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

MAYBE 18.822 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

((enumFrom :: 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

((enumFrom :: 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

((enumFrom :: 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

absReal1 x True = x

absReal1 x False = absReal0 x otherwise

absReal0 x True = `negate` x

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

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

gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy

gcd0Gcd' x xz = gcd0Gcd'2 x xz

gcd0Gcd' x y = gcd0Gcd'0 x y

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

mainModule Main

((enumFrom :: 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

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

module Main where

import qualified Prelude

Haskell To QDPs

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24[label="reduce2Reduce1 (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * vuz31) (primMulInt vuz31 (Pos (Succ Zero))) (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * vuz31) (primMulInt vuz31 (Pos (Succ Zero))) (primEqInt (primMulInt vuz31 (Pos (Succ Zero))) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];4658[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];24 -> 4658[label="",style="solid", color="burlywood", weight=9];
4658 -> 25[label="",style="solid", color="burlywood", weight=3];
4659[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];24 -> 4659[label="",style="solid", color="burlywood", weight=9];
4659 -> 26[label="",style="solid", color="burlywood", weight=3];
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4660 -> 29[label="",style="solid", color="burlywood", weight=3];
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4661 -> 30[label="",style="solid", color="burlywood", weight=3];
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4663 -> 32[label="",style="solid", color="burlywood", weight=3];
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361 -> 161[label="",style="dashed", color="red", weight=0];
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362 -> 161[label="",style="dashed", color="red", weight=0];
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212 -> 161[label="",style="dashed", color="red", weight=0];
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4675[label="vuz28/Zero",fontsize=10,color="white",style="solid",shape="box"];208 -> 4675[label="",style="solid", color="burlywood", weight=9];
4675 -> 326[label="",style="solid", color="burlywood", weight=3];
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462 -> 322[label="",style="dashed", color="red", weight=0];
462[label="primMulNat vuz3100 (Succ Zero)",fontsize=16,color="magenta"];462 -> 473[label="",style="dashed", color="magenta", weight=3];
161[label="primPlusNat vuz19 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];4677[label="vuz19/Succ vuz190",fontsize=10,color="white",style="solid",shape="box"];161 -> 4677[label="",style="solid", color="burlywood", weight=9];
4677 -> 166[label="",style="solid", color="burlywood", weight=3];
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4678 -> 167[label="",style="solid", color="burlywood", weight=3];
463 -> 322[label="",style="dashed", color="red", weight=0];
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464 -> 322[label="",style="dashed", color="red", weight=0];
464[label="primMulNat vuz3100 (Succ Zero)",fontsize=16,color="magenta"];464 -> 475[label="",style="dashed", color="magenta", weight=3];
465[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) (primEqInt (Pos (Succ vuz430)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];465 -> 476[label="",style="solid", color="black", weight=3];
466[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];466 -> 477[label="",style="solid", color="black", weight=3];
45[label="reduce2Reduce1 (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * Pos Zero) (Pos Zero) (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * Pos Zero) (Pos Zero) True",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3];
322[label="primMulNat vuz3100 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];4681[label="vuz3100/Succ vuz31000",fontsize=10,color="white",style="solid",shape="box"];322 -> 4681[label="",style="solid", color="burlywood", weight=9];
4681 -> 347[label="",style="solid", color="burlywood", weight=3];
4682[label="vuz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];322 -> 4682[label="",style="solid", color="burlywood", weight=9];
4682 -> 348[label="",style="solid", color="burlywood", weight=3];
323 -> 322[label="",style="dashed", color="red", weight=0];
323[label="primMulNat vuz3100 (Succ Zero)",fontsize=16,color="magenta"];324 -> 322[label="",style="dashed", color="red", weight=0];
324[label="primMulNat vuz3100 (Succ Zero)",fontsize=16,color="magenta"];325[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) (primEqInt (Neg (Succ vuz280)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];325 -> 349[label="",style="solid", color="black", weight=3];
326[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];326 -> 350[label="",style="solid", color="black", weight=3];
48[label="reduce2Reduce1 (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * Neg Zero) (Neg Zero) (vuz30 * Pos (Succ Zero) + Pos (Succ Zero) * Neg Zero) (Neg Zero) True",fontsize=16,color="black",shape="box"];48 -> 56[label="",style="solid", color="black", weight=3];
473[label="vuz3100",fontsize=16,color="green",shape="box"];166[label="primPlusNat (Succ vuz190) (Succ Zero)",fontsize=16,color="black",shape="box"];166 -> 332[label="",style="solid", color="black", weight=3];
167[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];167 -> 333[label="",style="solid", color="black", weight=3];
474[label="vuz3100",fontsize=16,color="green",shape="box"];475[label="vuz3100",fontsize=16,color="green",shape="box"];476[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) (primEqInt (Pos (Succ vuz430)) (Pos Zero))",fontsize=16,color="black",shape="box"];476 -> 483[label="",style="solid", color="black", weight=3];
477[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];477 -> 484[label="",style="solid", color="black", weight=3];
52[label="error []",fontsize=16,color="black",shape="triangle"];52 -> 60[label="",style="solid", color="black", weight=3];
347[label="primMulNat (Succ vuz31000) (Succ Zero)",fontsize=16,color="black",shape="box"];347 -> 467[label="",style="solid", color="black", weight=3];
348[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];348 -> 468[label="",style="solid", color="black", weight=3];
349[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) (primEqInt (Neg (Succ vuz280)) (Pos Zero))",fontsize=16,color="black",shape="box"];349 -> 469[label="",style="solid", color="black", weight=3];
350[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];350 -> 470[label="",style="solid", color="black", weight=3];
56 -> 52[label="",style="dashed", color="red", weight=0];
56[label="error []",fontsize=16,color="magenta"];332[label="Succ (Succ (primPlusNat vuz190 Zero))",fontsize=16,color="green",shape="box"];332 -> 356[label="",style="dashed", color="green", weight=3];
333[label="Succ Zero",fontsize=16,color="green",shape="box"];483[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) False",fontsize=16,color="black",shape="box"];483 -> 487[label="",style="solid", color="black", weight=3];
484[label="reduce2Reduce1 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) True",fontsize=16,color="black",shape="box"];484 -> 488[label="",style="solid", color="black", weight=3];
60[label="error []",fontsize=16,color="red",shape="box"];467 -> 161[label="",style="dashed", color="red", weight=0];
467[label="primPlusNat (primMulNat vuz31000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];467 -> 478[label="",style="dashed", color="magenta", weight=3];
468[label="Zero",fontsize=16,color="green",shape="box"];469[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) False",fontsize=16,color="black",shape="box"];469 -> 479[label="",style="solid", color="black", weight=3];
470[label="reduce2Reduce1 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) True",fontsize=16,color="black",shape="box"];470 -> 480[label="",style="solid", color="black", weight=3];
356[label="primPlusNat vuz190 Zero",fontsize=16,color="burlywood",shape="box"];4687[label="vuz190/Succ vuz1900",fontsize=10,color="white",style="solid",shape="box"];356 -> 4687[label="",style="solid", color="burlywood", weight=9];
4687 -> 471[label="",style="solid", color="burlywood", weight=3];
4688[label="vuz190/Zero",fontsize=10,color="white",style="solid",shape="box"];356 -> 4688[label="",style="solid", color="burlywood", weight=9];
4688 -> 472[label="",style="solid", color="burlywood", weight=3];
487[label="reduce2Reduce0 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) otherwise",fontsize=16,color="black",shape="box"];487 -> 490[label="",style="solid", color="black", weight=3];
488 -> 52[label="",style="dashed", color="red", weight=0];
488[label="error []",fontsize=16,color="magenta"];478 -> 322[label="",style="dashed", color="red", weight=0];
478[label="primMulNat vuz31000 (Succ Zero)",fontsize=16,color="magenta"];478 -> 485[label="",style="dashed", color="magenta", weight=3];
479[label="reduce2Reduce0 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) otherwise",fontsize=16,color="black",shape="box"];479 -> 486[label="",style="solid", color="black", weight=3];
480 -> 52[label="",style="dashed", color="red", weight=0];
480[label="error []",fontsize=16,color="magenta"];471[label="primPlusNat (Succ vuz1900) Zero",fontsize=16,color="black",shape="box"];471 -> 481[label="",style="solid", color="black", weight=3];
472[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];472 -> 482[label="",style="solid", color="black", weight=3];
490[label="reduce2Reduce0 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz41) True",fontsize=16,color="black",shape="box"];490 -> 493[label="",style="solid", color="black", weight=3];
485[label="vuz31000",fontsize=16,color="green",shape="box"];486[label="reduce2Reduce0 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz26) True",fontsize=16,color="black",shape="box"];486 -> 489[label="",style="solid", color="black", weight=3];
481[label="Succ vuz1900",fontsize=16,color="green",shape="box"];482[label="Zero",fontsize=16,color="green",shape="box"];493[label="(vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) `quot` reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42) :% (Pos vuz41 `quot` reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42))",fontsize=16,color="green",shape="box"];493 -> 496[label="",style="dashed", color="green", weight=3];
493 -> 497[label="",style="dashed", color="green", weight=3];
489[label="(vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) `quot` reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27) :% (Neg vuz26 `quot` reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27))",fontsize=16,color="green",shape="box"];489 -> 491[label="",style="dashed", color="green", weight=3];
489 -> 492[label="",style="dashed", color="green", weight=3];
496[label="(vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) `quot` reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];496 -> 500[label="",style="solid", color="black", weight=3];
497[label="Pos vuz41 `quot` reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];497 -> 501[label="",style="solid", color="black", weight=3];
491[label="(vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) `quot` reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];491 -> 494[label="",style="solid", color="black", weight=3];
492[label="Neg vuz26 `quot` reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];492 -> 495[label="",style="solid", color="black", weight=3];
500[label="primQuotInt (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42))",fontsize=16,color="black",shape="box"];500 -> 504[label="",style="solid", color="black", weight=3];
501 -> 1881[label="",style="dashed", color="red", weight=0];
501[label="primQuotInt (Pos vuz41) (reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42))",fontsize=16,color="magenta"];501 -> 1882[label="",style="dashed", color="magenta", weight=3];
494[label="primQuotInt (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27))",fontsize=16,color="black",shape="box"];494 -> 498[label="",style="solid", color="black", weight=3];
495 -> 2729[label="",style="dashed", color="red", weight=0];
495[label="primQuotInt (Neg vuz26) (reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27))",fontsize=16,color="magenta"];495 -> 2730[label="",style="dashed", color="magenta", weight=3];
504[label="primQuotInt (primPlusInt (vuz7 * Pos (Succ Zero)) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (vuz7 * Pos (Succ Zero)) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="black",shape="box"];504 -> 509[label="",style="solid", color="black", weight=3];
1882[label="reduce2D (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];1882 -> 2525[label="",style="solid", color="black", weight=3];
1881[label="primQuotInt (Pos vuz41) vuz106",fontsize=16,color="burlywood",shape="triangle"];4694[label="vuz106/Pos vuz1060",fontsize=10,color="white",style="solid",shape="box"];1881 -> 4694[label="",style="solid", color="burlywood", weight=9];
4694 -> 2526[label="",style="solid", color="burlywood", weight=3];
4695[label="vuz106/Neg vuz1060",fontsize=10,color="white",style="solid",shape="box"];1881 -> 4695[label="",style="solid", color="burlywood", weight=9];
4695 -> 2527[label="",style="solid", color="burlywood", weight=3];
498[label="primQuotInt (primPlusInt (vuz14 * Pos (Succ Zero)) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (vuz14 * Pos (Succ Zero)) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];498 -> 502[label="",style="solid", color="black", weight=3];
2730[label="reduce2D (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2730 -> 2992[label="",style="solid", color="black", weight=3];
2729[label="primQuotInt (Neg vuz26) vuz117",fontsize=16,color="burlywood",shape="triangle"];4696[label="vuz117/Pos vuz1170",fontsize=10,color="white",style="solid",shape="box"];2729 -> 4696[label="",style="solid", color="burlywood", weight=9];
4696 -> 2993[label="",style="solid", color="burlywood", weight=3];
4697[label="vuz117/Neg vuz1170",fontsize=10,color="white",style="solid",shape="box"];2729 -> 4697[label="",style="solid", color="burlywood", weight=9];
4697 -> 2994[label="",style="solid", color="burlywood", weight=3];
509[label="primQuotInt (primPlusInt (primMulInt vuz7 (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (primMulInt vuz7 (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="burlywood",shape="box"];4698[label="vuz7/Pos vuz70",fontsize=10,color="white",style="solid",shape="box"];509 -> 4698[label="",style="solid", color="burlywood", weight=9];
4698 -> 514[label="",style="solid", color="burlywood", weight=3];
4699[label="vuz7/Neg vuz70",fontsize=10,color="white",style="solid",shape="box"];509 -> 4699[label="",style="solid", color="burlywood", weight=9];
4699 -> 515[label="",style="solid", color="burlywood", weight=3];
2525[label="gcd (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2525 -> 2535[label="",style="solid", color="black", weight=3];
2526[label="primQuotInt (Pos vuz41) (Pos vuz1060)",fontsize=16,color="burlywood",shape="box"];4700[label="vuz1060/Succ vuz10600",fontsize=10,color="white",style="solid",shape="box"];2526 -> 4700[label="",style="solid", color="burlywood", weight=9];
4700 -> 2536[label="",style="solid", color="burlywood", weight=3];
4701[label="vuz1060/Zero",fontsize=10,color="white",style="solid",shape="box"];2526 -> 4701[label="",style="solid", color="burlywood", weight=9];
4701 -> 2537[label="",style="solid", color="burlywood", weight=3];
2527[label="primQuotInt (Pos vuz41) (Neg vuz1060)",fontsize=16,color="burlywood",shape="box"];4702[label="vuz1060/Succ vuz10600",fontsize=10,color="white",style="solid",shape="box"];2527 -> 4702[label="",style="solid", color="burlywood", weight=9];
4702 -> 2538[label="",style="solid", color="burlywood", weight=3];
4703[label="vuz1060/Zero",fontsize=10,color="white",style="solid",shape="box"];2527 -> 4703[label="",style="solid", color="burlywood", weight=9];
4703 -> 2539[label="",style="solid", color="burlywood", weight=3];
502[label="primQuotInt (primPlusInt (primMulInt vuz14 (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (primMulInt vuz14 (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="burlywood",shape="box"];4704[label="vuz14/Pos vuz140",fontsize=10,color="white",style="solid",shape="box"];502 -> 4704[label="",style="solid", color="burlywood", weight=9];
4704 -> 506[label="",style="solid", color="burlywood", weight=3];
4705[label="vuz14/Neg vuz140",fontsize=10,color="white",style="solid",shape="box"];502 -> 4705[label="",style="solid", color="burlywood", weight=9];
4705 -> 507[label="",style="solid", color="burlywood", weight=3];
2992[label="gcd (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2992 -> 3001[label="",style="solid", color="black", weight=3];
2993[label="primQuotInt (Neg vuz26) (Pos vuz1170)",fontsize=16,color="burlywood",shape="box"];4706[label="vuz1170/Succ vuz11700",fontsize=10,color="white",style="solid",shape="box"];2993 -> 4706[label="",style="solid", color="burlywood", weight=9];
4706 -> 3002[label="",style="solid", color="burlywood", weight=3];
4707[label="vuz1170/Zero",fontsize=10,color="white",style="solid",shape="box"];2993 -> 4707[label="",style="solid", color="burlywood", weight=9];
4707 -> 3003[label="",style="solid", color="burlywood", weight=3];
2994[label="primQuotInt (Neg vuz26) (Neg vuz1170)",fontsize=16,color="burlywood",shape="box"];4708[label="vuz1170/Succ vuz11700",fontsize=10,color="white",style="solid",shape="box"];2994 -> 4708[label="",style="solid", color="burlywood", weight=9];
4708 -> 3004[label="",style="solid", color="burlywood", weight=3];
4709[label="vuz1170/Zero",fontsize=10,color="white",style="solid",shape="box"];2994 -> 4709[label="",style="solid", color="burlywood", weight=9];
4709 -> 3005[label="",style="solid", color="burlywood", weight=3];
514[label="primQuotInt (primPlusInt (primMulInt (Pos vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (primMulInt (Pos vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="black",shape="box"];514 -> 520[label="",style="solid", color="black", weight=3];
515[label="primQuotInt (primPlusInt (primMulInt (Neg vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (primMulInt (Neg vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="black",shape="box"];515 -> 521[label="",style="solid", color="black", weight=3];
2535[label="gcd3 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2535 -> 2558[label="",style="solid", color="black", weight=3];
2536[label="primQuotInt (Pos vuz41) (Pos (Succ vuz10600))",fontsize=16,color="black",shape="box"];2536 -> 2559[label="",style="solid", color="black", weight=3];
2537[label="primQuotInt (Pos vuz41) (Pos Zero)",fontsize=16,color="black",shape="box"];2537 -> 2560[label="",style="solid", color="black", weight=3];
2538[label="primQuotInt (Pos vuz41) (Neg (Succ vuz10600))",fontsize=16,color="black",shape="box"];2538 -> 2561[label="",style="solid", color="black", weight=3];
2539[label="primQuotInt (Pos vuz41) (Neg Zero)",fontsize=16,color="black",shape="box"];2539 -> 2562[label="",style="solid", color="black", weight=3];
506[label="primQuotInt (primPlusInt (primMulInt (Pos vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (primMulInt (Pos vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];506 -> 511[label="",style="solid", color="black", weight=3];
507[label="primQuotInt (primPlusInt (primMulInt (Neg vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (primMulInt (Neg vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];507 -> 512[label="",style="solid", color="black", weight=3];
3001[label="gcd3 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3001 -> 3022[label="",style="solid", color="black", weight=3];
3002[label="primQuotInt (Neg vuz26) (Pos (Succ vuz11700))",fontsize=16,color="black",shape="box"];3002 -> 3023[label="",style="solid", color="black", weight=3];
3003[label="primQuotInt (Neg vuz26) (Pos Zero)",fontsize=16,color="black",shape="box"];3003 -> 3024[label="",style="solid", color="black", weight=3];
3004[label="primQuotInt (Neg vuz26) (Neg (Succ vuz11700))",fontsize=16,color="black",shape="box"];3004 -> 3025[label="",style="solid", color="black", weight=3];
3005[label="primQuotInt (Neg vuz26) (Neg Zero)",fontsize=16,color="black",shape="box"];3005 -> 3026[label="",style="solid", color="black", weight=3];
520 -> 526[label="",style="dashed", color="red", weight=0];
520[label="primQuotInt (primPlusInt (Pos (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (Pos (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="magenta"];520 -> 527[label="",style="dashed", color="magenta", weight=3];
520 -> 528[label="",style="dashed", color="magenta", weight=3];
521 -> 529[label="",style="dashed", color="red", weight=0];
521[label="primQuotInt (primPlusInt (Neg (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (Neg (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="magenta"];521 -> 530[label="",style="dashed", color="magenta", weight=3];
521 -> 531[label="",style="dashed", color="magenta", weight=3];
2558[label="gcd2 (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8) == fromInt (Pos Zero)) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2558 -> 2580[label="",style="solid", color="black", weight=3];
2559[label="Pos (primDivNatS vuz41 (Succ vuz10600))",fontsize=16,color="green",shape="box"];2559 -> 2581[label="",style="dashed", color="green", weight=3];
2560 -> 1311[label="",style="dashed", color="red", weight=0];
2560[label="error []",fontsize=16,color="magenta"];2561[label="Neg (primDivNatS vuz41 (Succ vuz10600))",fontsize=16,color="green",shape="box"];2561 -> 2582[label="",style="dashed", color="green", weight=3];
2562 -> 1311[label="",style="dashed", color="red", weight=0];
2562[label="error []",fontsize=16,color="magenta"];511 -> 517[label="",style="dashed", color="red", weight=0];
511[label="primQuotInt (primPlusInt (Pos (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (Pos (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="magenta"];511 -> 518[label="",style="dashed", color="magenta", weight=3];
511 -> 519[label="",style="dashed", color="magenta", weight=3];
512 -> 523[label="",style="dashed", color="red", weight=0];
512[label="primQuotInt (primPlusInt (Neg (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (Neg (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="magenta"];512 -> 524[label="",style="dashed", color="magenta", weight=3];
512 -> 525[label="",style="dashed", color="magenta", weight=3];
3022[label="gcd2 (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15) == fromInt (Pos Zero)) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3022 -> 3032[label="",style="solid", color="black", weight=3];
3023[label="Neg (primDivNatS vuz26 (Succ vuz11700))",fontsize=16,color="green",shape="box"];3023 -> 3033[label="",style="dashed", color="green", weight=3];
3024 -> 1311[label="",style="dashed", color="red", weight=0];
3024[label="error []",fontsize=16,color="magenta"];3025[label="Pos (primDivNatS vuz26 (Succ vuz11700))",fontsize=16,color="green",shape="box"];3025 -> 3034[label="",style="dashed", color="green", weight=3];
3026 -> 1311[label="",style="dashed", color="red", weight=0];
3026[label="error []",fontsize=16,color="magenta"];527 -> 322[label="",style="dashed", color="red", weight=0];
527[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];527 -> 534[label="",style="dashed", color="magenta", weight=3];
528 -> 322[label="",style="dashed", color="red", weight=0];
528[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];528 -> 535[label="",style="dashed", color="magenta", weight=3];
526[label="primQuotInt (primPlusInt (Pos vuz69) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (Pos vuz70) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="black",shape="triangle"];526 -> 536[label="",style="solid", color="black", weight=3];
530 -> 322[label="",style="dashed", color="red", weight=0];
530[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];530 -> 537[label="",style="dashed", color="magenta", weight=3];
531 -> 322[label="",style="dashed", color="red", weight=0];
531[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];531 -> 538[label="",style="dashed", color="magenta", weight=3];
529[label="primQuotInt (primPlusInt (Neg vuz71) (Pos (Succ Zero) * Pos (Succ vuz8))) (reduce2D (primPlusInt (Neg vuz72) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42))",fontsize=16,color="black",shape="triangle"];529 -> 539[label="",style="solid", color="black", weight=3];
2580[label="gcd2 (primEqInt (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (fromInt (Pos Zero))) (vuz7 * Pos (Succ Zero) + Pos (Succ Zero) * Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2580 -> 2604[label="",style="solid", color="black", weight=3];
2581 -> 1554[label="",style="dashed", color="red", weight=0];
2581[label="primDivNatS vuz41 (Succ vuz10600)",fontsize=16,color="magenta"];2581 -> 2605[label="",style="dashed", color="magenta", weight=3];
1311[label="error []",fontsize=16,color="black",shape="triangle"];1311 -> 1335[label="",style="solid", color="black", weight=3];
2582 -> 1554[label="",style="dashed", color="red", weight=0];
2582[label="primDivNatS vuz41 (Succ vuz10600)",fontsize=16,color="magenta"];2582 -> 2606[label="",style="dashed", color="magenta", weight=3];
518 -> 322[label="",style="dashed", color="red", weight=0];
518[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];518 -> 540[label="",style="dashed", color="magenta", weight=3];
519 -> 322[label="",style="dashed", color="red", weight=0];
519[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];519 -> 541[label="",style="dashed", color="magenta", weight=3];
517[label="primQuotInt (primPlusInt (Pos vuz65) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (Pos vuz66) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="triangle"];517 -> 542[label="",style="solid", color="black", weight=3];
524 -> 322[label="",style="dashed", color="red", weight=0];
524[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];524 -> 543[label="",style="dashed", color="magenta", weight=3];
525 -> 322[label="",style="dashed", color="red", weight=0];
525[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];525 -> 544[label="",style="dashed", color="magenta", weight=3];
523[label="primQuotInt (primPlusInt (Neg vuz67) (Pos (Succ Zero) * Neg (Succ vuz15))) (reduce2D (primPlusInt (Neg vuz68) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="triangle"];523 -> 545[label="",style="solid", color="black", weight=3];
3032[label="gcd2 (primEqInt (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (fromInt (Pos Zero))) (vuz14 * Pos (Succ Zero) + Pos (Succ Zero) * Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3032 -> 3038[label="",style="solid", color="black", weight=3];
3033 -> 1554[label="",style="dashed", color="red", weight=0];
3033[label="primDivNatS vuz26 (Succ vuz11700)",fontsize=16,color="magenta"];3033 -> 3039[label="",style="dashed", color="magenta", weight=3];
3033 -> 3040[label="",style="dashed", color="magenta", weight=3];
3034 -> 1554[label="",style="dashed", color="red", weight=0];
3034[label="primDivNatS vuz26 (Succ vuz11700)",fontsize=16,color="magenta"];3034 -> 3041[label="",style="dashed", color="magenta", weight=3];
3034 -> 3042[label="",style="dashed", color="magenta", weight=3];
534[label="vuz70",fontsize=16,color="green",shape="box"];535[label="vuz70",fontsize=16,color="green",shape="box"];536[label="primQuotInt (primPlusInt (Pos vuz69) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (reduce2D (primPlusInt (Pos vuz70) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (Pos vuz42))",fontsize=16,color="black",shape="box"];536 -> 548[label="",style="solid", color="black", weight=3];
537[label="vuz70",fontsize=16,color="green",shape="box"];538[label="vuz70",fontsize=16,color="green",shape="box"];539[label="primQuotInt (primPlusInt (Neg vuz71) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (reduce2D (primPlusInt (Neg vuz72) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (Pos vuz42))",fontsize=16,color="black",shape="box"];539 -> 549[label="",style="solid", color="black", weight=3];
2604[label="gcd2 (primEqInt (primPlusInt (vuz7 * Pos (Succ Zero)) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (vuz7 * Pos (Succ Zero)) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="black",shape="box"];2604 -> 2623[label="",style="solid", color="black", weight=3];
2605[label="vuz10600",fontsize=16,color="green",shape="box"];1554[label="primDivNatS vuz41 (Succ vuz8)",fontsize=16,color="burlywood",shape="triangle"];4730[label="vuz41/Succ vuz410",fontsize=10,color="white",style="solid",shape="box"];1554 -> 4730[label="",style="solid", color="burlywood", weight=9];
4730 -> 1578[label="",style="solid", color="burlywood", weight=3];
4731[label="vuz41/Zero",fontsize=10,color="white",style="solid",shape="box"];1554 -> 4731[label="",style="solid", color="burlywood", weight=9];
4731 -> 1579[label="",style="solid", color="burlywood", weight=3];
1335[label="error []",fontsize=16,color="red",shape="box"];2606[label="vuz10600",fontsize=16,color="green",shape="box"];540[label="vuz140",fontsize=16,color="green",shape="box"];541[label="vuz140",fontsize=16,color="green",shape="box"];542[label="primQuotInt (primPlusInt (Pos vuz65) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (reduce2D (primPlusInt (Pos vuz66) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (Neg vuz27))",fontsize=16,color="black",shape="box"];542 -> 550[label="",style="solid", color="black", weight=3];
543[label="vuz140",fontsize=16,color="green",shape="box"];544[label="vuz140",fontsize=16,color="green",shape="box"];545[label="primQuotInt (primPlusInt (Neg vuz67) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (reduce2D (primPlusInt (Neg vuz68) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (Neg vuz27))",fontsize=16,color="black",shape="box"];545 -> 551[label="",style="solid", color="black", weight=3];
3038[label="gcd2 (primEqInt (primPlusInt (vuz14 * Pos (Succ Zero)) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (vuz14 * Pos (Succ Zero)) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="black",shape="box"];3038 -> 3057[label="",style="solid", color="black", weight=3];
3039[label="vuz11700",fontsize=16,color="green",shape="box"];3040[label="vuz26",fontsize=16,color="green",shape="box"];3041[label="vuz11700",fontsize=16,color="green",shape="box"];3042[label="vuz26",fontsize=16,color="green",shape="box"];548[label="primQuotInt (primPlusInt (Pos vuz69) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (reduce2D (primPlusInt (Pos vuz70) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42))",fontsize=16,color="black",shape="box"];548 -> 556[label="",style="solid", color="black", weight=3];
549[label="primQuotInt (primPlusInt (Neg vuz71) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (reduce2D (primPlusInt (Neg vuz72) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42))",fontsize=16,color="black",shape="box"];549 -> 557[label="",style="solid", color="black", weight=3];
2623[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz7 (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz7 (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="burlywood",shape="box"];4732[label="vuz7/Pos vuz70",fontsize=10,color="white",style="solid",shape="box"];2623 -> 4732[label="",style="solid", color="burlywood", weight=9];
4732 -> 2639[label="",style="solid", color="burlywood", weight=3];
4733[label="vuz7/Neg vuz70",fontsize=10,color="white",style="solid",shape="box"];2623 -> 4733[label="",style="solid", color="burlywood", weight=9];
4733 -> 2640[label="",style="solid", color="burlywood", weight=3];
1578[label="primDivNatS (Succ vuz410) (Succ vuz8)",fontsize=16,color="black",shape="box"];1578 -> 1604[label="",style="solid", color="black", weight=3];
1579[label="primDivNatS Zero (Succ vuz8)",fontsize=16,color="black",shape="box"];1579 -> 1605[label="",style="solid", color="black", weight=3];
550[label="primQuotInt (primPlusInt (Pos vuz65) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (reduce2D (primPlusInt (Pos vuz66) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27))",fontsize=16,color="black",shape="box"];550 -> 558[label="",style="solid", color="black", weight=3];
551[label="primQuotInt (primPlusInt (Neg vuz67) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (reduce2D (primPlusInt (Neg vuz68) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27))",fontsize=16,color="black",shape="box"];551 -> 559[label="",style="solid", color="black", weight=3];
3057[label="gcd2 (primEqInt (primPlusInt (primMulInt vuz14 (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz14 (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="burlywood",shape="box"];4734[label="vuz14/Pos vuz140",fontsize=10,color="white",style="solid",shape="box"];3057 -> 4734[label="",style="solid", color="burlywood", weight=9];
4734 -> 3070[label="",style="solid", color="burlywood", weight=3];
4735[label="vuz14/Neg vuz140",fontsize=10,color="white",style="solid",shape="box"];3057 -> 4735[label="",style="solid", color="burlywood", weight=9];
4735 -> 3071[label="",style="solid", color="burlywood", weight=3];
556 -> 1881[label="",style="dashed", color="red", weight=0];
556[label="primQuotInt (Pos (primPlusNat vuz69 (primMulNat (Succ Zero) (Succ vuz8)))) (reduce2D (Pos (primPlusNat vuz69 (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42))",fontsize=16,color="magenta"];556 -> 1889[label="",style="dashed", color="magenta", weight=3];
556 -> 1890[label="",style="dashed", color="magenta", weight=3];
557[label="primQuotInt (primMinusNat (primMulNat (Succ Zero) (Succ vuz8)) vuz71) (reduce2D (primMinusNat (primMulNat (Succ Zero) (Succ vuz8)) vuz71) (Pos vuz42))",fontsize=16,color="black",shape="box"];557 -> 565[label="",style="solid", color="black", weight=3];
2639[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="black",shape="box"];2639 -> 2686[label="",style="solid", color="black", weight=3];
2640[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz70) (Pos (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="black",shape="box"];2640 -> 2687[label="",style="solid", color="black", weight=3];
1604 -> 1357[label="",style="dashed", color="red", weight=0];
1604[label="primDivNatS0 vuz410 vuz8 (primGEqNatS vuz410 vuz8)",fontsize=16,color="magenta"];1604 -> 1628[label="",style="dashed", color="magenta", weight=3];
1604 -> 1629[label="",style="dashed", color="magenta", weight=3];
1605[label="Zero",fontsize=16,color="green",shape="box"];558[label="primQuotInt (primMinusNat vuz65 (primMulNat (Succ Zero) (Succ vuz15))) (reduce2D (primMinusNat vuz65 (primMulNat (Succ Zero) (Succ vuz15))) (Neg vuz27))",fontsize=16,color="burlywood",shape="box"];4738[label="vuz65/Succ vuz650",fontsize=10,color="white",style="solid",shape="box"];558 -> 4738[label="",style="solid", color="burlywood", weight=9];
4738 -> 566[label="",style="solid", color="burlywood", weight=3];
4739[label="vuz65/Zero",fontsize=10,color="white",style="solid",shape="box"];558 -> 4739[label="",style="solid", color="burlywood", weight=9];
4739 -> 567[label="",style="solid", color="burlywood", weight=3];
559 -> 2729[label="",style="dashed", color="red", weight=0];
559[label="primQuotInt (Neg (primPlusNat vuz67 (primMulNat (Succ Zero) (Succ vuz15)))) (reduce2D (Neg (primPlusNat vuz67 (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27))",fontsize=16,color="magenta"];559 -> 2737[label="",style="dashed", color="magenta", weight=3];
559 -> 2738[label="",style="dashed", color="magenta", weight=3];
3070[label="gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="black",shape="box"];3070 -> 3089[label="",style="solid", color="black", weight=3];
3071[label="gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz140) (Pos (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="black",shape="box"];3071 -> 3090[label="",style="solid", color="black", weight=3];
1889 -> 745[label="",style="dashed", color="red", weight=0];
1889[label="primPlusNat vuz69 (primMulNat (Succ Zero) (Succ vuz8))",fontsize=16,color="magenta"];1889 -> 2528[label="",style="dashed", color="magenta", weight=3];
1889 -> 2529[label="",style="dashed", color="magenta", weight=3];
1890 -> 2530[label="",style="dashed", color="red", weight=0];
1890[label="reduce2D (Pos (primPlusNat vuz69 (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42)",fontsize=16,color="magenta"];1890 -> 2531[label="",style="dashed", color="magenta", weight=3];
565[label="primQuotInt (primMinusNat (primPlusNat (primMulNat Zero (Succ vuz8)) (Succ vuz8)) vuz71) (reduce2D (primMinusNat (primPlusNat (primMulNat Zero (Succ vuz8)) (Succ vuz8)) vuz71) (Pos vuz42))",fontsize=16,color="black",shape="box"];565 -> 582[label="",style="solid", color="black", weight=3];
2686 -> 2702[label="",style="dashed", color="red", weight=0];
2686[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="magenta"];2686 -> 2703[label="",style="dashed", color="magenta", weight=3];
2686 -> 2704[label="",style="dashed", color="magenta", weight=3];
2687 -> 2705[label="",style="dashed", color="red", weight=0];
2687[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz70 (Succ Zero))) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="magenta"];2687 -> 2706[label="",style="dashed", color="magenta", weight=3];
2687 -> 2707[label="",style="dashed", color="magenta", weight=3];
1628[label="vuz410",fontsize=16,color="green",shape="box"];1629[label="vuz8",fontsize=16,color="green",shape="box"];1357[label="primDivNatS0 vuz85 vuz8600 (primGEqNatS vuz85 vuz8600)",fontsize=16,color="burlywood",shape="triangle"];4745[label="vuz85/Succ vuz850",fontsize=10,color="white",style="solid",shape="box"];1357 -> 4745[label="",style="solid", color="burlywood", weight=9];
4745 -> 1378[label="",style="solid", color="burlywood", weight=3];
4746[label="vuz85/Zero",fontsize=10,color="white",style="solid",shape="box"];1357 -> 4746[label="",style="solid", color="burlywood", weight=9];
4746 -> 1379[label="",style="solid", color="burlywood", weight=3];
566[label="primQuotInt (primMinusNat (Succ vuz650) (primMulNat (Succ Zero) (Succ vuz15))) (reduce2D (primMinusNat (Succ vuz650) (primMulNat (Succ Zero) (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];566 -> 589[label="",style="solid", color="black", weight=3];
567[label="primQuotInt (primMinusNat Zero (primMulNat (Succ Zero) (Succ vuz15))) (reduce2D (primMinusNat Zero (primMulNat (Succ Zero) (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];567 -> 590[label="",style="solid", color="black", weight=3];
2737 -> 745[label="",style="dashed", color="red", weight=0];
2737[label="primPlusNat vuz67 (primMulNat (Succ Zero) (Succ vuz15))",fontsize=16,color="magenta"];2737 -> 2995[label="",style="dashed", color="magenta", weight=3];
2737 -> 2996[label="",style="dashed", color="magenta", weight=3];
2738 -> 2997[label="",style="dashed", color="red", weight=0];
2738[label="reduce2D (Neg (primPlusNat vuz67 (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27)",fontsize=16,color="magenta"];2738 -> 2998[label="",style="dashed", color="magenta", weight=3];
3089 -> 3104[label="",style="dashed", color="red", weight=0];
3089[label="gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="magenta"];3089 -> 3105[label="",style="dashed", color="magenta", weight=3];
3089 -> 3106[label="",style="dashed", color="magenta", weight=3];
3090 -> 3107[label="",style="dashed", color="red", weight=0];
3090[label="gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz140 (Succ Zero))) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="magenta"];3090 -> 3108[label="",style="dashed", color="magenta", weight=3];
3090 -> 3109[label="",style="dashed", color="magenta", weight=3];
2528[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="black",shape="triangle"];2528 -> 2540[label="",style="solid", color="black", weight=3];
2529[label="vuz69",fontsize=16,color="green",shape="box"];745[label="primPlusNat vuz670 vuz15",fontsize=16,color="burlywood",shape="triangle"];4751[label="vuz670/Succ vuz6700",fontsize=10,color="white",style="solid",shape="box"];745 -> 4751[label="",style="solid", color="burlywood", weight=9];
4751 -> 765[label="",style="solid", color="burlywood", weight=3];
4752[label="vuz670/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 4752[label="",style="solid", color="burlywood", weight=9];
4752 -> 766[label="",style="solid", color="burlywood", weight=3];
2531 -> 745[label="",style="dashed", color="red", weight=0];
2531[label="primPlusNat vuz69 (primMulNat (Succ Zero) (Succ vuz8))",fontsize=16,color="magenta"];2531 -> 2541[label="",style="dashed", color="magenta", weight=3];
2531 -> 2542[label="",style="dashed", color="magenta", weight=3];
2530[label="reduce2D (Pos vuz107) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];2530 -> 2543[label="",style="solid", color="black", weight=3];
582[label="primQuotInt (primMinusNat (primPlusNat Zero (Succ vuz8)) vuz71) (reduce2D (primMinusNat (primPlusNat Zero (Succ vuz8)) vuz71) (Pos vuz42))",fontsize=16,color="black",shape="box"];582 -> 599[label="",style="solid", color="black", weight=3];
2703 -> 322[label="",style="dashed", color="red", weight=0];
2703[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];2703 -> 2708[label="",style="dashed", color="magenta", weight=3];
2704 -> 322[label="",style="dashed", color="red", weight=0];
2704[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];2704 -> 2709[label="",style="dashed", color="magenta", weight=3];
2702[label="gcd2 (primEqInt (primPlusInt (Pos vuz114) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz113) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];2702 -> 2710[label="",style="solid", color="black", weight=3];
2706 -> 322[label="",style="dashed", color="red", weight=0];
2706[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];2706 -> 2711[label="",style="dashed", color="magenta", weight=3];
2707 -> 322[label="",style="dashed", color="red", weight=0];
2707[label="primMulNat vuz70 (Succ Zero)",fontsize=16,color="magenta"];2707 -> 2712[label="",style="dashed", color="magenta", weight=3];
2705[label="gcd2 (primEqInt (primPlusInt (Neg vuz116) (Pos (Succ Zero) * Pos (Succ vuz8))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz115) (Pos (Succ Zero) * Pos (Succ vuz8))) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];2705 -> 2713[label="",style="solid", color="black", weight=3];
1378[label="primDivNatS0 (Succ vuz850) vuz8600 (primGEqNatS (Succ vuz850) vuz8600)",fontsize=16,color="burlywood",shape="box"];4758[label="vuz8600/Succ vuz86000",fontsize=10,color="white",style="solid",shape="box"];1378 -> 4758[label="",style="solid", color="burlywood", weight=9];
4758 -> 1396[label="",style="solid", color="burlywood", weight=3];
4759[label="vuz8600/Zero",fontsize=10,color="white",style="solid",shape="box"];1378 -> 4759[label="",style="solid", color="burlywood", weight=9];
4759 -> 1397[label="",style="solid", color="burlywood", weight=3];
1379[label="primDivNatS0 Zero vuz8600 (primGEqNatS Zero vuz8600)",fontsize=16,color="burlywood",shape="box"];4760[label="vuz8600/Succ vuz86000",fontsize=10,color="white",style="solid",shape="box"];1379 -> 4760[label="",style="solid", color="burlywood", weight=9];
4760 -> 1398[label="",style="solid", color="burlywood", weight=3];
4761[label="vuz8600/Zero",fontsize=10,color="white",style="solid",shape="box"];1379 -> 4761[label="",style="solid", color="burlywood", weight=9];
4761 -> 1399[label="",style="solid", color="burlywood", weight=3];
589[label="primQuotInt (primMinusNat (Succ vuz650) (primPlusNat (primMulNat Zero (Succ vuz15)) (Succ vuz15))) (reduce2D (primMinusNat (Succ vuz650) (primPlusNat (primMulNat Zero (Succ vuz15)) (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];589 -> 602[label="",style="solid", color="black", weight=3];
590[label="primQuotInt (primMinusNat Zero (primPlusNat (primMulNat Zero (Succ vuz15)) (Succ vuz15))) (reduce2D (primMinusNat Zero (primPlusNat (primMulNat Zero (Succ vuz15)) (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];590 -> 603[label="",style="solid", color="black", weight=3];
2995 -> 2528[label="",style="dashed", color="red", weight=0];
2995[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];2995 -> 3006[label="",style="dashed", color="magenta", weight=3];
2996[label="vuz67",fontsize=16,color="green",shape="box"];2998 -> 745[label="",style="dashed", color="red", weight=0];
2998[label="primPlusNat vuz67 (primMulNat (Succ Zero) (Succ vuz15))",fontsize=16,color="magenta"];2998 -> 3007[label="",style="dashed", color="magenta", weight=3];
2998 -> 3008[label="",style="dashed", color="magenta", weight=3];
2997[label="reduce2D (Neg vuz118) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];2997 -> 3009[label="",style="solid", color="black", weight=3];
3105 -> 322[label="",style="dashed", color="red", weight=0];
3105[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];3105 -> 3110[label="",style="dashed", color="magenta", weight=3];
3106 -> 322[label="",style="dashed", color="red", weight=0];
3106[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];3106 -> 3111[label="",style="dashed", color="magenta", weight=3];
3104[label="gcd2 (primEqInt (primPlusInt (Pos vuz125) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz124) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];3104 -> 3112[label="",style="solid", color="black", weight=3];
3108 -> 322[label="",style="dashed", color="red", weight=0];
3108[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];3108 -> 3113[label="",style="dashed", color="magenta", weight=3];
3109 -> 322[label="",style="dashed", color="red", weight=0];
3109[label="primMulNat vuz140 (Succ Zero)",fontsize=16,color="magenta"];3109 -> 3114[label="",style="dashed", color="magenta", weight=3];
3107[label="gcd2 (primEqInt (primPlusInt (Neg vuz127) (Pos (Succ Zero) * Neg (Succ vuz15))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz126) (Pos (Succ Zero) * Neg (Succ vuz15))) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];3107 -> 3115[label="",style="solid", color="black", weight=3];
2540 -> 745[label="",style="dashed", color="red", weight=0];
2540[label="primPlusNat (primMulNat Zero (Succ vuz8)) (Succ vuz8)",fontsize=16,color="magenta"];2540 -> 2563[label="",style="dashed", color="magenta", weight=3];
2540 -> 2564[label="",style="dashed", color="magenta", weight=3];
765[label="primPlusNat (Succ vuz6700) vuz15",fontsize=16,color="burlywood",shape="box"];4769[label="vuz15/Succ vuz150",fontsize=10,color="white",style="solid",shape="box"];765 -> 4769[label="",style="solid", color="burlywood", weight=9];
4769 -> 794[label="",style="solid", color="burlywood", weight=3];
4770[label="vuz15/Zero",fontsize=10,color="white",style="solid",shape="box"];765 -> 4770[label="",style="solid", color="burlywood", weight=9];
4770 -> 795[label="",style="solid", color="burlywood", weight=3];
766[label="primPlusNat Zero vuz15",fontsize=16,color="burlywood",shape="box"];4771[label="vuz15/Succ vuz150",fontsize=10,color="white",style="solid",shape="box"];766 -> 4771[label="",style="solid", color="burlywood", weight=9];
4771 -> 796[label="",style="solid", color="burlywood", weight=3];
4772[label="vuz15/Zero",fontsize=10,color="white",style="solid",shape="box"];766 -> 4772[label="",style="solid", color="burlywood", weight=9];
4772 -> 797[label="",style="solid", color="burlywood", weight=3];
2541 -> 2528[label="",style="dashed", color="red", weight=0];
2541[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="magenta"];2542[label="vuz69",fontsize=16,color="green",shape="box"];2543[label="gcd (Pos vuz107) (Pos vuz42)",fontsize=16,color="black",shape="box"];2543 -> 2565[label="",style="solid", color="black", weight=3];
599[label="primQuotInt (primMinusNat (Succ vuz8) vuz71) (reduce2D (primMinusNat (Succ vuz8) vuz71) (Pos vuz42))",fontsize=16,color="burlywood",shape="box"];4774[label="vuz71/Succ vuz710",fontsize=10,color="white",style="solid",shape="box"];599 -> 4774[label="",style="solid", color="burlywood", weight=9];
4774 -> 608[label="",style="solid", color="burlywood", weight=3];
4775[label="vuz71/Zero",fontsize=10,color="white",style="solid",shape="box"];599 -> 4775[label="",style="solid", color="burlywood", weight=9];
4775 -> 609[label="",style="solid", color="burlywood", weight=3];
2708[label="vuz70",fontsize=16,color="green",shape="box"];2709[label="vuz70",fontsize=16,color="green",shape="box"];2710[label="gcd2 (primEqInt (primPlusInt (Pos vuz114) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz113) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (Pos vuz42)",fontsize=16,color="black",shape="box"];2710 -> 3010[label="",style="solid", color="black", weight=3];
2711[label="vuz70",fontsize=16,color="green",shape="box"];2712[label="vuz70",fontsize=16,color="green",shape="box"];2713[label="gcd2 (primEqInt (primPlusInt (Neg vuz116) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz115) (primMulInt (Pos (Succ Zero)) (Pos (Succ vuz8)))) (Pos vuz42)",fontsize=16,color="black",shape="box"];2713 -> 3011[label="",style="solid", color="black", weight=3];
1396[label="primDivNatS0 (Succ vuz850) (Succ vuz86000) (primGEqNatS (Succ vuz850) (Succ vuz86000))",fontsize=16,color="black",shape="box"];1396 -> 1416[label="",style="solid", color="black", weight=3];
1397[label="primDivNatS0 (Succ vuz850) Zero (primGEqNatS (Succ vuz850) Zero)",fontsize=16,color="black",shape="box"];1397 -> 1417[label="",style="solid", color="black", weight=3];
1398[label="primDivNatS0 Zero (Succ vuz86000) (primGEqNatS Zero (Succ vuz86000))",fontsize=16,color="black",shape="box"];1398 -> 1418[label="",style="solid", color="black", weight=3];
1399[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1399 -> 1419[label="",style="solid", color="black", weight=3];
602[label="primQuotInt (primMinusNat (Succ vuz650) (primPlusNat Zero (Succ vuz15))) (reduce2D (primMinusNat (Succ vuz650) (primPlusNat Zero (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];602 -> 612[label="",style="solid", color="black", weight=3];
603[label="primQuotInt (primMinusNat Zero (primPlusNat Zero (Succ vuz15))) (reduce2D (primMinusNat Zero (primPlusNat Zero (Succ vuz15))) (Neg vuz27))",fontsize=16,color="black",shape="box"];603 -> 613[label="",style="solid", color="black", weight=3];
3006[label="vuz15",fontsize=16,color="green",shape="box"];3007 -> 2528[label="",style="dashed", color="red", weight=0];
3007[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];3007 -> 3027[label="",style="dashed", color="magenta", weight=3];
3008[label="vuz67",fontsize=16,color="green",shape="box"];3009[label="gcd (Neg vuz118) (Neg vuz27)",fontsize=16,color="black",shape="box"];3009 -> 3028[label="",style="solid", color="black", weight=3];
3110[label="vuz140",fontsize=16,color="green",shape="box"];3111[label="vuz140",fontsize=16,color="green",shape="box"];3112[label="gcd2 (primEqInt (primPlusInt (Pos vuz125) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz124) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (Neg vuz27)",fontsize=16,color="black",shape="box"];3112 -> 3130[label="",style="solid", color="black", weight=3];
3113[label="vuz140",fontsize=16,color="green",shape="box"];3114[label="vuz140",fontsize=16,color="green",shape="box"];3115[label="gcd2 (primEqInt (primPlusInt (Neg vuz127) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz126) (primMulInt (Pos (Succ Zero)) (Neg (Succ vuz15)))) (Neg vuz27)",fontsize=16,color="black",shape="box"];3115 -> 3131[label="",style="solid", color="black", weight=3];
2563[label="Succ vuz8",fontsize=16,color="green",shape="box"];2564[label="primMulNat Zero (Succ vuz8)",fontsize=16,color="black",shape="box"];2564 -> 2583[label="",style="solid", color="black", weight=3];
794[label="primPlusNat (Succ vuz6700) (Succ vuz150)",fontsize=16,color="black",shape="box"];794 -> 819[label="",style="solid", color="black", weight=3];
795[label="primPlusNat (Succ vuz6700) Zero",fontsize=16,color="black",shape="box"];795 -> 820[label="",style="solid", color="black", weight=3];
796[label="primPlusNat Zero (Succ vuz150)",fontsize=16,color="black",shape="box"];796 -> 821[label="",style="solid", color="black", weight=3];
797[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];797 -> 822[label="",style="solid", color="black", weight=3];
2565[label="gcd3 (Pos vuz107) (Pos vuz42)",fontsize=16,color="black",shape="box"];2565 -> 2584[label="",style="solid", color="black", weight=3];
608[label="primQuotInt (primMinusNat (Succ vuz8) (Succ vuz710)) (reduce2D (primMinusNat (Succ vuz8) (Succ vuz710)) (Pos vuz42))",fontsize=16,color="black",shape="box"];608 -> 619[label="",style="solid", color="black", weight=3];
609[label="primQuotInt (primMinusNat (Succ vuz8) Zero) (reduce2D (primMinusNat (Succ vuz8) Zero) (Pos vuz42))",fontsize=16,color="black",shape="box"];609 -> 620[label="",style="solid", color="black", weight=3];
3010 -> 3029[label="",style="dashed", color="red", weight=0];
3010[label="gcd2 (primEqInt (primPlusInt (Pos vuz114) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz113) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42)",fontsize=16,color="magenta"];3010 -> 3030[label="",style="dashed", color="magenta", weight=3];
3010 -> 3031[label="",style="dashed", color="magenta", weight=3];
3011 -> 3035[label="",style="dashed", color="red", weight=0];
3011[label="gcd2 (primEqInt (primPlusInt (Neg vuz116) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz115) (Pos (primMulNat (Succ Zero) (Succ vuz8)))) (Pos vuz42)",fontsize=16,color="magenta"];3011 -> 3036[label="",style="dashed", color="magenta", weight=3];
3011 -> 3037[label="",style="dashed", color="magenta", weight=3];
1416 -> 2645[label="",style="dashed", color="red", weight=0];
1416[label="primDivNatS0 (Succ vuz850) (Succ vuz86000) (primGEqNatS vuz850 vuz86000)",fontsize=16,color="magenta"];1416 -> 2646[label="",style="dashed", color="magenta", weight=3];
1416 -> 2647[label="",style="dashed", color="magenta", weight=3];
1416 -> 2648[label="",style="dashed", color="magenta", weight=3];
1416 -> 2649[label="",style="dashed", color="magenta", weight=3];
1417[label="primDivNatS0 (Succ vuz850) Zero True",fontsize=16,color="black",shape="box"];1417 -> 1438[label="",style="solid", color="black", weight=3];
1418[label="primDivNatS0 Zero (Succ vuz86000) False",fontsize=16,color="black",shape="box"];1418 -> 1439[label="",style="solid", color="black", weight=3];
1419[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1419 -> 1440[label="",style="solid", color="black", weight=3];
612[label="primQuotInt (primMinusNat (Succ vuz650) (Succ vuz15)) (reduce2D (primMinusNat (Succ vuz650) (Succ vuz15)) (Neg vuz27))",fontsize=16,color="black",shape="box"];612 -> 624[label="",style="solid", color="black", weight=3];
613[label="primQuotInt (primMinusNat Zero (Succ vuz15)) (reduce2D (primMinusNat Zero (Succ vuz15)) (Neg vuz27))",fontsize=16,color="black",shape="box"];613 -> 625[label="",style="solid", color="black", weight=3];
3027[label="vuz15",fontsize=16,color="green",shape="box"];3028[label="gcd3 (Neg vuz118) (Neg vuz27)",fontsize=16,color="black",shape="box"];3028 -> 3043[label="",style="solid", color="black", weight=3];
3130 -> 3143[label="",style="dashed", color="red", weight=0];
3130[label="gcd2 (primEqInt (primPlusInt (Pos vuz125) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz124) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27)",fontsize=16,color="magenta"];3130 -> 3144[label="",style="dashed", color="magenta", weight=3];
3130 -> 3145[label="",style="dashed", color="magenta", weight=3];
3131 -> 3146[label="",style="dashed", color="red", weight=0];
3131[label="gcd2 (primEqInt (primPlusInt (Neg vuz127) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz126) (Neg (primMulNat (Succ Zero) (Succ vuz15)))) (Neg vuz27)",fontsize=16,color="magenta"];3131 -> 3147[label="",style="dashed", color="magenta", weight=3];
3131 -> 3148[label="",style="dashed", color="magenta", weight=3];
2583[label="Zero",fontsize=16,color="green",shape="box"];819[label="Succ (Succ (primPlusNat vuz6700 vuz150))",fontsize=16,color="green",shape="box"];819 -> 837[label="",style="dashed", color="green", weight=3];
820[label="Succ vuz6700",fontsize=16,color="green",shape="box"];821[label="Succ vuz150",fontsize=16,color="green",shape="box"];822[label="Zero",fontsize=16,color="green",shape="box"];2584[label="gcd2 (Pos vuz107 == fromInt (Pos Zero)) (Pos vuz107) (Pos vuz42)",fontsize=16,color="black",shape="box"];2584 -> 2607[label="",style="solid", color="black", weight=3];
619[label="primQuotInt (primMinusNat vuz8 vuz710) (reduce2D (primMinusNat vuz8 vuz710) (Pos vuz42))",fontsize=16,color="burlywood",shape="triangle"];4782[label="vuz8/Succ vuz80",fontsize=10,color="white",style="solid",shape="box"];619 -> 4782[label="",style="solid", color="burlywood", weight=9];
4782 -> 634[label="",style="solid", color="burlywood", weight=3];
4783[label="vuz8/Zero",fontsize=10,color="white",style="solid",shape="box"];619 -> 4783[label="",style="solid", color="burlywood", weight=9];
4783 -> 635[label="",style="solid", color="burlywood", weight=3];
620 -> 1881[label="",style="dashed", color="red", weight=0];
620[label="primQuotInt (Pos (Succ vuz8)) (reduce2D (Pos (Succ vuz8)) (Pos vuz42))",fontsize=16,color="magenta"];620 -> 1909[label="",style="dashed", color="magenta", weight=3];
620 -> 1910[label="",style="dashed", color="magenta", weight=3];
3030 -> 2528[label="",style="dashed", color="red", weight=0];
3030[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="magenta"];3031 -> 2528[label="",style="dashed", color="red", weight=0];
3031[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="magenta"];3029[label="gcd2 (primEqInt (primPlusInt (Pos vuz114) (Pos vuz121)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz113) (Pos vuz120)) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];3029 -> 3044[label="",style="solid", color="black", weight=3];
3036 -> 2528[label="",style="dashed", color="red", weight=0];
3036[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="magenta"];3037 -> 2528[label="",style="dashed", color="red", weight=0];
3037[label="primMulNat (Succ Zero) (Succ vuz8)",fontsize=16,color="magenta"];3035[label="gcd2 (primEqInt (primPlusInt (Neg vuz116) (Pos vuz123)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz115) (Pos vuz122)) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];3035 -> 3045[label="",style="solid", color="black", weight=3];
2646[label="vuz850",fontsize=16,color="green",shape="box"];2647[label="vuz86000",fontsize=16,color="green",shape="box"];2648[label="vuz86000",fontsize=16,color="green",shape="box"];2649[label="vuz850",fontsize=16,color="green",shape="box"];2645[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS vuz111 vuz112)",fontsize=16,color="burlywood",shape="triangle"];4789[label="vuz111/Succ vuz1110",fontsize=10,color="white",style="solid",shape="box"];2645 -> 4789[label="",style="solid", color="burlywood", weight=9];
4789 -> 2688[label="",style="solid", color="burlywood", weight=3];
4790[label="vuz111/Zero",fontsize=10,color="white",style="solid",shape="box"];2645 -> 4790[label="",style="solid", color="burlywood", weight=9];
4790 -> 2689[label="",style="solid", color="burlywood", weight=3];
1438[label="Succ (primDivNatS (primMinusNatS (Succ vuz850) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1438 -> 1462[label="",style="dashed", color="green", weight=3];
1439[label="Zero",fontsize=16,color="green",shape="box"];1440[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1440 -> 1463[label="",style="dashed", color="green", weight=3];
624[label="primQuotInt (primMinusNat vuz650 vuz15) (reduce2D (primMinusNat vuz650 vuz15) (Neg vuz27))",fontsize=16,color="burlywood",shape="triangle"];4791[label="vuz650/Succ vuz6500",fontsize=10,color="white",style="solid",shape="box"];624 -> 4791[label="",style="solid", color="burlywood", weight=9];
4791 -> 640[label="",style="solid", color="burlywood", weight=3];
4792[label="vuz650/Zero",fontsize=10,color="white",style="solid",shape="box"];624 -> 4792[label="",style="solid", color="burlywood", weight=9];
4792 -> 641[label="",style="solid", color="burlywood", weight=3];
625 -> 2729[label="",style="dashed", color="red", weight=0];
625[label="primQuotInt (Neg (Succ vuz15)) (reduce2D (Neg (Succ vuz15)) (Neg vuz27))",fontsize=16,color="magenta"];625 -> 2757[label="",style="dashed", color="magenta", weight=3];
625 -> 2758[label="",style="dashed", color="magenta", weight=3];
3043[label="gcd2 (Neg vuz118 == fromInt (Pos Zero)) (Neg vuz118) (Neg vuz27)",fontsize=16,color="black",shape="box"];3043 -> 3058[label="",style="solid", color="black", weight=3];
3144 -> 2528[label="",style="dashed", color="red", weight=0];
3144[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];3144 -> 3149[label="",style="dashed", color="magenta", weight=3];
3145 -> 2528[label="",style="dashed", color="red", weight=0];
3145[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];3145 -> 3150[label="",style="dashed", color="magenta", weight=3];
3143[label="gcd2 (primEqInt (primPlusInt (Pos vuz125) (Neg vuz129)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz124) (Neg vuz128)) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];3143 -> 3151[label="",style="solid", color="black", weight=3];
3147 -> 2528[label="",style="dashed", color="red", weight=0];
3147[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];3147 -> 3152[label="",style="dashed", color="magenta", weight=3];
3148 -> 2528[label="",style="dashed", color="red", weight=0];
3148[label="primMulNat (Succ Zero) (Succ vuz15)",fontsize=16,color="magenta"];3148 -> 3153[label="",style="dashed", color="magenta", weight=3];
3146[label="gcd2 (primEqInt (primPlusInt (Neg vuz127) (Neg vuz131)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz126) (Neg vuz130)) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];3146 -> 3154[label="",style="solid", color="black", weight=3];
837 -> 745[label="",style="dashed", color="red", weight=0];
837[label="primPlusNat vuz6700 vuz150",fontsize=16,color="magenta"];837 -> 850[label="",style="dashed", color="magenta", weight=3];
837 -> 851[label="",style="dashed", color="magenta", weight=3];
2607[label="gcd2 (primEqInt (Pos vuz107) (fromInt (Pos Zero))) (Pos vuz107) (Pos vuz42)",fontsize=16,color="burlywood",shape="triangle"];4799[label="vuz107/Succ vuz1070",fontsize=10,color="white",style="solid",shape="box"];2607 -> 4799[label="",style="solid", color="burlywood", weight=9];
4799 -> 2624[label="",style="solid", color="burlywood", weight=3];
4800[label="vuz107/Zero",fontsize=10,color="white",style="solid",shape="box"];2607 -> 4800[label="",style="solid", color="burlywood", weight=9];
4800 -> 2625[label="",style="solid", color="burlywood", weight=3];
634[label="primQuotInt (primMinusNat (Succ vuz80) vuz710) (reduce2D (primMinusNat (Succ vuz80) vuz710) (Pos vuz42))",fontsize=16,color="burlywood",shape="box"];4801[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];634 -> 4801[label="",style="solid", color="burlywood", weight=9];
4801 -> 651[label="",style="solid", color="burlywood", weight=3];
4802[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];634 -> 4802[label="",style="solid", color="burlywood", weight=9];
4802 -> 652[label="",style="solid", color="burlywood", weight=3];
635[label="primQuotInt (primMinusNat Zero vuz710) (reduce2D (primMinusNat Zero vuz710) (Pos vuz42))",fontsize=16,color="burlywood",shape="box"];4803[label="vuz710/Succ vuz7100",fontsize=10,color="white",style="solid",shape="box"];635 -> 4803[label="",style="solid", color="burlywood", weight=9];
4803 -> 653[label="",style="solid", color="burlywood", weight=3];
4804[label="vuz710/Zero",fontsize=10,color="white",style="solid",shape="box"];635 -> 4804[label="",style="solid", color="burlywood", weight=9];
4804 -> 654[label="",style="solid", color="burlywood", weight=3];
1909[label="Succ vuz8",fontsize=16,color="green",shape="box"];1910 -> 2530[label="",style="dashed", color="red", weight=0];
1910[label="reduce2D (Pos (Succ vuz8)) (Pos vuz42)",fontsize=16,color="magenta"];1910 -> 2532[label="",style="dashed", color="magenta", weight=3];
3044 -> 2607[label="",style="dashed", color="red", weight=0];
3044[label="gcd2 (primEqInt (Pos (primPlusNat vuz114 vuz121)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz114 vuz121)) (Pos vuz42)",fontsize=16,color="magenta"];3044 -> 3059[label="",style="dashed", color="magenta", weight=3];
3045[label="gcd2 (primEqInt (primMinusNat vuz123 vuz116) (fromInt (Pos Zero))) (primMinusNat vuz123 vuz116) (Pos vuz42)",fontsize=16,color="burlywood",shape="triangle"];4807[label="vuz123/Succ vuz1230",fontsize=10,color="white",style="solid",shape="box"];3045 -> 4807[label="",style="solid", color="burlywood", weight=9];
4807 -> 3060[label="",style="solid", color="burlywood", weight=3];
4808[label="vuz123/Zero",fontsize=10,color="white",style="solid",shape="box"];3045 -> 4808[label="",style="solid", color="burlywood", weight=9];
4808 -> 3061[label="",style="solid", color="burlywood", weight=3];
2688[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS (Succ vuz1110) vuz112)",fontsize=16,color="burlywood",shape="box"];4809[label="vuz112/Succ vuz1120",fontsize=10,color="white",style="solid",shape="box"];2688 -> 4809[label="",style="solid", color="burlywood", weight=9];
4809 -> 2714[label="",style="solid", color="burlywood", weight=3];
4810[label="vuz112/Zero",fontsize=10,color="white",style="solid",shape="box"];2688 -> 4810[label="",style="solid", color="burlywood", weight=9];
4810 -> 2715[label="",style="solid", color="burlywood", weight=3];
2689[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS Zero vuz112)",fontsize=16,color="burlywood",shape="box"];4811[label="vuz112/Succ vuz1120",fontsize=10,color="white",style="solid",shape="box"];2689 -> 4811[label="",style="solid", color="burlywood", weight=9];
4811 -> 2716[label="",style="solid", color="burlywood", weight=3];
4812[label="vuz112/Zero",fontsize=10,color="white",style="solid",shape="box"];2689 -> 4812[label="",style="solid", color="burlywood", weight=9];
4812 -> 2717[label="",style="solid", color="burlywood", weight=3];
1462[label="primDivNatS (primMinusNatS (Succ vuz850) Zero) (Succ Zero)",fontsize=16,color="black",shape="box"];1462 -> 1483[label="",style="solid", color="black", weight=3];
1463[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="black",shape="box"];1463 -> 1484[label="",style="solid", color="black", weight=3];
640[label="primQuotInt (primMinusNat (Succ vuz6500) vuz15) (reduce2D (primMinusNat (Succ vuz6500) vuz15) (Neg vuz27))",fontsize=16,color="burlywood",shape="box"];4813[label="vuz15/Succ vuz150",fontsize=10,color="white",style="solid",shape="box"];640 -> 4813[label="",style="solid", color="burlywood", weight=9];
4813 -> 659[label="",style="solid", color="burlywood", weight=3];
4814[label="vuz15/Zero",fontsize=10,color="white",style="solid",shape="box"];640 -> 4814[label="",style="solid", color="burlywood", weight=9];
4814 -> 660[label="",style="solid", color="burlywood", weight=3];
641[label="primQuotInt (primMinusNat Zero vuz15) (reduce2D (primMinusNat Zero vuz15) (Neg vuz27))",fontsize=16,color="burlywood",shape="box"];4815[label="vuz15/Succ vuz150",fontsize=10,color="white",style="solid",shape="box"];641 -> 4815[label="",style="solid", color="burlywood", weight=9];
4815 -> 661[label="",style="solid", color="burlywood", weight=3];
4816[label="vuz15/Zero",fontsize=10,color="white",style="solid",shape="box"];641 -> 4816[label="",style="solid", color="burlywood", weight=9];
4816 -> 662[label="",style="solid", color="burlywood", weight=3];
2757[label="Succ vuz15",fontsize=16,color="green",shape="box"];2758 -> 2997[label="",style="dashed", color="red", weight=0];
2758[label="reduce2D (Neg (Succ vuz15)) (Neg vuz27)",fontsize=16,color="magenta"];2758 -> 2999[label="",style="dashed", color="magenta", weight=3];
3058[label="gcd2 (primEqInt (Neg vuz118) (fromInt (Pos Zero))) (Neg vuz118) (Neg vuz27)",fontsize=16,color="burlywood",shape="triangle"];4818[label="vuz118/Succ vuz1180",fontsize=10,color="white",style="solid",shape="box"];3058 -> 4818[label="",style="solid", color="burlywood", weight=9];
4818 -> 3072[label="",style="solid", color="burlywood", weight=3];
4819[label="vuz118/Zero",fontsize=10,color="white",style="solid",shape="box"];3058 -> 4819[label="",style="solid", color="burlywood", weight=9];
4819 -> 3073[label="",style="solid", color="burlywood", weight=3];
3149[label="vuz15",fontsize=16,color="green",shape="box"];3150[label="vuz15",fontsize=16,color="green",shape="box"];3151[label="gcd2 (primEqInt (primMinusNat vuz125 vuz129) (fromInt (Pos Zero))) (primMinusNat vuz125 vuz129) (Neg vuz27)",fontsize=16,color="burlywood",shape="triangle"];4820[label="vuz125/Succ vuz1250",fontsize=10,color="white",style="solid",shape="box"];3151 -> 4820[label="",style="solid", color="burlywood", weight=9];
4820 -> 3166[label="",style="solid", color="burlywood", weight=3];
4821[label="vuz125/Zero",fontsize=10,color="white",style="solid",shape="box"];3151 -> 4821[label="",style="solid", color="burlywood", weight=9];
4821 -> 3167[label="",style="solid", color="burlywood", weight=3];
3152[label="vuz15",fontsize=16,color="green",shape="box"];3153[label="vuz15",fontsize=16,color="green",shape="box"];3154 -> 3058[label="",style="dashed", color="red", weight=0];
3154[label="gcd2 (primEqInt (Neg (primPlusNat vuz127 vuz131)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz127 vuz131)) (Neg vuz27)",fontsize=16,color="magenta"];3154 -> 3168[label="",style="dashed", color="magenta", weight=3];
850[label="vuz150",fontsize=16,color="green",shape="box"];851[label="vuz6700",fontsize=16,color="green",shape="box"];2624[label="gcd2 (primEqInt (Pos (Succ vuz1070)) (fromInt (Pos Zero))) (Pos (Succ vuz1070)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2624 -> 2641[label="",style="solid", color="black", weight=3];
2625[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];2625 -> 2642[label="",style="solid", color="black", weight=3];
651[label="primQuotInt (primMinusNat (Succ vuz80) (Succ vuz7100)) (reduce2D (primMinusNat (Succ vuz80) (Succ vuz7100)) (Pos vuz42))",fontsize=16,color="black",shape="box"];651 -> 672[label="",style="solid", color="black", weight=3];
652[label="primQuotInt (primMinusNat (Succ vuz80) Zero) (reduce2D (primMinusNat (Succ vuz80) Zero) (Pos vuz42))",fontsize=16,color="black",shape="box"];652 -> 673[label="",style="solid", color="black", weight=3];
653[label="primQuotInt (primMinusNat Zero (Succ vuz7100)) (reduce2D (primMinusNat Zero (Succ vuz7100)) (Pos vuz42))",fontsize=16,color="black",shape="box"];653 -> 674[label="",style="solid", color="black", weight=3];
654[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Pos vuz42))",fontsize=16,color="black",shape="box"];654 -> 675[label="",style="solid", color="black", weight=3];
2532[label="Succ vuz8",fontsize=16,color="green",shape="box"];3059 -> 745[label="",style="dashed", color="red", weight=0];
3059[label="primPlusNat vuz114 vuz121",fontsize=16,color="magenta"];3059 -> 3074[label="",style="dashed", color="magenta", weight=3];
3059 -> 3075[label="",style="dashed", color="magenta", weight=3];
3060[label="gcd2 (primEqInt (primMinusNat (Succ vuz1230) vuz116) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1230) vuz116) (Pos vuz42)",fontsize=16,color="burlywood",shape="box"];4824[label="vuz116/Succ vuz1160",fontsize=10,color="white",style="solid",shape="box"];3060 -> 4824[label="",style="solid", color="burlywood", weight=9];
4824 -> 3076[label="",style="solid", color="burlywood", weight=3];
4825[label="vuz116/Zero",fontsize=10,color="white",style="solid",shape="box"];3060 -> 4825[label="",style="solid", color="burlywood", weight=9];
4825 -> 3077[label="",style="solid", color="burlywood", weight=3];
3061[label="gcd2 (primEqInt (primMinusNat Zero vuz116) (fromInt (Pos Zero))) (primMinusNat Zero vuz116) (Pos vuz42)",fontsize=16,color="burlywood",shape="box"];4826[label="vuz116/Succ vuz1160",fontsize=10,color="white",style="solid",shape="box"];3061 -> 4826[label="",style="solid", color="burlywood", weight=9];
4826 -> 3078[label="",style="solid", color="burlywood", weight=3];
4827[label="vuz116/Zero",fontsize=10,color="white",style="solid",shape="box"];3061 -> 4827[label="",style="solid", color="burlywood", weight=9];
4827 -> 3079[label="",style="solid", color="burlywood", weight=3];
2714[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS (Succ vuz1110) (Succ vuz1120))",fontsize=16,color="black",shape="box"];2714 -> 3012[label="",style="solid", color="black", weight=3];
2715[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS (Succ vuz1110) Zero)",fontsize=16,color="black",shape="box"];2715 -> 3013[label="",style="solid", color="black", weight=3];
2716[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS Zero (Succ vuz1120))",fontsize=16,color="black",shape="box"];2716 -> 3014[label="",style="solid", color="black", weight=3];
2717[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2717 -> 3015[label="",style="solid", color="black", weight=3];
1483 -> 1334[label="",style="dashed", color="red", weight=0];
1483[label="primDivNatS (Succ vuz850) (Succ Zero)",fontsize=16,color="magenta"];1483 -> 1505[label="",style="dashed", color="magenta", weight=3];
1483 -> 1506[label="",style="dashed", color="magenta", weight=3];
1484[label="primDivNatS Zero (Succ Zero)",fontsize=16,color="black",shape="box"];1484 -> 1507[label="",style="solid", color="black", weight=3];
659[label="primQuotInt (primMinusNat (Succ vuz6500) (Succ vuz150)) (reduce2D (primMinusNat (Succ vuz6500) (Succ vuz150)) (Neg vuz27))",fontsize=16,color="black",shape="box"];659 -> 681[label="",style="solid", color="black", weight=3];
660[label="primQuotInt (primMinusNat (Succ vuz6500) Zero) (reduce2D (primMinusNat (Succ vuz6500) Zero) (Neg vuz27))",fontsize=16,color="black",shape="box"];660 -> 682[label="",style="solid", color="black", weight=3];
661[label="primQuotInt (primMinusNat Zero (Succ vuz150)) (reduce2D (primMinusNat Zero (Succ vuz150)) (Neg vuz27))",fontsize=16,color="black",shape="box"];661 -> 683[label="",style="solid", color="black", weight=3];
662[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero Zero) (Neg vuz27))",fontsize=16,color="black",shape="box"];662 -> 684[label="",style="solid", color="black", weight=3];
2999[label="Succ vuz15",fontsize=16,color="green",shape="box"];3072[label="gcd2 (primEqInt (Neg (Succ vuz1180)) (fromInt (Pos Zero))) (Neg (Succ vuz1180)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3072 -> 3091[label="",style="solid", color="black", weight=3];
3073[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3073 -> 3092[label="",style="solid", color="black", weight=3];
3166[label="gcd2 (primEqInt (primMinusNat (Succ vuz1250) vuz129) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1250) vuz129) (Neg vuz27)",fontsize=16,color="burlywood",shape="box"];4829[label="vuz129/Succ vuz1290",fontsize=10,color="white",style="solid",shape="box"];3166 -> 4829[label="",style="solid", color="burlywood", weight=9];
4829 -> 3179[label="",style="solid", color="burlywood", weight=3];
4830[label="vuz129/Zero",fontsize=10,color="white",style="solid",shape="box"];3166 -> 4830[label="",style="solid", color="burlywood", weight=9];
4830 -> 3180[label="",style="solid", color="burlywood", weight=3];
3167[label="gcd2 (primEqInt (primMinusNat Zero vuz129) (fromInt (Pos Zero))) (primMinusNat Zero vuz129) (Neg vuz27)",fontsize=16,color="burlywood",shape="box"];4831[label="vuz129/Succ vuz1290",fontsize=10,color="white",style="solid",shape="box"];3167 -> 4831[label="",style="solid", color="burlywood", weight=9];
4831 -> 3181[label="",style="solid", color="burlywood", weight=3];
4832[label="vuz129/Zero",fontsize=10,color="white",style="solid",shape="box"];3167 -> 4832[label="",style="solid", color="burlywood", weight=9];
4832 -> 3182[label="",style="solid", color="burlywood", weight=3];
3168 -> 745[label="",style="dashed", color="red", weight=0];
3168[label="primPlusNat vuz127 vuz131",fontsize=16,color="magenta"];3168 -> 3183[label="",style="dashed", color="magenta", weight=3];
3168 -> 3184[label="",style="dashed", color="magenta", weight=3];
2641[label="gcd2 (primEqInt (Pos (Succ vuz1070)) (Pos Zero)) (Pos (Succ vuz1070)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2641 -> 2690[label="",style="solid", color="black", weight=3];
2642[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];2642 -> 2691[label="",style="solid", color="black", weight=3];
672 -> 619[label="",style="dashed", color="red", weight=0];
672[label="primQuotInt (primMinusNat vuz80 vuz7100) (reduce2D (primMinusNat vuz80 vuz7100) (Pos vuz42))",fontsize=16,color="magenta"];672 -> 694[label="",style="dashed", color="magenta", weight=3];
672 -> 695[label="",style="dashed", color="magenta", weight=3];
673 -> 1881[label="",style="dashed", color="red", weight=0];
673[label="primQuotInt (Pos (Succ vuz80)) (reduce2D (Pos (Succ vuz80)) (Pos vuz42))",fontsize=16,color="magenta"];673 -> 1934[label="",style="dashed", color="magenta", weight=3];
673 -> 1935[label="",style="dashed", color="magenta", weight=3];
674 -> 2729[label="",style="dashed", color="red", weight=0];
674[label="primQuotInt (Neg (Succ vuz7100)) (reduce2D (Neg (Succ vuz7100)) (Pos vuz42))",fontsize=16,color="magenta"];674 -> 2777[label="",style="dashed", color="magenta", weight=3];
674 -> 2778[label="",style="dashed", color="magenta", weight=3];
675 -> 1881[label="",style="dashed", color="red", weight=0];
675[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz42))",fontsize=16,color="magenta"];675 -> 1936[label="",style="dashed", color="magenta", weight=3];
675 -> 1937[label="",style="dashed", color="magenta", weight=3];
3074[label="vuz121",fontsize=16,color="green",shape="box"];3075[label="vuz114",fontsize=16,color="green",shape="box"];3076[label="gcd2 (primEqInt (primMinusNat (Succ vuz1230) (Succ vuz1160)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1230) (Succ vuz1160)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3076 -> 3093[label="",style="solid", color="black", weight=3];
3077[label="gcd2 (primEqInt (primMinusNat (Succ vuz1230) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1230) Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];3077 -> 3094[label="",style="solid", color="black", weight=3];
3078[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz1160)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz1160)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3078 -> 3095[label="",style="solid", color="black", weight=3];
3079[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];3079 -> 3096[label="",style="solid", color="black", weight=3];
3012 -> 2645[label="",style="dashed", color="red", weight=0];
3012[label="primDivNatS0 (Succ vuz109) (Succ vuz110) (primGEqNatS vuz1110 vuz1120)",fontsize=16,color="magenta"];3012 -> 3046[label="",style="dashed", color="magenta", weight=3];
3012 -> 3047[label="",style="dashed", color="magenta", weight=3];
3013[label="primDivNatS0 (Succ vuz109) (Succ vuz110) True",fontsize=16,color="black",shape="triangle"];3013 -> 3048[label="",style="solid", color="black", weight=3];
3014[label="primDivNatS0 (Succ vuz109) (Succ vuz110) False",fontsize=16,color="black",shape="box"];3014 -> 3049[label="",style="solid", color="black", weight=3];
3015 -> 3013[label="",style="dashed", color="red", weight=0];
3015[label="primDivNatS0 (Succ vuz109) (Succ vuz110) True",fontsize=16,color="magenta"];1505[label="vuz850",fontsize=16,color="green",shape="box"];1506[label="Zero",fontsize=16,color="green",shape="box"];1334[label="primDivNatS (Succ vuz85) (Succ vuz8600)",fontsize=16,color="black",shape="triangle"];1334 -> 1357[label="",style="solid", color="black", weight=3];
1507[label="Zero",fontsize=16,color="green",shape="box"];681 -> 624[label="",style="dashed", color="red", weight=0];
681[label="primQuotInt (primMinusNat vuz6500 vuz150) (reduce2D (primMinusNat vuz6500 vuz150) (Neg vuz27))",fontsize=16,color="magenta"];681 -> 704[label="",style="dashed", color="magenta", weight=3];
681 -> 705[label="",style="dashed", color="magenta", weight=3];
682 -> 1881[label="",style="dashed", color="red", weight=0];
682[label="primQuotInt (Pos (Succ vuz6500)) (reduce2D (Pos (Succ vuz6500)) (Neg vuz27))",fontsize=16,color="magenta"];682 -> 1942[label="",style="dashed", color="magenta", weight=3];
682 -> 1943[label="",style="dashed", color="magenta", weight=3];
683 -> 2729[label="",style="dashed", color="red", weight=0];
683[label="primQuotInt (Neg (Succ vuz150)) (reduce2D (Neg (Succ vuz150)) (Neg vuz27))",fontsize=16,color="magenta"];683 -> 2779[label="",style="dashed", color="magenta", weight=3];
683 -> 2780[label="",style="dashed", color="magenta", weight=3];
684 -> 1881[label="",style="dashed", color="red", weight=0];
684[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz27))",fontsize=16,color="magenta"];684 -> 1944[label="",style="dashed", color="magenta", weight=3];
684 -> 1945[label="",style="dashed", color="magenta", weight=3];
3091[label="gcd2 (primEqInt (Neg (Succ vuz1180)) (Pos Zero)) (Neg (Succ vuz1180)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3091 -> 3116[label="",style="solid", color="black", weight=3];
3092[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3092 -> 3117[label="",style="solid", color="black", weight=3];
3179[label="gcd2 (primEqInt (primMinusNat (Succ vuz1250) (Succ vuz1290)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1250) (Succ vuz1290)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3179 -> 3194[label="",style="solid", color="black", weight=3];
3180[label="gcd2 (primEqInt (primMinusNat (Succ vuz1250) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz1250) Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3180 -> 3195[label="",style="solid", color="black", weight=3];
3181[label="gcd2 (primEqInt (primMinusNat Zero (Succ vuz1290)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz1290)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3181 -> 3196[label="",style="solid", color="black", weight=3];
3182[label="gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3182 -> 3197[label="",style="solid", color="black", weight=3];
3183[label="vuz131",fontsize=16,color="green",shape="box"];3184[label="vuz127",fontsize=16,color="green",shape="box"];2690[label="gcd2 False (Pos (Succ vuz1070)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2690 -> 2718[label="",style="solid", color="black", weight=3];
2691[label="gcd2 True (Pos Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];2691 -> 2719[label="",style="solid", color="black", weight=3];
694[label="vuz80",fontsize=16,color="green",shape="box"];695[label="vuz7100",fontsize=16,color="green",shape="box"];1934[label="Succ vuz80",fontsize=16,color="green",shape="box"];1935 -> 2530[label="",style="dashed", color="red", weight=0];
1935[label="reduce2D (Pos (Succ vuz80)) (Pos vuz42)",fontsize=16,color="magenta"];1935 -> 2533[label="",style="dashed", color="magenta", weight=3];
2777[label="Succ vuz7100",fontsize=16,color="green",shape="box"];2778[label="reduce2D (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2778 -> 3016[label="",style="solid", color="black", weight=3];
1936[label="Zero",fontsize=16,color="green",shape="box"];1937 -> 2530[label="",style="dashed", color="red", weight=0];
1937[label="reduce2D (Pos Zero) (Pos vuz42)",fontsize=16,color="magenta"];1937 -> 2534[label="",style="dashed", color="magenta", weight=3];
3093 -> 3045[label="",style="dashed", color="red", weight=0];
3093[label="gcd2 (primEqInt (primMinusNat vuz1230 vuz1160) (fromInt (Pos Zero))) (primMinusNat vuz1230 vuz1160) (Pos vuz42)",fontsize=16,color="magenta"];3093 -> 3118[label="",style="dashed", color="magenta", weight=3];
3093 -> 3119[label="",style="dashed", color="magenta", weight=3];
3094 -> 2607[label="",style="dashed", color="red", weight=0];
3094[label="gcd2 (primEqInt (Pos (Succ vuz1230)) (fromInt (Pos Zero))) (Pos (Succ vuz1230)) (Pos vuz42)",fontsize=16,color="magenta"];3094 -> 3120[label="",style="dashed", color="magenta", weight=3];
3095 -> 3082[label="",style="dashed", color="red", weight=0];
3095[label="gcd2 (primEqInt (Neg (Succ vuz1160)) (fromInt (Pos Zero))) (Neg (Succ vuz1160)) (Pos vuz42)",fontsize=16,color="magenta"];3095 -> 3121[label="",style="dashed", color="magenta", weight=3];
3096 -> 2607[label="",style="dashed", color="red", weight=0];
3096[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz42)",fontsize=16,color="magenta"];3096 -> 3122[label="",style="dashed", color="magenta", weight=3];
3046[label="vuz1120",fontsize=16,color="green",shape="box"];3047[label="vuz1110",fontsize=16,color="green",shape="box"];3048[label="Succ (primDivNatS (primMinusNatS (Succ vuz109) (Succ vuz110)) (Succ (Succ vuz110)))",fontsize=16,color="green",shape="box"];3048 -> 3062[label="",style="dashed", color="green", weight=3];
3049[label="Zero",fontsize=16,color="green",shape="box"];704[label="vuz150",fontsize=16,color="green",shape="box"];705[label="vuz6500",fontsize=16,color="green",shape="box"];1942[label="Succ vuz6500",fontsize=16,color="green",shape="box"];1943[label="reduce2D (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];1943 -> 2544[label="",style="solid", color="black", weight=3];
2779[label="Succ vuz150",fontsize=16,color="green",shape="box"];2780 -> 2997[label="",style="dashed", color="red", weight=0];
2780[label="reduce2D (Neg (Succ vuz150)) (Neg vuz27)",fontsize=16,color="magenta"];2780 -> 3000[label="",style="dashed", color="magenta", weight=3];
1944[label="Zero",fontsize=16,color="green",shape="box"];1945[label="reduce2D (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];1945 -> 2545[label="",style="solid", color="black", weight=3];
3116[label="gcd2 False (Neg (Succ vuz1180)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3116 -> 3132[label="",style="solid", color="black", weight=3];
3117[label="gcd2 True (Neg Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3117 -> 3133[label="",style="solid", color="black", weight=3];
3194 -> 3151[label="",style="dashed", color="red", weight=0];
3194[label="gcd2 (primEqInt (primMinusNat vuz1250 vuz1290) (fromInt (Pos Zero))) (primMinusNat vuz1250 vuz1290) (Neg vuz27)",fontsize=16,color="magenta"];3194 -> 3208[label="",style="dashed", color="magenta", weight=3];
3194 -> 3209[label="",style="dashed", color="magenta", weight=3];
3195 -> 2608[label="",style="dashed", color="red", weight=0];
3195[label="gcd2 (primEqInt (Pos (Succ vuz1250)) (fromInt (Pos Zero))) (Pos (Succ vuz1250)) (Neg vuz27)",fontsize=16,color="magenta"];3195 -> 3210[label="",style="dashed", color="magenta", weight=3];
3196 -> 3058[label="",style="dashed", color="red", weight=0];
3196[label="gcd2 (primEqInt (Neg (Succ vuz1290)) (fromInt (Pos Zero))) (Neg (Succ vuz1290)) (Neg vuz27)",fontsize=16,color="magenta"];3196 -> 3211[label="",style="dashed", color="magenta", weight=3];
3197 -> 2609[label="",style="dashed", color="red", weight=0];
3197[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz27)",fontsize=16,color="magenta"];2718[label="gcd0 (Pos (Succ vuz1070)) (Pos vuz42)",fontsize=16,color="black",shape="box"];2718 -> 3017[label="",style="solid", color="black", weight=3];
2719[label="gcd1 (Pos vuz42 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz42)",fontsize=16,color="black",shape="box"];2719 -> 3018[label="",style="solid", color="black", weight=3];
2533[label="Succ vuz80",fontsize=16,color="green",shape="box"];3016[label="gcd (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3016 -> 3050[label="",style="solid", color="black", weight=3];
2534[label="Zero",fontsize=16,color="green",shape="box"];3118[label="vuz1230",fontsize=16,color="green",shape="box"];3119[label="vuz1160",fontsize=16,color="green",shape="box"];3120[label="Succ vuz1230",fontsize=16,color="green",shape="box"];3121[label="vuz1160",fontsize=16,color="green",shape="box"];3082[label="gcd2 (primEqInt (Neg (Succ vuz7100)) (fromInt (Pos Zero))) (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="triangle"];3082 -> 3098[label="",style="solid", color="black", weight=3];
3122[label="Zero",fontsize=16,color="green",shape="box"];3062 -> 1554[label="",style="dashed", color="red", weight=0];
3062[label="primDivNatS (primMinusNatS (Succ vuz109) (Succ vuz110)) (Succ (Succ vuz110))",fontsize=16,color="magenta"];3062 -> 3080[label="",style="dashed", color="magenta", weight=3];
3062 -> 3081[label="",style="dashed", color="magenta", weight=3];
2544[label="gcd (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2544 -> 2566[label="",style="solid", color="black", weight=3];
3000[label="Succ vuz150",fontsize=16,color="green",shape="box"];2545[label="gcd (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2545 -> 2567[label="",style="solid", color="black", weight=3];
3132[label="gcd0 (Neg (Succ vuz1180)) (Neg vuz27)",fontsize=16,color="black",shape="box"];3132 -> 3155[label="",style="solid", color="black", weight=3];
3133[label="gcd1 (Neg vuz27 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];3133 -> 3156[label="",style="solid", color="black", weight=3];
3208[label="vuz1290",fontsize=16,color="green",shape="box"];3209[label="vuz1250",fontsize=16,color="green",shape="box"];3210[label="vuz1250",fontsize=16,color="green",shape="box"];2608[label="gcd2 (primEqInt (Pos (Succ vuz6500)) (fromInt (Pos Zero))) (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];2608 -> 2626[label="",style="solid", color="black", weight=3];
3211[label="Succ vuz1290",fontsize=16,color="green",shape="box"];2609[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="triangle"];2609 -> 2627[label="",style="solid", color="black", weight=3];
3017[label="gcd0Gcd' (abs (Pos (Succ vuz1070))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3017 -> 3051[label="",style="solid", color="black", weight=3];
3018[label="gcd1 (primEqInt (Pos vuz42) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz42)",fontsize=16,color="burlywood",shape="box"];4856[label="vuz42/Succ vuz420",fontsize=10,color="white",style="solid",shape="box"];3018 -> 4856[label="",style="solid", color="burlywood", weight=9];
4856 -> 3052[label="",style="solid", color="burlywood", weight=3];
4857[label="vuz42/Zero",fontsize=10,color="white",style="solid",shape="box"];3018 -> 4857[label="",style="solid", color="burlywood", weight=9];
4857 -> 3053[label="",style="solid", color="burlywood", weight=3];
3050[label="gcd3 (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3050 -> 3063[label="",style="solid", color="black", weight=3];
3098[label="gcd2 (primEqInt (Neg (Succ vuz7100)) (Pos Zero)) (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3098 -> 3125[label="",style="solid", color="black", weight=3];
3080[label="Succ vuz110",fontsize=16,color="green",shape="box"];3081[label="primMinusNatS (Succ vuz109) (Succ vuz110)",fontsize=16,color="black",shape="box"];3081 -> 3097[label="",style="solid", color="black", weight=3];
2566[label="gcd3 (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2566 -> 2585[label="",style="solid", color="black", weight=3];
2567[label="gcd3 (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2567 -> 2586[label="",style="solid", color="black", weight=3];
3155[label="gcd0Gcd' (abs (Neg (Succ vuz1180))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3155 -> 3169[label="",style="solid", color="black", weight=3];
3156[label="gcd1 (primEqInt (Neg vuz27) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz27)",fontsize=16,color="burlywood",shape="box"];4858[label="vuz27/Succ vuz270",fontsize=10,color="white",style="solid",shape="box"];3156 -> 4858[label="",style="solid", color="burlywood", weight=9];
4858 -> 3170[label="",style="solid", color="burlywood", weight=3];
4859[label="vuz27/Zero",fontsize=10,color="white",style="solid",shape="box"];3156 -> 4859[label="",style="solid", color="burlywood", weight=9];
4859 -> 3171[label="",style="solid", color="burlywood", weight=3];
2626[label="gcd2 (primEqInt (Pos (Succ vuz6500)) (Pos Zero)) (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2626 -> 2643[label="",style="solid", color="black", weight=3];
2627[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2627 -> 2644[label="",style="solid", color="black", weight=3];
3051[label="gcd0Gcd'2 (abs (Pos (Succ vuz1070))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3051 -> 3064[label="",style="solid", color="black", weight=3];
3052[label="gcd1 (primEqInt (Pos (Succ vuz420)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3052 -> 3065[label="",style="solid", color="black", weight=3];
3053[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];3053 -> 3066[label="",style="solid", color="black", weight=3];
3063[label="gcd2 (Neg (Succ vuz7100) == fromInt (Pos Zero)) (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3063 -> 3082[label="",style="solid", color="black", weight=3];
3125[label="gcd2 False (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3125 -> 3138[label="",style="solid", color="black", weight=3];
3097[label="primMinusNatS vuz109 vuz110",fontsize=16,color="burlywood",shape="triangle"];4860[label="vuz109/Succ vuz1090",fontsize=10,color="white",style="solid",shape="box"];3097 -> 4860[label="",style="solid", color="burlywood", weight=9];
4860 -> 3123[label="",style="solid", color="burlywood", weight=3];
4861[label="vuz109/Zero",fontsize=10,color="white",style="solid",shape="box"];3097 -> 4861[label="",style="solid", color="burlywood", weight=9];
4861 -> 3124[label="",style="solid", color="burlywood", weight=3];
2585[label="gcd2 (Pos (Succ vuz6500) == fromInt (Pos Zero)) (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2585 -> 2608[label="",style="solid", color="black", weight=3];
2586[label="gcd2 (Pos Zero == fromInt (Pos Zero)) (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2586 -> 2609[label="",style="solid", color="black", weight=3];
3169[label="gcd0Gcd'2 (abs (Neg (Succ vuz1180))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3169 -> 3185[label="",style="solid", color="black", weight=3];
3170[label="gcd1 (primEqInt (Neg (Succ vuz270)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3170 -> 3186[label="",style="solid", color="black", weight=3];
3171[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3171 -> 3187[label="",style="solid", color="black", weight=3];
2643[label="gcd2 False (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2643 -> 2692[label="",style="solid", color="black", weight=3];
2644[label="gcd2 True (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2644 -> 2693[label="",style="solid", color="black", weight=3];
3064[label="gcd0Gcd'1 (abs (Pos vuz42) == fromInt (Pos Zero)) (abs (Pos (Succ vuz1070))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3064 -> 3083[label="",style="solid", color="black", weight=3];
3065[label="gcd1 (primEqInt (Pos (Succ vuz420)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3065 -> 3084[label="",style="solid", color="black", weight=3];
3066[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];3066 -> 3085[label="",style="solid", color="black", weight=3];
3138[label="gcd0 (Neg (Succ vuz7100)) (Pos vuz42)",fontsize=16,color="black",shape="box"];3138 -> 3157[label="",style="solid", color="black", weight=3];
3123[label="primMinusNatS (Succ vuz1090) vuz110",fontsize=16,color="burlywood",shape="box"];4862[label="vuz110/Succ vuz1100",fontsize=10,color="white",style="solid",shape="box"];3123 -> 4862[label="",style="solid", color="burlywood", weight=9];
4862 -> 3134[label="",style="solid", color="burlywood", weight=3];
4863[label="vuz110/Zero",fontsize=10,color="white",style="solid",shape="box"];3123 -> 4863[label="",style="solid", color="burlywood", weight=9];
4863 -> 3135[label="",style="solid", color="burlywood", weight=3];
3124[label="primMinusNatS Zero vuz110",fontsize=16,color="burlywood",shape="box"];4864[label="vuz110/Succ vuz1100",fontsize=10,color="white",style="solid",shape="box"];3124 -> 4864[label="",style="solid", color="burlywood", weight=9];
4864 -> 3136[label="",style="solid", color="burlywood", weight=3];
4865[label="vuz110/Zero",fontsize=10,color="white",style="solid",shape="box"];3124 -> 4865[label="",style="solid", color="burlywood", weight=9];
4865 -> 3137[label="",style="solid", color="burlywood", weight=3];
3185[label="gcd0Gcd'1 (abs (Neg vuz27) == fromInt (Pos Zero)) (abs (Neg (Succ vuz1180))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3185 -> 3198[label="",style="solid", color="black", weight=3];
3186[label="gcd1 (primEqInt (Neg (Succ vuz270)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3186 -> 3199[label="",style="solid", color="black", weight=3];
3187[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3187 -> 3200[label="",style="solid", color="black", weight=3];
2692[label="gcd0 (Pos (Succ vuz6500)) (Neg vuz27)",fontsize=16,color="black",shape="box"];2692 -> 2720[label="",style="solid", color="black", weight=3];
2693[label="gcd1 (Neg vuz27 == fromInt (Pos Zero)) (Pos Zero) (Neg vuz27)",fontsize=16,color="black",shape="box"];2693 -> 2721[label="",style="solid", color="black", weight=3];
3083[label="gcd0Gcd'1 (primEqInt (abs (Pos vuz42)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3083 -> 3099[label="",style="solid", color="black", weight=3];
3084[label="gcd1 False (Pos Zero) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3084 -> 3100[label="",style="solid", color="black", weight=3];
3085[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];3085 -> 3101[label="",style="solid", color="black", weight=3];
3157[label="gcd0Gcd' (abs (Neg (Succ vuz7100))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3157 -> 3172[label="",style="solid", color="black", weight=3];
3134[label="primMinusNatS (Succ vuz1090) (Succ vuz1100)",fontsize=16,color="black",shape="box"];3134 -> 3158[label="",style="solid", color="black", weight=3];
3135[label="primMinusNatS (Succ vuz1090) Zero",fontsize=16,color="black",shape="box"];3135 -> 3159[label="",style="solid", color="black", weight=3];
3136[label="primMinusNatS Zero (Succ vuz1100)",fontsize=16,color="black",shape="box"];3136 -> 3160[label="",style="solid", color="black", weight=3];
3137[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];3137 -> 3161[label="",style="solid", color="black", weight=3];
3198[label="gcd0Gcd'1 (primEqInt (abs (Neg vuz27)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3198 -> 3212[label="",style="solid", color="black", weight=3];
3199[label="gcd1 False (Neg Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3199 -> 3213[label="",style="solid", color="black", weight=3];
3200[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3200 -> 3214[label="",style="solid", color="black", weight=3];
2720[label="gcd0Gcd' (abs (Pos (Succ vuz6500))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];2720 -> 3019[label="",style="solid", color="black", weight=3];
2721[label="gcd1 (primEqInt (Neg vuz27) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz27)",fontsize=16,color="burlywood",shape="box"];4866[label="vuz27/Succ vuz270",fontsize=10,color="white",style="solid",shape="box"];2721 -> 4866[label="",style="solid", color="burlywood", weight=9];
4866 -> 3020[label="",style="solid", color="burlywood", weight=3];
4867[label="vuz27/Zero",fontsize=10,color="white",style="solid",shape="box"];2721 -> 4867[label="",style="solid", color="burlywood", weight=9];
4867 -> 3021[label="",style="solid", color="burlywood", weight=3];
3099[label="gcd0Gcd'1 (primEqInt (absReal (Pos vuz42)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal (Pos vuz42))",fontsize=16,color="black",shape="box"];3099 -> 3126[label="",style="solid", color="black", weight=3];
3100[label="gcd0 (Pos Zero) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3100 -> 3127[label="",style="solid", color="black", weight=3];
3101 -> 1311[label="",style="dashed", color="red", weight=0];
3101[label="error []",fontsize=16,color="magenta"];3172[label="gcd0Gcd'2 (abs (Neg (Succ vuz7100))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3172 -> 3188[label="",style="solid", color="black", weight=3];
3158 -> 3097[label="",style="dashed", color="red", weight=0];
3158[label="primMinusNatS vuz1090 vuz1100",fontsize=16,color="magenta"];3158 -> 3173[label="",style="dashed", color="magenta", weight=3];
3158 -> 3174[label="",style="dashed", color="magenta", weight=3];
3159[label="Succ vuz1090",fontsize=16,color="green",shape="box"];3160[label="Zero",fontsize=16,color="green",shape="box"];3161[label="Zero",fontsize=16,color="green",shape="box"];3212[label="gcd0Gcd'1 (primEqInt (absReal (Neg vuz27)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal (Neg vuz27))",fontsize=16,color="black",shape="box"];3212 -> 3222[label="",style="solid", color="black", weight=3];
3213[label="gcd0 (Neg Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3213 -> 3223[label="",style="solid", color="black", weight=3];
3214 -> 1311[label="",style="dashed", color="red", weight=0];
3214[label="error []",fontsize=16,color="magenta"];3019[label="gcd0Gcd'2 (abs (Pos (Succ vuz6500))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3019 -> 3054[label="",style="solid", color="black", weight=3];
3020[label="gcd1 (primEqInt (Neg (Succ vuz270)) (fromInt (Pos Zero))) (Pos Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3020 -> 3055[label="",style="solid", color="black", weight=3];
3021[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3021 -> 3056[label="",style="solid", color="black", weight=3];
3126[label="gcd0Gcd'1 (primEqInt (absReal2 (Pos vuz42)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal2 (Pos vuz42))",fontsize=16,color="black",shape="box"];3126 -> 3139[label="",style="solid", color="black", weight=3];
3127[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3127 -> 3140[label="",style="solid", color="black", weight=3];
3188[label="gcd0Gcd'1 (abs (Pos vuz42) == fromInt (Pos Zero)) (abs (Neg (Succ vuz7100))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3188 -> 3201[label="",style="solid", color="black", weight=3];
3173[label="vuz1090",fontsize=16,color="green",shape="box"];3174[label="vuz1100",fontsize=16,color="green",shape="box"];3222[label="gcd0Gcd'1 (primEqInt (absReal2 (Neg vuz27)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal2 (Neg vuz27))",fontsize=16,color="black",shape="box"];3222 -> 3231[label="",style="solid", color="black", weight=3];
3223[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3223 -> 3232[label="",style="solid", color="black", weight=3];
3054[label="gcd0Gcd'1 (abs (Neg vuz27) == fromInt (Pos Zero)) (abs (Pos (Succ vuz6500))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3054 -> 3067[label="",style="solid", color="black", weight=3];
3055[label="gcd1 (primEqInt (Neg (Succ vuz270)) (Pos Zero)) (Pos Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3055 -> 3068[label="",style="solid", color="black", weight=3];
3056[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3056 -> 3069[label="",style="solid", color="black", weight=3];
3139[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (Pos vuz42 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos vuz42) (Pos vuz42 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3139 -> 3162[label="",style="solid", color="black", weight=3];
3140[label="gcd0Gcd'2 (abs (Pos Zero)) (abs (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3140 -> 3163[label="",style="solid", color="black", weight=3];
3201[label="gcd0Gcd'1 (primEqInt (abs (Pos vuz42)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (abs (Pos vuz42))",fontsize=16,color="black",shape="box"];3201 -> 3215[label="",style="solid", color="black", weight=3];
3231[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (Neg vuz27 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg vuz27) (Neg vuz27 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3231 -> 3240[label="",style="solid", color="black", weight=3];
3232[label="gcd0Gcd'2 (abs (Neg Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3232 -> 3241[label="",style="solid", color="black", weight=3];
3067[label="gcd0Gcd'1 (primEqInt (abs (Neg vuz27)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (abs (Neg vuz27))",fontsize=16,color="black",shape="box"];3067 -> 3086[label="",style="solid", color="black", weight=3];
3068[label="gcd1 False (Pos Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3068 -> 3087[label="",style="solid", color="black", weight=3];
3069[label="gcd1 True (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];3069 -> 3088[label="",style="solid", color="black", weight=3];
3162[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (compare (Pos vuz42) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos vuz42) (compare (Pos vuz42) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3162 -> 3175[label="",style="solid", color="black", weight=3];
3163[label="gcd0Gcd'1 (abs (Pos (Succ vuz420)) == fromInt (Pos Zero)) (abs (Pos Zero)) (abs (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3163 -> 3176[label="",style="solid", color="black", weight=3];
3215[label="gcd0Gcd'1 (primEqInt (absReal (Pos vuz42)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal (Pos vuz42))",fontsize=16,color="black",shape="box"];3215 -> 3224[label="",style="solid", color="black", weight=3];
3240[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (compare (Neg vuz27) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg vuz27) (compare (Neg vuz27) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3240 -> 3249[label="",style="solid", color="black", weight=3];
3241[label="gcd0Gcd'1 (abs (Neg (Succ vuz270)) == fromInt (Pos Zero)) (abs (Neg Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3241 -> 3250[label="",style="solid", color="black", weight=3];
3086[label="gcd0Gcd'1 (primEqInt (absReal (Neg vuz27)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal (Neg vuz27))",fontsize=16,color="black",shape="box"];3086 -> 3102[label="",style="solid", color="black", weight=3];
3087[label="gcd0 (Pos Zero) (Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3087 -> 3103[label="",style="solid", color="black", weight=3];
3088 -> 1311[label="",style="dashed", color="red", weight=0];
3088[label="error []",fontsize=16,color="magenta"];3175[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (not (compare (Pos vuz42) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos vuz42) (not (compare (Pos vuz42) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3175 -> 3189[label="",style="solid", color="black", weight=3];
3176[label="gcd0Gcd'1 (primEqInt (abs (Pos (Succ vuz420))) (fromInt (Pos Zero))) (abs (Pos Zero)) (abs (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3176 -> 3190[label="",style="solid", color="black", weight=3];
3224[label="gcd0Gcd'1 (primEqInt (absReal2 (Pos vuz42)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal2 (Pos vuz42))",fontsize=16,color="black",shape="box"];3224 -> 3233[label="",style="solid", color="black", weight=3];
3249[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (not (compare (Neg vuz27) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg vuz27) (not (compare (Neg vuz27) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3249 -> 3258[label="",style="solid", color="black", weight=3];
3250[label="gcd0Gcd'1 (primEqInt (abs (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Neg Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3250 -> 3259[label="",style="solid", color="black", weight=3];
3102[label="gcd0Gcd'1 (primEqInt (absReal2 (Neg vuz27)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal2 (Neg vuz27))",fontsize=16,color="black",shape="box"];3102 -> 3128[label="",style="solid", color="black", weight=3];
3103[label="gcd0Gcd' (abs (Pos Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3103 -> 3129[label="",style="solid", color="black", weight=3];
3189[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (not (primCmpInt (Pos vuz42) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos vuz42) (not (primCmpInt (Pos vuz42) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];4872[label="vuz42/Succ vuz420",fontsize=10,color="white",style="solid",shape="box"];3189 -> 4872[label="",style="solid", color="burlywood", weight=9];
4872 -> 3202[label="",style="solid", color="burlywood", weight=3];
4873[label="vuz42/Zero",fontsize=10,color="white",style="solid",shape="box"];3189 -> 4873[label="",style="solid", color="burlywood", weight=9];
4873 -> 3203[label="",style="solid", color="burlywood", weight=3];
3190[label="gcd0Gcd'1 (primEqInt (absReal (Pos (Succ vuz420))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3190 -> 3204[label="",style="solid", color="black", weight=3];
3233[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (Pos vuz42 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos vuz42) (Pos vuz42 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3233 -> 3242[label="",style="solid", color="black", weight=3];
3258[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (not (primCmpInt (Neg vuz27) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg vuz27) (not (primCmpInt (Neg vuz27) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];4874[label="vuz27/Succ vuz270",fontsize=10,color="white",style="solid",shape="box"];3258 -> 4874[label="",style="solid", color="burlywood", weight=9];
4874 -> 3267[label="",style="solid", color="burlywood", weight=3];
4875[label="vuz27/Zero",fontsize=10,color="white",style="solid",shape="box"];3258 -> 4875[label="",style="solid", color="burlywood", weight=9];
4875 -> 3268[label="",style="solid", color="burlywood", weight=3];
3259[label="gcd0Gcd'1 (primEqInt (absReal (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3259 -> 3269[label="",style="solid", color="black", weight=3];
3128[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (Neg vuz27 >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg vuz27) (Neg vuz27 >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3128 -> 3141[label="",style="solid", color="black", weight=3];
3129[label="gcd0Gcd'2 (abs (Pos Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3129 -> 3142[label="",style="solid", color="black", weight=3];
3202[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3202 -> 3216[label="",style="solid", color="black", weight=3];
3203[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3203 -> 3217[label="",style="solid", color="black", weight=3];
3204[label="gcd0Gcd'1 (primEqInt (absReal2 (Pos (Succ vuz420))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal2 (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3204 -> 3218[label="",style="solid", color="black", weight=3];
3242[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (compare (Pos vuz42) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos vuz42) (compare (Pos vuz42) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3242 -> 3251[label="",style="solid", color="black", weight=3];
3267[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3267 -> 3278[label="",style="solid", color="black", weight=3];
3268[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3268 -> 3279[label="",style="solid", color="black", weight=3];
3269[label="gcd0Gcd'1 (primEqInt (absReal2 (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal2 (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3269 -> 3280[label="",style="solid", color="black", weight=3];
3141[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (compare (Neg vuz27) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg vuz27) (compare (Neg vuz27) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3141 -> 3164[label="",style="solid", color="black", weight=3];
3142[label="gcd0Gcd'1 (abs (Neg (Succ vuz270)) == fromInt (Pos Zero)) (abs (Pos Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3142 -> 3165[label="",style="solid", color="black", weight=3];
3216[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3216 -> 3225[label="",style="solid", color="black", weight=3];
3217[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3217 -> 3226[label="",style="solid", color="black", weight=3];
3218[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (Pos (Succ vuz420) >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (Pos (Succ vuz420) >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3218 -> 3227[label="",style="solid", color="black", weight=3];
3251[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (not (compare (Pos vuz42) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos vuz42) (not (compare (Pos vuz42) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3251 -> 3260[label="",style="solid", color="black", weight=3];
3278[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3278 -> 3289[label="",style="solid", color="black", weight=3];
3279[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3279 -> 3290[label="",style="solid", color="black", weight=3];
3280[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (Neg (Succ vuz270) >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (Neg (Succ vuz270) >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3280 -> 3291[label="",style="solid", color="black", weight=3];
3164[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (not (compare (Neg vuz27) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg vuz27) (not (compare (Neg vuz27) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3164 -> 3177[label="",style="solid", color="black", weight=3];
3165[label="gcd0Gcd'1 (primEqInt (abs (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Pos Zero)) (abs (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3165 -> 3178[label="",style="solid", color="black", weight=3];
3225[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT)))",fontsize=16,color="black",shape="box"];3225 -> 3234[label="",style="solid", color="black", weight=3];
3226[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (EQ == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos Zero) (not (EQ == LT)))",fontsize=16,color="black",shape="box"];3226 -> 3235[label="",style="solid", color="black", weight=3];
3227[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (compare (Pos (Succ vuz420)) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (compare (Pos (Succ vuz420)) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3227 -> 3236[label="",style="solid", color="black", weight=3];
3260[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos vuz42) (not (primCmpInt (Pos vuz42) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos vuz42) (not (primCmpInt (Pos vuz42) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];4876[label="vuz42/Succ vuz420",fontsize=10,color="white",style="solid",shape="box"];3260 -> 4876[label="",style="solid", color="burlywood", weight=9];
4876 -> 3270[label="",style="solid", color="burlywood", weight=3];
4877[label="vuz42/Zero",fontsize=10,color="white",style="solid",shape="box"];3260 -> 4877[label="",style="solid", color="burlywood", weight=9];
4877 -> 3271[label="",style="solid", color="burlywood", weight=3];
3289[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg (Succ vuz270)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];3289 -> 3296[label="",style="solid", color="black", weight=3];
3290[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (EQ == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg Zero) (not (EQ == LT)))",fontsize=16,color="black",shape="box"];3290 -> 3297[label="",style="solid", color="black", weight=3];
3291[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3291 -> 3298[label="",style="solid", color="black", weight=3];
3177[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg vuz27) (not (primCmpInt (Neg vuz27) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg vuz27) (not (primCmpInt (Neg vuz27) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="burlywood",shape="box"];4878[label="vuz27/Succ vuz270",fontsize=10,color="white",style="solid",shape="box"];3177 -> 4878[label="",style="solid", color="burlywood", weight=9];
4878 -> 3191[label="",style="solid", color="burlywood", weight=3];
4879[label="vuz27/Zero",fontsize=10,color="white",style="solid",shape="box"];3177 -> 4879[label="",style="solid", color="burlywood", weight=9];
4879 -> 3192[label="",style="solid", color="burlywood", weight=3];
3178[label="gcd0Gcd'1 (primEqInt (absReal (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3178 -> 3193[label="",style="solid", color="black", weight=3];
3234[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) (not (GT == LT)))",fontsize=16,color="black",shape="box"];3234 -> 3243[label="",style="solid", color="black", weight=3];
3235[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not False)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos Zero) (not False))",fontsize=16,color="black",shape="box"];3235 -> 3244[label="",style="solid", color="black", weight=3];
3236[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (compare (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not (compare (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3236 -> 3245[label="",style="solid", color="black", weight=3];
3270[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3270 -> 3281[label="",style="solid", color="black", weight=3];
3271[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3271 -> 3282[label="",style="solid", color="black", weight=3];
3296[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not True)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg (Succ vuz270)) (not True))",fontsize=16,color="black",shape="box"];3296 -> 3309[label="",style="solid", color="black", weight=3];
3297[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not False)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg Zero) (not False))",fontsize=16,color="black",shape="box"];3297 -> 3310[label="",style="solid", color="black", weight=3];
3298[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (not (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3298 -> 3311[label="",style="solid", color="black", weight=3];
3191[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3191 -> 3205[label="",style="solid", color="black", weight=3];
3192[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3192 -> 3206[label="",style="solid", color="black", weight=3];
3193[label="gcd0Gcd'1 (primEqInt (absReal2 (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal2 (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3193 -> 3207[label="",style="solid", color="black", weight=3];
3243[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not False)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) (not False))",fontsize=16,color="black",shape="box"];3243 -> 3252[label="",style="solid", color="black", weight=3];
3244[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos Zero) True)",fontsize=16,color="black",shape="box"];3244 -> 3253[label="",style="solid", color="black", weight=3];
3245[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3245 -> 3254[label="",style="solid", color="black", weight=3];
3281[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3281 -> 3292[label="",style="solid", color="black", weight=3];
3282[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3282 -> 3293[label="",style="solid", color="black", weight=3];
3309[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) False) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg (Succ vuz270)) False)",fontsize=16,color="black",shape="box"];3309 -> 3318[label="",style="solid", color="black", weight=3];
3310[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal1 (Neg Zero) True)",fontsize=16,color="black",shape="box"];3310 -> 3319[label="",style="solid", color="black", weight=3];
3311[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3311 -> 3320[label="",style="solid", color="black", weight=3];
3205[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3205 -> 3219[label="",style="solid", color="black", weight=3];
3206[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3206 -> 3220[label="",style="solid", color="black", weight=3];
3207[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (Neg (Succ vuz270) >= fromInt (Pos Zero))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (Neg (Succ vuz270) >= fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];3207 -> 3221[label="",style="solid", color="black", weight=3];
3252[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (absReal1 (Pos (Succ vuz420)) True)",fontsize=16,color="black",shape="box"];3252 -> 3261[label="",style="solid", color="black", weight=3];
3253[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (Pos Zero)",fontsize=16,color="black",shape="box"];3253 -> 3262[label="",style="solid", color="black", weight=3];
3254[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not (primCmpInt (Pos (Succ vuz420)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3254 -> 3263[label="",style="solid", color="black", weight=3];
3292[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT)))",fontsize=16,color="black",shape="box"];3292 -> 3299[label="",style="solid", color="black", weight=3];
3293[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not (EQ == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos Zero) (not (EQ == LT)))",fontsize=16,color="black",shape="box"];3293 -> 3300[label="",style="solid", color="black", weight=3];
3318[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) otherwise) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal0 (Neg (Succ vuz270)) otherwise)",fontsize=16,color="black",shape="box"];3318 -> 3327[label="",style="solid", color="black", weight=3];
3319[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (Neg Zero)",fontsize=16,color="black",shape="box"];3319 -> 3328[label="",style="solid", color="black", weight=3];
3320[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3320 -> 3329[label="",style="solid", color="black", weight=3];
3219[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg (Succ vuz270)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];3219 -> 3228[label="",style="solid", color="black", weight=3];
3220[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not (EQ == LT))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg Zero) (not (EQ == LT)))",fontsize=16,color="black",shape="box"];3220 -> 3229[label="",style="solid", color="black", weight=3];
3221[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) /= LT)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) /= LT))",fontsize=16,color="black",shape="box"];3221 -> 3230[label="",style="solid", color="black", weight=3];
3261[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz1070))) (Pos (Succ vuz420))",fontsize=16,color="black",shape="triangle"];3261 -> 3272[label="",style="solid", color="black", weight=3];
3262[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (abs (Pos (Succ vuz1070))) (Pos Zero)",fontsize=16,color="black",shape="box"];3262 -> 3273[label="",style="solid", color="black", weight=3];
3263[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not (primCmpNat (Succ vuz420) Zero == LT)))",fontsize=16,color="black",shape="box"];3263 -> 3274[label="",style="solid", color="black", weight=3];
3299[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) (not (GT == LT)))",fontsize=16,color="black",shape="box"];3299 -> 3312[label="",style="solid", color="black", weight=3];
3300[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) (not False)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos Zero) (not False))",fontsize=16,color="black",shape="box"];3300 -> 3313[label="",style="solid", color="black", weight=3];
3327[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (absReal0 (Neg (Succ vuz270)) True)",fontsize=16,color="black",shape="box"];3327 -> 3336[label="",style="solid", color="black", weight=3];
3328[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (abs (Neg (Succ vuz1180))) (Neg Zero)",fontsize=16,color="black",shape="box"];3328 -> 3337[label="",style="solid", color="black", weight=3];
3329[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];3329 -> 3338[label="",style="solid", color="black", weight=3];
3228[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not True)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg (Succ vuz270)) (not True))",fontsize=16,color="black",shape="box"];3228 -> 3237[label="",style="solid", color="black", weight=3];
3229[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) (not False)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg Zero) (not False))",fontsize=16,color="black",shape="box"];3229 -> 3238[label="",style="solid", color="black", weight=3];
3230[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (not (compare (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3230 -> 3239[label="",style="solid", color="black", weight=3];
3272[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (Pos Zero)) (abs (Pos (Succ vuz1070))) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3272 -> 3283[label="",style="solid", color="black", weight=3];
3273[label="gcd0Gcd'1 True (abs (Pos (Succ vuz1070))) (Pos Zero)",fontsize=16,color="black",shape="box"];3273 -> 3284[label="",style="solid", color="black", weight=3];
3274[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not (GT == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not (GT == LT)))",fontsize=16,color="black",shape="box"];3274 -> 3285[label="",style="solid", color="black", weight=3];
3312[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not False)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) (not False))",fontsize=16,color="black",shape="box"];3312 -> 3321[label="",style="solid", color="black", weight=3];
3313[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos Zero) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos Zero) True)",fontsize=16,color="black",shape="box"];3313 -> 3322[label="",style="solid", color="black", weight=3];
3336[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuz270)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (`negate` Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3336 -> 3345[label="",style="solid", color="black", weight=3];
3337[label="gcd0Gcd'1 True (abs (Neg (Succ vuz1180))) (Neg Zero)",fontsize=16,color="black",shape="box"];3337 -> 3346[label="",style="solid", color="black", weight=3];
3338[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not True)) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) (not True))",fontsize=16,color="black",shape="box"];3338 -> 3347[label="",style="solid", color="black", weight=3];
3237[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) False) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg (Succ vuz270)) False)",fontsize=16,color="black",shape="box"];3237 -> 3246[label="",style="solid", color="black", weight=3];
3238[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg Zero) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal1 (Neg Zero) True)",fontsize=16,color="black",shape="box"];3238 -> 3247[label="",style="solid", color="black", weight=3];
3239[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (fromInt (Pos Zero)) == LT)))",fontsize=16,color="black",shape="box"];3239 -> 3248[label="",style="solid", color="black", weight=3];
3283 -> 3294[label="",style="dashed", color="red", weight=0];
3283[label="gcd0Gcd'1 False (abs (Pos (Succ vuz1070))) (Pos (Succ vuz420))",fontsize=16,color="magenta"];3283 -> 3295[label="",style="dashed", color="magenta", weight=3];
3284 -> 3276[label="",style="dashed", color="red", weight=0];
3284[label="abs (Pos (Succ vuz1070))",fontsize=16,color="magenta"];3284 -> 3301[label="",style="dashed", color="magenta", weight=3];
3285[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) (not False)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) (not False))",fontsize=16,color="black",shape="box"];3285 -> 3302[label="",style="solid", color="black", weight=3];
3321[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) True) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (absReal1 (Pos (Succ vuz420)) True)",fontsize=16,color="black",shape="box"];3321 -> 3330[label="",style="solid", color="black", weight=3];
3322[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (Pos Zero)",fontsize=16,color="black",shape="box"];3322 -> 3331[label="",style="solid", color="black", weight=3];
3345[label="gcd0Gcd'1 (primEqInt (primNegInt (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (primNegInt (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3345 -> 3353[label="",style="solid", color="black", weight=3];
3346[label="abs (Neg (Succ vuz1180))",fontsize=16,color="black",shape="triangle"];3346 -> 3354[label="",style="solid", color="black", weight=3];
3347[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) False) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal1 (Neg (Succ vuz270)) False)",fontsize=16,color="black",shape="box"];3347 -> 3355[label="",style="solid", color="black", weight=3];
3246[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) otherwise) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal0 (Neg (Succ vuz270)) otherwise)",fontsize=16,color="black",shape="box"];3246 -> 3255[label="",style="solid", color="black", weight=3];
3247[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (Neg Zero)",fontsize=16,color="black",shape="box"];3247 -> 3256[label="",style="solid", color="black", weight=3];
3248[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (not (primCmpInt (Neg (Succ vuz270)) (Pos Zero) == LT)))",fontsize=16,color="black",shape="box"];3248 -> 3257[label="",style="solid", color="black", weight=3];
3295 -> 3276[label="",style="dashed", color="red", weight=0];
3295[label="abs (Pos (Succ vuz1070))",fontsize=16,color="magenta"];3295 -> 3303[label="",style="dashed", color="magenta", weight=3];
3294[label="gcd0Gcd'1 False vuz132 (Pos (Succ vuz420))",fontsize=16,color="black",shape="triangle"];3294 -> 3304[label="",style="solid", color="black", weight=3];
3301[label="vuz1070",fontsize=16,color="green",shape="box"];3276[label="abs (Pos (Succ vuz6500))",fontsize=16,color="black",shape="triangle"];3276 -> 3287[label="",style="solid", color="black", weight=3];
3302[label="gcd0Gcd'1 (primEqInt (absReal1 (Pos (Succ vuz420)) True) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Pos (Succ vuz420)) True)",fontsize=16,color="black",shape="box"];3302 -> 3314[label="",style="solid", color="black", weight=3];
3330[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz7100))) (Pos (Succ vuz420))",fontsize=16,color="black",shape="triangle"];3330 -> 3339[label="",style="solid", color="black", weight=3];
3331[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (abs (Neg (Succ vuz7100))) (Pos Zero)",fontsize=16,color="black",shape="box"];3331 -> 3340[label="",style="solid", color="black", weight=3];
3353 -> 3330[label="",style="dashed", color="red", weight=0];
3353[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz270)) (fromInt (Pos Zero))) (abs (Neg (Succ vuz1180))) (Pos (Succ vuz270))",fontsize=16,color="magenta"];3353 -> 3362[label="",style="dashed", color="magenta", weight=3];
3353 -> 3363[label="",style="dashed", color="magenta", weight=3];
3354[label="absReal (Neg (Succ vuz1180))",fontsize=16,color="black",shape="box"];3354 -> 3364[label="",style="solid", color="black", weight=3];
3355[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) otherwise) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal0 (Neg (Succ vuz270)) otherwise)",fontsize=16,color="black",shape="box"];3355 -> 3365[label="",style="solid", color="black", weight=3];
3255[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) True) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (absReal0 (Neg (Succ vuz270)) True)",fontsize=16,color="black",shape="box"];3255 -> 3264[label="",style="solid", color="black", weight=3];
3256[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (abs (Pos (Succ vuz6500))) (Neg Zero)",fontsize=16,color="black",shape="box"];3256 -> 3265[label="",style="solid", color="black", weight=3];
3257[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not (LT == LT))) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (not (LT == LT)))",fontsize=16,color="black",shape="box"];3257 -> 3266[label="",style="solid", color="black", weight=3];
3303[label="vuz1070",fontsize=16,color="green",shape="box"];3304[label="gcd0Gcd'0 vuz132 (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3304 -> 3315[label="",style="solid", color="black", weight=3];
3287[label="absReal (Pos (Succ vuz6500))",fontsize=16,color="black",shape="box"];3287 -> 3307[label="",style="solid", color="black", weight=3];
3314[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (fromInt (Pos Zero))) (abs (Pos Zero)) (Pos (Succ vuz420))",fontsize=16,color="black",shape="triangle"];3314 -> 3323[label="",style="solid", color="black", weight=3];
3339[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (Pos Zero)) (abs (Neg (Succ vuz7100))) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3339 -> 3348[label="",style="solid", color="black", weight=3];
3340[label="gcd0Gcd'1 True (abs (Neg (Succ vuz7100))) (Pos Zero)",fontsize=16,color="black",shape="box"];3340 -> 3349[label="",style="solid", color="black", weight=3];
3362[label="vuz1180",fontsize=16,color="green",shape="box"];3363[label="vuz270",fontsize=16,color="green",shape="box"];3364[label="absReal2 (Neg (Succ vuz1180))",fontsize=16,color="black",shape="box"];3364 -> 3371[label="",style="solid", color="black", weight=3];
3365[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) True) (fromInt (Pos Zero))) (abs (Neg Zero)) (absReal0 (Neg (Succ vuz270)) True)",fontsize=16,color="black",shape="box"];3365 -> 3372[label="",style="solid", color="black", weight=3];
3264[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuz270)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (`negate` Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3264 -> 3275[label="",style="solid", color="black", weight=3];
3265[label="gcd0Gcd'1 True (abs (Pos (Succ vuz6500))) (Neg Zero)",fontsize=16,color="black",shape="box"];3265 -> 3276[label="",style="solid", color="black", weight=3];
3266[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) (not True)) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) (not True))",fontsize=16,color="black",shape="box"];3266 -> 3277[label="",style="solid", color="black", weight=3];
3315[label="gcd0Gcd' (Pos (Succ vuz420)) (vuz132 `rem` Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3315 -> 3324[label="",style="solid", color="black", weight=3];
3307[label="absReal2 (Pos (Succ vuz6500))",fontsize=16,color="black",shape="box"];3307 -> 3316[label="",style="solid", color="black", weight=3];
3323[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz420)) (Pos Zero)) (abs (Pos Zero)) (Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3323 -> 3332[label="",style="solid", color="black", weight=3];
3348 -> 3294[label="",style="dashed", color="red", weight=0];
3348[label="gcd0Gcd'1 False (abs (Neg (Succ vuz7100))) (Pos (Succ vuz420))",fontsize=16,color="magenta"];3348 -> 3356[label="",style="dashed", color="magenta", weight=3];
3349 -> 3346[label="",style="dashed", color="red", weight=0];
3349[label="abs (Neg (Succ vuz7100))",fontsize=16,color="magenta"];3349 -> 3357[label="",style="dashed", color="magenta", weight=3];
3371[label="absReal1 (Neg (Succ vuz1180)) (Neg (Succ vuz1180) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];3371 -> 3379[label="",style="solid", color="black", weight=3];
3372[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuz270)) (fromInt (Pos Zero))) (abs (Neg Zero)) (`negate` Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3372 -> 3380[label="",style="solid", color="black", weight=3];
3275[label="gcd0Gcd'1 (primEqInt (primNegInt (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (primNegInt (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3275 -> 3286[label="",style="solid", color="black", weight=3];
3277[label="gcd0Gcd'1 (primEqInt (absReal1 (Neg (Succ vuz270)) False) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal1 (Neg (Succ vuz270)) False)",fontsize=16,color="black",shape="box"];3277 -> 3288[label="",style="solid", color="black", weight=3];
3324[label="gcd0Gcd'2 (Pos (Succ vuz420)) (vuz132 `rem` Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3324 -> 3333[label="",style="solid", color="black", weight=3];
3316[label="absReal1 (Pos (Succ vuz6500)) (Pos (Succ vuz6500) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];3316 -> 3325[label="",style="solid", color="black", weight=3];
3332 -> 3294[label="",style="dashed", color="red", weight=0];
3332[label="gcd0Gcd'1 False (abs (Pos Zero)) (Pos (Succ vuz420))",fontsize=16,color="magenta"];3332 -> 3341[label="",style="dashed", color="magenta", weight=3];
3356 -> 3346[label="",style="dashed", color="red", weight=0];
3356[label="abs (Neg (Succ vuz7100))",fontsize=16,color="magenta"];3356 -> 3366[label="",style="dashed", color="magenta", weight=3];
3357[label="vuz7100",fontsize=16,color="green",shape="box"];3379[label="absReal1 (Neg (Succ vuz1180)) (compare (Neg (Succ vuz1180)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];3379 -> 3387[label="",style="solid", color="black", weight=3];
3380[label="gcd0Gcd'1 (primEqInt (primNegInt (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Neg Zero)) (primNegInt (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3380 -> 3388[label="",style="solid", color="black", weight=3];
3286 -> 3261[label="",style="dashed", color="red", weight=0];
3286[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz270)) (fromInt (Pos Zero))) (abs (Pos (Succ vuz6500))) (Pos (Succ vuz270))",fontsize=16,color="magenta"];3286 -> 3305[label="",style="dashed", color="magenta", weight=3];
3286 -> 3306[label="",style="dashed", color="magenta", weight=3];
3288[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) otherwise) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal0 (Neg (Succ vuz270)) otherwise)",fontsize=16,color="black",shape="box"];3288 -> 3308[label="",style="solid", color="black", weight=3];
3333[label="gcd0Gcd'1 (vuz132 `rem` Pos (Succ vuz420) == fromInt (Pos Zero)) (Pos (Succ vuz420)) (vuz132 `rem` Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3333 -> 3342[label="",style="solid", color="black", weight=3];
3325[label="absReal1 (Pos (Succ vuz6500)) (compare (Pos (Succ vuz6500)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];3325 -> 3334[label="",style="solid", color="black", weight=3];
3341[label="abs (Pos Zero)",fontsize=16,color="black",shape="box"];3341 -> 3350[label="",style="solid", color="black", weight=3];
3366[label="vuz7100",fontsize=16,color="green",shape="box"];3387[label="absReal1 (Neg (Succ vuz1180)) (not (compare (Neg (Succ vuz1180)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3387 -> 3397[label="",style="solid", color="black", weight=3];
3388[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz270)) (fromInt (Pos Zero))) (abs (Neg Zero)) (Pos (Succ vuz270))",fontsize=16,color="black",shape="box"];3388 -> 3398[label="",style="solid", color="black", weight=3];
3305[label="vuz6500",fontsize=16,color="green",shape="box"];3306[label="vuz270",fontsize=16,color="green",shape="box"];3308[label="gcd0Gcd'1 (primEqInt (absReal0 (Neg (Succ vuz270)) True) (fromInt (Pos Zero))) (abs (Pos Zero)) (absReal0 (Neg (Succ vuz270)) True)",fontsize=16,color="black",shape="box"];3308 -> 3317[label="",style="solid", color="black", weight=3];
3342[label="gcd0Gcd'1 (primEqInt (vuz132 `rem` Pos (Succ vuz420)) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (vuz132 `rem` Pos (Succ vuz420))",fontsize=16,color="black",shape="box"];3342 -> 3351[label="",style="solid", color="black", weight=3];
3334[label="absReal1 (Pos (Succ vuz6500)) (not (compare (Pos (Succ vuz6500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3334 -> 3343[label="",style="solid", color="black", weight=3];
3350[label="absReal (Pos Zero)",fontsize=16,color="black",shape="box"];3350 -> 3358[label="",style="solid", color="black", weight=3];
3397[label="absReal1 (Neg (Succ vuz1180)) (not (primCmpInt (Neg (Succ vuz1180)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3397 -> 3410[label="",style="solid", color="black", weight=3];
3398[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz270)) (Pos Zero)) (abs (Neg Zero)) (Pos (Succ vuz270))",fontsize=16,color="black",shape="box"];3398 -> 3411[label="",style="solid", color="black", weight=3];
3317[label="gcd0Gcd'1 (primEqInt (`negate` Neg (Succ vuz270)) (fromInt (Pos Zero))) (abs (Pos Zero)) (`negate` Neg (Succ vuz270))",fontsize=16,color="black",shape="box"];3317 -> 3326[label="",style="solid", color="black", weight=3];
3351[label="gcd0Gcd'1 (primEqInt (primRemInt vuz132 (Pos (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (primRemInt vuz132 (Pos (Succ vuz420)))",fontsize=16,color="burlywood",shape="box"];4889[label="vuz132/Pos vuz1320",fontsize=10,color="white",style="solid",shape="box"];3351 -> 4889[label="",style="solid", color="burlywood", weight=9];
4889 -> 3359[label="",style="solid", color="burlywood", weight=3];
4890[label="vuz132/Neg vuz1320",fontsize=10,color="white",style="solid",shape="box"];3351 -> 4890[label="",style="solid", color="burlywood", weight=9];
4890 -> 3360[label="",style="solid", color="burlywood", weight=3];
3343[label="absReal1 (Pos (Succ vuz6500)) (not (primCmpInt (Pos (Succ vuz6500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3343 -> 3352[label="",style="solid", color="black", weight=3];
3358[label="absReal2 (Pos Zero)",fontsize=16,color="black",shape="box"];3358 -> 3367[label="",style="solid", color="black", weight=3];
3410[label="absReal1 (Neg (Succ vuz1180)) (not (primCmpInt (Neg (Succ vuz1180)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];3410 -> 3423[label="",style="solid", color="black", weight=3];
3411 -> 3294[label="",style="dashed", color="red", weight=0];
3411[label="gcd0Gcd'1 False (abs (Neg Zero)) (Pos (Succ vuz270))",fontsize=16,color="magenta"];3411 -> 3424[label="",style="dashed", color="magenta", weight=3];
3411 -> 3425[label="",style="dashed", color="magenta", weight=3];
3326[label="gcd0Gcd'1 (primEqInt (primNegInt (Neg (Succ vuz270))) (fromInt (Pos Zero))) (abs (Pos Zero)) (primNegInt (Neg (Succ vuz270)))",fontsize=16,color="black",shape="box"];3326 -> 3335[label="",style="solid", color="black", weight=3];
3359[label="gcd0Gcd'1 (primEqInt (primRemInt (Pos vuz1320) (Pos (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (primRemInt (Pos vuz1320) (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3359 -> 3368[label="",style="solid", color="black", weight=3];
3360[label="gcd0Gcd'1 (primEqInt (primRemInt (Neg vuz1320) (Pos (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (primRemInt (Neg vuz1320) (Pos (Succ vuz420)))",fontsize=16,color="black",shape="box"];3360 -> 3369[label="",style="solid", color="black", weight=3];
3352[label="absReal1 (Pos (Succ vuz6500)) (not (primCmpInt (Pos (Succ vuz6500)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];3352 -> 3361[label="",style="solid", color="black", weight=3];
3367[label="absReal1 (Pos Zero) (Pos Zero >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];3367 -> 3373[label="",style="solid", color="black", weight=3];
3423[label="absReal1 (Neg (Succ vuz1180)) (not (LT == LT))",fontsize=16,color="black",shape="box"];3423 -> 3437[label="",style="solid", color="black", weight=3];
3424[label="abs (Neg Zero)",fontsize=16,color="black",shape="box"];3424 -> 3438[label="",style="solid", color="black", weight=3];
3425[label="vuz270",fontsize=16,color="green",shape="box"];3335 -> 3314[label="",style="dashed", color="red", weight=0];
3335[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz270)) (fromInt (Pos Zero))) (abs (Pos Zero)) (Pos (Succ vuz270))",fontsize=16,color="magenta"];3335 -> 3344[label="",style="dashed", color="magenta", weight=3];
3368[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS vuz1320 (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS vuz1320 (Succ vuz420)))",fontsize=16,color="burlywood",shape="triangle"];4893[label="vuz1320/Succ vuz13200",fontsize=10,color="white",style="solid",shape="box"];3368 -> 4893[label="",style="solid", color="burlywood", weight=9];
4893 -> 3374[label="",style="solid", color="burlywood", weight=3];
4894[label="vuz1320/Zero",fontsize=10,color="white",style="solid",shape="box"];3368 -> 4894[label="",style="solid", color="burlywood", weight=9];
4894 -> 3375[label="",style="solid", color="burlywood", weight=3];
3369[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS vuz1320 (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS vuz1320 (Succ vuz420)))",fontsize=16,color="burlywood",shape="triangle"];4895[label="vuz1320/Succ vuz13200",fontsize=10,color="white",style="solid",shape="box"];3369 -> 4895[label="",style="solid", color="burlywood", weight=9];
4895 -> 3376[label="",style="solid", color="burlywood", weight=3];
4896[label="vuz1320/Zero",fontsize=10,color="white",style="solid",shape="box"];3369 -> 4896[label="",style="solid", color="burlywood", weight=9];
4896 -> 3377[label="",style="solid", color="burlywood", weight=3];
3361[label="absReal1 (Pos (Succ vuz6500)) (not (primCmpNat (Succ vuz6500) Zero == LT))",fontsize=16,color="black",shape="box"];3361 -> 3370[label="",style="solid", color="black", weight=3];
3373[label="absReal1 (Pos Zero) (compare (Pos Zero) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];3373 -> 3381[label="",style="solid", color="black", weight=3];
3437[label="absReal1 (Neg (Succ vuz1180)) (not True)",fontsize=16,color="black",shape="box"];3437 -> 3458[label="",style="solid", color="black", weight=3];
3438[label="absReal (Neg Zero)",fontsize=16,color="black",shape="box"];3438 -> 3459[label="",style="solid", color="black", weight=3];
3344[label="vuz270",fontsize=16,color="green",shape="box"];3374[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuz13200) (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS (Succ vuz13200) (Succ vuz420)))",fontsize=16,color="black",shape="box"];3374 -> 3382[label="",style="solid", color="black", weight=3];
3375[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS Zero (Succ vuz420)))",fontsize=16,color="black",shape="box"];3375 -> 3383[label="",style="solid", color="black", weight=3];
3376[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (Succ vuz13200) (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS (Succ vuz13200) (Succ vuz420)))",fontsize=16,color="black",shape="box"];3376 -> 3384[label="",style="solid", color="black", weight=3];
3377[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS Zero (Succ vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS Zero (Succ vuz420)))",fontsize=16,color="black",shape="box"];3377 -> 3385[label="",style="solid", color="black", weight=3];
3370[label="absReal1 (Pos (Succ vuz6500)) (not (GT == LT))",fontsize=16,color="black",shape="box"];3370 -> 3378[label="",style="solid", color="black", weight=3];
3381[label="absReal1 (Pos Zero) (not (compare (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3381 -> 3389[label="",style="solid", color="black", weight=3];
3458[label="absReal1 (Neg (Succ vuz1180)) False",fontsize=16,color="black",shape="box"];3458 -> 3479[label="",style="solid", color="black", weight=3];
3459[label="absReal2 (Neg Zero)",fontsize=16,color="black",shape="box"];3459 -> 3480[label="",style="solid", color="black", weight=3];
3382[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 vuz13200 vuz420 (primGEqNatS vuz13200 vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS0 vuz13200 vuz420 (primGEqNatS vuz13200 vuz420)))",fontsize=16,color="burlywood",shape="box"];4897[label="vuz13200/Succ vuz132000",fontsize=10,color="white",style="solid",shape="box"];3382 -> 4897[label="",style="solid", color="burlywood", weight=9];
4897 -> 3390[label="",style="solid", color="burlywood", weight=3];
4898[label="vuz13200/Zero",fontsize=10,color="white",style="solid",shape="box"];3382 -> 4898[label="",style="solid", color="burlywood", weight=9];
4898 -> 3391[label="",style="solid", color="burlywood", weight=3];
3383[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos Zero)",fontsize=16,color="black",shape="box"];3383 -> 3392[label="",style="solid", color="black", weight=3];
3384[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 vuz13200 vuz420 (primGEqNatS vuz13200 vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS0 vuz13200 vuz420 (primGEqNatS vuz13200 vuz420)))",fontsize=16,color="burlywood",shape="box"];4899[label="vuz13200/Succ vuz132000",fontsize=10,color="white",style="solid",shape="box"];3384 -> 4899[label="",style="solid", color="burlywood", weight=9];
4899 -> 3393[label="",style="solid", color="burlywood", weight=3];
4900[label="vuz13200/Zero",fontsize=10,color="white",style="solid",shape="box"];3384 -> 4900[label="",style="solid", color="burlywood", weight=9];
4900 -> 3394[label="",style="solid", color="burlywood", weight=3];
3385[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg Zero)",fontsize=16,color="black",shape="box"];3385 -> 3395[label="",style="solid", color="black", weight=3];
3378[label="absReal1 (Pos (Succ vuz6500)) (not False)",fontsize=16,color="black",shape="box"];3378 -> 3386[label="",style="solid", color="black", weight=3];
3389[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3389 -> 3399[label="",style="solid", color="black", weight=3];
3479[label="absReal0 (Neg (Succ vuz1180)) otherwise",fontsize=16,color="black",shape="box"];3479 -> 3494[label="",style="solid", color="black", weight=3];
3480[label="absReal1 (Neg Zero) (Neg Zero >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];3480 -> 3495[label="",style="solid", color="black", weight=3];
3390[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz132000) vuz420 (primGEqNatS (Succ vuz132000) vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS0 (Succ vuz132000) vuz420 (primGEqNatS (Succ vuz132000) vuz420)))",fontsize=16,color="burlywood",shape="box"];4901[label="vuz420/Succ vuz4200",fontsize=10,color="white",style="solid",shape="box"];3390 -> 4901[label="",style="solid", color="burlywood", weight=9];
4901 -> 3400[label="",style="solid", color="burlywood", weight=3];
4902[label="vuz420/Zero",fontsize=10,color="white",style="solid",shape="box"];3390 -> 4902[label="",style="solid", color="burlywood", weight=9];
4902 -> 3401[label="",style="solid", color="burlywood", weight=3];
3391[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero vuz420 (primGEqNatS Zero vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Pos (primModNatS0 Zero vuz420 (primGEqNatS Zero vuz420)))",fontsize=16,color="burlywood",shape="box"];4903[label="vuz420/Succ vuz4200",fontsize=10,color="white",style="solid",shape="box"];3391 -> 4903[label="",style="solid", color="burlywood", weight=9];
4903 -> 3402[label="",style="solid", color="burlywood", weight=3];
4904[label="vuz420/Zero",fontsize=10,color="white",style="solid",shape="box"];3391 -> 4904[label="",style="solid", color="burlywood", weight=9];
4904 -> 3403[label="",style="solid", color="burlywood", weight=3];
3392[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ vuz420)) (Pos Zero)",fontsize=16,color="black",shape="box"];3392 -> 3404[label="",style="solid", color="black", weight=3];
3393[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz132000) vuz420 (primGEqNatS (Succ vuz132000) vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS0 (Succ vuz132000) vuz420 (primGEqNatS (Succ vuz132000) vuz420)))",fontsize=16,color="burlywood",shape="box"];4905[label="vuz420/Succ vuz4200",fontsize=10,color="white",style="solid",shape="box"];3393 -> 4905[label="",style="solid", color="burlywood", weight=9];
4905 -> 3405[label="",style="solid", color="burlywood", weight=3];
4906[label="vuz420/Zero",fontsize=10,color="white",style="solid",shape="box"];3393 -> 4906[label="",style="solid", color="burlywood", weight=9];
4906 -> 3406[label="",style="solid", color="burlywood", weight=3];
3394[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero vuz420 (primGEqNatS Zero vuz420))) (fromInt (Pos Zero))) (Pos (Succ vuz420)) (Neg (primModNatS0 Zero vuz420 (primGEqNatS Zero vuz420)))",fontsize=16,color="burlywood",shape="box"];4907[label="vuz420/Succ vuz4200",fontsize=10,color="white",style="solid",shape="box"];3394 -> 4907[label="",style="solid", color="burlywood", weight=9];
4907 -> 3407[label="",style="solid", color="burlywood", weight=3];
4908[label="vuz420/Zero",fontsize=10,color="white",style="solid",shape="box"];3394 -> 4908[label="",style="solid", color="burlywood", weight=9];
4908 -> 3408[label="",style="solid", color="burlywood", weight=3];
3395[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) (Pos (Succ vuz420)) (Neg Zero)",fontsize=16,color="black",shape="box"];3395 -> 3409[label="",style="solid", color="black", weight=3];
3386[label="absReal1 (Pos (Succ vuz6500)) True",fontsize=16,color="black",shape="box"];3386 -> 3396[label="",style="solid", color="black", weight=3];
3399[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];3399 -> 3412[label="",style="solid", color="black", weight=3];
3494[label="absReal0 (Neg (Succ vuz1180)) True",fontsize=16,color="black",shape="box"];3494 -> 3515[label="",style="solid", color="black", weight=3];
3495[label="absReal1 (Neg Zero) (compare (Neg Zero) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];3495 -> 3516[label="",style="solid", color="black", weight=3];
3400[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS (Succ vuz132000) (Succ vuz4200)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Pos (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS (Succ vuz132000) (Succ vuz4200))))",fontsize=16,color="black",shape="box"];3400 -> 3413[label="",style="solid", color="black", weight=3];
3401[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz132000) Zero (primGEqNatS (Succ vuz132000) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz132000) Zero (primGEqNatS (Succ vuz132000) Zero)))",fontsize=16,color="black",shape="box"];3401 -> 3414[label="",style="solid", color="black", weight=3];
3402[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz4200) (primGEqNatS Zero (Succ vuz4200)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Pos (primModNatS0 Zero (Succ vuz4200) (primGEqNatS Zero (Succ vuz4200))))",fontsize=16,color="black",shape="box"];3402 -> 3415[label="",style="solid", color="black", weight=3];
3403[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];3403 -> 3416[label="",style="solid", color="black", weight=3];
3404[label="gcd0Gcd'1 True (Pos (Succ vuz420)) (Pos Zero)",fontsize=16,color="black",shape="box"];3404 -> 3417[label="",style="solid", color="black", weight=3];
3405[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS (Succ vuz132000) (Succ vuz4200)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Neg (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS (Succ vuz132000) (Succ vuz4200))))",fontsize=16,color="black",shape="box"];3405 -> 3418[label="",style="solid", color="black", weight=3];
3406[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz132000) Zero (primGEqNatS (Succ vuz132000) Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 (Succ vuz132000) Zero (primGEqNatS (Succ vuz132000) Zero)))",fontsize=16,color="black",shape="box"];3406 -> 3419[label="",style="solid", color="black", weight=3];
3407[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero (Succ vuz4200) (primGEqNatS Zero (Succ vuz4200)))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Neg (primModNatS0 Zero (Succ vuz4200) (primGEqNatS Zero (Succ vuz4200))))",fontsize=16,color="black",shape="box"];3407 -> 3420[label="",style="solid", color="black", weight=3];
3408[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];3408 -> 3421[label="",style="solid", color="black", weight=3];
3409[label="gcd0Gcd'1 True (Pos (Succ vuz420)) (Neg Zero)",fontsize=16,color="black",shape="box"];3409 -> 3422[label="",style="solid", color="black", weight=3];
3396[label="Pos (Succ vuz6500)",fontsize=16,color="green",shape="box"];3412[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];3412 -> 3426[label="",style="solid", color="black", weight=3];
3515[label="`negate` Neg (Succ vuz1180)",fontsize=16,color="black",shape="box"];3515 -> 3536[label="",style="solid", color="black", weight=3];
3516[label="absReal1 (Neg Zero) (not (compare (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3516 -> 3537[label="",style="solid", color="black", weight=3];
3413 -> 3943[label="",style="dashed", color="red", weight=0];
3413[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS vuz132000 vuz4200))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Pos (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS vuz132000 vuz4200)))",fontsize=16,color="magenta"];3413 -> 3944[label="",style="dashed", color="magenta", weight=3];
3413 -> 3945[label="",style="dashed", color="magenta", weight=3];
3413 -> 3946[label="",style="dashed", color="magenta", weight=3];
3413 -> 3947[label="",style="dashed", color="magenta", weight=3];
3414 -> 3744[label="",style="dashed", color="red", weight=0];
3414[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz132000) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 (Succ vuz132000) Zero True))",fontsize=16,color="magenta"];3414 -> 3745[label="",style="dashed", color="magenta", weight=3];
3414 -> 3746[label="",style="dashed", color="magenta", weight=3];
3415[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz4200) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Pos (primModNatS0 Zero (Succ vuz4200) False))",fontsize=16,color="black",shape="box"];3415 -> 3430[label="",style="solid", color="black", weight=3];
3416[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];3416 -> 3431[label="",style="solid", color="black", weight=3];
3417[label="Pos (Succ vuz420)",fontsize=16,color="green",shape="box"];3418 -> 3987[label="",style="dashed", color="red", weight=0];
3418[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS vuz132000 vuz4200))) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Neg (primModNatS0 (Succ vuz132000) (Succ vuz4200) (primGEqNatS vuz132000 vuz4200)))",fontsize=16,color="magenta"];3418 -> 3988[label="",style="dashed", color="magenta", weight=3];
3418 -> 3989[label="",style="dashed", color="magenta", weight=3];
3418 -> 3990[label="",style="dashed", color="magenta", weight=3];
3418 -> 3991[label="",style="dashed", color="magenta", weight=3];
3419 -> 3777[label="",style="dashed", color="red", weight=0];
3419[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz132000) Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 (Succ vuz132000) Zero True))",fontsize=16,color="magenta"];3419 -> 3778[label="",style="dashed", color="magenta", weight=3];
3419 -> 3779[label="",style="dashed", color="magenta", weight=3];
3420[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero (Succ vuz4200) False)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Neg (primModNatS0 Zero (Succ vuz4200) False))",fontsize=16,color="black",shape="box"];3420 -> 3435[label="",style="solid", color="black", weight=3];
3421[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];3421 -> 3436[label="",style="solid", color="black", weight=3];
3422[label="Pos (Succ vuz420)",fontsize=16,color="green",shape="box"];3426[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];3426 -> 3439[label="",style="solid", color="black", weight=3];
3536[label="primNegInt (Neg (Succ vuz1180))",fontsize=16,color="black",shape="box"];3536 -> 3552[label="",style="solid", color="black", weight=3];
3537[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];3537 -> 3553[label="",style="solid", color="black", weight=3];
3944[label="vuz132000",fontsize=16,color="green",shape="box"];3945[label="vuz4200",fontsize=16,color="green",shape="box"];3946[label="Succ vuz4200",fontsize=16,color="green",shape="box"];3947[label="vuz132000",fontsize=16,color="green",shape="box"];3943[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS vuz162 vuz163))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS vuz162 vuz163)))",fontsize=16,color="burlywood",shape="triangle"];4913[label="vuz162/Succ vuz1620",fontsize=10,color="white",style="solid",shape="box"];3943 -> 4913[label="",style="solid", color="burlywood", weight=9];
4913 -> 3984[label="",style="solid", color="burlywood", weight=3];
4914[label="vuz162/Zero",fontsize=10,color="white",style="solid",shape="box"];3943 -> 4914[label="",style="solid", color="burlywood", weight=9];
4914 -> 3985[label="",style="solid", color="burlywood", weight=3];
3745[label="Zero",fontsize=16,color="green",shape="box"];3746[label="vuz132000",fontsize=16,color="green",shape="box"];3744[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz148) vuz149 True)) (fromInt (Pos Zero))) (Pos (Succ vuz149)) (Pos (primModNatS0 (Succ vuz148) vuz149 True))",fontsize=16,color="black",shape="triangle"];3744 -> 3767[label="",style="solid", color="black", weight=3];
3430[label="gcd0Gcd'1 (primEqInt (Pos (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];3430 -> 3446[label="",style="solid", color="black", weight=3];
3431 -> 3368[label="",style="dashed", color="red", weight=0];
3431[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];3431 -> 3447[label="",style="dashed", color="magenta", weight=3];
3431 -> 3448[label="",style="dashed", color="magenta", weight=3];
3988[label="Succ vuz4200",fontsize=16,color="green",shape="box"];3989[label="vuz4200",fontsize=16,color="green",shape="box"];3990[label="vuz132000",fontsize=16,color="green",shape="box"];3991[label="vuz132000",fontsize=16,color="green",shape="box"];3987[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS vuz167 vuz168))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS vuz167 vuz168)))",fontsize=16,color="burlywood",shape="triangle"];4916[label="vuz167/Succ vuz1670",fontsize=10,color="white",style="solid",shape="box"];3987 -> 4916[label="",style="solid", color="burlywood", weight=9];
4916 -> 4028[label="",style="solid", color="burlywood", weight=3];
4917[label="vuz167/Zero",fontsize=10,color="white",style="solid",shape="box"];3987 -> 4917[label="",style="solid", color="burlywood", weight=9];
4917 -> 4029[label="",style="solid", color="burlywood", weight=3];
3778[label="Zero",fontsize=16,color="green",shape="box"];3779[label="vuz132000",fontsize=16,color="green",shape="box"];3777[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz151) vuz152 True)) (fromInt (Pos Zero))) (Pos (Succ vuz152)) (Neg (primModNatS0 (Succ vuz151) vuz152 True))",fontsize=16,color="black",shape="triangle"];3777 -> 3800[label="",style="solid", color="black", weight=3];
3435 -> 3819[label="",style="dashed", color="red", weight=0];
3435[label="gcd0Gcd'1 (primEqInt (Neg (Succ Zero)) (fromInt (Pos Zero))) (Pos (Succ (Succ vuz4200))) (Neg (Succ Zero))",fontsize=16,color="magenta"];3435 -> 3820[label="",style="dashed", color="magenta", weight=3];
3435 -> 3821[label="",style="dashed", color="magenta", weight=3];
3436 -> 3369[label="",style="dashed", color="red", weight=0];
3436[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ Zero)) (Neg (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];3436 -> 3456[label="",style="dashed", color="magenta", weight=3];
3436 -> 3457[label="",style="dashed", color="magenta", weight=3];
3439[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];3439 -> 3460[label="",style="solid", color="black", weight=3];
3552[label="Pos (Succ vuz1180)",fontsize=16,color="green",shape="box"];3553[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];3553 -> 3574[label="",style="solid", color="black", weight=3];
3984[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) vuz163))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) vuz163)))",fontsize=16,color="burlywood",shape="box"];4920[label="vuz163/Succ vuz1630",fontsize=10,color="white",style="solid",shape="box"];3984 -> 4920[label="",style="solid", color="burlywood", weight=9];
4920 -> 4030[label="",style="solid", color="burlywood", weight=3];
4921[label="vuz163/Zero",fontsize=10,color="white",style="solid",shape="box"];3984 -> 4921[label="",style="solid", color="burlywood", weight=9];
4921 -> 4031[label="",style="solid", color="burlywood", weight=3];
3985[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero vuz163))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero vuz163)))",fontsize=16,color="burlywood",shape="box"];4922[label="vuz163/Succ vuz1630",fontsize=10,color="white",style="solid",shape="box"];3985 -> 4922[label="",style="solid", color="burlywood", weight=9];
4922 -> 4032[label="",style="solid", color="burlywood", weight=3];
4923[label="vuz163/Zero",fontsize=10,color="white",style="solid",shape="box"];3985 -> 4923[label="",style="solid", color="burlywood", weight=9];
4923 -> 4033[label="",style="solid", color="burlywood", weight=3];
3767 -> 3368[label="",style="dashed", color="red", weight=0];
3767[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz148) vuz149) (Succ vuz149))) (fromInt (Pos Zero))) (Pos (Succ vuz149)) (Pos (primModNatS (primMinusNatS (Succ vuz148) vuz149) (Succ vuz149)))",fontsize=16,color="magenta"];3767 -> 3801[label="",style="dashed", color="magenta", weight=3];
3767 -> 3802[label="",style="dashed", color="magenta", weight=3];
3446 -> 3882[label="",style="dashed", color="red", weight=0];
3446[label="gcd0Gcd'1 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ vuz4200))) (Pos (Succ Zero))",fontsize=16,color="magenta"];3446 -> 3883[label="",style="dashed", color="magenta", weight=3];
3446 -> 3884[label="",style="dashed", color="magenta", weight=3];
3447 -> 3097[label="",style="dashed", color="red", weight=0];
3447[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];3447 -> 3468[label="",style="dashed", color="magenta", weight=3];
3447 -> 3469[label="",style="dashed", color="magenta", weight=3];
3448[label="Zero",fontsize=16,color="green",shape="box"];4028[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) vuz168))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) vuz168)))",fontsize=16,color="burlywood",shape="box"];4927[label="vuz168/Succ vuz1680",fontsize=10,color="white",style="solid",shape="box"];4028 -> 4927[label="",style="solid", color="burlywood", weight=9];
4927 -> 4035[label="",style="solid", color="burlywood", weight=3];
4928[label="vuz168/Zero",fontsize=10,color="white",style="solid",shape="box"];4028 -> 4928[label="",style="solid", color="burlywood", weight=9];
4928 -> 4036[label="",style="solid", color="burlywood", weight=3];
4029[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero vuz168))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero vuz168)))",fontsize=16,color="burlywood",shape="box"];4929[label="vuz168/Succ vuz1680",fontsize=10,color="white",style="solid",shape="box"];4029 -> 4929[label="",style="solid", color="burlywood", weight=9];
4929 -> 4037[label="",style="solid", color="burlywood", weight=3];
4930[label="vuz168/Zero",fontsize=10,color="white",style="solid",shape="box"];4029 -> 4930[label="",style="solid", color="burlywood", weight=9];
4930 -> 4038[label="",style="solid", color="burlywood", weight=3];
3800 -> 3369[label="",style="dashed", color="red", weight=0];
3800[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS (primMinusNatS (Succ vuz151) vuz152) (Succ vuz152))) (fromInt (Pos Zero))) (Pos (Succ vuz152)) (Neg (primModNatS (primMinusNatS (Succ vuz151) vuz152) (Succ vuz152)))",fontsize=16,color="magenta"];3800 -> 3832[label="",style="dashed", color="magenta", weight=3];
3800 -> 3833[label="",style="dashed", color="magenta", weight=3];
3820[label="Succ vuz4200",fontsize=16,color="green",shape="box"];3821[label="Zero",fontsize=16,color="green",shape="box"];3819[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz154)) (fromInt (Pos Zero))) (Pos (Succ vuz155)) (Neg (Succ vuz154))",fontsize=16,color="black",shape="triangle"];3819 -> 3834[label="",style="solid", color="black", weight=3];
3456 -> 3097[label="",style="dashed", color="red", weight=0];
3456[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];3456 -> 3477[label="",style="dashed", color="magenta", weight=3];
3456 -> 3478[label="",style="dashed", color="magenta", weight=3];
3457[label="Zero",fontsize=16,color="green",shape="box"];3460[label="Pos Zero",fontsize=16,color="green",shape="box"];3574[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];3574 -> 3595[label="",style="solid", color="black", weight=3];
4030[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) (Succ vuz1630)))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) (Succ vuz1630))))",fontsize=16,color="black",shape="box"];4030 -> 4039[label="",style="solid", color="black", weight=3];
4031[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) Zero))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS (Succ vuz1620) Zero)))",fontsize=16,color="black",shape="box"];4031 -> 4040[label="",style="solid", color="black", weight=3];
4032[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero (Succ vuz1630)))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero (Succ vuz1630))))",fontsize=16,color="black",shape="box"];4032 -> 4041[label="",style="solid", color="black", weight=3];
4033[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];4033 -> 4042[label="",style="solid", color="black", weight=3];
3801 -> 3097[label="",style="dashed", color="red", weight=0];
3801[label="primMinusNatS (Succ vuz148) vuz149",fontsize=16,color="magenta"];3801 -> 3835[label="",style="dashed", color="magenta", weight=3];
3801 -> 3836[label="",style="dashed", color="magenta", weight=3];
3802[label="vuz149",fontsize=16,color="green",shape="box"];3883[label="Succ vuz4200",fontsize=16,color="green",shape="box"];3884[label="Zero",fontsize=16,color="green",shape="box"];3882[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz157)) (Pos Zero)) (Pos (Succ vuz158)) (Pos (Succ vuz157))",fontsize=16,color="black",shape="triangle"];3882 -> 3897[label="",style="solid", color="black", weight=3];
3468[label="Zero",fontsize=16,color="green",shape="box"];3469[label="Zero",fontsize=16,color="green",shape="box"];4035[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) (Succ vuz1680)))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) (Succ vuz1680))))",fontsize=16,color="black",shape="box"];4035 -> 4045[label="",style="solid", color="black", weight=3];
4036[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) Zero))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS (Succ vuz1670) Zero)))",fontsize=16,color="black",shape="box"];4036 -> 4046[label="",style="solid", color="black", weight=3];
4037[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero (Succ vuz1680)))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero (Succ vuz1680))))",fontsize=16,color="black",shape="box"];4037 -> 4047[label="",style="solid", color="black", weight=3];
4038[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];4038 -> 4048[label="",style="solid", color="black", weight=3];
3832 -> 3097[label="",style="dashed", color="red", weight=0];
3832[label="primMinusNatS (Succ vuz151) vuz152",fontsize=16,color="magenta"];3832 -> 3846[label="",style="dashed", color="magenta", weight=3];
3832 -> 3847[label="",style="dashed", color="magenta", weight=3];
3833[label="vuz152",fontsize=16,color="green",shape="box"];3834[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz154)) (Pos Zero)) (Pos (Succ vuz155)) (Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3834 -> 3848[label="",style="solid", color="black", weight=3];
3477[label="Zero",fontsize=16,color="green",shape="box"];3478[label="Zero",fontsize=16,color="green",shape="box"];3595[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];3595 -> 3611[label="",style="solid", color="black", weight=3];
4039 -> 3943[label="",style="dashed", color="red", weight=0];
4039[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS vuz1620 vuz1630))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 (primGEqNatS vuz1620 vuz1630)))",fontsize=16,color="magenta"];4039 -> 4049[label="",style="dashed", color="magenta", weight=3];
4039 -> 4050[label="",style="dashed", color="magenta", weight=3];
4040 -> 3744[label="",style="dashed", color="red", weight=0];
4040[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 True)) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 True))",fontsize=16,color="magenta"];4040 -> 4051[label="",style="dashed", color="magenta", weight=3];
4040 -> 4052[label="",style="dashed", color="magenta", weight=3];
4041[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 False)) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 False))",fontsize=16,color="black",shape="box"];4041 -> 4053[label="",style="solid", color="black", weight=3];
4042 -> 3744[label="",style="dashed", color="red", weight=0];
4042[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz160) vuz161 True)) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (primModNatS0 (Succ vuz160) vuz161 True))",fontsize=16,color="magenta"];4042 -> 4054[label="",style="dashed", color="magenta", weight=3];
4042 -> 4055[label="",style="dashed", color="magenta", weight=3];
3835[label="Succ vuz148",fontsize=16,color="green",shape="box"];3836[label="vuz149",fontsize=16,color="green",shape="box"];3897 -> 3294[label="",style="dashed", color="red", weight=0];
3897[label="gcd0Gcd'1 False (Pos (Succ vuz158)) (Pos (Succ vuz157))",fontsize=16,color="magenta"];3897 -> 3910[label="",style="dashed", color="magenta", weight=3];
3897 -> 3911[label="",style="dashed", color="magenta", weight=3];
4045 -> 3987[label="",style="dashed", color="red", weight=0];
4045[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS vuz1670 vuz1680))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 (primGEqNatS vuz1670 vuz1680)))",fontsize=16,color="magenta"];4045 -> 4060[label="",style="dashed", color="magenta", weight=3];
4045 -> 4061[label="",style="dashed", color="magenta", weight=3];
4046 -> 3777[label="",style="dashed", color="red", weight=0];
4046[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 True)) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 True))",fontsize=16,color="magenta"];4046 -> 4062[label="",style="dashed", color="magenta", weight=3];
4046 -> 4063[label="",style="dashed", color="magenta", weight=3];
4047[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 False)) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 False))",fontsize=16,color="black",shape="box"];4047 -> 4064[label="",style="solid", color="black", weight=3];
4048 -> 3777[label="",style="dashed", color="red", weight=0];
4048[label="gcd0Gcd'1 (primEqInt (Neg (primModNatS0 (Succ vuz165) vuz166 True)) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (primModNatS0 (Succ vuz165) vuz166 True))",fontsize=16,color="magenta"];4048 -> 4065[label="",style="dashed", color="magenta", weight=3];
4048 -> 4066[label="",style="dashed", color="magenta", weight=3];
3846[label="Succ vuz151",fontsize=16,color="green",shape="box"];3847[label="vuz152",fontsize=16,color="green",shape="box"];3848[label="gcd0Gcd'1 False (Pos (Succ vuz155)) (Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3848 -> 3865[label="",style="solid", color="black", weight=3];
3611[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];3611 -> 3633[label="",style="solid", color="black", weight=3];
4049[label="vuz1630",fontsize=16,color="green",shape="box"];4050[label="vuz1620",fontsize=16,color="green",shape="box"];4051[label="vuz161",fontsize=16,color="green",shape="box"];4052[label="vuz160",fontsize=16,color="green",shape="box"];4053[label="gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuz160))) (fromInt (Pos Zero))) (Pos (Succ vuz161)) (Pos (Succ (Succ vuz160)))",fontsize=16,color="black",shape="box"];4053 -> 4067[label="",style="solid", color="black", weight=3];
4054[label="vuz161",fontsize=16,color="green",shape="box"];4055[label="vuz160",fontsize=16,color="green",shape="box"];3910[label="Pos (Succ vuz158)",fontsize=16,color="green",shape="box"];3911[label="vuz157",fontsize=16,color="green",shape="box"];4060[label="vuz1680",fontsize=16,color="green",shape="box"];4061[label="vuz1670",fontsize=16,color="green",shape="box"];4062[label="vuz166",fontsize=16,color="green",shape="box"];4063[label="vuz165",fontsize=16,color="green",shape="box"];4064 -> 3819[label="",style="dashed", color="red", weight=0];
4064[label="gcd0Gcd'1 (primEqInt (Neg (Succ (Succ vuz165))) (fromInt (Pos Zero))) (Pos (Succ vuz166)) (Neg (Succ (Succ vuz165)))",fontsize=16,color="magenta"];4064 -> 4072[label="",style="dashed", color="magenta", weight=3];
4064 -> 4073[label="",style="dashed", color="magenta", weight=3];
4065[label="vuz166",fontsize=16,color="green",shape="box"];4066[label="vuz165",fontsize=16,color="green",shape="box"];3865[label="gcd0Gcd'0 (Pos (Succ vuz155)) (Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3865 -> 3877[label="",style="solid", color="black", weight=3];
3633[label="Neg Zero",fontsize=16,color="green",shape="box"];4067 -> 3882[label="",style="dashed", color="red", weight=0];
4067[label="gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuz160))) (Pos Zero)) (Pos (Succ vuz161)) (Pos (Succ (Succ vuz160)))",fontsize=16,color="magenta"];4067 -> 4074[label="",style="dashed", color="magenta", weight=3];
4067 -> 4075[label="",style="dashed", color="magenta", weight=3];
4072[label="vuz166",fontsize=16,color="green",shape="box"];4073[label="Succ vuz165",fontsize=16,color="green",shape="box"];3877[label="gcd0Gcd' (Neg (Succ vuz154)) (Pos (Succ vuz155) `rem` Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3877 -> 3898[label="",style="solid", color="black", weight=3];
4074[label="vuz161",fontsize=16,color="green",shape="box"];4075[label="Succ vuz160",fontsize=16,color="green",shape="box"];3898[label="gcd0Gcd'2 (Neg (Succ vuz154)) (Pos (Succ vuz155) `rem` Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3898 -> 3912[label="",style="solid", color="black", weight=3];
3912[label="gcd0Gcd'1 (Pos (Succ vuz155) `rem` Neg (Succ vuz154) == fromInt (Pos Zero)) (Neg (Succ vuz154)) (Pos (Succ vuz155) `rem` Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3912 -> 3925[label="",style="solid", color="black", weight=3];
3925[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz155) `rem` Neg (Succ vuz154)) (fromInt (Pos Zero))) (Neg (Succ vuz154)) (Pos (Succ vuz155) `rem` Neg (Succ vuz154))",fontsize=16,color="black",shape="box"];3925 -> 3938[label="",style="solid", color="black", weight=3];
3938[label="gcd0Gcd'1 (primEqInt (primRemInt (Pos (Succ vuz155)) (Neg (Succ vuz154))) (fromInt (Pos Zero))) (Neg (Succ vuz154)) (primRemInt (Pos (Succ vuz155)) (Neg (Succ vuz154)))",fontsize=16,color="black",shape="box"];3938 -> 3986[label="",style="solid", color="black", weight=3];
3986 -> 4305[label="",style="dashed", color="red", weight=0];
3986[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuz155) (Succ vuz154))) (fromInt (Pos Zero))) (Neg (Succ vuz154)) (Pos (primModNatS (Succ vuz155) (Succ vuz154)))",fontsize=16,color="magenta"];3986 -> 4306[label="",style="dashed", color="magenta", weight=3];
3986 -> 4307[label="",style="dashed", color="magenta", weight=3];
3986 -> 4308[label="",style="dashed", color="magenta", weight=3];
4306[label="vuz154",fontsize=16,color="green",shape="box"];4307[label="Succ vuz155",fontsize=16,color="green",shape="box"];4308[label="Succ vuz155",fontsize=16,color="green",shape="box"];4305[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS vuz189 (Succ vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS vuz188 (Succ vuz187)))",fontsize=16,color="burlywood",shape="triangle"];4945[label="vuz189/Succ vuz1890",fontsize=10,color="white",style="solid",shape="box"];4305 -> 4945[label="",style="solid", color="burlywood", weight=9];
4945 -> 4317[label="",style="solid", color="burlywood", weight=3];
4946[label="vuz189/Zero",fontsize=10,color="white",style="solid",shape="box"];4305 -> 4946[label="",style="solid", color="burlywood", weight=9];
4946 -> 4318[label="",style="solid", color="burlywood", weight=3];
4317[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (Succ vuz1890) (Succ vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS vuz188 (Succ vuz187)))",fontsize=16,color="black",shape="box"];4317 -> 4319[label="",style="solid", color="black", weight=3];
4318[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS Zero (Succ vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS vuz188 (Succ vuz187)))",fontsize=16,color="black",shape="box"];4318 -> 4320[label="",style="solid", color="black", weight=3];
4319[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 vuz1890 vuz187 (primGEqNatS vuz1890 vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS0 vuz1890 vuz187 (primGEqNatS vuz1890 vuz187)))",fontsize=16,color="burlywood",shape="box"];4947[label="vuz1890/Succ vuz18900",fontsize=10,color="white",style="solid",shape="box"];4319 -> 4947[label="",style="solid", color="burlywood", weight=9];
4947 -> 4321[label="",style="solid", color="burlywood", weight=3];
4948[label="vuz1890/Zero",fontsize=10,color="white",style="solid",shape="box"];4319 -> 4948[label="",style="solid", color="burlywood", weight=9];
4948 -> 4322[label="",style="solid", color="burlywood", weight=3];
4320[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos Zero)",fontsize=16,color="black",shape="box"];4320 -> 4323[label="",style="solid", color="black", weight=3];
4321[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz18900) vuz187 (primGEqNatS (Succ vuz18900) vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS0 (Succ vuz18900) vuz187 (primGEqNatS (Succ vuz18900) vuz187)))",fontsize=16,color="burlywood",shape="box"];4949[label="vuz187/Succ vuz1870",fontsize=10,color="white",style="solid",shape="box"];4321 -> 4949[label="",style="solid", color="burlywood", weight=9];
4949 -> 4324[label="",style="solid", color="burlywood", weight=3];
4950[label="vuz187/Zero",fontsize=10,color="white",style="solid",shape="box"];4321 -> 4950[label="",style="solid", color="burlywood", weight=9];
4950 -> 4325[label="",style="solid", color="burlywood", weight=3];
4322[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero vuz187 (primGEqNatS Zero vuz187))) (fromInt (Pos Zero))) (Neg (Succ vuz187)) (Pos (primModNatS0 Zero vuz187 (primGEqNatS Zero vuz187)))",fontsize=16,color="burlywood",shape="box"];4951[label="vuz187/Succ vuz1870",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4951[label="",style="solid", color="burlywood", weight=9];
4951 -> 4326[label="",style="solid", color="burlywood", weight=3];
4952[label="vuz187/Zero",fontsize=10,color="white",style="solid",shape="box"];4322 -> 4952[label="",style="solid", color="burlywood", weight=9];
4952 -> 4327[label="",style="solid", color="burlywood", weight=3];
4323[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) (Neg (Succ vuz187)) (Pos Zero)",fontsize=16,color="black",shape="box"];4323 -> 4328[label="",style="solid", color="black", weight=3];
4324[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz18900) (Succ vuz1870) (primGEqNatS (Succ vuz18900) (Succ vuz1870)))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz1870))) (Pos (primModNatS0 (Succ vuz18900) (Succ vuz1870) (primGEqNatS (Succ vuz18900) (Succ vuz1870))))",fontsize=16,color="black",shape="box"];4324 -> 4329[label="",style="solid", color="black", weight=3];
4325[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz18900) Zero (primGEqNatS (Succ vuz18900) Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 (Succ vuz18900) Zero (primGEqNatS (Succ vuz18900) Zero)))",fontsize=16,color="black",shape="box"];4325 -> 4330[label="",style="solid", color="black", weight=3];
4326[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz1870) (primGEqNatS Zero (Succ vuz1870)))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz1870))) (Pos (primModNatS0 Zero (Succ vuz1870) (primGEqNatS Zero (Succ vuz1870))))",fontsize=16,color="black",shape="box"];4326 -> 4331[label="",style="solid", color="black", weight=3];
4327[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 Zero Zero (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];4327 -> 4332[label="",style="solid", color="black", weight=3];
4328[label="gcd0Gcd'1 True (Neg (Succ vuz187)) (Pos Zero)",fontsize=16,color="black",shape="box"];4328 -> 4333[label="",style="solid", color="black", weight=3];
4329 -> 4593[label="",style="dashed", color="red", weight=0];
4329[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz18900) (Succ vuz1870) (primGEqNatS vuz18900 vuz1870))) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz1870))) (Pos (primModNatS0 (Succ vuz18900) (Succ vuz1870) (primGEqNatS vuz18900 vuz1870)))",fontsize=16,color="magenta"];4329 -> 4594[label="",style="dashed", color="magenta", weight=3];
4329 -> 4595[label="",style="dashed", color="magenta", weight=3];
4329 -> 4596[label="",style="dashed", color="magenta", weight=3];
4329 -> 4597[label="",style="dashed", color="magenta", weight=3];
4330 -> 4497[label="",style="dashed", color="red", weight=0];
4330[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz18900) Zero True)) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 (Succ vuz18900) Zero True))",fontsize=16,color="magenta"];4330 -> 4498[label="",style="dashed", color="magenta", weight=3];
4330 -> 4499[label="",style="dashed", color="magenta", weight=3];
4331[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero (Succ vuz1870) False)) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz1870))) (Pos (primModNatS0 Zero (Succ vuz1870) False))",fontsize=16,color="black",shape="box"];4331 -> 4337[label="",style="solid", color="black", weight=3];
4332[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 Zero Zero True)) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS0 Zero Zero True))",fontsize=16,color="black",shape="box"];4332 -> 4338[label="",style="solid", color="black", weight=3];
4333[label="Neg (Succ vuz187)",fontsize=16,color="green",shape="box"];4594[label="vuz18900",fontsize=16,color="green",shape="box"];4595[label="Succ vuz1870",fontsize=16,color="green",shape="box"];4596[label="vuz18900",fontsize=16,color="green",shape="box"];4597[label="vuz1870",fontsize=16,color="green",shape="box"];4593[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS vuz205 vuz206))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS vuz205 vuz206)))",fontsize=16,color="burlywood",shape="triangle"];4955[label="vuz205/Succ vuz2050",fontsize=10,color="white",style="solid",shape="box"];4593 -> 4955[label="",style="solid", color="burlywood", weight=9];
4955 -> 4634[label="",style="solid", color="burlywood", weight=3];
4956[label="vuz205/Zero",fontsize=10,color="white",style="solid",shape="box"];4593 -> 4956[label="",style="solid", color="burlywood", weight=9];
4956 -> 4635[label="",style="solid", color="burlywood", weight=3];
4498[label="vuz18900",fontsize=16,color="green",shape="box"];4499[label="Zero",fontsize=16,color="green",shape="box"];4497[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz197) vuz198 True)) (fromInt (Pos Zero))) (Neg (Succ vuz198)) (Pos (primModNatS0 (Succ vuz197) vuz198 True))",fontsize=16,color="black",shape="triangle"];4497 -> 4520[label="",style="solid", color="black", weight=3];
4337 -> 4553[label="",style="dashed", color="red", weight=0];
4337[label="gcd0Gcd'1 (primEqInt (Pos (Succ Zero)) (fromInt (Pos Zero))) (Neg (Succ (Succ vuz1870))) (Pos (Succ Zero))",fontsize=16,color="magenta"];4337 -> 4554[label="",style="dashed", color="magenta", weight=3];
4337 -> 4555[label="",style="dashed", color="magenta", weight=3];
4338 -> 4305[label="",style="dashed", color="red", weight=0];
4338[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero))) (fromInt (Pos Zero))) (Neg (Succ Zero)) (Pos (primModNatS (primMinusNatS Zero Zero) (Succ Zero)))",fontsize=16,color="magenta"];4338 -> 4347[label="",style="dashed", color="magenta", weight=3];
4338 -> 4348[label="",style="dashed", color="magenta", weight=3];
4338 -> 4349[label="",style="dashed", color="magenta", weight=3];
4634[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) vuz206))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) vuz206)))",fontsize=16,color="burlywood",shape="box"];4959[label="vuz206/Succ vuz2060",fontsize=10,color="white",style="solid",shape="box"];4634 -> 4959[label="",style="solid", color="burlywood", weight=9];
4959 -> 4636[label="",style="solid", color="burlywood", weight=3];
4960[label="vuz206/Zero",fontsize=10,color="white",style="solid",shape="box"];4634 -> 4960[label="",style="solid", color="burlywood", weight=9];
4960 -> 4637[label="",style="solid", color="burlywood", weight=3];
4635[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero vuz206))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero vuz206)))",fontsize=16,color="burlywood",shape="box"];4961[label="vuz206/Succ vuz2060",fontsize=10,color="white",style="solid",shape="box"];4635 -> 4961[label="",style="solid", color="burlywood", weight=9];
4961 -> 4638[label="",style="solid", color="burlywood", weight=3];
4962[label="vuz206/Zero",fontsize=10,color="white",style="solid",shape="box"];4635 -> 4962[label="",style="solid", color="burlywood", weight=9];
4962 -> 4639[label="",style="solid", color="burlywood", weight=3];
4520 -> 4305[label="",style="dashed", color="red", weight=0];
4520[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS (primMinusNatS (Succ vuz197) vuz198) (Succ vuz198))) (fromInt (Pos Zero))) (Neg (Succ vuz198)) (Pos (primModNatS (primMinusNatS (Succ vuz197) vuz198) (Succ vuz198)))",fontsize=16,color="magenta"];4520 -> 4528[label="",style="dashed", color="magenta", weight=3];
4520 -> 4529[label="",style="dashed", color="magenta", weight=3];
4520 -> 4530[label="",style="dashed", color="magenta", weight=3];
4554[label="Succ vuz1870",fontsize=16,color="green",shape="box"];4555[label="Zero",fontsize=16,color="green",shape="box"];4553[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz200)) (fromInt (Pos Zero))) (Neg (Succ vuz201)) (Pos (Succ vuz200))",fontsize=16,color="black",shape="triangle"];4553 -> 4568[label="",style="solid", color="black", weight=3];
4347[label="Zero",fontsize=16,color="green",shape="box"];4348 -> 3097[label="",style="dashed", color="red", weight=0];
4348[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];4348 -> 4359[label="",style="dashed", color="magenta", weight=3];
4348 -> 4360[label="",style="dashed", color="magenta", weight=3];
4349 -> 3097[label="",style="dashed", color="red", weight=0];
4349[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];4349 -> 4361[label="",style="dashed", color="magenta", weight=3];
4349 -> 4362[label="",style="dashed", color="magenta", weight=3];
4636[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) (Succ vuz2060)))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) (Succ vuz2060))))",fontsize=16,color="black",shape="box"];4636 -> 4640[label="",style="solid", color="black", weight=3];
4637[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) Zero))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS (Succ vuz2050) Zero)))",fontsize=16,color="black",shape="box"];4637 -> 4641[label="",style="solid", color="black", weight=3];
4638[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero (Succ vuz2060)))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero (Succ vuz2060))))",fontsize=16,color="black",shape="box"];4638 -> 4642[label="",style="solid", color="black", weight=3];
4639[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero Zero))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS Zero Zero)))",fontsize=16,color="black",shape="box"];4639 -> 4643[label="",style="solid", color="black", weight=3];
4528[label="vuz198",fontsize=16,color="green",shape="box"];4529 -> 3097[label="",style="dashed", color="red", weight=0];
4529[label="primMinusNatS (Succ vuz197) vuz198",fontsize=16,color="magenta"];4529 -> 4536[label="",style="dashed", color="magenta", weight=3];
4529 -> 4537[label="",style="dashed", color="magenta", weight=3];
4530 -> 3097[label="",style="dashed", color="red", weight=0];
4530[label="primMinusNatS (Succ vuz197) vuz198",fontsize=16,color="magenta"];4530 -> 4538[label="",style="dashed", color="magenta", weight=3];
4530 -> 4539[label="",style="dashed", color="magenta", weight=3];
4568[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz200)) (Pos Zero)) (Neg (Succ vuz201)) (Pos (Succ vuz200))",fontsize=16,color="black",shape="box"];4568 -> 4573[label="",style="solid", color="black", weight=3];
4359[label="Zero",fontsize=16,color="green",shape="box"];4360[label="Zero",fontsize=16,color="green",shape="box"];4361[label="Zero",fontsize=16,color="green",shape="box"];4362[label="Zero",fontsize=16,color="green",shape="box"];4640 -> 4593[label="",style="dashed", color="red", weight=0];
4640[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS vuz2050 vuz2060))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 (primGEqNatS vuz2050 vuz2060)))",fontsize=16,color="magenta"];4640 -> 4644[label="",style="dashed", color="magenta", weight=3];
4640 -> 4645[label="",style="dashed", color="magenta", weight=3];
4641 -> 4497[label="",style="dashed", color="red", weight=0];
4641[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 True)) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 True))",fontsize=16,color="magenta"];4641 -> 4646[label="",style="dashed", color="magenta", weight=3];
4641 -> 4647[label="",style="dashed", color="magenta", weight=3];
4642[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 False)) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 False))",fontsize=16,color="black",shape="box"];4642 -> 4648[label="",style="solid", color="black", weight=3];
4643 -> 4497[label="",style="dashed", color="red", weight=0];
4643[label="gcd0Gcd'1 (primEqInt (Pos (primModNatS0 (Succ vuz203) vuz204 True)) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (primModNatS0 (Succ vuz203) vuz204 True))",fontsize=16,color="magenta"];4643 -> 4649[label="",style="dashed", color="magenta", weight=3];
4643 -> 4650[label="",style="dashed", color="magenta", weight=3];
4536[label="Succ vuz197",fontsize=16,color="green",shape="box"];4537[label="vuz198",fontsize=16,color="green",shape="box"];4538[label="Succ vuz197",fontsize=16,color="green",shape="box"];4539[label="vuz198",fontsize=16,color="green",shape="box"];4573 -> 3294[label="",style="dashed", color="red", weight=0];
4573[label="gcd0Gcd'1 False (Neg (Succ vuz201)) (Pos (Succ vuz200))",fontsize=16,color="magenta"];4573 -> 4581[label="",style="dashed", color="magenta", weight=3];
4573 -> 4582[label="",style="dashed", color="magenta", weight=3];
4644[label="vuz2050",fontsize=16,color="green",shape="box"];4645[label="vuz2060",fontsize=16,color="green",shape="box"];4646[label="vuz203",fontsize=16,color="green",shape="box"];4647[label="vuz204",fontsize=16,color="green",shape="box"];4648 -> 4553[label="",style="dashed", color="red", weight=0];
4648[label="gcd0Gcd'1 (primEqInt (Pos (Succ (Succ vuz203))) (fromInt (Pos Zero))) (Neg (Succ vuz204)) (Pos (Succ (Succ vuz203)))",fontsize=16,color="magenta"];4648 -> 4651[label="",style="dashed", color="magenta", weight=3];
4648 -> 4652[label="",style="dashed", color="magenta", weight=3];
4649[label="vuz203",fontsize=16,color="green",shape="box"];4650[label="vuz204",fontsize=16,color="green",shape="box"];4581[label="Neg (Succ vuz201)",fontsize=16,color="green",shape="box"];4582[label="vuz200",fontsize=16,color="green",shape="box"];4651[label="vuz204",fontsize=16,color="green",shape="box"];4652[label="Succ vuz203",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

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primMulNat(Succ(vuz31000)) → new_primMulNat(vuz31000)

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_primMulNat(Succ(vuz31000)) → new_primMulNat(vuz31000)
The graph contains the following edges 1 > 1

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primPlusNat(Succ(vuz6700), Succ(vuz150)) → new_primPlusNat(vuz6700, vuz150)

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

new_primPlusNat(Succ(vuz6700), Succ(vuz150)) → new_primPlusNat(vuz6700, vuz150)
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

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primMinusNatS(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS(vuz1090, vuz1100)

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

new_primMinusNatS(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS(vuz1090, vuz1100)
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

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(vuz151, vuz152) → new_gcd0Gcd'17(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'11(vuz148, vuz149) → new_gcd0Gcd'1(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149)
new_gcd0Gcd'1(Succ(Zero), Zero) → new_gcd0Gcd'1(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'1(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'17(Succ(Zero), Zero) → new_gcd0Gcd'17(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'18(Succ(Zero), Zero, vuz188) → new_gcd0Gcd'18(new_primMinusNatS0(Zero, Zero), Zero, new_primMinusNatS0(Zero, Zero))
new_gcd0Gcd'13(Pos(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'12(vuz157, vuz158) → new_gcd0Gcd'13(Pos(Succ(vuz158)), vuz157)
new_gcd0Gcd'18(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'111(Zero, Succ(vuz1870))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'13(Neg(Succ(Zero)), Zero) → new_gcd0Gcd'17(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'111(vuz200, vuz201) → new_gcd0Gcd'13(Neg(Succ(vuz201)), vuz200)
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Pos(Succ(Zero)), Zero) → new_gcd0Gcd'1(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 5 less nodes.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'12(vuz157, vuz158) → new_gcd0Gcd'13(Pos(Succ(vuz158)), vuz157)
new_gcd0Gcd'13(Pos(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'11(vuz148, vuz149) → new_gcd0Gcd'1(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'1(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'11(vuz148, vuz149) → new_gcd0Gcd'1(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149) at position [0] we obtained the following new rules:

new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'13(Pos(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'1(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'12(vuz157, vuz158) → new_gcd0Gcd'13(Pos(Succ(vuz158)), vuz157)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                          ↳ QDP

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                          ↳ QDP

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                                  ↳ QDP

                                                    ↳ RuleRemovalProof

                                          ↳ QDP

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)

R is empty.
Q is empty.
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_gcd0Gcd'1(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'11(vuz132000, Zero)
new_gcd0Gcd'11(x0, Zero) → new_gcd0Gcd'1(Succ(x0), Zero)

Used ordering: POLO with Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + 2·x₁
POL(Zero) = 0
POL(new_gcd0Gcd'1(x₁, x₂)) = x₁ + x₂
POL(new_gcd0Gcd'11(x₁, x₂)) = 2 + 2·x₁ + x₂

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                                  ↳ QDP

                                                    ↳ RuleRemovalProof

                                                      ↳ QDP

                                                        ↳ PisEmptyProof

                                          ↳ QDP

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

Q DP problem:
P is empty.
R is empty.
Q is empty.
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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'12(vuz157, vuz158) → new_gcd0Gcd'13(Pos(Succ(vuz158)), vuz157)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'13(Pos(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'1(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'12(vuz157, vuz158) → new_gcd0Gcd'13(Pos(Succ(vuz158)), vuz157) we obtained the following new rules:

new_gcd0Gcd'12(Zero, Succ(z0)) → new_gcd0Gcd'13(Pos(Succ(Succ(z0))), Zero)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'12(Zero, Succ(z0)) → new_gcd0Gcd'13(Pos(Succ(Succ(z0))), Zero)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'13(Pos(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'1(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'12(Zero, Succ(vuz4200))
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_gcd0Gcd'1(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)

The remaining pairs can at least be oriented weakly.

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

Used ordering: Matrix interpretation [3]:
Non-tuple symbols:

M( new_primMinusNatS0(x₁, x₂) ) =

/	0	\
\	0	/

/	0	1	\
\	0	1	/

x₁

/	0	0	\
\	0	0	/

x₂

M( Succ(x₁) ) =

/	0	\
\	1	/

/	0	1	\
\	0	1	/

x₁

M( Zero ) =

/	0	\
\	0	/

M( Pos(x₁) ) =

/	0	\
\	0	/

/	0	0	\
\	1	0	/

x₁

Tuple symbols:

M( new_gcd0Gcd'10(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'11(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'1(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'12(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'13(x₁, x₂) ) =

[

]

x₁

[

]

x₂

Matrix type:
We used a basic matrix type which is not further parametrizeable.

As matrix orders are CE-compatible, we used usable rules w.r.t. argument filtering in the order.
The following usable rules [17] were oriented:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'11(x0, Succ(x1)) → new_gcd0Gcd'1(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'11(vuz160, vuz161)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                                          ↳ QDP

                                                            ↳ UsableRulesProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                                          ↳ QDP

                                                            ↳ UsableRulesProof

                                                              ↳ QDP

                                                                ↳ QReductionProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                                          ↳ QDP

                                                            ↳ UsableRulesProof

                                                              ↳ QDP

                                                                ↳ QReductionProof

                                                                  ↳ QDP

                                                                    ↳ NonInfProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The DP Problem is simplified using the Induction Calculus [18] with the following steps:
Note that final constraints are written in bold face.

For Pair new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200) the following chains were created:

We consider the chain new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0)), new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200) which results in the following constraint:
(1) (new_gcd0Gcd'13(Pos(Succ(x6)), Succ(x5))=new_gcd0Gcd'13(Pos(Succ(Succ(x7))), Succ(x8)) ⇒ new_gcd0Gcd'13(Pos(Succ(Succ(x7))), Succ(x8))≥new_gcd0Gcd'10(x7, Succ(x8), x7, x8))

We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
(2) (new_gcd0Gcd'13(Pos(Succ(Succ(x7))), Succ(x5))≥new_gcd0Gcd'10(x7, Succ(x5), x7, x5))

For Pair new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161) the following chains were created:

We consider the chain new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200), new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161) which results in the following constraint:
(3) (new_gcd0Gcd'10(x13, Succ(x14), x13, x14)=new_gcd0Gcd'10(x15, x16, Zero, Succ(x17)) ⇒ new_gcd0Gcd'10(x15, x16, Zero, Succ(x17))≥new_gcd0Gcd'12(Succ(x15), x16))

We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
(4) (new_gcd0Gcd'10(Zero, Succ(Succ(x17)), Zero, Succ(x17))≥new_gcd0Gcd'12(Succ(Zero), Succ(Succ(x17))))
We consider the chain new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630), new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161) which results in the following constraint:
(5) (new_gcd0Gcd'10(x23, x24, x25, x26)=new_gcd0Gcd'10(x27, x28, Zero, Succ(x29)) ⇒ new_gcd0Gcd'10(x27, x28, Zero, Succ(x29))≥new_gcd0Gcd'12(Succ(x27), x28))

We simplified constraint (5) using rules (I), (II), (III) which results in the following new constraint:
(6) (new_gcd0Gcd'10(x23, x24, Zero, Succ(x29))≥new_gcd0Gcd'12(Succ(x23), x24))

For Pair new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0)) the following chains were created:

We consider the chain new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161), new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0)) which results in the following constraint:
(7) (new_gcd0Gcd'12(Succ(x32), x33)=new_gcd0Gcd'12(Succ(x35), x36) ⇒ new_gcd0Gcd'12(Succ(x35), x36)≥new_gcd0Gcd'13(Pos(Succ(x36)), Succ(x35)))

We simplified constraint (7) using rules (I), (II), (III) which results in the following new constraint:
(8) (new_gcd0Gcd'12(Succ(x32), x33)≥new_gcd0Gcd'13(Pos(Succ(x33)), Succ(x32)))

For Pair new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630) the following chains were created:

We consider the chain new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200), new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630) which results in the following constraint:
(9) (new_gcd0Gcd'10(x43, Succ(x44), x43, x44)=new_gcd0Gcd'10(x45, x46, Succ(x47), Succ(x48)) ⇒ new_gcd0Gcd'10(x45, x46, Succ(x47), Succ(x48))≥new_gcd0Gcd'10(x45, x46, x47, x48))

We simplified constraint (9) using rules (I), (II), (III) which results in the following new constraint:
(10) (new_gcd0Gcd'10(Succ(x47), Succ(Succ(x48)), Succ(x47), Succ(x48))≥new_gcd0Gcd'10(Succ(x47), Succ(Succ(x48)), x47, x48))
We consider the chain new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630), new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630) which results in the following constraint:
(11) (new_gcd0Gcd'10(x54, x55, x56, x57)=new_gcd0Gcd'10(x58, x59, Succ(x60), Succ(x61)) ⇒ new_gcd0Gcd'10(x58, x59, Succ(x60), Succ(x61))≥new_gcd0Gcd'10(x58, x59, x60, x61))

We simplified constraint (11) using rules (I), (II), (III) which results in the following new constraint:
(12) (new_gcd0Gcd'10(x54, x55, Succ(x60), Succ(x61))≥new_gcd0Gcd'10(x54, x55, x60, x61))

To summarize, we get the following constraints P_≥ for the following pairs.

new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
- (new_gcd0Gcd'13(Pos(Succ(Succ(x7))), Succ(x5))≥new_gcd0Gcd'10(x7, Succ(x5), x7, x5))
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
- (new_gcd0Gcd'10(Zero, Succ(Succ(x17)), Zero, Succ(x17))≥new_gcd0Gcd'12(Succ(Zero), Succ(Succ(x17))))
- (new_gcd0Gcd'10(x23, x24, Zero, Succ(x29))≥new_gcd0Gcd'12(Succ(x23), x24))
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
- (new_gcd0Gcd'12(Succ(x32), x33)≥new_gcd0Gcd'13(Pos(Succ(x33)), Succ(x32)))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
- (new_gcd0Gcd'10(Succ(x47), Succ(Succ(x48)), Succ(x47), Succ(x48))≥new_gcd0Gcd'10(Succ(x47), Succ(Succ(x48)), x47, x48))
- (new_gcd0Gcd'10(x54, x55, Succ(x60), Succ(x61))≥new_gcd0Gcd'10(x54, x55, x60, x61))

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation [18]:

POL(Pos(x₁)) = 0
POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(c) = -1
POL(new_gcd0Gcd'10(x₁, x₂, x₃, x₄)) = -1 + x₁ - x₃ + x₄
POL(new_gcd0Gcd'12(x₁, x₂)) = -1 + x₁
POL(new_gcd0Gcd'13(x₁, x₂)) = -1 - x₁ + x₂

The following pairs are in P_>:

new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)

The following pairs are in P_bound:

new_gcd0Gcd'13(Pos(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'10(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))

There are no usable rules

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                                          ↳ QDP

                                                            ↳ UsableRulesProof

                                                              ↳ QDP

                                                                ↳ QReductionProof

                                                                  ↳ QDP

                                                                    ↳ NonInfProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'12(Succ(vuz160), vuz161)
new_gcd0Gcd'12(Succ(z0), z1) → new_gcd0Gcd'13(Pos(Succ(z1)), Succ(z0))
new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ DependencyGraphProof

                                                          ↳ QDP

                                                            ↳ UsableRulesProof

                                                              ↳ QDP

                                                                ↳ QReductionProof

                                                                  ↳ QDP

                                                                    ↳ NonInfProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ QDPSizeChangeProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)

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

new_gcd0Gcd'10(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'10(vuz160, vuz161, vuz1620, vuz1630)
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

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'15(vuz151, vuz152) → new_gcd0Gcd'17(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'18(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'111(Zero, Succ(vuz1870))
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'111(vuz200, vuz201) → new_gcd0Gcd'13(Neg(Succ(vuz201)), vuz200)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'15(vuz151, vuz152) → new_gcd0Gcd'17(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152) at position [0] we obtained the following new rules:

new_gcd0Gcd'15(x0, Zero) → new_gcd0Gcd'17(Succ(x0), Zero)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'15(x0, Zero) → new_gcd0Gcd'17(Succ(x0), Zero)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'111(Zero, Succ(vuz1870))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'111(vuz200, vuz201) → new_gcd0Gcd'13(Neg(Succ(vuz201)), vuz200)
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'15(x0, Zero) → new_gcd0Gcd'17(Succ(x0), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'15(x0, Zero) → new_gcd0Gcd'17(Succ(x0), Zero)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                                  ↳ QDP

                                                    ↳ RuleRemovalProof

                                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'17(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'15(vuz132000, Zero)
new_gcd0Gcd'15(x0, Zero) → new_gcd0Gcd'17(Succ(x0), Zero)

Used ordering: POLO with Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + 2·x₁
POL(Zero) = 0
POL(new_gcd0Gcd'15(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(new_gcd0Gcd'17(x₁, x₂)) = x₁ + x₂

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                            ↳ UsableRulesProof

                                              ↳ QDP

                                                ↳ QReductionProof

                                                  ↳ QDP

                                                    ↳ RuleRemovalProof

                                                      ↳ QDP

                                                        ↳ PisEmptyProof

                                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

Q DP problem:
P is empty.
R is empty.
Q is empty.
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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'18(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'111(Zero, Succ(vuz1870))
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'111(vuz200, vuz201) → new_gcd0Gcd'13(Neg(Succ(vuz201)), vuz200)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'111(vuz200, vuz201) → new_gcd0Gcd'13(Neg(Succ(vuz201)), vuz200) we obtained the following new rules:

new_gcd0Gcd'111(Zero, Succ(z0)) → new_gcd0Gcd'13(Neg(Succ(Succ(z0))), Zero)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'111(Zero, Succ(z0)) → new_gcd0Gcd'13(Neg(Succ(Succ(z0))), Zero)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'111(Zero, Succ(vuz1870))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_gcd0Gcd'13(Neg(Succ(Zero)), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))

The remaining pairs can at least be oriented weakly.

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

Used ordering: Matrix interpretation [3]:
Non-tuple symbols:

M( Neg(x₁) ) =

/	0	\
\	0	/

/	0	1	\
\	0	0	/

x₁

M( new_primMinusNatS0(x₁, x₂) ) =

/	0	\
\	0	/

/	0	0	\
\	0	0	/

x₁

/	0	0	\
\	0	0	/

x₂

M( Succ(x₁) ) =

/	0	\
\	0	/

/	0	0	\
\	1	0	/

x₁

M( Zero ) =

/	1	\
\	0	/

Tuple symbols:

M( new_gcd0Gcd'19(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'16(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'111(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'110(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'18(x₁, ..., x₃) ) =

[

]

x₁

[

]

x₂

[

]

x₃

M( new_gcd0Gcd'15(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'13(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'14(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'17(x₁, x₂) ) =

[

]

x₁

[

]

x₂

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_gcd0Gcd'17(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'16(Zero, Succ(vuz4200))

The remaining pairs can at least be oriented weakly.

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

Used ordering: Matrix interpretation [3]:
Non-tuple symbols:

M( Neg(x₁) ) =

/	0	\
\	0	/

/	1	0	\
\	0	0	/

x₁

M( new_primMinusNatS0(x₁, x₂) ) =

/	0	\
\	0	/

/	0	0	\
\	0	0	/

x₁

/	0	0	\
\	0	0	/

x₂

M( Succ(x₁) ) =

/	0	\
\	1	/

/	0	1	\
\	0	0	/

x₁

M( Zero ) =

/	0	\
\	0	/

Tuple symbols:

M( new_gcd0Gcd'19(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'16(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'111(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'110(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'18(x₁, ..., x₃) ) =

[

]

x₁

[

]

x₂

[

]

x₃

M( new_gcd0Gcd'15(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'13(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'14(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'17(x₁, x₂) ) =

[

]

x₁

[

]

x₂

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_gcd0Gcd'17(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'15(vuz165, vuz166)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'15(vuz165, vuz166)

The remaining pairs can at least be oriented weakly.

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))

Used ordering: Matrix interpretation [3]:
Non-tuple symbols:

M( Neg(x₁) ) =

/	0	\
\	0	/

/	0	0	\
\	1	0	/

x₁

M( new_primMinusNatS0(x₁, x₂) ) =

/	0	\
\	0	/

/	0	1	\
\	0	1	/

x₁

/	0	0	\
\	0	0	/

x₂

M( Succ(x₁) ) =

/	0	\
\	1	/

/	0	1	\
\	0	1	/

x₁

M( Zero ) =

/	0	\
\	0	/

Tuple symbols:

M( new_gcd0Gcd'19(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'16(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'111(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'110(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'18(x₁, ..., x₃) ) =

[

]

x₁

[

]

x₂

[

]

x₃

M( new_gcd0Gcd'15(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'13(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'14(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'17(x₁, x₂) ) =

[

]

x₁

[

]

x₂

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'15(x0, Succ(x1)) → new_gcd0Gcd'17(new_primMinusNatS0(x0, x1), Succ(x1))
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_gcd0Gcd'18(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'110(vuz18900, Zero)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'110(vuz203, vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'110(vuz203, vuz204)

The remaining pairs can at least be oriented weakly.

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

Used ordering: Matrix interpretation [3]:
Non-tuple symbols:

M( Neg(x₁) ) =

/	0	\
\	0	/

/	0	0	\
\	0	0	/

x₁

M( new_primMinusNatS0(x₁, x₂) ) =

/	0	\
\	1	/

/	1	0	\
\	0	0	/

x₁

/	0	0	\
\	0	0	/

x₂

M( Succ(x₁) ) =

/	0	\
\	1	/

/	1	1	\
\	0	0	/

x₁

M( Zero ) =

/	0	\
\	0	/

Tuple symbols:

M( new_gcd0Gcd'19(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

M( new_gcd0Gcd'16(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'111(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'18(x₁, ..., x₃) ) =

[

]

x₁

[

]

x₂

[

]

x₃

M( new_gcd0Gcd'110(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'13(x₁, x₂) ) =

[

]

x₁

[

]

x₂

M( new_gcd0Gcd'14(x₁, ..., x₄) ) =

[

]

x₁

[

]

x₂

[

]

x₃

[

]

x₄

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'110(vuz197, vuz198) → new_gcd0Gcd'18(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                                                                                  ↳ QDP

                                                                                    ↳ Instantiation

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'18(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'19(vuz18900, Succ(vuz1870), vuz18900, vuz1870) we obtained the following new rules:

new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                                                                                  ↳ QDP

                                                                                    ↳ Instantiation

                                                                                      ↳ QDP

                                                                                        ↳ NonInfProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The DP Problem is simplified using the Induction Calculus [18] with the following steps:
Note that final constraints are written in bold face.

For Pair new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204) the following chains were created:

We consider the chain new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060), new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204) which results in the following constraint:
(1) (new_gcd0Gcd'19(x3, x4, x5, x6)=new_gcd0Gcd'19(x7, x8, Zero, Succ(x9)) ⇒ new_gcd0Gcd'19(x7, x8, Zero, Succ(x9))≥new_gcd0Gcd'111(Succ(x7), x8))

We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
(2) (new_gcd0Gcd'19(x3, x4, Zero, Succ(x9))≥new_gcd0Gcd'111(Succ(x3), x4))
We consider the chain new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1), new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204) which results in the following constraint:
(3) (new_gcd0Gcd'19(x23, Succ(x24), x23, x24)=new_gcd0Gcd'19(x25, x26, Zero, Succ(x27)) ⇒ new_gcd0Gcd'19(x25, x26, Zero, Succ(x27))≥new_gcd0Gcd'111(Succ(x25), x26))

We simplified constraint (3) using rules (I), (II), (III) which results in the following new constraint:
(4) (new_gcd0Gcd'19(Zero, Succ(Succ(x27)), Zero, Succ(x27))≥new_gcd0Gcd'111(Succ(Zero), Succ(Succ(x27))))

For Pair new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060) the following chains were created:

We consider the chain new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060), new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060) which results in the following constraint:
(5) (new_gcd0Gcd'19(x31, x32, x33, x34)=new_gcd0Gcd'19(x35, x36, Succ(x37), Succ(x38)) ⇒ new_gcd0Gcd'19(x35, x36, Succ(x37), Succ(x38))≥new_gcd0Gcd'19(x35, x36, x37, x38))

We simplified constraint (5) using rules (I), (II), (III) which results in the following new constraint:
(6) (new_gcd0Gcd'19(x31, x32, Succ(x37), Succ(x38))≥new_gcd0Gcd'19(x31, x32, x37, x38))
We consider the chain new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1), new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060) which results in the following constraint:
(7) (new_gcd0Gcd'19(x52, Succ(x53), x52, x53)=new_gcd0Gcd'19(x54, x55, Succ(x56), Succ(x57)) ⇒ new_gcd0Gcd'19(x54, x55, Succ(x56), Succ(x57))≥new_gcd0Gcd'19(x54, x55, x56, x57))

We simplified constraint (7) using rules (I), (II), (III) which results in the following new constraint:
(8) (new_gcd0Gcd'19(Succ(x56), Succ(Succ(x57)), Succ(x56), Succ(x57))≥new_gcd0Gcd'19(Succ(x56), Succ(Succ(x57)), x56, x57))

For Pair new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680) the following chains were created:

We consider the chain new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680), new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680) which results in the following constraint:
(9) (new_gcd0Gcd'14(x65, x66, x67, x68)=new_gcd0Gcd'14(x69, x70, Succ(x71), Succ(x72)) ⇒ new_gcd0Gcd'14(x69, x70, Succ(x71), Succ(x72))≥new_gcd0Gcd'14(x69, x70, x71, x72))

We simplified constraint (9) using rules (I), (II), (III) which results in the following new constraint:
(10) (new_gcd0Gcd'14(x65, x66, Succ(x71), Succ(x72))≥new_gcd0Gcd'14(x65, x66, x71, x72))
We consider the chain new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200), new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680) which results in the following constraint:
(11) (new_gcd0Gcd'14(x75, Succ(x76), x75, x76)=new_gcd0Gcd'14(x77, x78, Succ(x79), Succ(x80)) ⇒ new_gcd0Gcd'14(x77, x78, Succ(x79), Succ(x80))≥new_gcd0Gcd'14(x77, x78, x79, x80))

We simplified constraint (11) using rules (I), (II), (III) which results in the following new constraint:
(12) (new_gcd0Gcd'14(Succ(x79), Succ(Succ(x80)), Succ(x79), Succ(x80))≥new_gcd0Gcd'14(Succ(x79), Succ(Succ(x80)), x79, x80))

For Pair new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155)) the following chains were created:

We consider the chain new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166), new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155)) which results in the following constraint:
(13) (new_gcd0Gcd'16(Succ(x105), x106)=new_gcd0Gcd'16(x108, x109) ⇒ new_gcd0Gcd'16(x108, x109)≥new_gcd0Gcd'18(Succ(x109), x108, Succ(x109)))

We simplified constraint (13) using rules (I), (II), (III) which results in the following new constraint:
(14) (new_gcd0Gcd'16(Succ(x105), x106)≥new_gcd0Gcd'18(Succ(x106), Succ(x105), Succ(x106)))

For Pair new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200) the following chains were created:

We consider the chain new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0)), new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200) which results in the following constraint:
(15) (new_gcd0Gcd'13(Neg(Succ(x128)), Succ(x127))=new_gcd0Gcd'13(Neg(Succ(Succ(x129))), Succ(x130)) ⇒ new_gcd0Gcd'13(Neg(Succ(Succ(x129))), Succ(x130))≥new_gcd0Gcd'14(x129, Succ(x130), x129, x130))

We simplified constraint (15) using rules (I), (II), (III) which results in the following new constraint:
(16) (new_gcd0Gcd'13(Neg(Succ(Succ(x129))), Succ(x127))≥new_gcd0Gcd'14(x129, Succ(x127), x129, x127))

For Pair new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0)) the following chains were created:

We consider the chain new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204), new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0)) which results in the following constraint:
(17) (new_gcd0Gcd'111(Succ(x136), x137)=new_gcd0Gcd'111(Succ(x139), x140) ⇒ new_gcd0Gcd'111(Succ(x139), x140)≥new_gcd0Gcd'13(Neg(Succ(x140)), Succ(x139)))

We simplified constraint (17) using rules (I), (II), (III) which results in the following new constraint:
(18) (new_gcd0Gcd'111(Succ(x136), x137)≥new_gcd0Gcd'13(Neg(Succ(x137)), Succ(x136)))

For Pair new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166) the following chains were created:

We consider the chain new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680), new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166) which results in the following constraint:
(19) (new_gcd0Gcd'14(x167, x168, x169, x170)=new_gcd0Gcd'14(x171, x172, Zero, Succ(x173)) ⇒ new_gcd0Gcd'14(x171, x172, Zero, Succ(x173))≥new_gcd0Gcd'16(Succ(x171), x172))

We simplified constraint (19) using rules (I), (II), (III) which results in the following new constraint:
(20) (new_gcd0Gcd'14(x167, x168, Zero, Succ(x173))≥new_gcd0Gcd'16(Succ(x167), x168))
We consider the chain new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200), new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166) which results in the following constraint:
(21) (new_gcd0Gcd'14(x176, Succ(x177), x176, x177)=new_gcd0Gcd'14(x178, x179, Zero, Succ(x180)) ⇒ new_gcd0Gcd'14(x178, x179, Zero, Succ(x180))≥new_gcd0Gcd'16(Succ(x178), x179))

We simplified constraint (21) using rules (I), (II), (III) which results in the following new constraint:
(22) (new_gcd0Gcd'14(Zero, Succ(Succ(x180)), Zero, Succ(x180))≥new_gcd0Gcd'16(Succ(Zero), Succ(Succ(x180))))

For Pair new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1) the following chains were created:

We consider the chain new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155)), new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1) which results in the following constraint:
(23) (new_gcd0Gcd'18(Succ(x200), x199, Succ(x200))=new_gcd0Gcd'18(Succ(Succ(x201)), Succ(x202), Succ(Succ(x201))) ⇒ new_gcd0Gcd'18(Succ(Succ(x201)), Succ(x202), Succ(Succ(x201)))≥new_gcd0Gcd'19(x201, Succ(x202), x201, x202))

We simplified constraint (23) using rules (I), (II), (III) which results in the following new constraint:
(24) (new_gcd0Gcd'18(Succ(Succ(x201)), Succ(x202), Succ(Succ(x201)))≥new_gcd0Gcd'19(x201, Succ(x202), x201, x202))

To summarize, we get the following constraints P_≥ for the following pairs.

new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
- (new_gcd0Gcd'19(x3, x4, Zero, Succ(x9))≥new_gcd0Gcd'111(Succ(x3), x4))
- (new_gcd0Gcd'19(Zero, Succ(Succ(x27)), Zero, Succ(x27))≥new_gcd0Gcd'111(Succ(Zero), Succ(Succ(x27))))
new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
- (new_gcd0Gcd'19(x31, x32, Succ(x37), Succ(x38))≥new_gcd0Gcd'19(x31, x32, x37, x38))
- (new_gcd0Gcd'19(Succ(x56), Succ(Succ(x57)), Succ(x56), Succ(x57))≥new_gcd0Gcd'19(Succ(x56), Succ(Succ(x57)), x56, x57))
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
- (new_gcd0Gcd'14(x65, x66, Succ(x71), Succ(x72))≥new_gcd0Gcd'14(x65, x66, x71, x72))
- (new_gcd0Gcd'14(Succ(x79), Succ(Succ(x80)), Succ(x79), Succ(x80))≥new_gcd0Gcd'14(Succ(x79), Succ(Succ(x80)), x79, x80))
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
- (new_gcd0Gcd'16(Succ(x105), x106)≥new_gcd0Gcd'18(Succ(x106), Succ(x105), Succ(x106)))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
- (new_gcd0Gcd'13(Neg(Succ(Succ(x129))), Succ(x127))≥new_gcd0Gcd'14(x129, Succ(x127), x129, x127))
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
- (new_gcd0Gcd'111(Succ(x136), x137)≥new_gcd0Gcd'13(Neg(Succ(x137)), Succ(x136)))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
- (new_gcd0Gcd'14(x167, x168, Zero, Succ(x173))≥new_gcd0Gcd'16(Succ(x167), x168))
- (new_gcd0Gcd'14(Zero, Succ(Succ(x180)), Zero, Succ(x180))≥new_gcd0Gcd'16(Succ(Zero), Succ(Succ(x180))))
new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1)
- (new_gcd0Gcd'18(Succ(Succ(x201)), Succ(x202), Succ(Succ(x201)))≥new_gcd0Gcd'19(x201, Succ(x202), x201, x202))

POL(Neg(x₁)) = x₁
POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(c) = -1
POL(new_gcd0Gcd'111(x₁, x₂)) = -1 + x₁
POL(new_gcd0Gcd'13(x₁, x₂)) = -1 + x₂
POL(new_gcd0Gcd'14(x₁, x₂, x₃, x₄)) = x₁ - x₃ + x₄
POL(new_gcd0Gcd'16(x₁, x₂)) = -1 + x₁
POL(new_gcd0Gcd'18(x₁, x₂, x₃)) = -1 + x₁ + x₂ - x₃
POL(new_gcd0Gcd'19(x₁, x₂, x₃, x₄)) = x₁ - x₃ + x₄

The following pairs are in P_>:

new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)

The following pairs are in P_bound:

new_gcd0Gcd'19(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'111(Succ(vuz203), vuz204)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'14(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'16(Succ(vuz165), vuz166)
new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1)

There are no usable rules

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                                                                                  ↳ QDP

                                                                                    ↳ Instantiation

                                                                                      ↳ QDP

                                                                                        ↳ NonInfProof

                                                                                          ↳ QDP

                                                                                            ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'111(Succ(z0), z1) → new_gcd0Gcd'13(Neg(Succ(z1)), Succ(z0))
new_gcd0Gcd'13(Neg(Succ(Succ(vuz132000))), Succ(vuz4200)) → new_gcd0Gcd'14(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_gcd0Gcd'16(vuz154, vuz155) → new_gcd0Gcd'18(Succ(vuz155), vuz154, Succ(vuz155))
new_gcd0Gcd'18(Succ(Succ(x0)), Succ(x1), Succ(Succ(x0))) → new_gcd0Gcd'19(x0, Succ(x1), x0, x1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 4 less nodes.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                                                                                  ↳ QDP

                                                                                    ↳ Instantiation

                                                                                      ↳ QDP

                                                                                        ↳ NonInfProof

                                                                                          ↳ QDP

                                                                                            ↳ DependencyGraphProof

                                                                                              ↳ AND

                                                                                                ↳ QDP

                                                                                                  ↳ QDPSizeChangeProof

                                                                                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)

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

new_gcd0Gcd'14(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'14(vuz165, vuz166, vuz1670, vuz1680)
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

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ AND

                                          ↳ QDP

                                          ↳ QDP

                                            ↳ Instantiation

                                              ↳ QDP

                                                ↳ DependencyGraphProof

                                                  ↳ QDP

                                                    ↳ QDPOrderProof

                                                      ↳ QDP

                                                        ↳ QDPOrderProof

                                                          ↳ QDP

                                                            ↳ QDPOrderProof

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ QDPOrderProof

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                                                                          ↳ QDP

                                                                            ↳ UsableRulesProof

                                                                              ↳ QDP

                                                                                ↳ QReductionProof

                                                                                  ↳ QDP

                                                                                    ↳ Instantiation

                                                                                      ↳ QDP

                                                                                        ↳ NonInfProof

                                                                                          ↳ QDP

                                                                                            ↳ DependencyGraphProof

                                                                                              ↳ AND

                                                                                                ↳ QDP

                                                                                                ↳ QDP

                                                                                                  ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)

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

new_gcd0Gcd'19(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'19(vuz203, vuz204, vuz2050, vuz2060)
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

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd2(Succ(vuz1250), Succ(vuz1290), vuz27) → new_gcd2(vuz1250, vuz1290, vuz27)

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

new_gcd2(Succ(vuz1250), Succ(vuz1290), vuz27) → new_gcd2(vuz1250, vuz1290, vuz27)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd20(Succ(vuz1230), Succ(vuz1160), vuz42) → new_gcd20(vuz1230, vuz1160, vuz42)

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

new_gcd20(Succ(vuz1230), Succ(vuz1160), vuz42) → new_gcd20(vuz1230, vuz1160, vuz42)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS1(Succ(vuz410), vuz8) → new_primDivNatS0(vuz410, vuz8)
new_primDivNatS0(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS00(vuz850, vuz86000, vuz850, vuz86000)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)
new_primDivNatS(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS00(vuz850, vuz86000, vuz850, vuz86000)
new_primDivNatS0(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS01(vuz109, vuz110) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS00(vuz109, vuz110, Zero, Zero) → new_primDivNatS01(vuz109, vuz110)
new_primDivNatS(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPSizeChangeProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)

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

new_primDivNatS(Succ(vuz850), Zero) → new_primDivNatS(vuz850, Zero)
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

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS1(Succ(vuz410), vuz8) → new_primDivNatS0(vuz410, vuz8)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)
new_primDivNatS0(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS00(vuz850, vuz86000, vuz850, vuz86000)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS01(vuz109, vuz110) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS00(vuz109, vuz110, Zero, Zero) → new_primDivNatS01(vuz109, vuz110)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Succ(x0), 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_primDivNatS0(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS00(vuz850, vuz86000, vuz850, vuz86000)

The remaining pairs can at least be oriented weakly.

new_primDivNatS1(Succ(vuz410), vuz8) → new_primDivNatS0(vuz410, vuz8)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS01(vuz109, vuz110) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS00(vuz109, vuz110, Zero, Zero) → new_primDivNatS01(vuz109, vuz110)

Used ordering: Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(new_primDivNatS0(x₁, x₂)) = 1 + x₁
POL(new_primDivNatS00(x₁, x₂, x₃, x₄)) = x₁
POL(new_primDivNatS01(x₁, x₂)) = x₁
POL(new_primDivNatS1(x₁, x₂)) = x₁
POL(new_primMinusNatS0(x₁, x₂)) = x₁

The following usable rules [17] were oriented:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ QDPOrderProof

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS1(Succ(vuz410), vuz8) → new_primDivNatS0(vuz410, vuz8)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)
new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS01(vuz109, vuz110) → new_primDivNatS1(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110))
new_primDivNatS00(vuz109, vuz110, Zero, Zero) → new_primDivNatS01(vuz109, vuz110)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ QDPOrderProof

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ QDPOrderProof

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ UsableRulesProof

                                            ↳ QDP

                                              ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ QDPOrderProof

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ UsableRulesProof

                                            ↳ QDP

                                              ↳ QReductionProof

                                                ↳ QDP

                                                  ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)

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

new_primDivNatS00(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS00(vuz109, vuz110, vuz1110, vuz1120)
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

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primQuotInt(Succ(vuz6500), Succ(vuz150), vuz27) → new_primQuotInt(vuz6500, vuz150, vuz27)

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

new_primQuotInt(Succ(vuz6500), Succ(vuz150), vuz27) → new_primQuotInt(vuz6500, vuz150, vuz27)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                      ↳ Narrow

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

new_primQuotInt0(Succ(vuz80), Succ(vuz7100), vuz42) → new_primQuotInt0(vuz80, vuz7100, vuz42)

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

new_primQuotInt0(Succ(vuz80), Succ(vuz7100), vuz42) → new_primQuotInt0(vuz80, vuz7100, vuz42)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ MNOCProof

                      ↳ Narrow

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

new_numericEnumFrom(vuz3) → new_numericEnumFrom(new_ps(vuz3))

The TRS R consists of the following rules:

new_gcd217(vuz127, vuz131, vuz126, vuz130, vuz27) → new_gcd22(new_primPlusNat0(vuz127, vuz131), vuz27)
new_primPlusNat2(Zero) → Zero
new_gcd26(Succ(vuz1230), Zero, vuz42) → new_gcd27(Succ(vuz1230), vuz42)
new_primQuotInt3(Zero, Succ(vuz7100), vuz42) → new_primQuotInt7(Succ(vuz7100), new_gcd21(vuz7100, vuz42))
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'118(vuz160, vuz161, vuz1620, vuz1630)
new_primQuotInt9(vuz67, vuz15, vuz68, vuz27) → new_primQuotInt7(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), new_reduce2D0(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), vuz27))
new_gcd22(Succ(vuz1180), Succ(vuz270)) → new_gcd0Gcd'116(vuz270, vuz1180)
new_gcd0Gcd'123(vuz151, vuz152) → new_gcd0Gcd'124(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152)
new_gcd0Gcd'117(Neg(vuz1320), vuz420) → new_gcd0Gcd'124(vuz1320, vuz420)
new_ps(:%(vuz30, Neg(Zero))) → new_error0
new_gcd0Gcd'124(Succ(Zero), Zero) → new_gcd0Gcd'124(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Zero) → Zero
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS03(vuz109, vuz110, vuz1110, vuz1120)
new_primQuotInt7(vuz26, Neg(Zero)) → new_error
new_gcd0Gcd'122(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd21(vuz7100, Succ(vuz420)) → new_gcd0Gcd'116(vuz420, vuz7100)
new_gcd0Gcd'127(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd27(Zero, Succ(vuz420)) → new_gcd0Gcd'125(vuz420)
new_gcd0Gcd'115(vuz200, vuz201) → new_gcd0Gcd'117(Neg(Succ(vuz201)), vuz200)
new_gcd213(vuz127, vuz15, vuz126, vuz27) → new_gcd217(vuz127, new_primMulNat0(vuz15), vuz126, new_primMulNat0(vuz15), vuz27)
new_primDivNatS02(Zero, Succ(vuz86000)) → Zero
new_gcd27(Succ(vuz1070), Succ(vuz420)) → new_gcd0Gcd'121(vuz420, vuz1070)
new_gcd0Gcd'121(vuz420, vuz1070) → new_gcd0Gcd'117(new_abs0(vuz1070), vuz420)
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd0Gcd'112(Succ(Zero), Zero, vuz188) → new_gcd0Gcd'112(new_primMinusNatS0(Zero, Zero), Zero, new_primMinusNatS0(Zero, Zero))
new_primQuotInt5(vuz69, vuz8, vuz70, vuz42) → new_primQuotInt1(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), new_reduce2D(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), vuz42))
new_abs0(vuz6500) → Pos(Succ(vuz6500))
new_gcd0Gcd'119(vuz148, vuz149) → new_gcd0Gcd'122(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149)
new_ps(:%(vuz30, Pos(Zero))) → new_error0
new_gcd22(Zero, Zero) → new_error
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)
new_primQuotInt4(Neg(vuz70), vuz8, vuz42) → new_primQuotInt2(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd25(vuz6500, Succ(vuz270)) → new_gcd0Gcd'121(vuz270, vuz6500)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'123(vuz132000, Zero)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'113(vuz203, vuz204, vuz2050, vuz2060)
new_primQuotInt3(Succ(vuz80), Zero, vuz42) → new_primQuotInt1(Succ(vuz80), new_reduce2D(Succ(vuz80), vuz42))
new_error0 → error([])
new_gcd0Gcd'127(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'126(Succ(vuz165), vuz166)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Zero) → new_error0
new_gcd216(Zero, Zero, vuz27) → new_gcd214(vuz27)
new_gcd0Gcd'114(vuz197, vuz198) → new_gcd0Gcd'112(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_primMulNat0(vuz8) → new_primPlusNat0(Zero, Succ(vuz8))
new_gcd0Gcd'118(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Succ(vuz430)) → :%(new_primQuotInt4(vuz7, vuz8, vuz42), new_primQuotInt1(vuz41, new_gcd210(vuz7, vuz8, vuz42)))
new_abs(vuz1180) → Pos(Succ(vuz1180))
new_reduce2D(vuz107, vuz42) → new_gcd27(vuz107, vuz42)
new_primQuotInt2(Succ(vuz710), vuz8, vuz72, vuz42) → new_primQuotInt3(vuz8, vuz710, vuz42)
new_gcd26(Zero, Succ(vuz1160), vuz42) → new_gcd21(vuz1160, vuz42)
new_gcd211(Neg(vuz140), vuz15, vuz27) → new_gcd213(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd211(Pos(vuz140), vuz15, vuz27) → new_gcd212(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'122(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'120(Zero, Succ(vuz4200))
new_gcd28(vuz114, vuz8, vuz113, vuz42) → new_gcd29(vuz114, new_primMulNat0(vuz8), vuz113, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'124(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'126(Zero, Succ(vuz4200))
new_primDivNatS03(vuz109, vuz110, Zero, Succ(vuz1120)) → Zero
new_gcd215(vuz125, vuz129, vuz124, vuz128, vuz27) → new_gcd216(vuz125, vuz129, vuz27)
new_gcd0Gcd'122(Succ(Zero), Zero) → new_gcd0Gcd'122(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'119(vuz132000, Zero)
new_primQuotInt2(Zero, vuz8, vuz72, vuz42) → new_primQuotInt1(Succ(vuz8), new_reduce2D(Succ(vuz8), vuz42))
new_gcd21(vuz7100, Zero) → new_abs(vuz7100)
new_primQuotInt7(vuz26, Pos(Succ(vuz11700))) → Neg(new_primDivNatS2(vuz26, vuz11700))
new_gcd27(Succ(vuz1070), Zero) → new_abs0(vuz1070)
new_primDivNatS02(Zero, Zero) → Succ(Zero)
new_gcd0Gcd'124(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd216(Zero, Succ(vuz1290), vuz27) → new_gcd22(Succ(vuz1290), vuz27)
new_gcd26(Zero, Zero, vuz42) → new_gcd27(Zero, vuz42)
new_primPlusNat2(Succ(vuz1900)) → Succ(vuz1900)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'114(vuz18900, Zero)
new_primPlusNat1(Zero) → Succ(Zero)
new_gcd0Gcd'112(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'115(Zero, Succ(vuz1870))
new_gcd210(Pos(vuz70), vuz8, vuz42) → new_gcd28(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'118(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'120(Succ(vuz160), vuz161)
new_primQuotInt6(Neg(vuz140), vuz15, vuz27) → new_primQuotInt9(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_primMulNat1(Zero) → Zero
new_primQuotInt7(vuz26, Pos(Zero)) → new_error
new_primDivNatS02(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS03(vuz850, vuz86000, vuz850, vuz86000)
new_primPlusNat0(Succ(vuz6700), Succ(vuz150)) → Succ(Succ(new_primPlusNat0(vuz6700, vuz150)))
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'127(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'116(vuz420, vuz7100) → new_gcd0Gcd'117(new_abs(vuz7100), vuz420)
new_primQuotInt3(Succ(vuz80), Succ(vuz7100), vuz42) → new_primQuotInt3(vuz80, vuz7100, vuz42)
new_gcd22(Zero, Succ(vuz270)) → new_gcd0Gcd'117(Neg(Zero), vuz270)
new_primDivNatS02(Succ(vuz850), Zero) → Succ(new_primDivNatS3(vuz850, Zero))
new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_gcd214(Succ(vuz270)) → new_gcd0Gcd'125(vuz270)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'113(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_primPlusNat0(Zero, Zero) → Zero
new_primDivNatS2(Zero, vuz8) → Zero
new_primQuotInt10(Zero, Zero, vuz27) → new_primQuotInt1(Zero, new_gcd214(vuz27))
new_gcd212(vuz125, vuz15, vuz124, vuz27) → new_gcd215(vuz125, new_primMulNat0(vuz15), vuz124, new_primMulNat0(vuz15), vuz27)
new_gcd27(Zero, Zero) → new_error
new_primQuotInt1(vuz41, Pos(Zero)) → new_error
new_gcd210(Neg(vuz70), vuz8, vuz42) → new_gcd23(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_primQuotInt7(vuz26, Neg(Succ(vuz11700))) → Pos(new_primDivNatS2(vuz26, vuz11700))
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Zero) → new_error0
new_gcd26(Succ(vuz1230), Succ(vuz1160), vuz42) → new_gcd26(vuz1230, vuz1160, vuz42)
new_primQuotInt10(Succ(vuz6500), Zero, vuz27) → new_primQuotInt1(Succ(vuz6500), new_gcd25(vuz6500, vuz27))
new_primPlusNat1(Succ(vuz190)) → Succ(Succ(new_primPlusNat2(vuz190)))
new_primQuotInt8(Succ(vuz650), vuz15, vuz66, vuz27) → new_primQuotInt10(vuz650, vuz15, vuz27)
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_gcd216(Succ(vuz1250), Zero, vuz27) → new_gcd25(vuz1250, vuz27)
new_gcd24(vuz116, vuz123, vuz115, vuz122, vuz42) → new_gcd26(vuz123, vuz116, vuz42)
new_primMulNat1(Succ(vuz31000)) → new_primPlusNat1(new_primMulNat1(vuz31000))
new_primQuotInt3(Zero, Zero, vuz42) → new_primQuotInt1(Zero, new_reduce2D(Zero, vuz42))
new_primDivNatS3(vuz85, vuz8600) → new_primDivNatS02(vuz85, vuz8600)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Succ(vuz280)) → :%(new_primQuotInt6(vuz14, vuz15, vuz27), new_primQuotInt7(vuz26, new_gcd211(vuz14, vuz15, vuz27)))
new_ps(:%(vuz30, Neg(Succ(vuz3100)))) → new_reduce2Reduce10(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))
new_primQuotInt1(vuz41, Neg(Succ(vuz10600))) → Neg(new_primDivNatS2(vuz41, vuz10600))
new_primQuotInt1(vuz41, Neg(Zero)) → new_error
new_primQuotInt6(Pos(vuz140), vuz15, vuz27) → new_primQuotInt8(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'125(vuz420) → new_gcd0Gcd'117(Pos(Zero), vuz420)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'127(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_error → error([])
new_primDivNatS2(Succ(vuz410), vuz8) → new_primDivNatS02(vuz410, vuz8)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_primQuotInt10(Zero, Succ(vuz150), vuz27) → new_primQuotInt7(Succ(vuz150), new_reduce2D0(Succ(vuz150), vuz27))
new_gcd29(vuz114, vuz121, vuz113, vuz120, vuz42) → new_gcd27(new_primPlusNat0(vuz114, vuz121), vuz42)
new_gcd22(Succ(vuz1180), Zero) → new_abs(vuz1180)
new_primDivNatS04(vuz109, vuz110) → Succ(new_primDivNatS2(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110)))
new_gcd25(vuz6500, Zero) → new_abs0(vuz6500)
new_gcd0Gcd'112(Zero, vuz187, vuz188) → Neg(Succ(vuz187))
new_gcd0Gcd'126(vuz154, vuz155) → new_gcd0Gcd'112(Succ(vuz155), vuz154, Succ(vuz155))
new_primQuotInt4(Pos(vuz70), vuz8, vuz42) → new_primQuotInt5(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'115(Succ(vuz203), vuz204)
new_primQuotInt10(Succ(vuz6500), Succ(vuz150), vuz27) → new_primQuotInt10(vuz6500, vuz150, vuz27)
new_primQuotInt8(Zero, vuz15, vuz66, vuz27) → new_primQuotInt7(Succ(vuz15), new_reduce2D0(Succ(vuz15), vuz27))
new_primQuotInt1(vuz41, Pos(Succ(vuz10600))) → Pos(new_primDivNatS2(vuz41, vuz10600))
new_gcd0Gcd'117(Pos(vuz1320), vuz420) → new_gcd0Gcd'122(vuz1320, vuz420)
new_gcd214(Zero) → new_error
new_primDivNatS03(vuz109, vuz110, Zero, Zero) → new_primDivNatS04(vuz109, vuz110)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'118(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_primPlusNat0(Zero, Succ(vuz150)) → Succ(vuz150)
new_primPlusNat0(Succ(vuz6700), Zero) → Succ(vuz6700)
new_gcd23(vuz116, vuz8, vuz115, vuz42) → new_gcd24(vuz116, new_primMulNat0(vuz8), vuz115, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'120(vuz157, vuz158) → new_gcd0Gcd'117(Pos(Succ(vuz158)), vuz157)
new_reduce2D0(vuz118, vuz27) → new_gcd22(vuz118, vuz27)
new_gcd216(Succ(vuz1250), Succ(vuz1290), vuz27) → new_gcd216(vuz1250, vuz1290, vuz27)
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS04(vuz109, vuz110)
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_ps(:%(vuz30, Pos(Succ(vuz3100)))) → new_reduce2Reduce1(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))

The set Q consists of the following terms:

new_gcd0Gcd'117(Neg(x0), x1)
new_primQuotInt4(Neg(x0), x1, x2)
new_gcd22(Succ(x0), Zero)
new_gcd0Gcd'122(Succ(Succ(x0)), Zero)
new_primQuotInt1(x0, Neg(Succ(x1)))
new_primQuotInt8(Zero, x0, x1, x2)
new_primQuotInt10(Zero, Succ(x0), x1)
new_gcd0Gcd'113(x0, x1, Zero, Succ(x2))
new_gcd0Gcd'113(x0, x1, Succ(x2), Zero)
new_gcd0Gcd'123(x0, x1)
new_primQuotInt6(Neg(x0), x1, x2)
new_gcd27(Succ(x0), Zero)
new_gcd216(Succ(x0), Zero, x1)
new_primQuotInt1(x0, Neg(Zero))
new_gcd0Gcd'124(Zero, x0)
new_primPlusNat0(Zero, Succ(x0))
new_error
new_primPlusNat2(Zero)
new_primQuotInt3(Succ(x0), Succ(x1), x2)
new_primDivNatS03(x0, x1, Zero, Zero)
new_primQuotInt5(x0, x1, x2, x3)
new_gcd26(Zero, Succ(x0), x1)
new_primQuotInt10(Zero, Zero, x0)
new_gcd21(x0, Zero)
new_gcd0Gcd'112(Zero, x0, x1)
new_gcd0Gcd'126(x0, x1)
new_gcd29(x0, x1, x2, x3, x4)
new_gcd22(Zero, Succ(x0))
new_abs0(x0)
new_gcd22(Succ(x0), Succ(x1))
new_gcd0Gcd'112(Succ(Zero), Zero, x0)
new_gcd216(Succ(x0), Succ(x1), x2)
new_ps(:%(x0, Neg(Zero)))
new_gcd0Gcd'116(x0, x1)
new_gcd0Gcd'112(Succ(Succ(x0)), Succ(x1), x2)
new_gcd0Gcd'117(Pos(x0), x1)
new_primQuotInt3(Succ(x0), Zero, x1)
new_gcd0Gcd'122(Succ(Zero), Succ(x0))
new_gcd27(Zero, Succ(x0))
new_gcd0Gcd'121(x0, x1)
new_gcd23(x0, x1, x2, x3)
new_reduce2Reduce1(x0, x1, x2, x3, Succ(x4))
new_primPlusNat1(Zero)
new_primDivNatS02(Succ(x0), Zero)
new_reduce2D0(x0, x1)
new_gcd0Gcd'118(x0, x1, Zero, Zero)
new_primDivNatS03(x0, x1, Zero, Succ(x2))
new_reduce2Reduce1(x0, x1, x2, x3, Zero)
new_gcd213(x0, x1, x2, x3)
new_gcd0Gcd'124(Succ(Succ(x0)), Zero)
new_gcd210(Neg(x0), x1, x2)
new_gcd0Gcd'127(x0, x1, Zero, Zero)
new_gcd0Gcd'112(Succ(Zero), Succ(x0), x1)
new_gcd217(x0, x1, x2, x3, x4)
new_gcd0Gcd'127(x0, x1, Zero, Succ(x2))
new_gcd26(Zero, Zero, x0)
new_primQuotInt1(x0, Pos(Succ(x1)))
new_ps(:%(x0, Pos(Succ(x1))))
new_gcd0Gcd'120(x0, x1)
new_gcd0Gcd'122(Zero, x0)
new_ps(:%(x0, Neg(Succ(x1))))
new_primQuotInt6(Pos(x0), x1, x2)
new_gcd24(x0, x1, x2, x3, x4)
new_gcd26(Succ(x0), Succ(x1), x2)
new_gcd210(Pos(x0), x1, x2)
new_gcd28(x0, x1, x2, x3)
new_primQuotInt4(Pos(x0), x1, x2)
new_primQuotInt8(Succ(x0), x1, x2, x3)
new_primDivNatS03(x0, x1, Succ(x2), Succ(x3))
new_primQuotInt2(Zero, x0, x1, x2)
new_primMulNat1(Zero)
new_primMinusNatS0(Zero, Zero)
new_primQuotInt7(x0, Pos(Succ(x1)))
new_gcd216(Zero, Zero, x0)
new_gcd0Gcd'112(Succ(Succ(x0)), Zero, x1)
new_gcd26(Succ(x0), Zero, x1)
new_reduce2Reduce10(x0, x1, x2, x3, Zero)
new_primPlusNat1(Succ(x0))
new_reduce2D(x0, x1)
new_primDivNatS04(x0, x1)
new_gcd0Gcd'125(x0)
new_gcd27(Succ(x0), Succ(x1))
new_error0
new_primPlusNat2(Succ(x0))
new_primQuotInt1(x0, Pos(Zero))
new_gcd0Gcd'122(Succ(Succ(x0)), Succ(x1))
new_reduce2Reduce10(x0, x1, x2, x3, Succ(x4))
new_gcd0Gcd'124(Succ(Zero), Zero)
new_gcd27(Zero, Zero)
new_primPlusNat0(Zero, Zero)
new_gcd0Gcd'119(x0, x1)
new_primQuotInt3(Zero, Succ(x0), x1)
new_gcd21(x0, Succ(x1))
new_primMulNat1(Succ(x0))
new_primQuotInt7(x0, Neg(Succ(x1)))
new_primPlusNat0(Succ(x0), Zero)
new_gcd0Gcd'124(Succ(Zero), Succ(x0))
new_primQuotInt2(Succ(x0), x1, x2, x3)
new_gcd0Gcd'113(x0, x1, Succ(x2), Succ(x3))
new_gcd0Gcd'113(x0, x1, Zero, Zero)
new_primMulNat0(x0)
new_gcd214(Zero)
new_primQuotInt10(Succ(x0), Succ(x1), x2)
new_primQuotInt7(x0, Neg(Zero))
new_primQuotInt3(Zero, Zero, x0)
new_ps(:%(x0, Pos(Zero)))
new_gcd211(Neg(x0), x1, x2)
new_primMinusNatS0(Succ(x0), Zero)
new_primDivNatS02(Zero, Zero)
new_primQuotInt10(Succ(x0), Zero, x1)
new_gcd0Gcd'114(x0, x1)
new_gcd216(Zero, Succ(x0), x1)
new_primDivNatS2(Succ(x0), x1)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_gcd0Gcd'118(x0, x1, Succ(x2), Zero)
new_abs(x0)
new_primQuotInt9(x0, x1, x2, x3)
new_gcd0Gcd'127(x0, x1, Succ(x2), Zero)
new_primMinusNatS0(Zero, Succ(x0))
new_gcd0Gcd'118(x0, x1, Zero, Succ(x2))
new_gcd0Gcd'127(x0, x1, Succ(x2), Succ(x3))
new_primDivNatS03(x0, x1, Succ(x2), Zero)
new_gcd0Gcd'115(x0, x1)
new_gcd0Gcd'124(Succ(Succ(x0)), Succ(x1))
new_gcd25(x0, Succ(x1))
new_gcd22(Zero, Zero)
new_gcd212(x0, x1, x2, x3)
new_primDivNatS02(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primQuotInt7(x0, Pos(Zero))
new_primDivNatS02(Zero, Succ(x0))
new_gcd0Gcd'118(x0, x1, Succ(x2), Succ(x3))
new_gcd215(x0, x1, x2, x3, x4)
new_gcd211(Pos(x0), x1, x2)
new_gcd214(Succ(x0))
new_primDivNatS2(Zero, x0)
new_gcd0Gcd'122(Succ(Zero), Zero)
new_gcd25(x0, Zero)
new_primDivNatS3(x0, x1)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ MNOCProof

                              ↳ QDP

                                ↳ NonTerminationProof

                      ↳ Narrow

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

new_numericEnumFrom(vuz3) → new_numericEnumFrom(new_ps(vuz3))

The TRS R consists of the following rules:

new_gcd217(vuz127, vuz131, vuz126, vuz130, vuz27) → new_gcd22(new_primPlusNat0(vuz127, vuz131), vuz27)
new_primPlusNat2(Zero) → Zero
new_gcd26(Succ(vuz1230), Zero, vuz42) → new_gcd27(Succ(vuz1230), vuz42)
new_primQuotInt3(Zero, Succ(vuz7100), vuz42) → new_primQuotInt7(Succ(vuz7100), new_gcd21(vuz7100, vuz42))
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'118(vuz160, vuz161, vuz1620, vuz1630)
new_primQuotInt9(vuz67, vuz15, vuz68, vuz27) → new_primQuotInt7(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), new_reduce2D0(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), vuz27))
new_gcd22(Succ(vuz1180), Succ(vuz270)) → new_gcd0Gcd'116(vuz270, vuz1180)
new_gcd0Gcd'123(vuz151, vuz152) → new_gcd0Gcd'124(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152)
new_gcd0Gcd'117(Neg(vuz1320), vuz420) → new_gcd0Gcd'124(vuz1320, vuz420)
new_ps(:%(vuz30, Neg(Zero))) → new_error0
new_gcd0Gcd'124(Succ(Zero), Zero) → new_gcd0Gcd'124(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Zero) → Zero
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS03(vuz109, vuz110, vuz1110, vuz1120)
new_primQuotInt7(vuz26, Neg(Zero)) → new_error
new_gcd0Gcd'122(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd21(vuz7100, Succ(vuz420)) → new_gcd0Gcd'116(vuz420, vuz7100)
new_gcd0Gcd'127(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd27(Zero, Succ(vuz420)) → new_gcd0Gcd'125(vuz420)
new_gcd0Gcd'115(vuz200, vuz201) → new_gcd0Gcd'117(Neg(Succ(vuz201)), vuz200)
new_gcd213(vuz127, vuz15, vuz126, vuz27) → new_gcd217(vuz127, new_primMulNat0(vuz15), vuz126, new_primMulNat0(vuz15), vuz27)
new_primDivNatS02(Zero, Succ(vuz86000)) → Zero
new_gcd27(Succ(vuz1070), Succ(vuz420)) → new_gcd0Gcd'121(vuz420, vuz1070)
new_gcd0Gcd'121(vuz420, vuz1070) → new_gcd0Gcd'117(new_abs0(vuz1070), vuz420)
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd0Gcd'112(Succ(Zero), Zero, vuz188) → new_gcd0Gcd'112(new_primMinusNatS0(Zero, Zero), Zero, new_primMinusNatS0(Zero, Zero))
new_primQuotInt5(vuz69, vuz8, vuz70, vuz42) → new_primQuotInt1(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), new_reduce2D(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), vuz42))
new_abs0(vuz6500) → Pos(Succ(vuz6500))
new_gcd0Gcd'119(vuz148, vuz149) → new_gcd0Gcd'122(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149)
new_ps(:%(vuz30, Pos(Zero))) → new_error0
new_gcd22(Zero, Zero) → new_error
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)
new_primQuotInt4(Neg(vuz70), vuz8, vuz42) → new_primQuotInt2(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd25(vuz6500, Succ(vuz270)) → new_gcd0Gcd'121(vuz270, vuz6500)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'123(vuz132000, Zero)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'113(vuz203, vuz204, vuz2050, vuz2060)
new_primQuotInt3(Succ(vuz80), Zero, vuz42) → new_primQuotInt1(Succ(vuz80), new_reduce2D(Succ(vuz80), vuz42))
new_error0 → error([])
new_gcd0Gcd'127(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'126(Succ(vuz165), vuz166)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Zero) → new_error0
new_gcd216(Zero, Zero, vuz27) → new_gcd214(vuz27)
new_gcd0Gcd'114(vuz197, vuz198) → new_gcd0Gcd'112(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_primMulNat0(vuz8) → new_primPlusNat0(Zero, Succ(vuz8))
new_gcd0Gcd'118(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Succ(vuz430)) → :%(new_primQuotInt4(vuz7, vuz8, vuz42), new_primQuotInt1(vuz41, new_gcd210(vuz7, vuz8, vuz42)))
new_abs(vuz1180) → Pos(Succ(vuz1180))
new_reduce2D(vuz107, vuz42) → new_gcd27(vuz107, vuz42)
new_primQuotInt2(Succ(vuz710), vuz8, vuz72, vuz42) → new_primQuotInt3(vuz8, vuz710, vuz42)
new_gcd26(Zero, Succ(vuz1160), vuz42) → new_gcd21(vuz1160, vuz42)
new_gcd211(Neg(vuz140), vuz15, vuz27) → new_gcd213(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd211(Pos(vuz140), vuz15, vuz27) → new_gcd212(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'122(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'120(Zero, Succ(vuz4200))
new_gcd28(vuz114, vuz8, vuz113, vuz42) → new_gcd29(vuz114, new_primMulNat0(vuz8), vuz113, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'124(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'126(Zero, Succ(vuz4200))
new_primDivNatS03(vuz109, vuz110, Zero, Succ(vuz1120)) → Zero
new_gcd215(vuz125, vuz129, vuz124, vuz128, vuz27) → new_gcd216(vuz125, vuz129, vuz27)
new_gcd0Gcd'122(Succ(Zero), Zero) → new_gcd0Gcd'122(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'119(vuz132000, Zero)
new_primQuotInt2(Zero, vuz8, vuz72, vuz42) → new_primQuotInt1(Succ(vuz8), new_reduce2D(Succ(vuz8), vuz42))
new_gcd21(vuz7100, Zero) → new_abs(vuz7100)
new_primQuotInt7(vuz26, Pos(Succ(vuz11700))) → Neg(new_primDivNatS2(vuz26, vuz11700))
new_gcd27(Succ(vuz1070), Zero) → new_abs0(vuz1070)
new_primDivNatS02(Zero, Zero) → Succ(Zero)
new_gcd0Gcd'124(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd216(Zero, Succ(vuz1290), vuz27) → new_gcd22(Succ(vuz1290), vuz27)
new_gcd26(Zero, Zero, vuz42) → new_gcd27(Zero, vuz42)
new_primPlusNat2(Succ(vuz1900)) → Succ(vuz1900)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'114(vuz18900, Zero)
new_primPlusNat1(Zero) → Succ(Zero)
new_gcd0Gcd'112(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'115(Zero, Succ(vuz1870))
new_gcd210(Pos(vuz70), vuz8, vuz42) → new_gcd28(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'118(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'120(Succ(vuz160), vuz161)
new_primQuotInt6(Neg(vuz140), vuz15, vuz27) → new_primQuotInt9(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_primMulNat1(Zero) → Zero
new_primQuotInt7(vuz26, Pos(Zero)) → new_error
new_primDivNatS02(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS03(vuz850, vuz86000, vuz850, vuz86000)
new_primPlusNat0(Succ(vuz6700), Succ(vuz150)) → Succ(Succ(new_primPlusNat0(vuz6700, vuz150)))
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'127(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'116(vuz420, vuz7100) → new_gcd0Gcd'117(new_abs(vuz7100), vuz420)
new_primQuotInt3(Succ(vuz80), Succ(vuz7100), vuz42) → new_primQuotInt3(vuz80, vuz7100, vuz42)
new_gcd22(Zero, Succ(vuz270)) → new_gcd0Gcd'117(Neg(Zero), vuz270)
new_primDivNatS02(Succ(vuz850), Zero) → Succ(new_primDivNatS3(vuz850, Zero))
new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_gcd214(Succ(vuz270)) → new_gcd0Gcd'125(vuz270)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'113(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_primPlusNat0(Zero, Zero) → Zero
new_primDivNatS2(Zero, vuz8) → Zero
new_primQuotInt10(Zero, Zero, vuz27) → new_primQuotInt1(Zero, new_gcd214(vuz27))
new_gcd212(vuz125, vuz15, vuz124, vuz27) → new_gcd215(vuz125, new_primMulNat0(vuz15), vuz124, new_primMulNat0(vuz15), vuz27)
new_gcd27(Zero, Zero) → new_error
new_primQuotInt1(vuz41, Pos(Zero)) → new_error
new_gcd210(Neg(vuz70), vuz8, vuz42) → new_gcd23(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_primQuotInt7(vuz26, Neg(Succ(vuz11700))) → Pos(new_primDivNatS2(vuz26, vuz11700))
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Zero) → new_error0
new_gcd26(Succ(vuz1230), Succ(vuz1160), vuz42) → new_gcd26(vuz1230, vuz1160, vuz42)
new_primQuotInt10(Succ(vuz6500), Zero, vuz27) → new_primQuotInt1(Succ(vuz6500), new_gcd25(vuz6500, vuz27))
new_primPlusNat1(Succ(vuz190)) → Succ(Succ(new_primPlusNat2(vuz190)))
new_primQuotInt8(Succ(vuz650), vuz15, vuz66, vuz27) → new_primQuotInt10(vuz650, vuz15, vuz27)
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_gcd216(Succ(vuz1250), Zero, vuz27) → new_gcd25(vuz1250, vuz27)
new_gcd24(vuz116, vuz123, vuz115, vuz122, vuz42) → new_gcd26(vuz123, vuz116, vuz42)
new_primMulNat1(Succ(vuz31000)) → new_primPlusNat1(new_primMulNat1(vuz31000))
new_primQuotInt3(Zero, Zero, vuz42) → new_primQuotInt1(Zero, new_reduce2D(Zero, vuz42))
new_primDivNatS3(vuz85, vuz8600) → new_primDivNatS02(vuz85, vuz8600)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Succ(vuz280)) → :%(new_primQuotInt6(vuz14, vuz15, vuz27), new_primQuotInt7(vuz26, new_gcd211(vuz14, vuz15, vuz27)))
new_ps(:%(vuz30, Neg(Succ(vuz3100)))) → new_reduce2Reduce10(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))
new_primQuotInt1(vuz41, Neg(Succ(vuz10600))) → Neg(new_primDivNatS2(vuz41, vuz10600))
new_primQuotInt1(vuz41, Neg(Zero)) → new_error
new_primQuotInt6(Pos(vuz140), vuz15, vuz27) → new_primQuotInt8(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'125(vuz420) → new_gcd0Gcd'117(Pos(Zero), vuz420)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'127(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_error → error([])
new_primDivNatS2(Succ(vuz410), vuz8) → new_primDivNatS02(vuz410, vuz8)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_primQuotInt10(Zero, Succ(vuz150), vuz27) → new_primQuotInt7(Succ(vuz150), new_reduce2D0(Succ(vuz150), vuz27))
new_gcd29(vuz114, vuz121, vuz113, vuz120, vuz42) → new_gcd27(new_primPlusNat0(vuz114, vuz121), vuz42)
new_gcd22(Succ(vuz1180), Zero) → new_abs(vuz1180)
new_primDivNatS04(vuz109, vuz110) → Succ(new_primDivNatS2(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110)))
new_gcd25(vuz6500, Zero) → new_abs0(vuz6500)
new_gcd0Gcd'112(Zero, vuz187, vuz188) → Neg(Succ(vuz187))
new_gcd0Gcd'126(vuz154, vuz155) → new_gcd0Gcd'112(Succ(vuz155), vuz154, Succ(vuz155))
new_primQuotInt4(Pos(vuz70), vuz8, vuz42) → new_primQuotInt5(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'115(Succ(vuz203), vuz204)
new_primQuotInt10(Succ(vuz6500), Succ(vuz150), vuz27) → new_primQuotInt10(vuz6500, vuz150, vuz27)
new_primQuotInt8(Zero, vuz15, vuz66, vuz27) → new_primQuotInt7(Succ(vuz15), new_reduce2D0(Succ(vuz15), vuz27))
new_primQuotInt1(vuz41, Pos(Succ(vuz10600))) → Pos(new_primDivNatS2(vuz41, vuz10600))
new_gcd0Gcd'117(Pos(vuz1320), vuz420) → new_gcd0Gcd'122(vuz1320, vuz420)
new_gcd214(Zero) → new_error
new_primDivNatS03(vuz109, vuz110, Zero, Zero) → new_primDivNatS04(vuz109, vuz110)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'118(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_primPlusNat0(Zero, Succ(vuz150)) → Succ(vuz150)
new_primPlusNat0(Succ(vuz6700), Zero) → Succ(vuz6700)
new_gcd23(vuz116, vuz8, vuz115, vuz42) → new_gcd24(vuz116, new_primMulNat0(vuz8), vuz115, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'120(vuz157, vuz158) → new_gcd0Gcd'117(Pos(Succ(vuz158)), vuz157)
new_reduce2D0(vuz118, vuz27) → new_gcd22(vuz118, vuz27)
new_gcd216(Succ(vuz1250), Succ(vuz1290), vuz27) → new_gcd216(vuz1250, vuz1290, vuz27)
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS04(vuz109, vuz110)
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_ps(:%(vuz30, Pos(Succ(vuz3100)))) → new_reduce2Reduce1(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))

Q is empty.
We have to consider all (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

The TRS P consists of the following rules:

new_numericEnumFrom(vuz3) → new_numericEnumFrom(new_ps(vuz3))

The TRS R consists of the following rules:

new_gcd217(vuz127, vuz131, vuz126, vuz130, vuz27) → new_gcd22(new_primPlusNat0(vuz127, vuz131), vuz27)
new_primPlusNat2(Zero) → Zero
new_gcd26(Succ(vuz1230), Zero, vuz42) → new_gcd27(Succ(vuz1230), vuz42)
new_primQuotInt3(Zero, Succ(vuz7100), vuz42) → new_primQuotInt7(Succ(vuz7100), new_gcd21(vuz7100, vuz42))
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Succ(vuz1630)) → new_gcd0Gcd'118(vuz160, vuz161, vuz1620, vuz1630)
new_primQuotInt9(vuz67, vuz15, vuz68, vuz27) → new_primQuotInt7(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), new_reduce2D0(new_primPlusNat0(vuz67, new_primMulNat0(vuz15)), vuz27))
new_gcd22(Succ(vuz1180), Succ(vuz270)) → new_gcd0Gcd'116(vuz270, vuz1180)
new_gcd0Gcd'123(vuz151, vuz152) → new_gcd0Gcd'124(new_primMinusNatS0(Succ(vuz151), vuz152), vuz152)
new_gcd0Gcd'117(Neg(vuz1320), vuz420) → new_gcd0Gcd'124(vuz1320, vuz420)
new_ps(:%(vuz30, Neg(Zero))) → new_error0
new_gcd0Gcd'124(Succ(Zero), Zero) → new_gcd0Gcd'124(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Zero) → Zero
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Succ(vuz1120)) → new_primDivNatS03(vuz109, vuz110, vuz1110, vuz1120)
new_primQuotInt7(vuz26, Neg(Zero)) → new_error
new_gcd0Gcd'122(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd21(vuz7100, Succ(vuz420)) → new_gcd0Gcd'116(vuz420, vuz7100)
new_gcd0Gcd'127(vuz165, vuz166, Zero, Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd27(Zero, Succ(vuz420)) → new_gcd0Gcd'125(vuz420)
new_gcd0Gcd'115(vuz200, vuz201) → new_gcd0Gcd'117(Neg(Succ(vuz201)), vuz200)
new_gcd213(vuz127, vuz15, vuz126, vuz27) → new_gcd217(vuz127, new_primMulNat0(vuz15), vuz126, new_primMulNat0(vuz15), vuz27)
new_primDivNatS02(Zero, Succ(vuz86000)) → Zero
new_gcd27(Succ(vuz1070), Succ(vuz420)) → new_gcd0Gcd'121(vuz420, vuz1070)
new_gcd0Gcd'121(vuz420, vuz1070) → new_gcd0Gcd'117(new_abs0(vuz1070), vuz420)
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Zero) → new_gcd0Gcd'123(vuz165, vuz166)
new_gcd0Gcd'112(Succ(Zero), Zero, vuz188) → new_gcd0Gcd'112(new_primMinusNatS0(Zero, Zero), Zero, new_primMinusNatS0(Zero, Zero))
new_primQuotInt5(vuz69, vuz8, vuz70, vuz42) → new_primQuotInt1(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), new_reduce2D(new_primPlusNat0(vuz69, new_primMulNat0(vuz8)), vuz42))
new_abs0(vuz6500) → Pos(Succ(vuz6500))
new_gcd0Gcd'119(vuz148, vuz149) → new_gcd0Gcd'122(new_primMinusNatS0(Succ(vuz148), vuz149), vuz149)
new_ps(:%(vuz30, Pos(Zero))) → new_error0
new_gcd22(Zero, Zero) → new_error
new_primMinusNatS0(Succ(vuz1090), Zero) → Succ(vuz1090)
new_primQuotInt4(Neg(vuz70), vuz8, vuz42) → new_primQuotInt2(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd25(vuz6500, Succ(vuz270)) → new_gcd0Gcd'121(vuz270, vuz6500)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'123(vuz132000, Zero)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Succ(vuz2060)) → new_gcd0Gcd'113(vuz203, vuz204, vuz2050, vuz2060)
new_primQuotInt3(Succ(vuz80), Zero, vuz42) → new_primQuotInt1(Succ(vuz80), new_reduce2D(Succ(vuz80), vuz42))
new_error0 → error([])
new_gcd0Gcd'127(vuz165, vuz166, Zero, Succ(vuz1680)) → new_gcd0Gcd'126(Succ(vuz165), vuz166)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Zero) → new_error0
new_gcd216(Zero, Zero, vuz27) → new_gcd214(vuz27)
new_gcd0Gcd'114(vuz197, vuz198) → new_gcd0Gcd'112(new_primMinusNatS0(Succ(vuz197), vuz198), vuz198, new_primMinusNatS0(Succ(vuz197), vuz198))
new_primMulNat0(vuz8) → new_primPlusNat0(Zero, Succ(vuz8))
new_gcd0Gcd'118(vuz160, vuz161, Zero, Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Succ(vuz430)) → :%(new_primQuotInt4(vuz7, vuz8, vuz42), new_primQuotInt1(vuz41, new_gcd210(vuz7, vuz8, vuz42)))
new_abs(vuz1180) → Pos(Succ(vuz1180))
new_reduce2D(vuz107, vuz42) → new_gcd27(vuz107, vuz42)
new_primQuotInt2(Succ(vuz710), vuz8, vuz72, vuz42) → new_primQuotInt3(vuz8, vuz710, vuz42)
new_gcd26(Zero, Succ(vuz1160), vuz42) → new_gcd21(vuz1160, vuz42)
new_gcd211(Neg(vuz140), vuz15, vuz27) → new_gcd213(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd211(Pos(vuz140), vuz15, vuz27) → new_gcd212(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'122(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'120(Zero, Succ(vuz4200))
new_gcd28(vuz114, vuz8, vuz113, vuz42) → new_gcd29(vuz114, new_primMulNat0(vuz8), vuz113, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'124(Succ(Zero), Succ(vuz4200)) → new_gcd0Gcd'126(Zero, Succ(vuz4200))
new_primDivNatS03(vuz109, vuz110, Zero, Succ(vuz1120)) → Zero
new_gcd215(vuz125, vuz129, vuz124, vuz128, vuz27) → new_gcd216(vuz125, vuz129, vuz27)
new_gcd0Gcd'122(Succ(Zero), Zero) → new_gcd0Gcd'122(new_primMinusNatS0(Zero, Zero), Zero)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Zero) → new_gcd0Gcd'119(vuz132000, Zero)
new_primQuotInt2(Zero, vuz8, vuz72, vuz42) → new_primQuotInt1(Succ(vuz8), new_reduce2D(Succ(vuz8), vuz42))
new_gcd21(vuz7100, Zero) → new_abs(vuz7100)
new_primQuotInt7(vuz26, Pos(Succ(vuz11700))) → Neg(new_primDivNatS2(vuz26, vuz11700))
new_gcd27(Succ(vuz1070), Zero) → new_abs0(vuz1070)
new_primDivNatS02(Zero, Zero) → Succ(Zero)
new_gcd0Gcd'124(Zero, vuz420) → Pos(Succ(vuz420))
new_gcd216(Zero, Succ(vuz1290), vuz27) → new_gcd22(Succ(vuz1290), vuz27)
new_gcd26(Zero, Zero, vuz42) → new_gcd27(Zero, vuz42)
new_primPlusNat2(Succ(vuz1900)) → Succ(vuz1900)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Zero, vuz188) → new_gcd0Gcd'114(vuz18900, Zero)
new_primPlusNat1(Zero) → Succ(Zero)
new_gcd0Gcd'112(Succ(Zero), Succ(vuz1870), vuz188) → new_gcd0Gcd'115(Zero, Succ(vuz1870))
new_gcd210(Pos(vuz70), vuz8, vuz42) → new_gcd28(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'118(vuz160, vuz161, Zero, Succ(vuz1630)) → new_gcd0Gcd'120(Succ(vuz160), vuz161)
new_primQuotInt6(Neg(vuz140), vuz15, vuz27) → new_primQuotInt9(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_primMulNat1(Zero) → Zero
new_primQuotInt7(vuz26, Pos(Zero)) → new_error
new_primDivNatS02(Succ(vuz850), Succ(vuz86000)) → new_primDivNatS03(vuz850, vuz86000, vuz850, vuz86000)
new_primPlusNat0(Succ(vuz6700), Succ(vuz150)) → Succ(Succ(new_primPlusNat0(vuz6700, vuz150)))
new_gcd0Gcd'127(vuz165, vuz166, Succ(vuz1670), Succ(vuz1680)) → new_gcd0Gcd'127(vuz165, vuz166, vuz1670, vuz1680)
new_gcd0Gcd'116(vuz420, vuz7100) → new_gcd0Gcd'117(new_abs(vuz7100), vuz420)
new_primQuotInt3(Succ(vuz80), Succ(vuz7100), vuz42) → new_primQuotInt3(vuz80, vuz7100, vuz42)
new_gcd22(Zero, Succ(vuz270)) → new_gcd0Gcd'117(Neg(Zero), vuz270)
new_primDivNatS02(Succ(vuz850), Zero) → Succ(new_primDivNatS3(vuz850, Zero))
new_primMinusNatS0(Zero, Succ(vuz1100)) → Zero
new_gcd214(Succ(vuz270)) → new_gcd0Gcd'125(vuz270)
new_gcd0Gcd'112(Succ(Succ(vuz18900)), Succ(vuz1870), vuz188) → new_gcd0Gcd'113(vuz18900, Succ(vuz1870), vuz18900, vuz1870)
new_primPlusNat0(Zero, Zero) → Zero
new_primDivNatS2(Zero, vuz8) → Zero
new_primQuotInt10(Zero, Zero, vuz27) → new_primQuotInt1(Zero, new_gcd214(vuz27))
new_gcd212(vuz125, vuz15, vuz124, vuz27) → new_gcd215(vuz125, new_primMulNat0(vuz15), vuz124, new_primMulNat0(vuz15), vuz27)
new_gcd27(Zero, Zero) → new_error
new_primQuotInt1(vuz41, Pos(Zero)) → new_error
new_gcd210(Neg(vuz70), vuz8, vuz42) → new_gcd23(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_primQuotInt7(vuz26, Neg(Succ(vuz11700))) → Pos(new_primDivNatS2(vuz26, vuz11700))
new_reduce2Reduce1(vuz7, vuz8, vuz42, vuz41, Zero) → new_error0
new_gcd26(Succ(vuz1230), Succ(vuz1160), vuz42) → new_gcd26(vuz1230, vuz1160, vuz42)
new_primQuotInt10(Succ(vuz6500), Zero, vuz27) → new_primQuotInt1(Succ(vuz6500), new_gcd25(vuz6500, vuz27))
new_primPlusNat1(Succ(vuz190)) → Succ(Succ(new_primPlusNat2(vuz190)))
new_primQuotInt8(Succ(vuz650), vuz15, vuz66, vuz27) → new_primQuotInt10(vuz650, vuz15, vuz27)
new_gcd0Gcd'118(vuz160, vuz161, Succ(vuz1620), Zero) → new_gcd0Gcd'119(vuz160, vuz161)
new_gcd216(Succ(vuz1250), Zero, vuz27) → new_gcd25(vuz1250, vuz27)
new_gcd24(vuz116, vuz123, vuz115, vuz122, vuz42) → new_gcd26(vuz123, vuz116, vuz42)
new_primMulNat1(Succ(vuz31000)) → new_primPlusNat1(new_primMulNat1(vuz31000))
new_primQuotInt3(Zero, Zero, vuz42) → new_primQuotInt1(Zero, new_reduce2D(Zero, vuz42))
new_primDivNatS3(vuz85, vuz8600) → new_primDivNatS02(vuz85, vuz8600)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_reduce2Reduce10(vuz14, vuz15, vuz27, vuz26, Succ(vuz280)) → :%(new_primQuotInt6(vuz14, vuz15, vuz27), new_primQuotInt7(vuz26, new_gcd211(vuz14, vuz15, vuz27)))
new_ps(:%(vuz30, Neg(Succ(vuz3100)))) → new_reduce2Reduce10(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))
new_primQuotInt1(vuz41, Neg(Succ(vuz10600))) → Neg(new_primDivNatS2(vuz41, vuz10600))
new_primQuotInt1(vuz41, Neg(Zero)) → new_error
new_primQuotInt6(Pos(vuz140), vuz15, vuz27) → new_primQuotInt8(new_primMulNat1(vuz140), vuz15, new_primMulNat1(vuz140), vuz27)
new_gcd0Gcd'125(vuz420) → new_gcd0Gcd'117(Pos(Zero), vuz420)
new_gcd0Gcd'124(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'127(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_error → error([])
new_primDivNatS2(Succ(vuz410), vuz8) → new_primDivNatS02(vuz410, vuz8)
new_gcd0Gcd'113(vuz203, vuz204, Succ(vuz2050), Zero) → new_gcd0Gcd'114(vuz203, vuz204)
new_primQuotInt10(Zero, Succ(vuz150), vuz27) → new_primQuotInt7(Succ(vuz150), new_reduce2D0(Succ(vuz150), vuz27))
new_gcd29(vuz114, vuz121, vuz113, vuz120, vuz42) → new_gcd27(new_primPlusNat0(vuz114, vuz121), vuz42)
new_gcd22(Succ(vuz1180), Zero) → new_abs(vuz1180)
new_primDivNatS04(vuz109, vuz110) → Succ(new_primDivNatS2(new_primMinusNatS0(vuz109, vuz110), Succ(vuz110)))
new_gcd25(vuz6500, Zero) → new_abs0(vuz6500)
new_gcd0Gcd'112(Zero, vuz187, vuz188) → Neg(Succ(vuz187))
new_gcd0Gcd'126(vuz154, vuz155) → new_gcd0Gcd'112(Succ(vuz155), vuz154, Succ(vuz155))
new_primQuotInt4(Pos(vuz70), vuz8, vuz42) → new_primQuotInt5(new_primMulNat1(vuz70), vuz8, new_primMulNat1(vuz70), vuz42)
new_gcd0Gcd'113(vuz203, vuz204, Zero, Succ(vuz2060)) → new_gcd0Gcd'115(Succ(vuz203), vuz204)
new_primQuotInt10(Succ(vuz6500), Succ(vuz150), vuz27) → new_primQuotInt10(vuz6500, vuz150, vuz27)
new_primQuotInt8(Zero, vuz15, vuz66, vuz27) → new_primQuotInt7(Succ(vuz15), new_reduce2D0(Succ(vuz15), vuz27))
new_primQuotInt1(vuz41, Pos(Succ(vuz10600))) → Pos(new_primDivNatS2(vuz41, vuz10600))
new_gcd0Gcd'117(Pos(vuz1320), vuz420) → new_gcd0Gcd'122(vuz1320, vuz420)
new_gcd214(Zero) → new_error
new_primDivNatS03(vuz109, vuz110, Zero, Zero) → new_primDivNatS04(vuz109, vuz110)
new_gcd0Gcd'122(Succ(Succ(vuz132000)), Succ(vuz4200)) → new_gcd0Gcd'118(vuz132000, Succ(vuz4200), vuz132000, vuz4200)
new_primPlusNat0(Zero, Succ(vuz150)) → Succ(vuz150)
new_primPlusNat0(Succ(vuz6700), Zero) → Succ(vuz6700)
new_gcd23(vuz116, vuz8, vuz115, vuz42) → new_gcd24(vuz116, new_primMulNat0(vuz8), vuz115, new_primMulNat0(vuz8), vuz42)
new_gcd0Gcd'120(vuz157, vuz158) → new_gcd0Gcd'117(Pos(Succ(vuz158)), vuz157)
new_reduce2D0(vuz118, vuz27) → new_gcd22(vuz118, vuz27)
new_gcd216(Succ(vuz1250), Succ(vuz1290), vuz27) → new_gcd216(vuz1250, vuz1290, vuz27)
new_primDivNatS03(vuz109, vuz110, Succ(vuz1110), Zero) → new_primDivNatS04(vuz109, vuz110)
new_primMinusNatS0(Succ(vuz1090), Succ(vuz1100)) → new_primMinusNatS0(vuz1090, vuz1100)
new_ps(:%(vuz30, Pos(Succ(vuz3100)))) → new_reduce2Reduce1(vuz30, vuz3100, new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)), new_primPlusNat1(new_primMulNat1(vuz3100)))

s = new_numericEnumFrom(vuz3) evaluates to t =new_numericEnumFrom(new_ps(vuz3))

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Matcher: [vuz3 / new_ps(vuz3)]
Semiunifier: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_numericEnumFrom(vuz3) to new_numericEnumFrom(new_ps(vuz3)).

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