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

MAYBE 97.177 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

((product :: [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

((product :: [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

((product :: [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

((product :: [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

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

reduce2D vux vuy = gcd 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'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'1 True x xz = x

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

mainModule Main

((product :: [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

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

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="product",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="product vuz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="foldl' (*) (fromInt (Pos (Succ Zero))) vuz3",fontsize=16,color="burlywood",shape="box"];6703[label="vuz3/vuz30 : vuz31",fontsize=10,color="white",style="solid",shape="box"];4 -> 6703[label="",style="solid", color="burlywood", weight=9];
6703 -> 5[label="",style="solid", color="burlywood", weight=3];
6704[label="vuz3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 6704[label="",style="solid", color="burlywood", weight=9];
6704 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="foldl' (*) (fromInt (Pos (Succ Zero))) (vuz30 : vuz31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="foldl' (*) (fromInt (Pos (Succ Zero))) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="(foldl' (*) $! (*) fromInt (Pos (Succ Zero)) vuz30)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];8 -> 10[label="",style="solid", color="black", weight=3];
9 -> 11[label="",style="dashed", color="red", weight=0];
9[label="((*) fromInt (Pos (Succ Zero)) vuz30 `seq` foldl' (*) ((*) fromInt (Pos (Succ Zero)) vuz30))",fontsize=16,color="magenta"];9 -> 12[label="",style="dashed", color="magenta", weight=3];
9 -> 13[label="",style="dashed", color="magenta", weight=3];
10[label="intToRatio (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
12 -> 8[label="",style="dashed", color="red", weight=0];
12[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];13 -> 8[label="",style="dashed", color="red", weight=0];
13[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];11[label="((*) vuz4 vuz30 `seq` foldl' (*) ((*) vuz5 vuz30))",fontsize=16,color="black",shape="triangle"];11 -> 15[label="",style="solid", color="black", weight=3];
14[label="fromInt (Pos (Succ Zero)) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];14 -> 16[label="",style="dashed", color="green", weight=3];
14 -> 17[label="",style="dashed", color="green", weight=3];
15[label="enforceWHNF (WHNF ((*) vuz4 vuz30)) (foldl' (*) ((*) vuz5 vuz30)) vuz31",fontsize=16,color="burlywood",shape="box"];6708[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];15 -> 6708[label="",style="solid", color="burlywood", weight=9];
6708 -> 18[label="",style="solid", color="burlywood", weight=3];
16[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3];
17 -> 16[label="",style="dashed", color="red", weight=0];
17[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];18[label="enforceWHNF (WHNF ((*) (vuz40 :% vuz41) vuz30)) (foldl' (*) ((*) vuz5 vuz30)) vuz31",fontsize=16,color="burlywood",shape="box"];6710[label="vuz30/vuz300 :% vuz301",fontsize=10,color="white",style="solid",shape="box"];18 -> 6710[label="",style="solid", color="burlywood", weight=9];
6710 -> 20[label="",style="solid", color="burlywood", weight=3];
19[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];20[label="enforceWHNF (WHNF ((*) (vuz40 :% vuz41) (vuz300 :% vuz301))) (foldl' (*) ((*) vuz5 (vuz300 :% vuz301))) vuz31",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
21[label="enforceWHNF (WHNF (reduce (vuz40 * vuz300) (vuz41 * vuz301))) (foldl' (*) (reduce (vuz40 * vuz300) (vuz41 * vuz301))) vuz31",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="enforceWHNF (WHNF (reduce2 (vuz40 * vuz300) (vuz41 * vuz301))) (foldl' (*) (reduce2 (vuz40 * vuz300) (vuz41 * vuz301))) vuz31",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
23[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (vuz41 * vuz301) (vuz40 * vuz300) (vuz41 * vuz301) (vuz41 * vuz301 == fromInt (Pos Zero)))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (vuz41 * vuz301) (vuz40 * vuz300) (vuz41 * vuz301) (vuz41 * vuz301 == fromInt (Pos Zero)))) vuz31",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
24[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (vuz41 * vuz301) (vuz40 * vuz300) (vuz41 * vuz301) (primEqInt (vuz41 * vuz301) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (vuz41 * vuz301) (vuz40 * vuz300) (vuz41 * vuz301) (primEqInt (vuz41 * vuz301) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3];
25[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt vuz41 vuz301) (vuz40 * vuz300) (primMulInt vuz41 vuz301) (primEqInt (primMulInt vuz41 vuz301) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt vuz41 vuz301) (vuz40 * vuz300) (primMulInt vuz41 vuz301) (primEqInt (primMulInt vuz41 vuz301) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="burlywood",shape="box"];6711[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6711[label="",style="solid", color="burlywood", weight=9];
6711 -> 26[label="",style="solid", color="burlywood", weight=3];
6712[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];25 -> 6712[label="",style="solid", color="burlywood", weight=9];
6712 -> 27[label="",style="solid", color="burlywood", weight=3];
26[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) vuz301) (vuz40 * vuz300) (primMulInt (Pos vuz410) vuz301) (primEqInt (primMulInt (Pos vuz410) vuz301) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) vuz301) (vuz40 * vuz300) (primMulInt (Pos vuz410) vuz301) (primEqInt (primMulInt (Pos vuz410) vuz301) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="burlywood",shape="box"];6713[label="vuz301/Pos vuz3010",fontsize=10,color="white",style="solid",shape="box"];26 -> 6713[label="",style="solid", color="burlywood", weight=9];
6713 -> 28[label="",style="solid", color="burlywood", weight=3];
6714[label="vuz301/Neg vuz3010",fontsize=10,color="white",style="solid",shape="box"];26 -> 6714[label="",style="solid", color="burlywood", weight=9];
6714 -> 29[label="",style="solid", color="burlywood", weight=3];
27[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) vuz301) (vuz40 * vuz300) (primMulInt (Neg vuz410) vuz301) (primEqInt (primMulInt (Neg vuz410) vuz301) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) vuz301) (vuz40 * vuz300) (primMulInt (Neg vuz410) vuz301) (primEqInt (primMulInt (Neg vuz410) vuz301) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="burlywood",shape="box"];6715[label="vuz301/Pos vuz3010",fontsize=10,color="white",style="solid",shape="box"];27 -> 6715[label="",style="solid", color="burlywood", weight=9];
6715 -> 30[label="",style="solid", color="burlywood", weight=3];
6716[label="vuz301/Neg vuz3010",fontsize=10,color="white",style="solid",shape="box"];27 -> 6716[label="",style="solid", color="burlywood", weight=9];
6716 -> 31[label="",style="solid", color="burlywood", weight=3];
28[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) (Pos vuz3010)) (vuz40 * vuz300) (primMulInt (Pos vuz410) (Pos vuz3010)) (primEqInt (primMulInt (Pos vuz410) (Pos vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) (Pos vuz3010)) (vuz40 * vuz300) (primMulInt (Pos vuz410) (Pos vuz3010)) (primEqInt (primMulInt (Pos vuz410) (Pos vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) (Neg vuz3010)) (vuz40 * vuz300) (primMulInt (Pos vuz410) (Neg vuz3010)) (primEqInt (primMulInt (Pos vuz410) (Neg vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Pos vuz410) (Neg vuz3010)) (vuz40 * vuz300) (primMulInt (Pos vuz410) (Neg vuz3010)) (primEqInt (primMulInt (Pos vuz410) (Neg vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
30[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) (Pos vuz3010)) (vuz40 * vuz300) (primMulInt (Neg vuz410) (Pos vuz3010)) (primEqInt (primMulInt (Neg vuz410) (Pos vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) (Pos vuz3010)) (vuz40 * vuz300) (primMulInt (Neg vuz410) (Pos vuz3010)) (primEqInt (primMulInt (Neg vuz410) (Pos vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) (Neg vuz3010)) (vuz40 * vuz300) (primMulInt (Neg vuz410) (Neg vuz3010)) (primEqInt (primMulInt (Neg vuz410) (Neg vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (primMulInt (Neg vuz410) (Neg vuz3010)) (vuz40 * vuz300) (primMulInt (Neg vuz410) (Neg vuz3010)) (primEqInt (primMulInt (Neg vuz410) (Neg vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32 -> 304[label="",style="dashed", color="red", weight=0];
32[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (primEqInt (Pos (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (primEqInt (Pos (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="magenta"];32 -> 305[label="",style="dashed", color="magenta", weight=3];
32 -> 306[label="",style="dashed", color="magenta", weight=3];
32 -> 307[label="",style="dashed", color="magenta", weight=3];
32 -> 308[label="",style="dashed", color="magenta", weight=3];
32 -> 309[label="",style="dashed", color="magenta", weight=3];
32 -> 310[label="",style="dashed", color="magenta", weight=3];
33 -> 393[label="",style="dashed", color="red", weight=0];
33[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (primEqInt (Neg (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (primEqInt (Neg (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="magenta"];33 -> 394[label="",style="dashed", color="magenta", weight=3];
33 -> 395[label="",style="dashed", color="magenta", weight=3];
33 -> 396[label="",style="dashed", color="magenta", weight=3];
33 -> 397[label="",style="dashed", color="magenta", weight=3];
33 -> 398[label="",style="dashed", color="magenta", weight=3];
33 -> 399[label="",style="dashed", color="magenta", weight=3];
34 -> 393[label="",style="dashed", color="red", weight=0];
34[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (primEqInt (Neg (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Neg (primMulNat vuz410 vuz3010)) (primEqInt (Neg (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="magenta"];34 -> 400[label="",style="dashed", color="magenta", weight=3];
34 -> 401[label="",style="dashed", color="magenta", weight=3];
34 -> 402[label="",style="dashed", color="magenta", weight=3];
34 -> 403[label="",style="dashed", color="magenta", weight=3];
34 -> 404[label="",style="dashed", color="magenta", weight=3];
34 -> 405[label="",style="dashed", color="magenta", weight=3];
35 -> 304[label="",style="dashed", color="red", weight=0];
35[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (primEqInt (Pos (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (vuz40 * vuz300) (Pos (primMulNat vuz410 vuz3010)) (primEqInt (Pos (primMulNat vuz410 vuz3010)) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="magenta"];35 -> 311[label="",style="dashed", color="magenta", weight=3];
35 -> 312[label="",style="dashed", color="magenta", weight=3];
35 -> 313[label="",style="dashed", color="magenta", weight=3];
35 -> 314[label="",style="dashed", color="magenta", weight=3];
35 -> 315[label="",style="dashed", color="magenta", weight=3];
35 -> 316[label="",style="dashed", color="magenta", weight=3];
305[label="primMulNat vuz410 vuz3010",fontsize=16,color="burlywood",shape="triangle"];6721[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];305 -> 6721[label="",style="solid", color="burlywood", weight=9];
6721 -> 377[label="",style="solid", color="burlywood", weight=3];
6722[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];305 -> 6722[label="",style="solid", color="burlywood", weight=9];
6722 -> 378[label="",style="solid", color="burlywood", weight=3];
306 -> 305[label="",style="dashed", color="red", weight=0];
306[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];307 -> 305[label="",style="dashed", color="red", weight=0];
307[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];308 -> 305[label="",style="dashed", color="red", weight=0];
308[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];309 -> 305[label="",style="dashed", color="red", weight=0];
309[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];310 -> 305[label="",style="dashed", color="red", weight=0];
310[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];304[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) (primEqInt (Pos vuz30) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) (primEqInt (Pos vuz29) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="burlywood",shape="triangle"];6728[label="vuz30/Succ vuz300",fontsize=10,color="white",style="solid",shape="box"];304 -> 6728[label="",style="solid", color="burlywood", weight=9];
6728 -> 379[label="",style="solid", color="burlywood", weight=3];
6729[label="vuz30/Zero",fontsize=10,color="white",style="solid",shape="box"];304 -> 6729[label="",style="solid", color="burlywood", weight=9];
6729 -> 380[label="",style="solid", color="burlywood", weight=3];
394 -> 305[label="",style="dashed", color="red", weight=0];
394[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];394 -> 466[label="",style="dashed", color="magenta", weight=3];
395 -> 305[label="",style="dashed", color="red", weight=0];
395[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];395 -> 467[label="",style="dashed", color="magenta", weight=3];
396 -> 305[label="",style="dashed", color="red", weight=0];
396[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];396 -> 468[label="",style="dashed", color="magenta", weight=3];
397 -> 305[label="",style="dashed", color="red", weight=0];
397[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];397 -> 469[label="",style="dashed", color="magenta", weight=3];
398 -> 305[label="",style="dashed", color="red", weight=0];
398[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];398 -> 470[label="",style="dashed", color="magenta", weight=3];
399 -> 305[label="",style="dashed", color="red", weight=0];
399[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];399 -> 471[label="",style="dashed", color="magenta", weight=3];
393[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) (primEqInt (Neg vuz36) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) (primEqInt (Neg vuz35) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="burlywood",shape="triangle"];6736[label="vuz36/Succ vuz360",fontsize=10,color="white",style="solid",shape="box"];393 -> 6736[label="",style="solid", color="burlywood", weight=9];
6736 -> 472[label="",style="solid", color="burlywood", weight=3];
6737[label="vuz36/Zero",fontsize=10,color="white",style="solid",shape="box"];393 -> 6737[label="",style="solid", color="burlywood", weight=9];
6737 -> 473[label="",style="solid", color="burlywood", weight=3];
400 -> 305[label="",style="dashed", color="red", weight=0];
400[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];400 -> 474[label="",style="dashed", color="magenta", weight=3];
401 -> 305[label="",style="dashed", color="red", weight=0];
401[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];401 -> 475[label="",style="dashed", color="magenta", weight=3];
402 -> 305[label="",style="dashed", color="red", weight=0];
402[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];402 -> 476[label="",style="dashed", color="magenta", weight=3];
403 -> 305[label="",style="dashed", color="red", weight=0];
403[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];403 -> 477[label="",style="dashed", color="magenta", weight=3];
404 -> 305[label="",style="dashed", color="red", weight=0];
404[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];404 -> 478[label="",style="dashed", color="magenta", weight=3];
405 -> 305[label="",style="dashed", color="red", weight=0];
405[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];405 -> 479[label="",style="dashed", color="magenta", weight=3];
311 -> 305[label="",style="dashed", color="red", weight=0];
311[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];311 -> 381[label="",style="dashed", color="magenta", weight=3];
311 -> 382[label="",style="dashed", color="magenta", weight=3];
312 -> 305[label="",style="dashed", color="red", weight=0];
312[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];312 -> 383[label="",style="dashed", color="magenta", weight=3];
312 -> 384[label="",style="dashed", color="magenta", weight=3];
313 -> 305[label="",style="dashed", color="red", weight=0];
313[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];313 -> 385[label="",style="dashed", color="magenta", weight=3];
313 -> 386[label="",style="dashed", color="magenta", weight=3];
314 -> 305[label="",style="dashed", color="red", weight=0];
314[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];314 -> 387[label="",style="dashed", color="magenta", weight=3];
314 -> 388[label="",style="dashed", color="magenta", weight=3];
315 -> 305[label="",style="dashed", color="red", weight=0];
315[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];315 -> 389[label="",style="dashed", color="magenta", weight=3];
315 -> 390[label="",style="dashed", color="magenta", weight=3];
316 -> 305[label="",style="dashed", color="red", weight=0];
316[label="primMulNat vuz410 vuz3010",fontsize=16,color="magenta"];316 -> 391[label="",style="dashed", color="magenta", weight=3];
316 -> 392[label="",style="dashed", color="magenta", weight=3];
377[label="primMulNat (Succ vuz4100) vuz3010",fontsize=16,color="burlywood",shape="box"];6750[label="vuz3010/Succ vuz30100",fontsize=10,color="white",style="solid",shape="box"];377 -> 6750[label="",style="solid", color="burlywood", weight=9];
6750 -> 480[label="",style="solid", color="burlywood", weight=3];
6751[label="vuz3010/Zero",fontsize=10,color="white",style="solid",shape="box"];377 -> 6751[label="",style="solid", color="burlywood", weight=9];
6751 -> 481[label="",style="solid", color="burlywood", weight=3];
378[label="primMulNat Zero vuz3010",fontsize=16,color="burlywood",shape="box"];6752[label="vuz3010/Succ vuz30100",fontsize=10,color="white",style="solid",shape="box"];378 -> 6752[label="",style="solid", color="burlywood", weight=9];
6752 -> 482[label="",style="solid", color="burlywood", weight=3];
6753[label="vuz3010/Zero",fontsize=10,color="white",style="solid",shape="box"];378 -> 6753[label="",style="solid", color="burlywood", weight=9];
6753 -> 483[label="",style="solid", color="burlywood", weight=3];
379[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) (primEqInt (Pos (Succ vuz300)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) (primEqInt (Pos vuz29) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];379 -> 484[label="",style="solid", color="black", weight=3];
380[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) (primEqInt (Pos Zero) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) (primEqInt (Pos vuz29) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];380 -> 485[label="",style="solid", color="black", weight=3];
466[label="vuz3010",fontsize=16,color="green",shape="box"];467[label="vuz3010",fontsize=16,color="green",shape="box"];468[label="vuz3010",fontsize=16,color="green",shape="box"];469[label="vuz3010",fontsize=16,color="green",shape="box"];470[label="vuz3010",fontsize=16,color="green",shape="box"];471[label="vuz3010",fontsize=16,color="green",shape="box"];472[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) (primEqInt (Neg (Succ vuz360)) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) (primEqInt (Neg vuz35) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];472 -> 486[label="",style="solid", color="black", weight=3];
473[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) (primEqInt (Neg Zero) (fromInt (Pos Zero))))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) (primEqInt (Neg vuz35) (fromInt (Pos Zero))))) vuz31",fontsize=16,color="black",shape="box"];473 -> 487[label="",style="solid", color="black", weight=3];
474[label="vuz410",fontsize=16,color="green",shape="box"];475[label="vuz410",fontsize=16,color="green",shape="box"];476[label="vuz410",fontsize=16,color="green",shape="box"];477[label="vuz410",fontsize=16,color="green",shape="box"];478[label="vuz410",fontsize=16,color="green",shape="box"];479[label="vuz410",fontsize=16,color="green",shape="box"];381[label="vuz410",fontsize=16,color="green",shape="box"];382[label="vuz3010",fontsize=16,color="green",shape="box"];383[label="vuz410",fontsize=16,color="green",shape="box"];384[label="vuz3010",fontsize=16,color="green",shape="box"];385[label="vuz410",fontsize=16,color="green",shape="box"];386[label="vuz3010",fontsize=16,color="green",shape="box"];387[label="vuz410",fontsize=16,color="green",shape="box"];388[label="vuz3010",fontsize=16,color="green",shape="box"];389[label="vuz410",fontsize=16,color="green",shape="box"];390[label="vuz3010",fontsize=16,color="green",shape="box"];391[label="vuz410",fontsize=16,color="green",shape="box"];392[label="vuz3010",fontsize=16,color="green",shape="box"];480[label="primMulNat (Succ vuz4100) (Succ vuz30100)",fontsize=16,color="black",shape="box"];480 -> 488[label="",style="solid", color="black", weight=3];
481[label="primMulNat (Succ vuz4100) Zero",fontsize=16,color="black",shape="box"];481 -> 489[label="",style="solid", color="black", weight=3];
482[label="primMulNat Zero (Succ vuz30100)",fontsize=16,color="black",shape="box"];482 -> 490[label="",style="solid", color="black", weight=3];
483[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];483 -> 491[label="",style="solid", color="black", weight=3];
484[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) (primEqInt (Pos (Succ vuz300)) (Pos Zero)))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) (primEqInt (Pos vuz29) (Pos Zero)))) vuz31",fontsize=16,color="black",shape="box"];484 -> 492[label="",style="solid", color="black", weight=3];
485[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) (primEqInt (Pos Zero) (Pos Zero)))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) (primEqInt (Pos vuz29) (Pos Zero)))) vuz31",fontsize=16,color="black",shape="box"];485 -> 493[label="",style="solid", color="black", weight=3];
486[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) (primEqInt (Neg (Succ vuz360)) (Pos Zero)))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) (primEqInt (Neg vuz35) (Pos Zero)))) vuz31",fontsize=16,color="black",shape="box"];486 -> 494[label="",style="solid", color="black", weight=3];
487[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) (primEqInt (Neg Zero) (Pos Zero)))) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) (primEqInt (Neg vuz35) (Pos Zero)))) vuz31",fontsize=16,color="black",shape="box"];487 -> 495[label="",style="solid", color="black", weight=3];
488 -> 496[label="",style="dashed", color="red", weight=0];
488[label="primPlusNat (primMulNat vuz4100 (Succ vuz30100)) (Succ vuz30100)",fontsize=16,color="magenta"];488 -> 497[label="",style="dashed", color="magenta", weight=3];
489[label="Zero",fontsize=16,color="green",shape="box"];490[label="Zero",fontsize=16,color="green",shape="box"];491[label="Zero",fontsize=16,color="green",shape="box"];492[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) False)) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) False)) vuz31",fontsize=16,color="black",shape="box"];492 -> 498[label="",style="solid", color="black", weight=3];
493[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) True)) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Pos vuz26) (vuz40 * vuz300) (Pos vuz25) True)) vuz31",fontsize=16,color="black",shape="box"];493 -> 499[label="",style="solid", color="black", weight=3];
494[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) False)) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) False)) vuz31",fontsize=16,color="black",shape="box"];494 -> 500[label="",style="solid", color="black", weight=3];
495[label="enforceWHNF (WHNF (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) True)) (foldl' (*) (reduce2Reduce1 (vuz40 * vuz300) (Neg vuz32) (vuz40 * vuz300) (Neg vuz31) True)) vuz31",fontsize=16,color="black",shape="box"];495 -> 501[label="",style="solid", color="black", weight=3];
497 -> 305[label="",style="dashed", color="red", weight=0];
497[label="primMulNat vuz4100 (Succ vuz30100)",fontsize=16,color="magenta"];497 -> 502[label="",style="dashed", color="magenta", weight=3];
497 -> 503[label="",style="dashed", color="magenta", weight=3];
496[label="primPlusNat vuz37 (Succ vuz30100)",fontsize=16,color="burlywood",shape="triangle"];6756[label="vuz37/Succ vuz370",fontsize=10,color="white",style="solid",shape="box"];496 -> 6756[label="",style="solid", color="burlywood", weight=9];
6756 -> 504[label="",style="solid", color="burlywood", weight=3];
6757[label="vuz37/Zero",fontsize=10,color="white",style="solid",shape="box"];496 -> 6757[label="",style="solid", color="burlywood", weight=9];
6757 -> 505[label="",style="solid", color="burlywood", weight=3];
498[label="enforceWHNF (WHNF (reduce2Reduce0 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) otherwise)) (foldl' (*) (reduce2Reduce0 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) otherwise)) vuz31",fontsize=16,color="black",shape="box"];498 -> 506[label="",style="solid", color="black", weight=3];
499[label="enforceWHNF (WHNF (error [])) (foldl' (*) (error [])) vuz31",fontsize=16,color="black",shape="triangle"];499 -> 507[label="",style="solid", color="black", weight=3];
500[label="enforceWHNF (WHNF (reduce2Reduce0 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) otherwise)) (foldl' (*) (reduce2Reduce0 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) otherwise)) vuz31",fontsize=16,color="black",shape="box"];500 -> 508[label="",style="solid", color="black", weight=3];
501 -> 499[label="",style="dashed", color="red", weight=0];
501[label="enforceWHNF (WHNF (error [])) (foldl' (*) (error [])) vuz31",fontsize=16,color="magenta"];502[label="vuz4100",fontsize=16,color="green",shape="box"];503[label="Succ vuz30100",fontsize=16,color="green",shape="box"];504[label="primPlusNat (Succ vuz370) (Succ vuz30100)",fontsize=16,color="black",shape="box"];504 -> 509[label="",style="solid", color="black", weight=3];
505[label="primPlusNat Zero (Succ vuz30100)",fontsize=16,color="black",shape="box"];505 -> 510[label="",style="solid", color="black", weight=3];
506[label="enforceWHNF (WHNF (reduce2Reduce0 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) True)) (foldl' (*) (reduce2Reduce0 (vuz40 * vuz300) (Pos vuz28) (vuz40 * vuz300) (Pos vuz27) True)) vuz31",fontsize=16,color="black",shape="box"];506 -> 511[label="",style="solid", color="black", weight=3];
507[label="error []",fontsize=16,color="red",shape="box"];508[label="enforceWHNF (WHNF (reduce2Reduce0 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) True)) (foldl' (*) (reduce2Reduce0 (vuz40 * vuz300) (Neg vuz34) (vuz40 * vuz300) (Neg vuz33) True)) vuz31",fontsize=16,color="black",shape="box"];508 -> 512[label="",style="solid", color="black", weight=3];
509[label="Succ (Succ (primPlusNat vuz370 vuz30100))",fontsize=16,color="green",shape="box"];509 -> 513[label="",style="dashed", color="green", weight=3];
510[label="Succ vuz30100",fontsize=16,color="green",shape="box"];511 -> 1782[label="",style="dashed", color="red", weight=0];
511[label="enforceWHNF (WHNF (vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28) :% (Pos vuz27 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)))) (foldl' (*) (vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28) :% (Pos vuz27 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)))) vuz31",fontsize=16,color="magenta"];511 -> 1783[label="",style="dashed", color="magenta", weight=3];
511 -> 1784[label="",style="dashed", color="magenta", weight=3];
511 -> 1785[label="",style="dashed", color="magenta", weight=3];
511 -> 1786[label="",style="dashed", color="magenta", weight=3];
512 -> 1782[label="",style="dashed", color="red", weight=0];
512[label="enforceWHNF (WHNF (vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34) :% (Neg vuz33 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)))) (foldl' (*) (vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34) :% (Neg vuz33 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)))) vuz31",fontsize=16,color="magenta"];512 -> 1787[label="",style="dashed", color="magenta", weight=3];
512 -> 1788[label="",style="dashed", color="magenta", weight=3];
512 -> 1789[label="",style="dashed", color="magenta", weight=3];
512 -> 1790[label="",style="dashed", color="magenta", weight=3];
513[label="primPlusNat vuz370 vuz30100",fontsize=16,color="burlywood",shape="triangle"];6761[label="vuz370/Succ vuz3700",fontsize=10,color="white",style="solid",shape="box"];513 -> 6761[label="",style="solid", color="burlywood", weight=9];
6761 -> 516[label="",style="solid", color="burlywood", weight=3];
6762[label="vuz370/Zero",fontsize=10,color="white",style="solid",shape="box"];513 -> 6762[label="",style="solid", color="burlywood", weight=9];
6762 -> 517[label="",style="solid", color="burlywood", weight=3];
1783[label="Pos vuz27 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="triangle"];1783 -> 3901[label="",style="solid", color="black", weight=3];
1784[label="vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="triangle"];1784 -> 3902[label="",style="solid", color="black", weight=3];
1785 -> 1783[label="",style="dashed", color="red", weight=0];
1785[label="Pos vuz27 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="magenta"];1786 -> 1784[label="",style="dashed", color="red", weight=0];
1786[label="vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="magenta"];1782[label="enforceWHNF (WHNF (vuz104 :% vuz90)) (foldl' (*) (vuz103 :% vuz89)) vuz31",fontsize=16,color="black",shape="triangle"];1782 -> 3903[label="",style="solid", color="black", weight=3];
1787[label="Neg vuz33 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="triangle"];1787 -> 3904[label="",style="solid", color="black", weight=3];
1788[label="vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="triangle"];1788 -> 3905[label="",style="solid", color="black", weight=3];
1789 -> 1787[label="",style="dashed", color="red", weight=0];
1789[label="Neg vuz33 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="magenta"];1790 -> 1788[label="",style="dashed", color="red", weight=0];
1790[label="vuz40 * vuz300 `quot` reduce2D (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="magenta"];516[label="primPlusNat (Succ vuz3700) vuz30100",fontsize=16,color="burlywood",shape="box"];6767[label="vuz30100/Succ vuz301000",fontsize=10,color="white",style="solid",shape="box"];516 -> 6767[label="",style="solid", color="burlywood", weight=9];
6767 -> 520[label="",style="solid", color="burlywood", weight=3];
6768[label="vuz30100/Zero",fontsize=10,color="white",style="solid",shape="box"];516 -> 6768[label="",style="solid", color="burlywood", weight=9];
6768 -> 521[label="",style="solid", color="burlywood", weight=3];
517[label="primPlusNat Zero vuz30100",fontsize=16,color="burlywood",shape="box"];6769[label="vuz30100/Succ vuz301000",fontsize=10,color="white",style="solid",shape="box"];517 -> 6769[label="",style="solid", color="burlywood", weight=9];
6769 -> 522[label="",style="solid", color="burlywood", weight=3];
6770[label="vuz30100/Zero",fontsize=10,color="white",style="solid",shape="box"];517 -> 6770[label="",style="solid", color="burlywood", weight=9];
6770 -> 523[label="",style="solid", color="burlywood", weight=3];
3901 -> 5759[label="",style="dashed", color="red", weight=0];
3901[label="primQuotInt (Pos vuz27) (reduce2D (vuz40 * vuz300) (Pos vuz28))",fontsize=16,color="magenta"];3901 -> 5760[label="",style="dashed", color="magenta", weight=3];
3902[label="primQuotInt (vuz40 * vuz300) (reduce2D (vuz40 * vuz300) (Pos vuz28))",fontsize=16,color="black",shape="box"];3902 -> 3907[label="",style="solid", color="black", weight=3];
3903[label="foldl' (*) (vuz103 :% vuz89) vuz31",fontsize=16,color="burlywood",shape="box"];6772[label="vuz31/vuz310 : vuz311",fontsize=10,color="white",style="solid",shape="box"];3903 -> 6772[label="",style="solid", color="burlywood", weight=9];
6772 -> 3908[label="",style="solid", color="burlywood", weight=3];
6773[label="vuz31/[]",fontsize=10,color="white",style="solid",shape="box"];3903 -> 6773[label="",style="solid", color="burlywood", weight=9];
6773 -> 3909[label="",style="solid", color="burlywood", weight=3];
3904 -> 4543[label="",style="dashed", color="red", weight=0];
3904[label="primQuotInt (Neg vuz33) (reduce2D (vuz40 * vuz300) (Neg vuz34))",fontsize=16,color="magenta"];3904 -> 4544[label="",style="dashed", color="magenta", weight=3];
3904 -> 4545[label="",style="dashed", color="magenta", weight=3];
3905[label="primQuotInt (vuz40 * vuz300) (reduce2D (vuz40 * vuz300) (Neg vuz34))",fontsize=16,color="black",shape="box"];3905 -> 3911[label="",style="solid", color="black", weight=3];
520[label="primPlusNat (Succ vuz3700) (Succ vuz301000)",fontsize=16,color="black",shape="box"];520 -> 528[label="",style="solid", color="black", weight=3];
521[label="primPlusNat (Succ vuz3700) Zero",fontsize=16,color="black",shape="box"];521 -> 529[label="",style="solid", color="black", weight=3];
522[label="primPlusNat Zero (Succ vuz301000)",fontsize=16,color="black",shape="box"];522 -> 530[label="",style="solid", color="black", weight=3];
523[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];523 -> 531[label="",style="solid", color="black", weight=3];
5760[label="reduce2D (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="box"];5760 -> 6169[label="",style="solid", color="black", weight=3];
5759[label="primQuotInt (Pos vuz27) vuz166",fontsize=16,color="burlywood",shape="triangle"];6775[label="vuz166/Pos vuz1660",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6775[label="",style="solid", color="burlywood", weight=9];
6775 -> 6170[label="",style="solid", color="burlywood", weight=3];
6776[label="vuz166/Neg vuz1660",fontsize=10,color="white",style="solid",shape="box"];5759 -> 6776[label="",style="solid", color="burlywood", weight=9];
6776 -> 6171[label="",style="solid", color="burlywood", weight=3];
3907[label="primQuotInt (primMulInt vuz40 vuz300) (reduce2D (primMulInt vuz40 vuz300) (Pos vuz28))",fontsize=16,color="burlywood",shape="box"];6777[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];3907 -> 6777[label="",style="solid", color="burlywood", weight=9];
6777 -> 3913[label="",style="solid", color="burlywood", weight=3];
6778[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];3907 -> 6778[label="",style="solid", color="burlywood", weight=9];
6778 -> 3914[label="",style="solid", color="burlywood", weight=3];
3908[label="foldl' (*) (vuz103 :% vuz89) (vuz310 : vuz311)",fontsize=16,color="black",shape="box"];3908 -> 3915[label="",style="solid", color="black", weight=3];
3909[label="foldl' (*) (vuz103 :% vuz89) []",fontsize=16,color="black",shape="box"];3909 -> 3916[label="",style="solid", color="black", weight=3];
4544[label="reduce2D (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="box"];4544 -> 4990[label="",style="solid", color="black", weight=3];
4545[label="vuz33",fontsize=16,color="green",shape="box"];4543[label="primQuotInt (Neg vuz122) vuz123",fontsize=16,color="burlywood",shape="triangle"];6779[label="vuz123/Pos vuz1230",fontsize=10,color="white",style="solid",shape="box"];4543 -> 6779[label="",style="solid", color="burlywood", weight=9];
6779 -> 4991[label="",style="solid", color="burlywood", weight=3];
6780[label="vuz123/Neg vuz1230",fontsize=10,color="white",style="solid",shape="box"];4543 -> 6780[label="",style="solid", color="burlywood", weight=9];
6780 -> 4992[label="",style="solid", color="burlywood", weight=3];
3911[label="primQuotInt (primMulInt vuz40 vuz300) (reduce2D (primMulInt vuz40 vuz300) (Neg vuz34))",fontsize=16,color="burlywood",shape="box"];6781[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];3911 -> 6781[label="",style="solid", color="burlywood", weight=9];
6781 -> 3918[label="",style="solid", color="burlywood", weight=3];
6782[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];3911 -> 6782[label="",style="solid", color="burlywood", weight=9];
6782 -> 3919[label="",style="solid", color="burlywood", weight=3];
528[label="Succ (Succ (primPlusNat vuz3700 vuz301000))",fontsize=16,color="green",shape="box"];528 -> 540[label="",style="dashed", color="green", weight=3];
529[label="Succ vuz3700",fontsize=16,color="green",shape="box"];530[label="Succ vuz301000",fontsize=16,color="green",shape="box"];531[label="Zero",fontsize=16,color="green",shape="box"];6169[label="gcd (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="box"];6169 -> 6177[label="",style="solid", color="black", weight=3];
6170[label="primQuotInt (Pos vuz27) (Pos vuz1660)",fontsize=16,color="burlywood",shape="box"];6783[label="vuz1660/Succ vuz16600",fontsize=10,color="white",style="solid",shape="box"];6170 -> 6783[label="",style="solid", color="burlywood", weight=9];
6783 -> 6178[label="",style="solid", color="burlywood", weight=3];
6784[label="vuz1660/Zero",fontsize=10,color="white",style="solid",shape="box"];6170 -> 6784[label="",style="solid", color="burlywood", weight=9];
6784 -> 6179[label="",style="solid", color="burlywood", weight=3];
6171[label="primQuotInt (Pos vuz27) (Neg vuz1660)",fontsize=16,color="burlywood",shape="box"];6785[label="vuz1660/Succ vuz16600",fontsize=10,color="white",style="solid",shape="box"];6171 -> 6785[label="",style="solid", color="burlywood", weight=9];
6785 -> 6180[label="",style="solid", color="burlywood", weight=3];
6786[label="vuz1660/Zero",fontsize=10,color="white",style="solid",shape="box"];6171 -> 6786[label="",style="solid", color="burlywood", weight=9];
6786 -> 6181[label="",style="solid", color="burlywood", weight=3];
3913[label="primQuotInt (primMulInt (Pos vuz400) vuz300) (reduce2D (primMulInt (Pos vuz400) vuz300) (Pos vuz28))",fontsize=16,color="burlywood",shape="box"];6787[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];3913 -> 6787[label="",style="solid", color="burlywood", weight=9];
6787 -> 3921[label="",style="solid", color="burlywood", weight=3];
6788[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];3913 -> 6788[label="",style="solid", color="burlywood", weight=9];
6788 -> 3922[label="",style="solid", color="burlywood", weight=3];
3914[label="primQuotInt (primMulInt (Neg vuz400) vuz300) (reduce2D (primMulInt (Neg vuz400) vuz300) (Pos vuz28))",fontsize=16,color="burlywood",shape="box"];6789[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];3914 -> 6789[label="",style="solid", color="burlywood", weight=9];
6789 -> 3923[label="",style="solid", color="burlywood", weight=3];
6790[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];3914 -> 6790[label="",style="solid", color="burlywood", weight=9];
6790 -> 3924[label="",style="solid", color="burlywood", weight=3];
3915[label="(foldl' (*) $! (*) (vuz103 :% vuz89) vuz310)",fontsize=16,color="black",shape="box"];3915 -> 3925[label="",style="solid", color="black", weight=3];
3916[label="vuz103 :% vuz89",fontsize=16,color="green",shape="box"];4990[label="gcd (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="box"];4990 -> 4996[label="",style="solid", color="black", weight=3];
4991[label="primQuotInt (Neg vuz122) (Pos vuz1230)",fontsize=16,color="burlywood",shape="box"];6791[label="vuz1230/Succ vuz12300",fontsize=10,color="white",style="solid",shape="box"];4991 -> 6791[label="",style="solid", color="burlywood", weight=9];
6791 -> 4997[label="",style="solid", color="burlywood", weight=3];
6792[label="vuz1230/Zero",fontsize=10,color="white",style="solid",shape="box"];4991 -> 6792[label="",style="solid", color="burlywood", weight=9];
6792 -> 4998[label="",style="solid", color="burlywood", weight=3];
4992[label="primQuotInt (Neg vuz122) (Neg vuz1230)",fontsize=16,color="burlywood",shape="box"];6793[label="vuz1230/Succ vuz12300",fontsize=10,color="white",style="solid",shape="box"];4992 -> 6793[label="",style="solid", color="burlywood", weight=9];
6793 -> 4999[label="",style="solid", color="burlywood", weight=3];
6794[label="vuz1230/Zero",fontsize=10,color="white",style="solid",shape="box"];4992 -> 6794[label="",style="solid", color="burlywood", weight=9];
6794 -> 5000[label="",style="solid", color="burlywood", weight=3];
3918[label="primQuotInt (primMulInt (Pos vuz400) vuz300) (reduce2D (primMulInt (Pos vuz400) vuz300) (Neg vuz34))",fontsize=16,color="burlywood",shape="box"];6795[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];3918 -> 6795[label="",style="solid", color="burlywood", weight=9];
6795 -> 3927[label="",style="solid", color="burlywood", weight=3];
6796[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];3918 -> 6796[label="",style="solid", color="burlywood", weight=9];
6796 -> 3928[label="",style="solid", color="burlywood", weight=3];
3919[label="primQuotInt (primMulInt (Neg vuz400) vuz300) (reduce2D (primMulInt (Neg vuz400) vuz300) (Neg vuz34))",fontsize=16,color="burlywood",shape="box"];6797[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];3919 -> 6797[label="",style="solid", color="burlywood", weight=9];
6797 -> 3929[label="",style="solid", color="burlywood", weight=3];
6798[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];3919 -> 6798[label="",style="solid", color="burlywood", weight=9];
6798 -> 3930[label="",style="solid", color="burlywood", weight=3];
540 -> 513[label="",style="dashed", color="red", weight=0];
540[label="primPlusNat vuz3700 vuz301000",fontsize=16,color="magenta"];540 -> 549[label="",style="dashed", color="magenta", weight=3];
540 -> 550[label="",style="dashed", color="magenta", weight=3];
6177[label="gcd3 (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="box"];6177 -> 6189[label="",style="solid", color="black", weight=3];
6178[label="primQuotInt (Pos vuz27) (Pos (Succ vuz16600))",fontsize=16,color="black",shape="box"];6178 -> 6190[label="",style="solid", color="black", weight=3];
6179[label="primQuotInt (Pos vuz27) (Pos Zero)",fontsize=16,color="black",shape="box"];6179 -> 6191[label="",style="solid", color="black", weight=3];
6180[label="primQuotInt (Pos vuz27) (Neg (Succ vuz16600))",fontsize=16,color="black",shape="box"];6180 -> 6192[label="",style="solid", color="black", weight=3];
6181[label="primQuotInt (Pos vuz27) (Neg Zero)",fontsize=16,color="black",shape="box"];6181 -> 6193[label="",style="solid", color="black", weight=3];
3921[label="primQuotInt (primMulInt (Pos vuz400) (Pos vuz3000)) (reduce2D (primMulInt (Pos vuz400) (Pos vuz3000)) (Pos vuz28))",fontsize=16,color="black",shape="box"];3921 -> 3932[label="",style="solid", color="black", weight=3];
3922[label="primQuotInt (primMulInt (Pos vuz400) (Neg vuz3000)) (reduce2D (primMulInt (Pos vuz400) (Neg vuz3000)) (Pos vuz28))",fontsize=16,color="black",shape="box"];3922 -> 3933[label="",style="solid", color="black", weight=3];
3923[label="primQuotInt (primMulInt (Neg vuz400) (Pos vuz3000)) (reduce2D (primMulInt (Neg vuz400) (Pos vuz3000)) (Pos vuz28))",fontsize=16,color="black",shape="box"];3923 -> 3934[label="",style="solid", color="black", weight=3];
3924[label="primQuotInt (primMulInt (Neg vuz400) (Neg vuz3000)) (reduce2D (primMulInt (Neg vuz400) (Neg vuz3000)) (Pos vuz28))",fontsize=16,color="black",shape="box"];3924 -> 3935[label="",style="solid", color="black", weight=3];
3925 -> 11[label="",style="dashed", color="red", weight=0];
3925[label="((*) (vuz103 :% vuz89) vuz310 `seq` foldl' (*) ((*) (vuz103 :% vuz89) vuz310))",fontsize=16,color="magenta"];3925 -> 3936[label="",style="dashed", color="magenta", weight=3];
3925 -> 3937[label="",style="dashed", color="magenta", weight=3];
3925 -> 3938[label="",style="dashed", color="magenta", weight=3];
3925 -> 3939[label="",style="dashed", color="magenta", weight=3];
4996[label="gcd3 (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="box"];4996 -> 5008[label="",style="solid", color="black", weight=3];
4997[label="primQuotInt (Neg vuz122) (Pos (Succ vuz12300))",fontsize=16,color="black",shape="box"];4997 -> 5009[label="",style="solid", color="black", weight=3];
4998[label="primQuotInt (Neg vuz122) (Pos Zero)",fontsize=16,color="black",shape="box"];4998 -> 5010[label="",style="solid", color="black", weight=3];
4999[label="primQuotInt (Neg vuz122) (Neg (Succ vuz12300))",fontsize=16,color="black",shape="box"];4999 -> 5011[label="",style="solid", color="black", weight=3];
5000[label="primQuotInt (Neg vuz122) (Neg Zero)",fontsize=16,color="black",shape="box"];5000 -> 5012[label="",style="solid", color="black", weight=3];
3927[label="primQuotInt (primMulInt (Pos vuz400) (Pos vuz3000)) (reduce2D (primMulInt (Pos vuz400) (Pos vuz3000)) (Neg vuz34))",fontsize=16,color="black",shape="box"];3927 -> 3941[label="",style="solid", color="black", weight=3];
3928[label="primQuotInt (primMulInt (Pos vuz400) (Neg vuz3000)) (reduce2D (primMulInt (Pos vuz400) (Neg vuz3000)) (Neg vuz34))",fontsize=16,color="black",shape="box"];3928 -> 3942[label="",style="solid", color="black", weight=3];
3929[label="primQuotInt (primMulInt (Neg vuz400) (Pos vuz3000)) (reduce2D (primMulInt (Neg vuz400) (Pos vuz3000)) (Neg vuz34))",fontsize=16,color="black",shape="box"];3929 -> 3943[label="",style="solid", color="black", weight=3];
3930[label="primQuotInt (primMulInt (Neg vuz400) (Neg vuz3000)) (reduce2D (primMulInt (Neg vuz400) (Neg vuz3000)) (Neg vuz34))",fontsize=16,color="black",shape="box"];3930 -> 3944[label="",style="solid", color="black", weight=3];
549[label="vuz301000",fontsize=16,color="green",shape="box"];550[label="vuz3700",fontsize=16,color="green",shape="box"];6189[label="gcd2 (vuz40 * vuz300 == fromInt (Pos Zero)) (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="box"];6189 -> 6216[label="",style="solid", color="black", weight=3];
6190[label="Pos (primDivNatS vuz27 (Succ vuz16600))",fontsize=16,color="green",shape="box"];6190 -> 6217[label="",style="dashed", color="green", weight=3];
6191 -> 5010[label="",style="dashed", color="red", weight=0];
6191[label="error []",fontsize=16,color="magenta"];6192[label="Neg (primDivNatS vuz27 (Succ vuz16600))",fontsize=16,color="green",shape="box"];6192 -> 6218[label="",style="dashed", color="green", weight=3];
6193 -> 5010[label="",style="dashed", color="red", weight=0];
6193[label="error []",fontsize=16,color="magenta"];3932 -> 5759[label="",style="dashed", color="red", weight=0];
3932[label="primQuotInt (Pos (primMulNat vuz400 vuz3000)) (reduce2D (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28))",fontsize=16,color="magenta"];3932 -> 5765[label="",style="dashed", color="magenta", weight=3];
3932 -> 5766[label="",style="dashed", color="magenta", weight=3];
3933 -> 4543[label="",style="dashed", color="red", weight=0];
3933[label="primQuotInt (Neg (primMulNat vuz400 vuz3000)) (reduce2D (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28))",fontsize=16,color="magenta"];3933 -> 4552[label="",style="dashed", color="magenta", weight=3];
3933 -> 4553[label="",style="dashed", color="magenta", weight=3];
3934 -> 4543[label="",style="dashed", color="red", weight=0];
3934[label="primQuotInt (Neg (primMulNat vuz400 vuz3000)) (reduce2D (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28))",fontsize=16,color="magenta"];3934 -> 4554[label="",style="dashed", color="magenta", weight=3];
3934 -> 4555[label="",style="dashed", color="magenta", weight=3];
3935 -> 5759[label="",style="dashed", color="red", weight=0];
3935[label="primQuotInt (Pos (primMulNat vuz400 vuz3000)) (reduce2D (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28))",fontsize=16,color="magenta"];3935 -> 5767[label="",style="dashed", color="magenta", weight=3];
3935 -> 5768[label="",style="dashed", color="magenta", weight=3];
3936[label="vuz103 :% vuz89",fontsize=16,color="green",shape="box"];3937[label="vuz310",fontsize=16,color="green",shape="box"];3938[label="vuz311",fontsize=16,color="green",shape="box"];3939[label="vuz103 :% vuz89",fontsize=16,color="green",shape="box"];5008[label="gcd2 (vuz40 * vuz300 == fromInt (Pos Zero)) (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="box"];5008 -> 5033[label="",style="solid", color="black", weight=3];
5009[label="Neg (primDivNatS vuz122 (Succ vuz12300))",fontsize=16,color="green",shape="box"];5009 -> 5034[label="",style="dashed", color="green", weight=3];
5010[label="error []",fontsize=16,color="black",shape="triangle"];5010 -> 5035[label="",style="solid", color="black", weight=3];
5011[label="Pos (primDivNatS vuz122 (Succ vuz12300))",fontsize=16,color="green",shape="box"];5011 -> 5036[label="",style="dashed", color="green", weight=3];
5012 -> 5010[label="",style="dashed", color="red", weight=0];
5012[label="error []",fontsize=16,color="magenta"];3941 -> 5759[label="",style="dashed", color="red", weight=0];
3941[label="primQuotInt (Pos (primMulNat vuz400 vuz3000)) (reduce2D (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34))",fontsize=16,color="magenta"];3941 -> 5769[label="",style="dashed", color="magenta", weight=3];
3941 -> 5770[label="",style="dashed", color="magenta", weight=3];
3942 -> 4543[label="",style="dashed", color="red", weight=0];
3942[label="primQuotInt (Neg (primMulNat vuz400 vuz3000)) (reduce2D (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34))",fontsize=16,color="magenta"];3942 -> 4558[label="",style="dashed", color="magenta", weight=3];
3942 -> 4559[label="",style="dashed", color="magenta", weight=3];
3943 -> 4543[label="",style="dashed", color="red", weight=0];
3943[label="primQuotInt (Neg (primMulNat vuz400 vuz3000)) (reduce2D (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34))",fontsize=16,color="magenta"];3943 -> 4560[label="",style="dashed", color="magenta", weight=3];
3943 -> 4561[label="",style="dashed", color="magenta", weight=3];
3944 -> 5759[label="",style="dashed", color="red", weight=0];
3944[label="primQuotInt (Pos (primMulNat vuz400 vuz3000)) (reduce2D (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34))",fontsize=16,color="magenta"];3944 -> 5771[label="",style="dashed", color="magenta", weight=3];
3944 -> 5772[label="",style="dashed", color="magenta", weight=3];
6216[label="gcd2 (primEqInt (vuz40 * vuz300) (fromInt (Pos Zero))) (vuz40 * vuz300) (Pos vuz28)",fontsize=16,color="black",shape="box"];6216 -> 6232[label="",style="solid", color="black", weight=3];
6217 -> 5034[label="",style="dashed", color="red", weight=0];
6217[label="primDivNatS vuz27 (Succ vuz16600)",fontsize=16,color="magenta"];6217 -> 6233[label="",style="dashed", color="magenta", weight=3];
6217 -> 6234[label="",style="dashed", color="magenta", weight=3];
6218 -> 5034[label="",style="dashed", color="red", weight=0];
6218[label="primDivNatS vuz27 (Succ vuz16600)",fontsize=16,color="magenta"];6218 -> 6235[label="",style="dashed", color="magenta", weight=3];
6218 -> 6236[label="",style="dashed", color="magenta", weight=3];
5765 -> 305[label="",style="dashed", color="red", weight=0];
5765[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5765 -> 6172[label="",style="dashed", color="magenta", weight=3];
5765 -> 6173[label="",style="dashed", color="magenta", weight=3];
5766 -> 6174[label="",style="dashed", color="red", weight=0];
5766[label="reduce2D (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];5766 -> 6175[label="",style="dashed", color="magenta", weight=3];
4552 -> 4993[label="",style="dashed", color="red", weight=0];
4552[label="reduce2D (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];4552 -> 4994[label="",style="dashed", color="magenta", weight=3];
4553 -> 305[label="",style="dashed", color="red", weight=0];
4553[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4553 -> 5001[label="",style="dashed", color="magenta", weight=3];
4553 -> 5002[label="",style="dashed", color="magenta", weight=3];
4554 -> 4993[label="",style="dashed", color="red", weight=0];
4554[label="reduce2D (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];4554 -> 4995[label="",style="dashed", color="magenta", weight=3];
4555 -> 305[label="",style="dashed", color="red", weight=0];
4555[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4555 -> 5003[label="",style="dashed", color="magenta", weight=3];
4555 -> 5004[label="",style="dashed", color="magenta", weight=3];
5767 -> 305[label="",style="dashed", color="red", weight=0];
5767[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5767 -> 6182[label="",style="dashed", color="magenta", weight=3];
5767 -> 6183[label="",style="dashed", color="magenta", weight=3];
5768 -> 6174[label="",style="dashed", color="red", weight=0];
5768[label="reduce2D (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];5768 -> 6176[label="",style="dashed", color="magenta", weight=3];
5033[label="gcd2 (primEqInt (vuz40 * vuz300) (fromInt (Pos Zero))) (vuz40 * vuz300) (Neg vuz34)",fontsize=16,color="black",shape="box"];5033 -> 5047[label="",style="solid", color="black", weight=3];
5034[label="primDivNatS vuz122 (Succ vuz12300)",fontsize=16,color="burlywood",shape="triangle"];6822[label="vuz122/Succ vuz1220",fontsize=10,color="white",style="solid",shape="box"];5034 -> 6822[label="",style="solid", color="burlywood", weight=9];
6822 -> 5048[label="",style="solid", color="burlywood", weight=3];
6823[label="vuz122/Zero",fontsize=10,color="white",style="solid",shape="box"];5034 -> 6823[label="",style="solid", color="burlywood", weight=9];
6823 -> 5049[label="",style="solid", color="burlywood", weight=3];
5035[label="error []",fontsize=16,color="red",shape="box"];5036 -> 5034[label="",style="dashed", color="red", weight=0];
5036[label="primDivNatS vuz122 (Succ vuz12300)",fontsize=16,color="magenta"];5036 -> 5050[label="",style="dashed", color="magenta", weight=3];
5769 -> 305[label="",style="dashed", color="red", weight=0];
5769[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5769 -> 6184[label="",style="dashed", color="magenta", weight=3];
5769 -> 6185[label="",style="dashed", color="magenta", weight=3];
5770 -> 6186[label="",style="dashed", color="red", weight=0];
5770[label="reduce2D (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5770 -> 6187[label="",style="dashed", color="magenta", weight=3];
4558 -> 5005[label="",style="dashed", color="red", weight=0];
4558[label="reduce2D (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];4558 -> 5006[label="",style="dashed", color="magenta", weight=3];
4559 -> 305[label="",style="dashed", color="red", weight=0];
4559[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4559 -> 5013[label="",style="dashed", color="magenta", weight=3];
4559 -> 5014[label="",style="dashed", color="magenta", weight=3];
4560 -> 5005[label="",style="dashed", color="red", weight=0];
4560[label="reduce2D (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];4560 -> 5007[label="",style="dashed", color="magenta", weight=3];
4561 -> 305[label="",style="dashed", color="red", weight=0];
4561[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4561 -> 5015[label="",style="dashed", color="magenta", weight=3];
4561 -> 5016[label="",style="dashed", color="magenta", weight=3];
5771 -> 305[label="",style="dashed", color="red", weight=0];
5771[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5771 -> 6194[label="",style="dashed", color="magenta", weight=3];
5771 -> 6195[label="",style="dashed", color="magenta", weight=3];
5772 -> 6186[label="",style="dashed", color="red", weight=0];
5772[label="reduce2D (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5772 -> 6188[label="",style="dashed", color="magenta", weight=3];
6232[label="gcd2 (primEqInt (primMulInt vuz40 vuz300) (fromInt (Pos Zero))) (primMulInt vuz40 vuz300) (Pos vuz28)",fontsize=16,color="burlywood",shape="box"];6833[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];6232 -> 6833[label="",style="solid", color="burlywood", weight=9];
6833 -> 6248[label="",style="solid", color="burlywood", weight=3];
6834[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];6232 -> 6834[label="",style="solid", color="burlywood", weight=9];
6834 -> 6249[label="",style="solid", color="burlywood", weight=3];
6233[label="vuz27",fontsize=16,color="green",shape="box"];6234[label="vuz16600",fontsize=16,color="green",shape="box"];6235[label="vuz27",fontsize=16,color="green",shape="box"];6236[label="vuz16600",fontsize=16,color="green",shape="box"];6172[label="vuz400",fontsize=16,color="green",shape="box"];6173[label="vuz3000",fontsize=16,color="green",shape="box"];6175 -> 305[label="",style="dashed", color="red", weight=0];
6175[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6175 -> 6196[label="",style="dashed", color="magenta", weight=3];
6175 -> 6197[label="",style="dashed", color="magenta", weight=3];
6174[label="reduce2D (Pos vuz167) (Pos vuz28)",fontsize=16,color="black",shape="triangle"];6174 -> 6198[label="",style="solid", color="black", weight=3];
4994 -> 305[label="",style="dashed", color="red", weight=0];
4994[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4994 -> 5017[label="",style="dashed", color="magenta", weight=3];
4994 -> 5018[label="",style="dashed", color="magenta", weight=3];
4993[label="reduce2D (Neg vuz124) (Pos vuz28)",fontsize=16,color="black",shape="triangle"];4993 -> 5019[label="",style="solid", color="black", weight=3];
5001[label="vuz400",fontsize=16,color="green",shape="box"];5002[label="vuz3000",fontsize=16,color="green",shape="box"];4995 -> 305[label="",style="dashed", color="red", weight=0];
4995[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];4995 -> 5020[label="",style="dashed", color="magenta", weight=3];
4995 -> 5021[label="",style="dashed", color="magenta", weight=3];
5003[label="vuz400",fontsize=16,color="green",shape="box"];5004[label="vuz3000",fontsize=16,color="green",shape="box"];6182[label="vuz400",fontsize=16,color="green",shape="box"];6183[label="vuz3000",fontsize=16,color="green",shape="box"];6176 -> 305[label="",style="dashed", color="red", weight=0];
6176[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6176 -> 6199[label="",style="dashed", color="magenta", weight=3];
6176 -> 6200[label="",style="dashed", color="magenta", weight=3];
5047[label="gcd2 (primEqInt (primMulInt vuz40 vuz300) (fromInt (Pos Zero))) (primMulInt vuz40 vuz300) (Neg vuz34)",fontsize=16,color="burlywood",shape="box"];6839[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];5047 -> 6839[label="",style="solid", color="burlywood", weight=9];
6839 -> 5059[label="",style="solid", color="burlywood", weight=3];
6840[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];5047 -> 6840[label="",style="solid", color="burlywood", weight=9];
6840 -> 5060[label="",style="solid", color="burlywood", weight=3];
5048[label="primDivNatS (Succ vuz1220) (Succ vuz12300)",fontsize=16,color="black",shape="box"];5048 -> 5061[label="",style="solid", color="black", weight=3];
5049[label="primDivNatS Zero (Succ vuz12300)",fontsize=16,color="black",shape="box"];5049 -> 5062[label="",style="solid", color="black", weight=3];
5050[label="vuz12300",fontsize=16,color="green",shape="box"];6184[label="vuz400",fontsize=16,color="green",shape="box"];6185[label="vuz3000",fontsize=16,color="green",shape="box"];6187 -> 305[label="",style="dashed", color="red", weight=0];
6187[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6187 -> 6201[label="",style="dashed", color="magenta", weight=3];
6187 -> 6202[label="",style="dashed", color="magenta", weight=3];
6186[label="reduce2D (Pos vuz168) (Neg vuz34)",fontsize=16,color="black",shape="triangle"];6186 -> 6203[label="",style="solid", color="black", weight=3];
5006 -> 305[label="",style="dashed", color="red", weight=0];
5006[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5006 -> 5022[label="",style="dashed", color="magenta", weight=3];
5006 -> 5023[label="",style="dashed", color="magenta", weight=3];
5005[label="reduce2D (Neg vuz125) (Neg vuz34)",fontsize=16,color="black",shape="triangle"];5005 -> 5024[label="",style="solid", color="black", weight=3];
5013[label="vuz400",fontsize=16,color="green",shape="box"];5014[label="vuz3000",fontsize=16,color="green",shape="box"];5007 -> 305[label="",style="dashed", color="red", weight=0];
5007[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5007 -> 5025[label="",style="dashed", color="magenta", weight=3];
5007 -> 5026[label="",style="dashed", color="magenta", weight=3];
5015[label="vuz400",fontsize=16,color="green",shape="box"];5016[label="vuz3000",fontsize=16,color="green",shape="box"];6194[label="vuz400",fontsize=16,color="green",shape="box"];6195[label="vuz3000",fontsize=16,color="green",shape="box"];6188 -> 305[label="",style="dashed", color="red", weight=0];
6188[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6188 -> 6204[label="",style="dashed", color="magenta", weight=3];
6188 -> 6205[label="",style="dashed", color="magenta", weight=3];
6248[label="gcd2 (primEqInt (primMulInt (Pos vuz400) vuz300) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) vuz300) (Pos vuz28)",fontsize=16,color="burlywood",shape="box"];6845[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];6248 -> 6845[label="",style="solid", color="burlywood", weight=9];
6845 -> 6259[label="",style="solid", color="burlywood", weight=3];
6846[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];6248 -> 6846[label="",style="solid", color="burlywood", weight=9];
6846 -> 6260[label="",style="solid", color="burlywood", weight=3];
6249[label="gcd2 (primEqInt (primMulInt (Neg vuz400) vuz300) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) vuz300) (Pos vuz28)",fontsize=16,color="burlywood",shape="box"];6847[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];6249 -> 6847[label="",style="solid", color="burlywood", weight=9];
6847 -> 6261[label="",style="solid", color="burlywood", weight=3];
6848[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];6249 -> 6848[label="",style="solid", color="burlywood", weight=9];
6848 -> 6262[label="",style="solid", color="burlywood", weight=3];
6196[label="vuz400",fontsize=16,color="green",shape="box"];6197[label="vuz3000",fontsize=16,color="green",shape="box"];6198[label="gcd (Pos vuz167) (Pos vuz28)",fontsize=16,color="black",shape="box"];6198 -> 6219[label="",style="solid", color="black", weight=3];
5017[label="vuz400",fontsize=16,color="green",shape="box"];5018[label="vuz3000",fontsize=16,color="green",shape="box"];5019[label="gcd (Neg vuz124) (Pos vuz28)",fontsize=16,color="black",shape="box"];5019 -> 5037[label="",style="solid", color="black", weight=3];
5020[label="vuz400",fontsize=16,color="green",shape="box"];5021[label="vuz3000",fontsize=16,color="green",shape="box"];6199[label="vuz400",fontsize=16,color="green",shape="box"];6200[label="vuz3000",fontsize=16,color="green",shape="box"];5059[label="gcd2 (primEqInt (primMulInt (Pos vuz400) vuz300) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) vuz300) (Neg vuz34)",fontsize=16,color="burlywood",shape="box"];6849[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];5059 -> 6849[label="",style="solid", color="burlywood", weight=9];
6849 -> 5071[label="",style="solid", color="burlywood", weight=3];
6850[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];5059 -> 6850[label="",style="solid", color="burlywood", weight=9];
6850 -> 5072[label="",style="solid", color="burlywood", weight=3];
5060[label="gcd2 (primEqInt (primMulInt (Neg vuz400) vuz300) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) vuz300) (Neg vuz34)",fontsize=16,color="burlywood",shape="box"];6851[label="vuz300/Pos vuz3000",fontsize=10,color="white",style="solid",shape="box"];5060 -> 6851[label="",style="solid", color="burlywood", weight=9];
6851 -> 5073[label="",style="solid", color="burlywood", weight=3];
6852[label="vuz300/Neg vuz3000",fontsize=10,color="white",style="solid",shape="box"];5060 -> 6852[label="",style="solid", color="burlywood", weight=9];
6852 -> 5074[label="",style="solid", color="burlywood", weight=3];
5061[label="primDivNatS0 vuz1220 vuz12300 (primGEqNatS vuz1220 vuz12300)",fontsize=16,color="burlywood",shape="box"];6853[label="vuz1220/Succ vuz12200",fontsize=10,color="white",style="solid",shape="box"];5061 -> 6853[label="",style="solid", color="burlywood", weight=9];
6853 -> 5075[label="",style="solid", color="burlywood", weight=3];
6854[label="vuz1220/Zero",fontsize=10,color="white",style="solid",shape="box"];5061 -> 6854[label="",style="solid", color="burlywood", weight=9];
6854 -> 5076[label="",style="solid", color="burlywood", weight=3];
5062[label="Zero",fontsize=16,color="green",shape="box"];6201[label="vuz400",fontsize=16,color="green",shape="box"];6202[label="vuz3000",fontsize=16,color="green",shape="box"];6203[label="gcd (Pos vuz168) (Neg vuz34)",fontsize=16,color="black",shape="box"];6203 -> 6220[label="",style="solid", color="black", weight=3];
5022[label="vuz400",fontsize=16,color="green",shape="box"];5023[label="vuz3000",fontsize=16,color="green",shape="box"];5024[label="gcd (Neg vuz125) (Neg vuz34)",fontsize=16,color="black",shape="box"];5024 -> 5038[label="",style="solid", color="black", weight=3];
5025[label="vuz400",fontsize=16,color="green",shape="box"];5026[label="vuz3000",fontsize=16,color="green",shape="box"];6204[label="vuz400",fontsize=16,color="green",shape="box"];6205[label="vuz3000",fontsize=16,color="green",shape="box"];6259[label="gcd2 (primEqInt (primMulInt (Pos vuz400) (Pos vuz3000)) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) (Pos vuz3000)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6259 -> 6275[label="",style="solid", color="black", weight=3];
6260[label="gcd2 (primEqInt (primMulInt (Pos vuz400) (Neg vuz3000)) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) (Neg vuz3000)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6260 -> 6276[label="",style="solid", color="black", weight=3];
6261[label="gcd2 (primEqInt (primMulInt (Neg vuz400) (Pos vuz3000)) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) (Pos vuz3000)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6261 -> 6277[label="",style="solid", color="black", weight=3];
6262[label="gcd2 (primEqInt (primMulInt (Neg vuz400) (Neg vuz3000)) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) (Neg vuz3000)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6262 -> 6278[label="",style="solid", color="black", weight=3];
6219[label="gcd3 (Pos vuz167) (Pos vuz28)",fontsize=16,color="black",shape="box"];6219 -> 6237[label="",style="solid", color="black", weight=3];
5037[label="gcd3 (Neg vuz124) (Pos vuz28)",fontsize=16,color="black",shape="box"];5037 -> 5051[label="",style="solid", color="black", weight=3];
5071[label="gcd2 (primEqInt (primMulInt (Pos vuz400) (Pos vuz3000)) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) (Pos vuz3000)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5071 -> 5088[label="",style="solid", color="black", weight=3];
5072[label="gcd2 (primEqInt (primMulInt (Pos vuz400) (Neg vuz3000)) (fromInt (Pos Zero))) (primMulInt (Pos vuz400) (Neg vuz3000)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5072 -> 5089[label="",style="solid", color="black", weight=3];
5073[label="gcd2 (primEqInt (primMulInt (Neg vuz400) (Pos vuz3000)) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) (Pos vuz3000)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5073 -> 5090[label="",style="solid", color="black", weight=3];
5074[label="gcd2 (primEqInt (primMulInt (Neg vuz400) (Neg vuz3000)) (fromInt (Pos Zero))) (primMulInt (Neg vuz400) (Neg vuz3000)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5074 -> 5091[label="",style="solid", color="black", weight=3];
5075[label="primDivNatS0 (Succ vuz12200) vuz12300 (primGEqNatS (Succ vuz12200) vuz12300)",fontsize=16,color="burlywood",shape="box"];6855[label="vuz12300/Succ vuz123000",fontsize=10,color="white",style="solid",shape="box"];5075 -> 6855[label="",style="solid", color="burlywood", weight=9];
6855 -> 5092[label="",style="solid", color="burlywood", weight=3];
6856[label="vuz12300/Zero",fontsize=10,color="white",style="solid",shape="box"];5075 -> 6856[label="",style="solid", color="burlywood", weight=9];
6856 -> 5093[label="",style="solid", color="burlywood", weight=3];
5076[label="primDivNatS0 Zero vuz12300 (primGEqNatS Zero vuz12300)",fontsize=16,color="burlywood",shape="box"];6857[label="vuz12300/Succ vuz123000",fontsize=10,color="white",style="solid",shape="box"];5076 -> 6857[label="",style="solid", color="burlywood", weight=9];
6857 -> 5094[label="",style="solid", color="burlywood", weight=3];
6858[label="vuz12300/Zero",fontsize=10,color="white",style="solid",shape="box"];5076 -> 6858[label="",style="solid", color="burlywood", weight=9];
6858 -> 5095[label="",style="solid", color="burlywood", weight=3];
6220[label="gcd3 (Pos vuz168) (Neg vuz34)",fontsize=16,color="black",shape="box"];6220 -> 6238[label="",style="solid", color="black", weight=3];
5038[label="gcd3 (Neg vuz125) (Neg vuz34)",fontsize=16,color="black",shape="box"];5038 -> 5052[label="",style="solid", color="black", weight=3];
6275 -> 6250[label="",style="dashed", color="red", weight=0];
6275[label="gcd2 (primEqInt (Pos (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];6275 -> 6290[label="",style="dashed", color="magenta", weight=3];
6276 -> 5063[label="",style="dashed", color="red", weight=0];
6276[label="gcd2 (primEqInt (Neg (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];6276 -> 6291[label="",style="dashed", color="magenta", weight=3];
6277 -> 5063[label="",style="dashed", color="red", weight=0];
6277[label="gcd2 (primEqInt (Neg (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Neg (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];6277 -> 6292[label="",style="dashed", color="magenta", weight=3];
6278 -> 6250[label="",style="dashed", color="red", weight=0];
6278[label="gcd2 (primEqInt (Pos (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Pos (primMulNat vuz400 vuz3000)) (Pos vuz28)",fontsize=16,color="magenta"];6278 -> 6293[label="",style="dashed", color="magenta", weight=3];
6237[label="gcd2 (Pos vuz167 == fromInt (Pos Zero)) (Pos vuz167) (Pos vuz28)",fontsize=16,color="black",shape="box"];6237 -> 6250[label="",style="solid", color="black", weight=3];
5051[label="gcd2 (Neg vuz124 == fromInt (Pos Zero)) (Neg vuz124) (Pos vuz28)",fontsize=16,color="black",shape="box"];5051 -> 5063[label="",style="solid", color="black", weight=3];
5088 -> 5105[label="",style="dashed", color="red", weight=0];
5088[label="gcd2 (primEqInt (Pos (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5088 -> 5106[label="",style="dashed", color="magenta", weight=3];
5088 -> 5107[label="",style="dashed", color="magenta", weight=3];
5089 -> 5064[label="",style="dashed", color="red", weight=0];
5089[label="gcd2 (primEqInt (Neg (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5089 -> 5110[label="",style="dashed", color="magenta", weight=3];
5090 -> 5064[label="",style="dashed", color="red", weight=0];
5090[label="gcd2 (primEqInt (Neg (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Neg (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5090 -> 5111[label="",style="dashed", color="magenta", weight=3];
5091 -> 5105[label="",style="dashed", color="red", weight=0];
5091[label="gcd2 (primEqInt (Pos (primMulNat vuz400 vuz3000)) (fromInt (Pos Zero))) (Pos (primMulNat vuz400 vuz3000)) (Neg vuz34)",fontsize=16,color="magenta"];5091 -> 5108[label="",style="dashed", color="magenta", weight=3];
5091 -> 5109[label="",style="dashed", color="magenta", weight=3];
5092[label="primDivNatS0 (Succ vuz12200) (Succ vuz123000) (primGEqNatS (Succ vuz12200) (Succ vuz123000))",fontsize=16,color="black",shape="box"];5092 -> 5112[label="",style="solid", color="black", weight=3];
5093[label="primDivNatS0 (Succ vuz12200) Zero (primGEqNatS (Succ vuz12200) Zero)",fontsize=16,color="black",shape="box"];5093 -> 5113[label="",style="solid", color="black", weight=3];
5094[label="primDivNatS0 Zero (Succ vuz123000) (primGEqNatS Zero (Succ vuz123000))",fontsize=16,color="black",shape="box"];5094 -> 5114[label="",style="solid", color="black", weight=3];
5095[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];5095 -> 5115[label="",style="solid", color="black", weight=3];
6238[label="gcd2 (Pos vuz168 == fromInt (Pos Zero)) (Pos vuz168) (Neg vuz34)",fontsize=16,color="black",shape="box"];6238 -> 6251[label="",style="solid", color="black", weight=3];
5052[label="gcd2 (Neg vuz125 == fromInt (Pos Zero)) (Neg vuz125) (Neg vuz34)",fontsize=16,color="black",shape="box"];5052 -> 5064[label="",style="solid", color="black", weight=3];
6290 -> 305[label="",style="dashed", color="red", weight=0];
6290[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6290 -> 6306[label="",style="dashed", color="magenta", weight=3];
6290 -> 6307[label="",style="dashed", color="magenta", weight=3];
6250[label="gcd2 (primEqInt (Pos vuz167) (fromInt (Pos Zero))) (Pos vuz167) (Pos vuz28)",fontsize=16,color="burlywood",shape="triangle"];6868[label="vuz167/Succ vuz1670",fontsize=10,color="white",style="solid",shape="box"];6250 -> 6868[label="",style="solid", color="burlywood", weight=9];
6868 -> 6263[label="",style="solid", color="burlywood", weight=3];
6869[label="vuz167/Zero",fontsize=10,color="white",style="solid",shape="box"];6250 -> 6869[label="",style="solid", color="burlywood", weight=9];
6869 -> 6264[label="",style="solid", color="burlywood", weight=3];
6291 -> 305[label="",style="dashed", color="red", weight=0];
6291[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6291 -> 6308[label="",style="dashed", color="magenta", weight=3];
6291 -> 6309[label="",style="dashed", color="magenta", weight=3];
5063[label="gcd2 (primEqInt (Neg vuz124) (fromInt (Pos Zero))) (Neg vuz124) (Pos vuz28)",fontsize=16,color="burlywood",shape="triangle"];6871[label="vuz124/Succ vuz1240",fontsize=10,color="white",style="solid",shape="box"];5063 -> 6871[label="",style="solid", color="burlywood", weight=9];
6871 -> 5077[label="",style="solid", color="burlywood", weight=3];
6872[label="vuz124/Zero",fontsize=10,color="white",style="solid",shape="box"];5063 -> 6872[label="",style="solid", color="burlywood", weight=9];
6872 -> 5078[label="",style="solid", color="burlywood", weight=3];
6292 -> 305[label="",style="dashed", color="red", weight=0];
6292[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6292 -> 6310[label="",style="dashed", color="magenta", weight=3];
6292 -> 6311[label="",style="dashed", color="magenta", weight=3];
6293 -> 305[label="",style="dashed", color="red", weight=0];
6293[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];6293 -> 6312[label="",style="dashed", color="magenta", weight=3];
6293 -> 6313[label="",style="dashed", color="magenta", weight=3];
5106 -> 305[label="",style="dashed", color="red", weight=0];
5106[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5106 -> 5116[label="",style="dashed", color="magenta", weight=3];
5106 -> 5117[label="",style="dashed", color="magenta", weight=3];
5107 -> 305[label="",style="dashed", color="red", weight=0];
5107[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5107 -> 5118[label="",style="dashed", color="magenta", weight=3];
5107 -> 5119[label="",style="dashed", color="magenta", weight=3];
5105[label="gcd2 (primEqInt (Pos vuz127) (fromInt (Pos Zero))) (Pos vuz126) (Neg vuz34)",fontsize=16,color="burlywood",shape="triangle"];6877[label="vuz127/Succ vuz1270",fontsize=10,color="white",style="solid",shape="box"];5105 -> 6877[label="",style="solid", color="burlywood", weight=9];
6877 -> 5120[label="",style="solid", color="burlywood", weight=3];
6878[label="vuz127/Zero",fontsize=10,color="white",style="solid",shape="box"];5105 -> 6878[label="",style="solid", color="burlywood", weight=9];
6878 -> 5121[label="",style="solid", color="burlywood", weight=3];
5110 -> 305[label="",style="dashed", color="red", weight=0];
5110[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5110 -> 5134[label="",style="dashed", color="magenta", weight=3];
5110 -> 5135[label="",style="dashed", color="magenta", weight=3];
5064[label="gcd2 (primEqInt (Neg vuz125) (fromInt (Pos Zero))) (Neg vuz125) (Neg vuz34)",fontsize=16,color="burlywood",shape="triangle"];6880[label="vuz125/Succ vuz1250",fontsize=10,color="white",style="solid",shape="box"];5064 -> 6880[label="",style="solid", color="burlywood", weight=9];
6880 -> 5079[label="",style="solid", color="burlywood", weight=3];
6881[label="vuz125/Zero",fontsize=10,color="white",style="solid",shape="box"];5064 -> 6881[label="",style="solid", color="burlywood", weight=9];
6881 -> 5080[label="",style="solid", color="burlywood", weight=3];
5111 -> 305[label="",style="dashed", color="red", weight=0];
5111[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5111 -> 5136[label="",style="dashed", color="magenta", weight=3];
5111 -> 5137[label="",style="dashed", color="magenta", weight=3];
5108 -> 305[label="",style="dashed", color="red", weight=0];
5108[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5108 -> 5122[label="",style="dashed", color="magenta", weight=3];
5108 -> 5123[label="",style="dashed", color="magenta", weight=3];
5109 -> 305[label="",style="dashed", color="red", weight=0];
5109[label="primMulNat vuz400 vuz3000",fontsize=16,color="magenta"];5109 -> 5124[label="",style="dashed", color="magenta", weight=3];
5109 -> 5125[label="",style="dashed", color="magenta", weight=3];
5112 -> 5710[label="",style="dashed", color="red", weight=0];
5112[label="primDivNatS0 (Succ vuz12200) (Succ vuz123000) (primGEqNatS vuz12200 vuz123000)",fontsize=16,color="magenta"];5112 -> 5711[label="",style="dashed", color="magenta", weight=3];
5112 -> 5712[label="",style="dashed", color="magenta", weight=3];
5112 -> 5713[label="",style="dashed", color="magenta", weight=3];
5112 -> 5714[label="",style="dashed", color="magenta", weight=3];
5113[label="primDivNatS0 (Succ vuz12200) Zero True",fontsize=16,color="black",shape="box"];5113 -> 5140[label="",style="solid", color="black", weight=3];
5114[label="primDivNatS0 Zero (Succ vuz123000) False",fontsize=16,color="black",shape="box"];5114 -> 5141[label="",style="solid", color="black", weight=3];
5115[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];5115 -> 5142[label="",style="solid", color="black", weight=3];
6251 -> 5105[label="",style="dashed", color="red", weight=0];
6251[label="gcd2 (primEqInt (Pos vuz168) (fromInt (Pos Zero))) (Pos vuz168) (Neg vuz34)",fontsize=16,color="magenta"];6251 -> 6265[label="",style="dashed", color="magenta", weight=3];
6251 -> 6266[label="",style="dashed", color="magenta", weight=3];
6306[label="vuz400",fontsize=16,color="green",shape="box"];6307[label="vuz3000",fontsize=16,color="green",shape="box"];6263[label="gcd2 (primEqInt (Pos (Succ vuz1670)) (fromInt (Pos Zero))) (Pos (Succ vuz1670)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6263 -> 6279[label="",style="solid", color="black", weight=3];
6264[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];6264 -> 6280[label="",style="solid", color="black", weight=3];
6308[label="vuz400",fontsize=16,color="green",shape="box"];6309[label="vuz3000",fontsize=16,color="green",shape="box"];5077[label="gcd2 (primEqInt (Neg (Succ vuz1240)) (fromInt (Pos Zero))) (Neg (Succ vuz1240)) (Pos vuz28)",fontsize=16,color="black",shape="box"];5077 -> 5096[label="",style="solid", color="black", weight=3];
5078[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];5078 -> 5097[label="",style="solid", color="black", weight=3];
6310[label="vuz400",fontsize=16,color="green",shape="box"];6311[label="vuz3000",fontsize=16,color="green",shape="box"];6312[label="vuz400",fontsize=16,color="green",shape="box"];6313[label="vuz3000",fontsize=16,color="green",shape="box"];5116[label="vuz400",fontsize=16,color="green",shape="box"];5117[label="vuz3000",fontsize=16,color="green",shape="box"];5118[label="vuz400",fontsize=16,color="green",shape="box"];5119[label="vuz3000",fontsize=16,color="green",shape="box"];5120[label="gcd2 (primEqInt (Pos (Succ vuz1270)) (fromInt (Pos Zero))) (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5120 -> 5143[label="",style="solid", color="black", weight=3];
5121[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5121 -> 5144[label="",style="solid", color="black", weight=3];
5134[label="vuz400",fontsize=16,color="green",shape="box"];5135[label="vuz3000",fontsize=16,color="green",shape="box"];5079[label="gcd2 (primEqInt (Neg (Succ vuz1250)) (fromInt (Pos Zero))) (Neg (Succ vuz1250)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5079 -> 5098[label="",style="solid", color="black", weight=3];
5080[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz34)",fontsize=16,color="black",shape="box"];5080 -> 5099[label="",style="solid", color="black", weight=3];
5136[label="vuz400",fontsize=16,color="green",shape="box"];5137[label="vuz3000",fontsize=16,color="green",shape="box"];5122[label="vuz400",fontsize=16,color="green",shape="box"];5123[label="vuz3000",fontsize=16,color="green",shape="box"];5124[label="vuz400",fontsize=16,color="green",shape="box"];5125[label="vuz3000",fontsize=16,color="green",shape="box"];5711[label="vuz123000",fontsize=16,color="green",shape="box"];5712[label="vuz12200",fontsize=16,color="green",shape="box"];5713[label="vuz123000",fontsize=16,color="green",shape="box"];5714[label="vuz12200",fontsize=16,color="green",shape="box"];5710[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS vuz164 vuz165)",fontsize=16,color="burlywood",shape="triangle"];6887[label="vuz164/Succ vuz1640",fontsize=10,color="white",style="solid",shape="box"];5710 -> 6887[label="",style="solid", color="burlywood", weight=9];
6887 -> 5751[label="",style="solid", color="burlywood", weight=3];
6888[label="vuz164/Zero",fontsize=10,color="white",style="solid",shape="box"];5710 -> 6888[label="",style="solid", color="burlywood", weight=9];
6888 -> 5752[label="",style="solid", color="burlywood", weight=3];
5140[label="Succ (primDivNatS (primMinusNatS (Succ vuz12200) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];5140 -> 5157[label="",style="dashed", color="green", weight=3];
5141[label="Zero",fontsize=16,color="green",shape="box"];5142[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];5142 -> 5158[label="",style="dashed", color="green", weight=3];
6265[label="vuz168",fontsize=16,color="green",shape="box"];6266[label="vuz168",fontsize=16,color="green",shape="box"];6279[label="gcd2 (primEqInt (Pos (Succ vuz1670)) (Pos Zero)) (Pos (Succ vuz1670)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6279 -> 6294[label="",style="solid", color="black", weight=3];
6280[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];6280 -> 6295[label="",style="solid", color="black", weight=3];
5096[label="gcd2 (primEqInt (Neg (Succ vuz1240)) (Pos Zero)) (Neg (Succ vuz1240)) (Pos vuz28)",fontsize=16,color="black",shape="box"];5096 -> 5126[label="",style="solid", color="black", weight=3];
5097[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];5097 -> 5127[label="",style="solid", color="black", weight=3];
5143[label="gcd2 (primEqInt (Pos (Succ vuz1270)) (Pos Zero)) (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5143 -> 5159[label="",style="solid", color="black", weight=3];
5144[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5144 -> 5160[label="",style="solid", color="black", weight=3];
5098[label="gcd2 (primEqInt (Neg (Succ vuz1250)) (Pos Zero)) (Neg (Succ vuz1250)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5098 -> 5128[label="",style="solid", color="black", weight=3];
5099[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz34)",fontsize=16,color="black",shape="box"];5099 -> 5129[label="",style="solid", color="black", weight=3];
5751[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS (Succ vuz1640) vuz165)",fontsize=16,color="burlywood",shape="box"];6889[label="vuz165/Succ vuz1650",fontsize=10,color="white",style="solid",shape="box"];5751 -> 6889[label="",style="solid", color="burlywood", weight=9];
6889 -> 6206[label="",style="solid", color="burlywood", weight=3];
6890[label="vuz165/Zero",fontsize=10,color="white",style="solid",shape="box"];5751 -> 6890[label="",style="solid", color="burlywood", weight=9];
6890 -> 6207[label="",style="solid", color="burlywood", weight=3];
5752[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS Zero vuz165)",fontsize=16,color="burlywood",shape="box"];6891[label="vuz165/Succ vuz1650",fontsize=10,color="white",style="solid",shape="box"];5752 -> 6891[label="",style="solid", color="burlywood", weight=9];
6891 -> 6208[label="",style="solid", color="burlywood", weight=3];
6892[label="vuz165/Zero",fontsize=10,color="white",style="solid",shape="box"];5752 -> 6892[label="",style="solid", color="burlywood", weight=9];
6892 -> 6209[label="",style="solid", color="burlywood", weight=3];
5157 -> 5034[label="",style="dashed", color="red", weight=0];
5157[label="primDivNatS (primMinusNatS (Succ vuz12200) Zero) (Succ Zero)",fontsize=16,color="magenta"];5157 -> 5173[label="",style="dashed", color="magenta", weight=3];
5157 -> 5174[label="",style="dashed", color="magenta", weight=3];
5158 -> 5034[label="",style="dashed", color="red", weight=0];
5158[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];5158 -> 5175[label="",style="dashed", color="magenta", weight=3];
5158 -> 5176[label="",style="dashed", color="magenta", weight=3];
6294[label="gcd2 False (Pos (Succ vuz1670)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6294 -> 6314[label="",style="solid", color="black", weight=3];
6295[label="gcd2 True (Pos Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];6295 -> 6315[label="",style="solid", color="black", weight=3];
5126[label="gcd2 False (Neg (Succ vuz1240)) (Pos vuz28)",fontsize=16,color="black",shape="box"];5126 -> 5145[label="",style="solid", color="black", weight=3];
5127[label="gcd2 True (Neg Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];5127 -> 5146[label="",style="solid", color="black", weight=3];
5159[label="gcd2 False (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5159 -> 5177[label="",style="solid", color="black", weight=3];
5160[label="gcd2 True (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5160 -> 5178[label="",style="solid", color="black", weight=3];
5128[label="gcd2 False (Neg (Succ vuz1250)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5128 -> 5147[label="",style="solid", color="black", weight=3];
5129[label="gcd2 True (Neg Zero) (Neg vuz34)",fontsize=16,color="black",shape="box"];5129 -> 5148[label="",style="solid", color="black", weight=3];
6206[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS (Succ vuz1640) (Succ vuz1650))",fontsize=16,color="black",shape="box"];6206 -> 6221[label="",style="solid", color="black", weight=3];
6207[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS (Succ vuz1640) Zero)",fontsize=16,color="black",shape="box"];6207 -> 6222[label="",style="solid", color="black", weight=3];
6208[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS Zero (Succ vuz1650))",fontsize=16,color="black",shape="box"];6208 -> 6223[label="",style="solid", color="black", weight=3];
6209[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6209 -> 6224[label="",style="solid", color="black", weight=3];
5173[label="primMinusNatS (Succ vuz12200) Zero",fontsize=16,color="black",shape="triangle"];5173 -> 5194[label="",style="solid", color="black", weight=3];
5174[label="Zero",fontsize=16,color="green",shape="box"];5175[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];5175 -> 5195[label="",style="solid", color="black", weight=3];
5176[label="Zero",fontsize=16,color="green",shape="box"];6314[label="gcd0 (Pos (Succ vuz1670)) (Pos vuz28)",fontsize=16,color="black",shape="box"];6314 -> 6330[label="",style="solid", color="black", weight=3];
6315[label="gcd1 (Pos vuz28 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];6315 -> 6331[label="",style="solid", color="black", weight=3];
5145[label="gcd0 (Neg (Succ vuz1240)) (Pos vuz28)",fontsize=16,color="black",shape="box"];5145 -> 5161[label="",style="solid", color="black", weight=3];
5146[label="gcd1 (Pos vuz28 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz28)",fontsize=16,color="black",shape="box"];5146 -> 5162[label="",style="solid", color="black", weight=3];
5177[label="gcd0 (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="triangle"];5177 -> 5196[label="",style="solid", color="black", weight=3];
5178[label="gcd1 (Neg vuz34 == fromInt (Pos Zero)) (Pos vuz126) (Neg vuz34)",fontsize=16,color="black",shape="box"];5178 -> 5197[label="",style="solid", color="black", weight=3];
5147[label="gcd0 (Neg (Succ vuz1250)) (Neg vuz34)",fontsize=16,color="black",shape="box"];5147 -> 5163[label="",style="solid", color="black", weight=3];
5148[label="gcd1 (Neg vuz34 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz34)",fontsize=16,color="black",shape="box"];5148 -> 5164[label="",style="solid", color="black", weight=3];
6221 -> 5710[label="",style="dashed", color="red", weight=0];
6221[label="primDivNatS0 (Succ vuz162) (Succ vuz163) (primGEqNatS vuz1640 vuz1650)",fontsize=16,color="magenta"];6221 -> 6239[label="",style="dashed", color="magenta", weight=3];
6221 -> 6240[label="",style="dashed", color="magenta", weight=3];
6222[label="primDivNatS0 (Succ vuz162) (Succ vuz163) True",fontsize=16,color="black",shape="triangle"];6222 -> 6241[label="",style="solid", color="black", weight=3];
6223[label="primDivNatS0 (Succ vuz162) (Succ vuz163) False",fontsize=16,color="black",shape="box"];6223 -> 6242[label="",style="solid", color="black", weight=3];
6224 -> 6222[label="",style="dashed", color="red", weight=0];
6224[label="primDivNatS0 (Succ vuz162) (Succ vuz163) True",fontsize=16,color="magenta"];5194[label="Succ vuz12200",fontsize=16,color="green",shape="box"];5195[label="Zero",fontsize=16,color="green",shape="box"];6330 -> 6349[label="",style="dashed", color="red", weight=0];
6330[label="gcd0Gcd' (abs (Pos (Succ vuz1670))) (abs (Pos vuz28))",fontsize=16,color="magenta"];6330 -> 6350[label="",style="dashed", color="magenta", weight=3];
6330 -> 6351[label="",style="dashed", color="magenta", weight=3];
6331[label="gcd1 (primEqInt (Pos vuz28) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz28)",fontsize=16,color="burlywood",shape="box"];6898[label="vuz28/Succ vuz280",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6898[label="",style="solid", color="burlywood", weight=9];
6898 -> 6364[label="",style="solid", color="burlywood", weight=3];
6899[label="vuz28/Zero",fontsize=10,color="white",style="solid",shape="box"];6331 -> 6899[label="",style="solid", color="burlywood", weight=9];
6899 -> 6365[label="",style="solid", color="burlywood", weight=3];
5161 -> 6349[label="",style="dashed", color="red", weight=0];
5161[label="gcd0Gcd' (abs (Neg (Succ vuz1240))) (abs (Pos vuz28))",fontsize=16,color="magenta"];5161 -> 6352[label="",style="dashed", color="magenta", weight=3];
5161 -> 6353[label="",style="dashed", color="magenta", weight=3];
5162[label="gcd1 (primEqInt (Pos vuz28) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz28)",fontsize=16,color="burlywood",shape="box"];6901[label="vuz28/Succ vuz280",fontsize=10,color="white",style="solid",shape="box"];5162 -> 6901[label="",style="solid", color="burlywood", weight=9];
6901 -> 5180[label="",style="solid", color="burlywood", weight=3];
6902[label="vuz28/Zero",fontsize=10,color="white",style="solid",shape="box"];5162 -> 6902[label="",style="solid", color="burlywood", weight=9];
6902 -> 5181[label="",style="solid", color="burlywood", weight=3];
5196 -> 6349[label="",style="dashed", color="red", weight=0];
5196[label="gcd0Gcd' (abs (Pos vuz126)) (abs (Neg vuz34))",fontsize=16,color="magenta"];5196 -> 6354[label="",style="dashed", color="magenta", weight=3];
5196 -> 6355[label="",style="dashed", color="magenta", weight=3];
5197[label="gcd1 (primEqInt (Neg vuz34) (fromInt (Pos Zero))) (Pos vuz126) (Neg vuz34)",fontsize=16,color="burlywood",shape="box"];6904[label="vuz34/Succ vuz340",fontsize=10,color="white",style="solid",shape="box"];5197 -> 6904[label="",style="solid", color="burlywood", weight=9];
6904 -> 5216[label="",style="solid", color="burlywood", weight=3];
6905[label="vuz34/Zero",fontsize=10,color="white",style="solid",shape="box"];5197 -> 6905[label="",style="solid", color="burlywood", weight=9];
6905 -> 5217[label="",style="solid", color="burlywood", weight=3];
5163 -> 6349[label="",style="dashed", color="red", weight=0];
5163[label="gcd0Gcd' (abs (Neg (Succ vuz1250))) (abs (Neg vuz34))",fontsize=16,color="magenta"];5163 -> 6356[label="",style="dashed", color="magenta", weight=3];
5163 -> 6357[label="",style="dashed", color="magenta", weight=3];
5164[label="gcd1 (primEqInt (Neg vuz34) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz34)",fontsize=16,color="burlywood",shape="box"];6907[label="vuz34/Succ vuz340",fontsize=10,color="white",style="solid",shape="box"];5164 -> 6907[label="",style="solid", color="burlywood", weight=9];
6907 -> 5183[label="",style="solid", color="burlywood", weight=3];
6908[label="vuz34/Zero",fontsize=10,color="white",style="solid",shape="box"];5164 -> 6908[label="",style="solid", color="burlywood", weight=9];
6908 -> 5184[label="",style="solid", color="burlywood", weight=3];
6239[label="vuz1650",fontsize=16,color="green",shape="box"];6240[label="vuz1640",fontsize=16,color="green",shape="box"];6241[label="Succ (primDivNatS (primMinusNatS (Succ vuz162) (Succ vuz163)) (Succ (Succ vuz163)))",fontsize=16,color="green",shape="box"];6241 -> 6252[label="",style="dashed", color="green", weight=3];
6242[label="Zero",fontsize=16,color="green",shape="box"];6350[label="abs (Pos vuz28)",fontsize=16,color="black",shape="triangle"];6350 -> 6366[label="",style="solid", color="black", weight=3];
6351 -> 6350[label="",style="dashed", color="red", weight=0];
6351[label="abs (Pos (Succ vuz1670))",fontsize=16,color="magenta"];6351 -> 6367[label="",style="dashed", color="magenta", weight=3];
6349[label="gcd0Gcd' vuz170 vuz169",fontsize=16,color="black",shape="triangle"];6349 -> 6368[label="",style="solid", color="black", weight=3];
6364[label="gcd1 (primEqInt (Pos (Succ vuz280)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];6364 -> 6379[label="",style="solid", color="black", weight=3];
6365[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6365 -> 6380[label="",style="solid", color="black", weight=3];
6352 -> 6350[label="",style="dashed", color="red", weight=0];
6352[label="abs (Pos vuz28)",fontsize=16,color="magenta"];6353[label="abs (Neg (Succ vuz1240))",fontsize=16,color="black",shape="box"];6353 -> 6369[label="",style="solid", color="black", weight=3];
5180[label="gcd1 (primEqInt (Pos (Succ vuz280)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];5180 -> 5199[label="",style="solid", color="black", weight=3];
5181[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];5181 -> 5200[label="",style="solid", color="black", weight=3];
6354[label="abs (Neg vuz34)",fontsize=16,color="black",shape="triangle"];6354 -> 6370[label="",style="solid", color="black", weight=3];
6355 -> 6350[label="",style="dashed", color="red", weight=0];
6355[label="abs (Pos vuz126)",fontsize=16,color="magenta"];6355 -> 6371[label="",style="dashed", color="magenta", weight=3];
5216[label="gcd1 (primEqInt (Neg (Succ vuz340)) (fromInt (Pos Zero))) (Pos vuz126) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5216 -> 5240[label="",style="solid", color="black", weight=3];
5217[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz126) (Neg Zero)",fontsize=16,color="black",shape="box"];5217 -> 5241[label="",style="solid", color="black", weight=3];
6356 -> 6354[label="",style="dashed", color="red", weight=0];
6356[label="abs (Neg vuz34)",fontsize=16,color="magenta"];6357 -> 6354[label="",style="dashed", color="red", weight=0];
6357[label="abs (Neg (Succ vuz1250))",fontsize=16,color="magenta"];6357 -> 6372[label="",style="dashed", color="magenta", weight=3];
5183[label="gcd1 (primEqInt (Neg (Succ vuz340)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5183 -> 5202[label="",style="solid", color="black", weight=3];
5184[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];5184 -> 5203[label="",style="solid", color="black", weight=3];
6252 -> 5034[label="",style="dashed", color="red", weight=0];
6252[label="primDivNatS (primMinusNatS (Succ vuz162) (Succ vuz163)) (Succ (Succ vuz163))",fontsize=16,color="magenta"];6252 -> 6267[label="",style="dashed", color="magenta", weight=3];
6252 -> 6268[label="",style="dashed", color="magenta", weight=3];
6366[label="absReal (Pos vuz28)",fontsize=16,color="black",shape="box"];6366 -> 6381[label="",style="solid", color="black", weight=3];
6367[label="Succ vuz1670",fontsize=16,color="green",shape="box"];6368[label="gcd0Gcd'2 vuz170 vuz169",fontsize=16,color="black",shape="box"];6368 -> 6382[label="",style="solid", color="black", weight=3];
6379[label="gcd1 (primEqInt (Pos (Succ vuz280)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];6379 -> 6385[label="",style="solid", color="black", weight=3];
6380[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6380 -> 6386[label="",style="solid", color="black", weight=3];
6369[label="absReal (Neg (Succ vuz1240))",fontsize=16,color="black",shape="box"];6369 -> 6383[label="",style="solid", color="black", weight=3];
5199[label="gcd1 (primEqInt (Pos (Succ vuz280)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];5199 -> 5219[label="",style="solid", color="black", weight=3];
5200[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];5200 -> 5220[label="",style="solid", color="black", weight=3];
6370[label="absReal (Neg vuz34)",fontsize=16,color="black",shape="box"];6370 -> 6384[label="",style="solid", color="black", weight=3];
6371[label="vuz126",fontsize=16,color="green",shape="box"];5240[label="gcd1 (primEqInt (Neg (Succ vuz340)) (Pos Zero)) (Pos vuz126) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5240 -> 5262[label="",style="solid", color="black", weight=3];
5241[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz126) (Neg Zero)",fontsize=16,color="black",shape="box"];5241 -> 5263[label="",style="solid", color="black", weight=3];
6372[label="Succ vuz1250",fontsize=16,color="green",shape="box"];5202[label="gcd1 (primEqInt (Neg (Succ vuz340)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5202 -> 5222[label="",style="solid", color="black", weight=3];
5203[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];5203 -> 5223[label="",style="solid", color="black", weight=3];
6267[label="primMinusNatS (Succ vuz162) (Succ vuz163)",fontsize=16,color="black",shape="box"];6267 -> 6281[label="",style="solid", color="black", weight=3];
6268[label="Succ vuz163",fontsize=16,color="green",shape="box"];6381[label="absReal2 (Pos vuz28)",fontsize=16,color="black",shape="box"];6381 -> 6387[label="",style="solid", color="black", weight=3];
6382[label="gcd0Gcd'1 (vuz169 == fromInt (Pos Zero)) vuz170 vuz169",fontsize=16,color="black",shape="box"];6382 -> 6388[label="",style="solid", color="black", weight=3];
6385[label="gcd1 False (Pos Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];6385 -> 6391[label="",style="solid", color="black", weight=3];
6386[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];6386 -> 6392[label="",style="solid", color="black", weight=3];
6383[label="absReal2 (Neg (Succ vuz1240))",fontsize=16,color="black",shape="box"];6383 -> 6389[label="",style="solid", color="black", weight=3];
5219[label="gcd1 False (Neg Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];5219 -> 5243[label="",style="solid", color="black", weight=3];
5220[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];5220 -> 5244[label="",style="solid", color="black", weight=3];
6384[label="absReal2 (Neg vuz34)",fontsize=16,color="black",shape="box"];6384 -> 6390[label="",style="solid", color="black", weight=3];
5262[label="gcd1 False (Pos vuz126) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5262 -> 5281[label="",style="solid", color="black", weight=3];
5263[label="gcd1 True (Pos vuz126) (Neg Zero)",fontsize=16,color="black",shape="box"];5263 -> 5282[label="",style="solid", color="black", weight=3];
5222[label="gcd1 False (Neg Zero) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5222 -> 5246[label="",style="solid", color="black", weight=3];
5223[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];5223 -> 5247[label="",style="solid", color="black", weight=3];
6281[label="primMinusNatS vuz162 vuz163",fontsize=16,color="burlywood",shape="triangle"];6915[label="vuz162/Succ vuz1620",fontsize=10,color="white",style="solid",shape="box"];6281 -> 6915[label="",style="solid", color="burlywood", weight=9];
6915 -> 6296[label="",style="solid", color="burlywood", weight=3];
6916[label="vuz162/Zero",fontsize=10,color="white",style="solid",shape="box"];6281 -> 6916[label="",style="solid", color="burlywood", weight=9];
6916 -> 6297[label="",style="solid", color="burlywood", weight=3];
6387[label="absReal1 (Pos vuz28) (Pos vuz28 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6387 -> 6393[label="",style="solid", color="black", weight=3];
6388[label="gcd0Gcd'1 (primEqInt vuz169 (fromInt (Pos Zero))) vuz170 vuz169",fontsize=16,color="burlywood",shape="box"];6917[label="vuz169/Pos vuz1690",fontsize=10,color="white",style="solid",shape="box"];6388 -> 6917[label="",style="solid", color="burlywood", weight=9];
6917 -> 6394[label="",style="solid", color="burlywood", weight=3];
6918[label="vuz169/Neg vuz1690",fontsize=10,color="white",style="solid",shape="box"];6388 -> 6918[label="",style="solid", color="burlywood", weight=9];
6918 -> 6395[label="",style="solid", color="burlywood", weight=3];
6391[label="gcd0 (Pos Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];6391 -> 6398[label="",style="solid", color="black", weight=3];
6392 -> 5010[label="",style="dashed", color="red", weight=0];
6392[label="error []",fontsize=16,color="magenta"];6389[label="absReal1 (Neg (Succ vuz1240)) (Neg (Succ vuz1240) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6389 -> 6396[label="",style="solid", color="black", weight=3];
5243[label="gcd0 (Neg Zero) (Pos (Succ vuz280))",fontsize=16,color="black",shape="box"];5243 -> 5265[label="",style="solid", color="black", weight=3];
5244 -> 5010[label="",style="dashed", color="red", weight=0];
5244[label="error []",fontsize=16,color="magenta"];6390[label="absReal1 (Neg vuz34) (Neg vuz34 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6390 -> 6397[label="",style="solid", color="black", weight=3];
5281 -> 5177[label="",style="dashed", color="red", weight=0];
5281[label="gcd0 (Pos vuz126) (Neg (Succ vuz340))",fontsize=16,color="magenta"];5281 -> 5305[label="",style="dashed", color="magenta", weight=3];
5282 -> 5010[label="",style="dashed", color="red", weight=0];
5282[label="error []",fontsize=16,color="magenta"];5246[label="gcd0 (Neg Zero) (Neg (Succ vuz340))",fontsize=16,color="black",shape="box"];5246 -> 5267[label="",style="solid", color="black", weight=3];
5247 -> 5010[label="",style="dashed", color="red", weight=0];
5247[label="error []",fontsize=16,color="magenta"];6296[label="primMinusNatS (Succ vuz1620) vuz163",fontsize=16,color="burlywood",shape="box"];6924[label="vuz163/Succ vuz1630",fontsize=10,color="white",style="solid",shape="box"];6296 -> 6924[label="",style="solid", color="burlywood", weight=9];
6924 -> 6316[label="",style="solid", color="burlywood", weight=3];
6925[label="vuz163/Zero",fontsize=10,color="white",style="solid",shape="box"];6296 -> 6925[label="",style="solid", color="burlywood", weight=9];
6925 -> 6317[label="",style="solid", color="burlywood", weight=3];
6297[label="primMinusNatS Zero vuz163",fontsize=16,color="burlywood",shape="box"];6926[label="vuz163/Succ vuz1630",fontsize=10,color="white",style="solid",shape="box"];6297 -> 6926[label="",style="solid", color="burlywood", weight=9];
6926 -> 6318[label="",style="solid", color="burlywood", weight=3];
6927[label="vuz163/Zero",fontsize=10,color="white",style="solid",shape="box"];6297 -> 6927[label="",style="solid", color="burlywood", weight=9];
6927 -> 6319[label="",style="solid", color="burlywood", weight=3];
6393[label="absReal1 (Pos vuz28) (compare (Pos vuz28) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6393 -> 6399[label="",style="solid", color="black", weight=3];
6394[label="gcd0Gcd'1 (primEqInt (Pos vuz1690) (fromInt (Pos Zero))) vuz170 (Pos vuz1690)",fontsize=16,color="burlywood",shape="box"];6928[label="vuz1690/Succ vuz16900",fontsize=10,color="white",style="solid",shape="box"];6394 -> 6928[label="",style="solid", color="burlywood", weight=9];
6928 -> 6400[label="",style="solid", color="burlywood", weight=3];
6929[label="vuz1690/Zero",fontsize=10,color="white",style="solid",shape="box"];6394 -> 6929[label="",style="solid", color="burlywood", weight=9];
6929 -> 6401[label="",style="solid", color="burlywood", weight=3];
6395[label="gcd0Gcd'1 (primEqInt (Neg vuz1690) (fromInt (Pos Zero))) vuz170 (Neg vuz1690)",fontsize=16,color="burlywood",shape="box"];6930[label="vuz1690/Succ vuz16900",fontsize=10,color="white",style="solid",shape="box"];6395 -> 6930[label="",style="solid", color="burlywood", weight=9];
6930 -> 6402[label="",style="solid", color="burlywood", weight=3];
6931[label="vuz1690/Zero",fontsize=10,color="white",style="solid",shape="box"];6395 -> 6931[label="",style="solid", color="burlywood", weight=9];
6931 -> 6403[label="",style="solid", color="burlywood", weight=3];
6398 -> 6349[label="",style="dashed", color="red", weight=0];
6398[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz280)))",fontsize=16,color="magenta"];6398 -> 6406[label="",style="dashed", color="magenta", weight=3];
6398 -> 6407[label="",style="dashed", color="magenta", weight=3];
6396[label="absReal1 (Neg (Succ vuz1240)) (compare (Neg (Succ vuz1240)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6396 -> 6404[label="",style="solid", color="black", weight=3];
5265 -> 6349[label="",style="dashed", color="red", weight=0];
5265[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz280)))",fontsize=16,color="magenta"];5265 -> 6358[label="",style="dashed", color="magenta", weight=3];
5265 -> 6359[label="",style="dashed", color="magenta", weight=3];
6397[label="absReal1 (Neg vuz34) (compare (Neg vuz34) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];6397 -> 6405[label="",style="solid", color="black", weight=3];
5305[label="Succ vuz340",fontsize=16,color="green",shape="box"];5267 -> 6349[label="",style="dashed", color="red", weight=0];
5267[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz340)))",fontsize=16,color="magenta"];5267 -> 6360[label="",style="dashed", color="magenta", weight=3];
5267 -> 6361[label="",style="dashed", color="magenta", weight=3];
6316[label="primMinusNatS (Succ vuz1620) (Succ vuz1630)",fontsize=16,color="black",shape="box"];6316 -> 6332[label="",style="solid", color="black", weight=3];
6317[label="primMinusNatS (Succ vuz1620) Zero",fontsize=16,color="black",shape="box"];6317 -> 6333[label="",style="solid", color="black", weight=3];
6318[label="primMinusNatS Zero (Succ vuz1630)",fontsize=16,color="black",shape="box"];6318 -> 6334[label="",style="solid", color="black", weight=3];
6319[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];6319 -> 6335[label="",style="solid", color="black", weight=3];
6399[label="absReal1 (Pos vuz28) (not (compare (Pos vuz28) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6399 -> 6408[label="",style="solid", color="black", weight=3];
6400[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz16900)) (fromInt (Pos Zero))) vuz170 (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6400 -> 6409[label="",style="solid", color="black", weight=3];
6401[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz170 (Pos Zero)",fontsize=16,color="black",shape="box"];6401 -> 6410[label="",style="solid", color="black", weight=3];
6402[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz16900)) (fromInt (Pos Zero))) vuz170 (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6402 -> 6411[label="",style="solid", color="black", weight=3];
6403[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz170 (Neg Zero)",fontsize=16,color="black",shape="box"];6403 -> 6412[label="",style="solid", color="black", weight=3];
6406 -> 6350[label="",style="dashed", color="red", weight=0];
6406[label="abs (Pos (Succ vuz280))",fontsize=16,color="magenta"];6406 -> 6415[label="",style="dashed", color="magenta", weight=3];
6407 -> 6350[label="",style="dashed", color="red", weight=0];
6407[label="abs (Pos Zero)",fontsize=16,color="magenta"];6407 -> 6416[label="",style="dashed", color="magenta", weight=3];
6404[label="absReal1 (Neg (Succ vuz1240)) (not (compare (Neg (Succ vuz1240)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6404 -> 6413[label="",style="solid", color="black", weight=3];
6358 -> 6350[label="",style="dashed", color="red", weight=0];
6358[label="abs (Pos (Succ vuz280))",fontsize=16,color="magenta"];6358 -> 6373[label="",style="dashed", color="magenta", weight=3];
6359 -> 6354[label="",style="dashed", color="red", weight=0];
6359[label="abs (Neg Zero)",fontsize=16,color="magenta"];6359 -> 6374[label="",style="dashed", color="magenta", weight=3];
6405[label="absReal1 (Neg vuz34) (not (compare (Neg vuz34) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6405 -> 6414[label="",style="solid", color="black", weight=3];
6360 -> 6354[label="",style="dashed", color="red", weight=0];
6360[label="abs (Neg (Succ vuz340))",fontsize=16,color="magenta"];6360 -> 6375[label="",style="dashed", color="magenta", weight=3];
6361 -> 6354[label="",style="dashed", color="red", weight=0];
6361[label="abs (Neg Zero)",fontsize=16,color="magenta"];6361 -> 6376[label="",style="dashed", color="magenta", weight=3];
6332 -> 6281[label="",style="dashed", color="red", weight=0];
6332[label="primMinusNatS vuz1620 vuz1630",fontsize=16,color="magenta"];6332 -> 6377[label="",style="dashed", color="magenta", weight=3];
6332 -> 6378[label="",style="dashed", color="magenta", weight=3];
6333[label="Succ vuz1620",fontsize=16,color="green",shape="box"];6334[label="Zero",fontsize=16,color="green",shape="box"];6335[label="Zero",fontsize=16,color="green",shape="box"];6408[label="absReal1 (Pos vuz28) (not (primCmpInt (Pos vuz28) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6942[label="vuz28/Succ vuz280",fontsize=10,color="white",style="solid",shape="box"];6408 -> 6942[label="",style="solid", color="burlywood", weight=9];
6942 -> 6417[label="",style="solid", color="burlywood", weight=3];
6943[label="vuz28/Zero",fontsize=10,color="white",style="solid",shape="box"];6408 -> 6943[label="",style="solid", color="burlywood", weight=9];
6943 -> 6418[label="",style="solid", color="burlywood", weight=3];
6409[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz16900)) (Pos Zero)) vuz170 (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6409 -> 6419[label="",style="solid", color="black", weight=3];
6410[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz170 (Pos Zero)",fontsize=16,color="black",shape="box"];6410 -> 6420[label="",style="solid", color="black", weight=3];
6411[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz16900)) (Pos Zero)) vuz170 (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6411 -> 6421[label="",style="solid", color="black", weight=3];
6412[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz170 (Neg Zero)",fontsize=16,color="black",shape="box"];6412 -> 6422[label="",style="solid", color="black", weight=3];
6415[label="Succ vuz280",fontsize=16,color="green",shape="box"];6416[label="Zero",fontsize=16,color="green",shape="box"];6413[label="absReal1 (Neg (Succ vuz1240)) (not (primCmpInt (Neg (Succ vuz1240)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6413 -> 6423[label="",style="solid", color="black", weight=3];
6373[label="Succ vuz280",fontsize=16,color="green",shape="box"];6374[label="Zero",fontsize=16,color="green",shape="box"];6414[label="absReal1 (Neg vuz34) (not (primCmpInt (Neg vuz34) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];6944[label="vuz34/Succ vuz340",fontsize=10,color="white",style="solid",shape="box"];6414 -> 6944[label="",style="solid", color="burlywood", weight=9];
6944 -> 6424[label="",style="solid", color="burlywood", weight=3];
6945[label="vuz34/Zero",fontsize=10,color="white",style="solid",shape="box"];6414 -> 6945[label="",style="solid", color="burlywood", weight=9];
6945 -> 6425[label="",style="solid", color="burlywood", weight=3];
6375[label="Succ vuz340",fontsize=16,color="green",shape="box"];6376[label="Zero",fontsize=16,color="green",shape="box"];6377[label="vuz1630",fontsize=16,color="green",shape="box"];6378[label="vuz1620",fontsize=16,color="green",shape="box"];6417[label="absReal1 (Pos (Succ vuz280)) (not (primCmpInt (Pos (Succ vuz280)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6417 -> 6426[label="",style="solid", color="black", weight=3];
6418[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6418 -> 6427[label="",style="solid", color="black", weight=3];
6419[label="gcd0Gcd'1 False vuz170 (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6419 -> 6428[label="",style="solid", color="black", weight=3];
6420[label="gcd0Gcd'1 True vuz170 (Pos Zero)",fontsize=16,color="black",shape="box"];6420 -> 6429[label="",style="solid", color="black", weight=3];
6421[label="gcd0Gcd'1 False vuz170 (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6421 -> 6430[label="",style="solid", color="black", weight=3];
6422[label="gcd0Gcd'1 True vuz170 (Neg Zero)",fontsize=16,color="black",shape="box"];6422 -> 6431[label="",style="solid", color="black", weight=3];
6423[label="absReal1 (Neg (Succ vuz1240)) (not (primCmpInt (Neg (Succ vuz1240)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];6423 -> 6432[label="",style="solid", color="black", weight=3];
6424[label="absReal1 (Neg (Succ vuz340)) (not (primCmpInt (Neg (Succ vuz340)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6424 -> 6433[label="",style="solid", color="black", weight=3];
6425[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];6425 -> 6434[label="",style="solid", color="black", weight=3];
6426[label="absReal1 (Pos (Succ vuz280)) (not (primCmpInt (Pos (Succ vuz280)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6426 -> 6435[label="",style="solid", color="black", weight=3];
6427[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6427 -> 6436[label="",style="solid", color="black", weight=3];
6428[label="gcd0Gcd'0 vuz170 (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6428 -> 6437[label="",style="solid", color="black", weight=3];
6429[label="vuz170",fontsize=16,color="green",shape="box"];6430[label="gcd0Gcd'0 vuz170 (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6430 -> 6438[label="",style="solid", color="black", weight=3];
6431[label="vuz170",fontsize=16,color="green",shape="box"];6432[label="absReal1 (Neg (Succ vuz1240)) (not (LT == LT))",fontsize=16,color="black",shape="box"];6432 -> 6439[label="",style="solid", color="black", weight=3];
6433 -> 6423[label="",style="dashed", color="red", weight=0];
6433[label="absReal1 (Neg (Succ vuz340)) (not (primCmpInt (Neg (Succ vuz340)) (Pos Zero) == LT))",fontsize=16,color="magenta"];6433 -> 6440[label="",style="dashed", color="magenta", weight=3];
6434[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];6434 -> 6441[label="",style="solid", color="black", weight=3];
6435[label="absReal1 (Pos (Succ vuz280)) (not (primCmpNat (Succ vuz280) Zero == LT))",fontsize=16,color="black",shape="box"];6435 -> 6442[label="",style="solid", color="black", weight=3];
6436[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6436 -> 6443[label="",style="solid", color="black", weight=3];
6437 -> 6349[label="",style="dashed", color="red", weight=0];
6437[label="gcd0Gcd' (Pos (Succ vuz16900)) (vuz170 `rem` Pos (Succ vuz16900))",fontsize=16,color="magenta"];6437 -> 6444[label="",style="dashed", color="magenta", weight=3];
6437 -> 6445[label="",style="dashed", color="magenta", weight=3];
6438 -> 6349[label="",style="dashed", color="red", weight=0];
6438[label="gcd0Gcd' (Neg (Succ vuz16900)) (vuz170 `rem` Neg (Succ vuz16900))",fontsize=16,color="magenta"];6438 -> 6446[label="",style="dashed", color="magenta", weight=3];
6438 -> 6447[label="",style="dashed", color="magenta", weight=3];
6439[label="absReal1 (Neg (Succ vuz1240)) (not True)",fontsize=16,color="black",shape="box"];6439 -> 6448[label="",style="solid", color="black", weight=3];
6440[label="vuz340",fontsize=16,color="green",shape="box"];6441[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];6441 -> 6449[label="",style="solid", color="black", weight=3];
6442[label="absReal1 (Pos (Succ vuz280)) (not (GT == LT))",fontsize=16,color="black",shape="box"];6442 -> 6450[label="",style="solid", color="black", weight=3];
6443[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];6443 -> 6451[label="",style="solid", color="black", weight=3];
6444[label="vuz170 `rem` Pos (Succ vuz16900)",fontsize=16,color="black",shape="box"];6444 -> 6452[label="",style="solid", color="black", weight=3];
6445[label="Pos (Succ vuz16900)",fontsize=16,color="green",shape="box"];6446[label="vuz170 `rem` Neg (Succ vuz16900)",fontsize=16,color="black",shape="box"];6446 -> 6453[label="",style="solid", color="black", weight=3];
6447[label="Neg (Succ vuz16900)",fontsize=16,color="green",shape="box"];6448[label="absReal1 (Neg (Succ vuz1240)) False",fontsize=16,color="black",shape="box"];6448 -> 6454[label="",style="solid", color="black", weight=3];
6449[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];6449 -> 6455[label="",style="solid", color="black", weight=3];
6450[label="absReal1 (Pos (Succ vuz280)) (not False)",fontsize=16,color="black",shape="box"];6450 -> 6456[label="",style="solid", color="black", weight=3];
6451[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];6451 -> 6457[label="",style="solid", color="black", weight=3];
6452[label="primRemInt vuz170 (Pos (Succ vuz16900))",fontsize=16,color="burlywood",shape="box"];6949[label="vuz170/Pos vuz1700",fontsize=10,color="white",style="solid",shape="box"];6452 -> 6949[label="",style="solid", color="burlywood", weight=9];
6949 -> 6458[label="",style="solid", color="burlywood", weight=3];
6950[label="vuz170/Neg vuz1700",fontsize=10,color="white",style="solid",shape="box"];6452 -> 6950[label="",style="solid", color="burlywood", weight=9];
6950 -> 6459[label="",style="solid", color="burlywood", weight=3];
6453[label="primRemInt vuz170 (Neg (Succ vuz16900))",fontsize=16,color="burlywood",shape="box"];6951[label="vuz170/Pos vuz1700",fontsize=10,color="white",style="solid",shape="box"];6453 -> 6951[label="",style="solid", color="burlywood", weight=9];
6951 -> 6460[label="",style="solid", color="burlywood", weight=3];
6952[label="vuz170/Neg vuz1700",fontsize=10,color="white",style="solid",shape="box"];6453 -> 6952[label="",style="solid", color="burlywood", weight=9];
6952 -> 6461[label="",style="solid", color="burlywood", weight=3];
6454[label="absReal0 (Neg (Succ vuz1240)) otherwise",fontsize=16,color="black",shape="box"];6454 -> 6462[label="",style="solid", color="black", weight=3];
6455[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];6455 -> 6463[label="",style="solid", color="black", weight=3];
6456[label="absReal1 (Pos (Succ vuz280)) True",fontsize=16,color="black",shape="box"];6456 -> 6464[label="",style="solid", color="black", weight=3];
6457[label="Pos Zero",fontsize=16,color="green",shape="box"];6458[label="primRemInt (Pos vuz1700) (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6458 -> 6465[label="",style="solid", color="black", weight=3];
6459[label="primRemInt (Neg vuz1700) (Pos (Succ vuz16900))",fontsize=16,color="black",shape="box"];6459 -> 6466[label="",style="solid", color="black", weight=3];
6460[label="primRemInt (Pos vuz1700) (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6460 -> 6467[label="",style="solid", color="black", weight=3];
6461[label="primRemInt (Neg vuz1700) (Neg (Succ vuz16900))",fontsize=16,color="black",shape="box"];6461 -> 6468[label="",style="solid", color="black", weight=3];
6462[label="absReal0 (Neg (Succ vuz1240)) True",fontsize=16,color="black",shape="box"];6462 -> 6469[label="",style="solid", color="black", weight=3];
6463[label="Neg Zero",fontsize=16,color="green",shape="box"];6464[label="Pos (Succ vuz280)",fontsize=16,color="green",shape="box"];6465[label="Pos (primModNatS vuz1700 (Succ vuz16900))",fontsize=16,color="green",shape="box"];6465 -> 6470[label="",style="dashed", color="green", weight=3];
6466[label="Neg (primModNatS vuz1700 (Succ vuz16900))",fontsize=16,color="green",shape="box"];6466 -> 6471[label="",style="dashed", color="green", weight=3];
6467[label="Pos (primModNatS vuz1700 (Succ vuz16900))",fontsize=16,color="green",shape="box"];6467 -> 6472[label="",style="dashed", color="green", weight=3];
6468[label="Neg (primModNatS vuz1700 (Succ vuz16900))",fontsize=16,color="green",shape="box"];6468 -> 6473[label="",style="dashed", color="green", weight=3];
6469[label="`negate` Neg (Succ vuz1240)",fontsize=16,color="black",shape="box"];6469 -> 6474[label="",style="solid", color="black", weight=3];
6470[label="primModNatS vuz1700 (Succ vuz16900)",fontsize=16,color="burlywood",shape="triangle"];6953[label="vuz1700/Succ vuz17000",fontsize=10,color="white",style="solid",shape="box"];6470 -> 6953[label="",style="solid", color="burlywood", weight=9];
6953 -> 6475[label="",style="solid", color="burlywood", weight=3];
6954[label="vuz1700/Zero",fontsize=10,color="white",style="solid",shape="box"];6470 -> 6954[label="",style="solid", color="burlywood", weight=9];
6954 -> 6476[label="",style="solid", color="burlywood", weight=3];
6471 -> 6470[label="",style="dashed", color="red", weight=0];
6471[label="primModNatS vuz1700 (Succ vuz16900)",fontsize=16,color="magenta"];6471 -> 6477[label="",style="dashed", color="magenta", weight=3];
6472 -> 6470[label="",style="dashed", color="red", weight=0];
6472[label="primModNatS vuz1700 (Succ vuz16900)",fontsize=16,color="magenta"];6472 -> 6478[label="",style="dashed", color="magenta", weight=3];
6473 -> 6470[label="",style="dashed", color="red", weight=0];
6473[label="primModNatS vuz1700 (Succ vuz16900)",fontsize=16,color="magenta"];6473 -> 6479[label="",style="dashed", color="magenta", weight=3];
6473 -> 6480[label="",style="dashed", color="magenta", weight=3];
6474[label="primNegInt (Neg (Succ vuz1240))",fontsize=16,color="black",shape="box"];6474 -> 6481[label="",style="solid", color="black", weight=3];
6475[label="primModNatS (Succ vuz17000) (Succ vuz16900)",fontsize=16,color="black",shape="box"];6475 -> 6482[label="",style="solid", color="black", weight=3];
6476[label="primModNatS Zero (Succ vuz16900)",fontsize=16,color="black",shape="box"];6476 -> 6483[label="",style="solid", color="black", weight=3];
6477[label="vuz1700",fontsize=16,color="green",shape="box"];6478[label="vuz16900",fontsize=16,color="green",shape="box"];6479[label="vuz16900",fontsize=16,color="green",shape="box"];6480[label="vuz1700",fontsize=16,color="green",shape="box"];6481[label="Pos (Succ vuz1240)",fontsize=16,color="green",shape="box"];6482[label="primModNatS0 vuz17000 vuz16900 (primGEqNatS vuz17000 vuz16900)",fontsize=16,color="burlywood",shape="box"];6958[label="vuz17000/Succ vuz170000",fontsize=10,color="white",style="solid",shape="box"];6482 -> 6958[label="",style="solid", color="burlywood", weight=9];
6958 -> 6484[label="",style="solid", color="burlywood", weight=3];
6959[label="vuz17000/Zero",fontsize=10,color="white",style="solid",shape="box"];6482 -> 6959[label="",style="solid", color="burlywood", weight=9];
6959 -> 6485[label="",style="solid", color="burlywood", weight=3];
6483[label="Zero",fontsize=16,color="green",shape="box"];6484[label="primModNatS0 (Succ vuz170000) vuz16900 (primGEqNatS (Succ vuz170000) vuz16900)",fontsize=16,color="burlywood",shape="box"];6960[label="vuz16900/Succ vuz169000",fontsize=10,color="white",style="solid",shape="box"];6484 -> 6960[label="",style="solid", color="burlywood", weight=9];
6960 -> 6486[label="",style="solid", color="burlywood", weight=3];
6961[label="vuz16900/Zero",fontsize=10,color="white",style="solid",shape="box"];6484 -> 6961[label="",style="solid", color="burlywood", weight=9];
6961 -> 6487[label="",style="solid", color="burlywood", weight=3];
6485[label="primModNatS0 Zero vuz16900 (primGEqNatS Zero vuz16900)",fontsize=16,color="burlywood",shape="box"];6962[label="vuz16900/Succ vuz169000",fontsize=10,color="white",style="solid",shape="box"];6485 -> 6962[label="",style="solid", color="burlywood", weight=9];
6962 -> 6488[label="",style="solid", color="burlywood", weight=3];
6963[label="vuz16900/Zero",fontsize=10,color="white",style="solid",shape="box"];6485 -> 6963[label="",style="solid", color="burlywood", weight=9];
6963 -> 6489[label="",style="solid", color="burlywood", weight=3];
6486[label="primModNatS0 (Succ vuz170000) (Succ vuz169000) (primGEqNatS (Succ vuz170000) (Succ vuz169000))",fontsize=16,color="black",shape="box"];6486 -> 6490[label="",style="solid", color="black", weight=3];
6487[label="primModNatS0 (Succ vuz170000) Zero (primGEqNatS (Succ vuz170000) Zero)",fontsize=16,color="black",shape="box"];6487 -> 6491[label="",style="solid", color="black", weight=3];
6488[label="primModNatS0 Zero (Succ vuz169000) (primGEqNatS Zero (Succ vuz169000))",fontsize=16,color="black",shape="box"];6488 -> 6492[label="",style="solid", color="black", weight=3];
6489[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6489 -> 6493[label="",style="solid", color="black", weight=3];
6490 -> 6652[label="",style="dashed", color="red", weight=0];
6490[label="primModNatS0 (Succ vuz170000) (Succ vuz169000) (primGEqNatS vuz170000 vuz169000)",fontsize=16,color="magenta"];6490 -> 6653[label="",style="dashed", color="magenta", weight=3];
6490 -> 6654[label="",style="dashed", color="magenta", weight=3];
6490 -> 6655[label="",style="dashed", color="magenta", weight=3];
6490 -> 6656[label="",style="dashed", color="magenta", weight=3];
6491[label="primModNatS0 (Succ vuz170000) Zero True",fontsize=16,color="black",shape="box"];6491 -> 6496[label="",style="solid", color="black", weight=3];
6492[label="primModNatS0 Zero (Succ vuz169000) False",fontsize=16,color="black",shape="box"];6492 -> 6497[label="",style="solid", color="black", weight=3];
6493[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];6493 -> 6498[label="",style="solid", color="black", weight=3];
6653[label="vuz169000",fontsize=16,color="green",shape="box"];6654[label="vuz169000",fontsize=16,color="green",shape="box"];6655[label="vuz170000",fontsize=16,color="green",shape="box"];6656[label="vuz170000",fontsize=16,color="green",shape="box"];6652[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS vuz189 vuz190)",fontsize=16,color="burlywood",shape="triangle"];6965[label="vuz189/Succ vuz1890",fontsize=10,color="white",style="solid",shape="box"];6652 -> 6965[label="",style="solid", color="burlywood", weight=9];
6965 -> 6685[label="",style="solid", color="burlywood", weight=3];
6966[label="vuz189/Zero",fontsize=10,color="white",style="solid",shape="box"];6652 -> 6966[label="",style="solid", color="burlywood", weight=9];
6966 -> 6686[label="",style="solid", color="burlywood", weight=3];
6496 -> 6470[label="",style="dashed", color="red", weight=0];
6496[label="primModNatS (primMinusNatS (Succ vuz170000) Zero) (Succ Zero)",fontsize=16,color="magenta"];6496 -> 6503[label="",style="dashed", color="magenta", weight=3];
6496 -> 6504[label="",style="dashed", color="magenta", weight=3];
6497[label="Succ Zero",fontsize=16,color="green",shape="box"];6498 -> 6470[label="",style="dashed", color="red", weight=0];
6498[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];6498 -> 6505[label="",style="dashed", color="magenta", weight=3];
6498 -> 6506[label="",style="dashed", color="magenta", weight=3];
6685[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS (Succ vuz1890) vuz190)",fontsize=16,color="burlywood",shape="box"];6969[label="vuz190/Succ vuz1900",fontsize=10,color="white",style="solid",shape="box"];6685 -> 6969[label="",style="solid", color="burlywood", weight=9];
6969 -> 6687[label="",style="solid", color="burlywood", weight=3];
6970[label="vuz190/Zero",fontsize=10,color="white",style="solid",shape="box"];6685 -> 6970[label="",style="solid", color="burlywood", weight=9];
6970 -> 6688[label="",style="solid", color="burlywood", weight=3];
6686[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS Zero vuz190)",fontsize=16,color="burlywood",shape="box"];6971[label="vuz190/Succ vuz1900",fontsize=10,color="white",style="solid",shape="box"];6686 -> 6971[label="",style="solid", color="burlywood", weight=9];
6971 -> 6689[label="",style="solid", color="burlywood", weight=3];
6972[label="vuz190/Zero",fontsize=10,color="white",style="solid",shape="box"];6686 -> 6972[label="",style="solid", color="burlywood", weight=9];
6972 -> 6690[label="",style="solid", color="burlywood", weight=3];
6503[label="Zero",fontsize=16,color="green",shape="box"];6504 -> 6281[label="",style="dashed", color="red", weight=0];
6504[label="primMinusNatS (Succ vuz170000) Zero",fontsize=16,color="magenta"];6504 -> 6511[label="",style="dashed", color="magenta", weight=3];
6504 -> 6512[label="",style="dashed", color="magenta", weight=3];
6505[label="Zero",fontsize=16,color="green",shape="box"];6506 -> 6281[label="",style="dashed", color="red", weight=0];
6506[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];6506 -> 6513[label="",style="dashed", color="magenta", weight=3];
6506 -> 6514[label="",style="dashed", color="magenta", weight=3];
6687[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS (Succ vuz1890) (Succ vuz1900))",fontsize=16,color="black",shape="box"];6687 -> 6691[label="",style="solid", color="black", weight=3];
6688[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS (Succ vuz1890) Zero)",fontsize=16,color="black",shape="box"];6688 -> 6692[label="",style="solid", color="black", weight=3];
6689[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS Zero (Succ vuz1900))",fontsize=16,color="black",shape="box"];6689 -> 6693[label="",style="solid", color="black", weight=3];
6690[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];6690 -> 6694[label="",style="solid", color="black", weight=3];
6511[label="Zero",fontsize=16,color="green",shape="box"];6512[label="Succ vuz170000",fontsize=16,color="green",shape="box"];6513[label="Zero",fontsize=16,color="green",shape="box"];6514[label="Zero",fontsize=16,color="green",shape="box"];6691 -> 6652[label="",style="dashed", color="red", weight=0];
6691[label="primModNatS0 (Succ vuz187) (Succ vuz188) (primGEqNatS vuz1890 vuz1900)",fontsize=16,color="magenta"];6691 -> 6695[label="",style="dashed", color="magenta", weight=3];
6691 -> 6696[label="",style="dashed", color="magenta", weight=3];
6692[label="primModNatS0 (Succ vuz187) (Succ vuz188) True",fontsize=16,color="black",shape="triangle"];6692 -> 6697[label="",style="solid", color="black", weight=3];
6693[label="primModNatS0 (Succ vuz187) (Succ vuz188) False",fontsize=16,color="black",shape="box"];6693 -> 6698[label="",style="solid", color="black", weight=3];
6694 -> 6692[label="",style="dashed", color="red", weight=0];
6694[label="primModNatS0 (Succ vuz187) (Succ vuz188) True",fontsize=16,color="magenta"];6695[label="vuz1900",fontsize=16,color="green",shape="box"];6696[label="vuz1890",fontsize=16,color="green",shape="box"];6697 -> 6470[label="",style="dashed", color="red", weight=0];
6697[label="primModNatS (primMinusNatS (Succ vuz187) (Succ vuz188)) (Succ (Succ vuz188))",fontsize=16,color="magenta"];6697 -> 6699[label="",style="dashed", color="magenta", weight=3];
6697 -> 6700[label="",style="dashed", color="magenta", weight=3];
6698[label="Succ (Succ vuz187)",fontsize=16,color="green",shape="box"];6699[label="Succ vuz188",fontsize=16,color="green",shape="box"];6700 -> 6281[label="",style="dashed", color="red", weight=0];
6700[label="primMinusNatS (Succ vuz187) (Succ vuz188)",fontsize=16,color="magenta"];6700 -> 6701[label="",style="dashed", color="magenta", weight=3];
6700 -> 6702[label="",style="dashed", color="magenta", weight=3];
6701[label="Succ vuz188",fontsize=16,color="green",shape="box"];6702[label="Succ vuz187",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

                      ↳ Narrow

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

new_primPlusNat(Succ(vuz3700), Succ(vuz301000)) → new_primPlusNat(vuz3700, vuz301000)

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

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

new_primPlusNat(Succ(vuz3700), Succ(vuz301000)) → new_primPlusNat(vuz3700, vuz301000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primMulNat(Succ(vuz4100), Succ(vuz30100)) → new_primMulNat(vuz4100, Succ(vuz30100))

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

new_primMulNat(Succ(vuz4100), Succ(vuz30100)) → new_primMulNat(vuz4100, Succ(vuz30100))
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

                      ↳ Narrow

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

new_primMinusNatS(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS(vuz1620, vuz1630)

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

new_primMinusNatS(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS(vuz1620, vuz1630)
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

                      ↳ Narrow

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

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS0(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS(Succ(Zero), Zero) → new_primModNatS(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS(Succ(Succ(vuz170000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

                                  ↳ UsableRulesProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS(Succ(Succ(vuz170000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ RuleRemovalProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS(Succ(Succ(vuz170000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

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

new_primModNatS(Succ(Succ(vuz170000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

Strictly oriented rules of the TRS R:

new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

Used ordering: POLO with Polynomial interpretation [25]:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ RuleRemovalProof

                                        ↳ QDP

                                          ↳ PisEmptyProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS0(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188)) at position [0] we obtained the following new rules:

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS0(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188)) at position [0] we obtained the following new rules:

new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS0(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Zero, Succ(x0))
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_primModNatS(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS0(vuz170000, vuz169000, vuz170000, vuz169000)

The remaining pairs can at least be oriented weakly.

new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)

Used ordering: Polynomial interpretation [25]:

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

The following usable rules [17] were oriented:

new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS00(vuz187, vuz188) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS(new_primMinusNatS0(vuz187, vuz188), Succ(vuz188))
new_primModNatS0(vuz187, vuz188, Zero, Zero) → new_primModNatS00(vuz187, vuz188)
new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)

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

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

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ 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_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)

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

new_primModNatS0(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS0(vuz187, vuz188, vuz1890, vuz1900)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz170, Neg(Succ(vuz16900))) → new_gcd0Gcd'(Neg(Succ(vuz16900)), new_primRemInt0(vuz170, vuz16900))
new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primRemInt0(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primRemInt0(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'(vuz170, Neg(Succ(vuz16900))) → new_gcd0Gcd'(Neg(Succ(vuz16900)), new_primRemInt0(vuz170, vuz16900)) at position [1] we obtained the following new rules:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primRemInt0(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primRemInt0(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                    ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primRemInt0(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primRemInt0(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                    ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                    ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                                ↳ QDP

                                                  ↳ MNOCProof

                                    ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                                ↳ QDP

                                                  ↳ MNOCProof

                                                    ↳ QDP

                                    ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primRemInt0(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primRemInt0(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900)) at position [1] we obtained the following new rules:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                      ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                      ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                      ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ MNOCProof

                                                      ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ MNOCProof

                                                                      ↳ QDP

                                                      ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                                                                      ↳ QDP

                                                                        ↳ MNOCProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                                                                      ↳ QDP

                                                                        ↳ MNOCProof

                                                                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_primModNatS1(Zero, vuz16900) → Zero
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Zero) → Zero
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Zero, Zero) → new_primDivNatS00(vuz162, vuz163)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS0(vuz12200, vuz123000, vuz12200, vuz123000)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS(Succ(Zero), Zero) → new_primDivNatS(new_primMinusNatS2, Zero)
new_primDivNatS(Succ(Succ(vuz12200)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz12200), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz12200) → Succ(vuz12200)
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz12200)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz12200), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz12200) → Succ(vuz12200)
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz12200)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz12200), Zero)

The TRS R consists of the following rules:

new_primMinusNatS1(vuz12200) → Succ(vuz12200)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS1(x0)
new_primMinusNatS2
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Zero, Succ(x0))
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_primMinusNatS2
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Zero, Succ(x0))
new_primMinusNatS0(Succ(x0), Zero)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ RuleRemovalProof

                                ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz12200)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz12200), Zero)

The TRS R consists of the following rules:

new_primMinusNatS1(vuz12200) → Succ(vuz12200)

The set Q consists of the following terms:

new_primMinusNatS1(x0)

new_primDivNatS(Succ(Succ(vuz12200)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz12200), Zero)

Strictly oriented rules of the TRS R:

new_primMinusNatS1(vuz12200) → Succ(vuz12200)

Used ordering: POLO with Polynomial interpretation [25]:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ RuleRemovalProof

                                            ↳ QDP

                                              ↳ PisEmptyProof

                                ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primMinusNatS1(x0)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Zero, Zero) → new_primDivNatS00(vuz162, vuz163)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
new_primDivNatS(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS0(vuz12200, vuz123000, vuz12200, vuz123000)
new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz12200) → Succ(vuz12200)
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Zero, Zero) → new_primDivNatS00(vuz162, vuz163)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
new_primDivNatS(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS0(vuz12200, vuz123000, vuz12200, vuz123000)
new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS1(x0)
new_primMinusNatS2
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Zero, Succ(x0))
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_primMinusNatS1(x0)
new_primMinusNatS2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Zero, Zero) → new_primDivNatS00(vuz162, vuz163)
new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS0(vuz12200, vuz123000, vuz12200, vuz123000)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

new_primMinusNatS0(Succ(x0), Succ(x1))
new_primMinusNatS0(Zero, Zero)
new_primMinusNatS0(Zero, Succ(x0))
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(vuz162, vuz163, Zero, Zero) → new_primDivNatS00(vuz162, vuz163)
new_primDivNatS(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS0(vuz12200, vuz123000, vuz12200, vuz123000)
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))

The remaining pairs can at least be oriented weakly.

new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))
new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)

Used ordering: Polynomial interpretation [25]:

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

The following usable rules [17] were oriented:

new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
new_primDivNatS00(vuz162, vuz163) → new_primDivNatS(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                                                        ↳ QDP

                                                          ↳ QDPSizeChangeProof

                          ↳ QDP

                      ↳ Narrow

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

new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)

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

new_primDivNatS0(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS0(vuz162, vuz163, vuz1640, vuz1650)
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

                            ↳ QDPSizeChangeProof

                      ↳ Narrow

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

new_enforceWHNF0(vuz104, vuz90, vuz103, vuz89, :(vuz310, vuz311)) → new_seq(:%(vuz103, vuz89), vuz310, :%(vuz103, vuz89), vuz311)
new_enforceWHNF(vuz40, vuz300, vuz28, vuz27, Succ(vuz300), vuz26, vuz25, vuz29, vuz31) → new_enforceWHNF0(new_quot0(vuz40, vuz300, vuz28), new_quot(vuz27, vuz40, vuz300, vuz28), new_quot0(vuz40, vuz300, vuz28), new_quot(vuz27, vuz40, vuz300, vuz28), vuz31)
new_seq(:%(vuz40, Pos(vuz410)), :%(vuz300, Pos(vuz3010)), vuz5, vuz31) → new_enforceWHNF(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
new_enforceWHNF1(vuz40, vuz300, vuz34, vuz33, Succ(vuz360), vuz32, vuz31, vuz35, vuz31) → new_enforceWHNF0(new_quot2(vuz40, vuz300, vuz34), new_quot1(vuz33, vuz40, vuz300, vuz34), new_quot2(vuz40, vuz300, vuz34), new_quot1(vuz33, vuz40, vuz300, vuz34), vuz31)
new_seq(:%(vuz40, Pos(vuz410)), :%(vuz300, Neg(vuz3010)), vuz5, vuz31) → new_enforceWHNF1(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
new_seq(:%(vuz40, Neg(vuz410)), :%(vuz300, Pos(vuz3010)), vuz5, vuz31) → new_enforceWHNF1(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
new_seq(:%(vuz40, Neg(vuz410)), :%(vuz300, Neg(vuz3010)), vuz5, vuz31) → new_enforceWHNF(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)

The TRS R consists of the following rules:

new_gcd0Gcd'0(vuz170, Pos(Succ(vuz16900))) → new_gcd0Gcd'0(Pos(Succ(vuz16900)), new_primRemInt(vuz170, vuz16900))
new_primDivNatS1(Succ(Zero), Zero) → Succ(new_primDivNatS1(new_primMinusNatS2, Zero))
new_primModNatS01(vuz187, vuz188) → new_primModNatS1(new_primMinusNatS0(Succ(vuz187), Succ(vuz188)), Succ(vuz188))
new_primModNatS1(Succ(Zero), Succ(vuz169000)) → Succ(Zero)
new_abs(Zero) → Neg(Zero)
new_quot(vuz27, vuz40, vuz300, vuz28) → new_primQuotInt(vuz27, new_gcd22(vuz40, vuz300, vuz28))
new_primModNatS02(vuz187, vuz188, Zero, Succ(vuz1900)) → Succ(Succ(vuz187))
new_primRemInt0(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_gcd22(Pos(vuz400), Pos(vuz3000), vuz28) → new_gcd23(new_primMulNat0(vuz400, vuz3000), vuz28)
new_quot2(Pos(vuz400), Pos(vuz3000), vuz34) → new_primQuotInt(new_primMulNat0(vuz400, vuz3000), new_reduce2D2(new_primMulNat0(vuz400, vuz3000), vuz34))
new_primQuotInt(vuz27, Neg(Zero)) → new_error
new_primPlusNat1(Succ(vuz3700), Succ(vuz301000)) → Succ(Succ(new_primPlusNat1(vuz3700, vuz301000)))
new_primQuotInt0(vuz122, Pos(Zero)) → new_error
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Zero) → new_primModNatS01(vuz187, vuz188)
new_primMulNat0(Zero, Succ(vuz30100)) → Zero
new_primMulNat0(Succ(vuz4100), Zero) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_reduce2D1(vuz125, vuz34) → new_gcd21(vuz125, vuz34)
new_primPlusNat1(Zero, Zero) → Zero
new_primDivNatS02(vuz162, vuz163, Zero, Succ(vuz1650)) → Zero
new_primMinusNatS0(Zero, Succ(vuz1630)) → Zero
new_abs(Succ(vuz340)) → new_absReal1(vuz340)
new_quot2(Neg(vuz400), Pos(vuz3000), vuz34) → new_primQuotInt0(new_primMulNat0(vuz400, vuz3000), new_reduce2D1(new_primMulNat0(vuz400, vuz3000), vuz34))
new_quot2(Pos(vuz400), Neg(vuz3000), vuz34) → new_primQuotInt0(new_primMulNat0(vuz400, vuz3000), new_reduce2D1(new_primMulNat0(vuz400, vuz3000), vuz34))
new_gcd23(Succ(vuz1670), vuz28) → new_gcd0Gcd'0(new_abs0(Succ(vuz1670)), new_abs0(vuz28))
new_primDivNatS02(vuz162, vuz163, Succ(vuz1640), Zero) → new_primDivNatS01(vuz162, vuz163)
new_primDivNatS1(Succ(Succ(vuz12200)), Zero) → Succ(new_primDivNatS1(new_primMinusNatS1(vuz12200), Zero))
new_gcd21(Zero, Zero) → new_error
new_gcd20(Pos(vuz400), Neg(vuz3000), vuz34) → new_gcd21(new_primMulNat0(vuz400, vuz3000), vuz34)
new_gcd20(Neg(vuz400), Pos(vuz3000), vuz34) → new_gcd21(new_primMulNat0(vuz400, vuz3000), vuz34)
new_reduce2D2(vuz168, vuz34) → new_gcd2(vuz168, vuz168, vuz34)
new_gcd21(Succ(vuz1250), vuz34) → new_gcd0Gcd'0(new_abs(Succ(vuz1250)), new_abs(vuz34))
new_gcd23(Zero, Succ(vuz280)) → new_gcd0Gcd'0(new_abs0(Zero), new_abs0(Succ(vuz280)))
new_primMulNat0(Succ(vuz4100), Succ(vuz30100)) → new_primPlusNat0(new_primMulNat0(vuz4100, Succ(vuz30100)), vuz30100)
new_gcd22(Neg(vuz400), Neg(vuz3000), vuz28) → new_gcd23(new_primMulNat0(vuz400, vuz3000), vuz28)
new_gcd2(Succ(vuz1270), vuz126, vuz34) → new_gcd0(vuz126, vuz34)
new_gcd0(vuz126, vuz34) → new_gcd0Gcd'0(new_abs0(vuz126), new_abs(vuz34))
new_primDivNatS02(vuz162, vuz163, Succ(vuz1640), Succ(vuz1650)) → new_primDivNatS02(vuz162, vuz163, vuz1640, vuz1650)
new_gcd23(Zero, Zero) → new_error
new_gcd0Gcd'0(vuz170, Neg(Succ(vuz16900))) → new_gcd0Gcd'0(Neg(Succ(vuz16900)), new_primRemInt0(vuz170, vuz16900))
new_primQuotInt(vuz27, Pos(Succ(vuz16600))) → Pos(new_primDivNatS1(vuz27, vuz16600))
new_absReal1(vuz1240) → Pos(Succ(vuz1240))
new_primModNatS02(vuz187, vuz188, Zero, Zero) → new_primModNatS01(vuz187, vuz188)
new_primMinusNatS1(vuz12200) → Succ(vuz12200)
new_primDivNatS01(vuz162, vuz163) → Succ(new_primDivNatS1(new_primMinusNatS0(vuz162, vuz163), Succ(vuz163)))
new_quot0(Neg(vuz400), Pos(vuz3000), vuz28) → new_primQuotInt0(new_primMulNat0(vuz400, vuz3000), new_reduce2D0(new_primMulNat0(vuz400, vuz3000), vuz28))
new_quot0(Pos(vuz400), Neg(vuz3000), vuz28) → new_primQuotInt0(new_primMulNat0(vuz400, vuz3000), new_reduce2D0(new_primMulNat0(vuz400, vuz3000), vuz28))
new_primQuotInt(vuz27, Pos(Zero)) → new_error
new_primMinusNatS0(Succ(vuz1620), Zero) → Succ(vuz1620)
new_primDivNatS1(Zero, vuz12300) → Zero
new_primQuotInt0(vuz122, Neg(Zero)) → new_error
new_abs0(Zero) → Pos(Zero)
new_primMulNat0(Zero, Zero) → Zero
new_primRemInt0(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primPlusNat0(Succ(vuz370), vuz30100) → Succ(Succ(new_primPlusNat1(vuz370, vuz30100)))
new_error → error([])
new_primModNatS1(Zero, vuz16900) → Zero
new_quot2(Neg(vuz400), Neg(vuz3000), vuz34) → new_primQuotInt(new_primMulNat0(vuz400, vuz3000), new_reduce2D2(new_primMulNat0(vuz400, vuz3000), vuz34))
new_quot0(Neg(vuz400), Neg(vuz3000), vuz28) → new_primQuotInt(new_primMulNat0(vuz400, vuz3000), new_reduce2D(new_primMulNat0(vuz400, vuz3000), vuz28))
new_reduce2D(vuz167, vuz28) → new_gcd23(vuz167, vuz28)
new_gcd20(Neg(vuz400), Neg(vuz3000), vuz34) → new_gcd2(new_primMulNat0(vuz400, vuz3000), new_primMulNat0(vuz400, vuz3000), vuz34)
new_gcd2(Zero, vuz126, Succ(vuz340)) → new_gcd0(vuz126, Succ(vuz340))
new_gcd22(Neg(vuz400), Pos(vuz3000), vuz28) → new_gcd24(new_primMulNat0(vuz400, vuz3000), vuz28)
new_gcd22(Pos(vuz400), Neg(vuz3000), vuz28) → new_gcd24(new_primMulNat0(vuz400, vuz3000), vuz28)
new_abs0(Succ(vuz280)) → Pos(Succ(vuz280))
new_gcd0Gcd'0(vuz170, Neg(Zero)) → vuz170
new_primPlusNat0(Zero, vuz30100) → Succ(vuz30100)
new_gcd21(Zero, Succ(vuz340)) → new_gcd0Gcd'0(new_abs(Zero), new_abs(Succ(vuz340)))
new_primQuotInt(vuz27, Neg(Succ(vuz16600))) → Neg(new_primDivNatS1(vuz27, vuz16600))
new_primModNatS02(vuz187, vuz188, Succ(vuz1890), Succ(vuz1900)) → new_primModNatS02(vuz187, vuz188, vuz1890, vuz1900)
new_reduce2D0(vuz124, vuz28) → new_gcd24(vuz124, vuz28)
new_primRemInt(Pos(vuz1700), vuz16900) → Pos(new_primModNatS1(vuz1700, vuz16900))
new_primDivNatS1(Succ(Succ(vuz12200)), Succ(vuz123000)) → new_primDivNatS02(vuz12200, vuz123000, vuz12200, vuz123000)
new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_quot1(vuz33, vuz40, vuz300, vuz34) → new_primQuotInt0(vuz33, new_gcd20(vuz40, vuz300, vuz34))
new_primDivNatS02(vuz162, vuz163, Zero, Zero) → new_primDivNatS01(vuz162, vuz163)
new_primRemInt(Neg(vuz1700), vuz16900) → Neg(new_primModNatS1(vuz1700, vuz16900))
new_primPlusNat1(Zero, Succ(vuz301000)) → Succ(vuz301000)
new_primPlusNat1(Succ(vuz3700), Zero) → Succ(vuz3700)
new_gcd24(Zero, Zero) → new_error
new_gcd20(Pos(vuz400), Pos(vuz3000), vuz34) → new_gcd2(new_primMulNat0(vuz400, vuz3000), new_primMulNat0(vuz400, vuz3000), vuz34)
new_primMinusNatS2 → Zero
new_primModNatS1(Succ(Succ(vuz170000)), Succ(vuz169000)) → new_primModNatS02(vuz170000, vuz169000, vuz170000, vuz169000)
new_primQuotInt0(vuz122, Pos(Succ(vuz12300))) → Neg(new_primDivNatS1(vuz122, vuz12300))
new_quot0(Pos(vuz400), Pos(vuz3000), vuz28) → new_primQuotInt(new_primMulNat0(vuz400, vuz3000), new_reduce2D(new_primMulNat0(vuz400, vuz3000), vuz28))
new_gcd24(Succ(vuz1240), vuz28) → new_gcd0Gcd'0(new_absReal1(vuz1240), new_abs0(vuz28))
new_gcd2(Zero, vuz126, Zero) → new_error
new_primQuotInt0(vuz122, Neg(Succ(vuz12300))) → Pos(new_primDivNatS1(vuz122, vuz12300))
new_gcd24(Zero, Succ(vuz280)) → new_gcd0Gcd'0(new_abs(Zero), new_abs0(Succ(vuz280)))
new_primDivNatS1(Succ(Zero), Succ(vuz123000)) → Zero
new_gcd0Gcd'0(vuz170, Pos(Zero)) → vuz170
new_primMinusNatS0(Succ(vuz1620), Succ(vuz1630)) → new_primMinusNatS0(vuz1620, vuz1630)
new_primModNatS1(Succ(Succ(vuz170000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz170000), Zero), Zero)

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), Zero)
new_primDivNatS1(Succ(Succ(x0)), Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primDivNatS1(Succ(Zero), Succ(x0))
new_primPlusNat0(Zero, x0)
new_gcd24(Zero, Succ(x0))
new_primMinusNatS2
new_gcd21(Succ(x0), x1)
new_gcd22(Neg(x0), Neg(x1), x2)
new_gcd2(Succ(x0), x1, x2)
new_primModNatS1(Succ(Zero), Succ(x0))
new_primMulNat0(Zero, Zero)
new_primQuotInt(x0, Neg(Zero))
new_primMinusNatS0(Succ(x0), Zero)
new_primQuotInt0(x0, Pos(Zero))
new_absReal1(x0)
new_primDivNatS1(Succ(Succ(x0)), Zero)
new_primMinusNatS1(x0)
new_gcd22(Pos(x0), Pos(x1), x2)
new_primRemInt(Neg(x0), x1)
new_quot0(Pos(x0), Neg(x1), x2)
new_quot0(Neg(x0), Pos(x1), x2)
new_abs0(Succ(x0))
new_gcd23(Zero, Succ(x0))
new_gcd0Gcd'0(x0, Neg(Zero))
new_primPlusNat1(Zero, Succ(x0))
new_primQuotInt0(x0, Neg(Zero))
new_primMinusNatS0(Zero, Zero)
new_quot2(Neg(x0), Pos(x1), x2)
new_quot2(Pos(x0), Neg(x1), x2)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_abs(Succ(x0))
new_gcd0Gcd'0(x0, Neg(Succ(x1)))
new_primModNatS02(x0, x1, Succ(x2), Succ(x3))
new_reduce2D2(x0, x1)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primDivNatS1(Succ(Zero), Zero)
new_gcd21(Zero, Succ(x0))
new_primQuotInt(x0, Neg(Succ(x1)))
new_gcd21(Zero, Zero)
new_reduce2D0(x0, x1)
new_primPlusNat1(Zero, Zero)
new_error
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS02(x0, x1, Succ(x2), Zero)
new_quot(x0, x1, x2, x3)
new_primQuotInt0(x0, Pos(Succ(x1)))
new_quot0(Neg(x0), Neg(x1), x2)
new_gcd23(Succ(x0), x1)
new_gcd24(Zero, Zero)
new_quot2(Neg(x0), Neg(x1), x2)
new_primModNatS1(Succ(Zero), Zero)
new_gcd24(Succ(x0), x1)
new_primRemInt0(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primDivNatS02(x0, x1, Succ(x2), Succ(x3))
new_gcd2(Zero, x0, Zero)
new_primRemInt0(Pos(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_quot0(Pos(x0), Pos(x1), x2)
new_primQuotInt0(x0, Neg(Succ(x1)))
new_primDivNatS1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), x1)
new_primQuotInt(x0, Pos(Succ(x1)))
new_gcd2(Zero, x0, Succ(x1))
new_primModNatS1(Zero, x0)
new_primDivNatS02(x0, x1, Zero, Succ(x2))
new_gcd20(Neg(x0), Neg(x1), x2)
new_primDivNatS02(x0, x1, Zero, Zero)
new_gcd0Gcd'0(x0, Pos(Succ(x1)))
new_gcd23(Zero, Zero)
new_gcd22(Neg(x0), Pos(x1), x2)
new_gcd22(Pos(x0), Neg(x1), x2)
new_primQuotInt(x0, Pos(Zero))
new_gcd0Gcd'0(x0, Pos(Zero))
new_primDivNatS02(x0, x1, Succ(x2), Zero)
new_reduce2D1(x0, x1)
new_primModNatS01(x0, x1)
new_primRemInt(Pos(x0), x1)
new_primDivNatS01(x0, x1)
new_quot2(Pos(x0), Pos(x1), x2)
new_gcd0(x0, x1)
new_primMulNat0(Succ(x0), Succ(x1))
new_reduce2D(x0, x1)
new_abs0(Zero)
new_primModNatS02(x0, x1, Zero, Succ(x2))
new_gcd20(Neg(x0), Pos(x1), x2)
new_gcd20(Pos(x0), Neg(x1), x2)
new_quot1(x0, x1, x2, x3)
new_abs(Zero)
new_primModNatS02(x0, x1, Zero, Zero)
new_gcd20(Pos(x0), Pos(x1), x2)

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_enforceWHNF0(vuz104, vuz90, vuz103, vuz89, :(vuz310, vuz311)) → new_seq(:%(vuz103, vuz89), vuz310, :%(vuz103, vuz89), vuz311)
The graph contains the following edges 5 > 2, 5 > 4
new_enforceWHNF(vuz40, vuz300, vuz28, vuz27, Succ(vuz300), vuz26, vuz25, vuz29, vuz31) → new_enforceWHNF0(new_quot0(vuz40, vuz300, vuz28), new_quot(vuz27, vuz40, vuz300, vuz28), new_quot0(vuz40, vuz300, vuz28), new_quot(vuz27, vuz40, vuz300, vuz28), vuz31)
The graph contains the following edges 9 >= 5
new_enforceWHNF1(vuz40, vuz300, vuz34, vuz33, Succ(vuz360), vuz32, vuz31, vuz35, vuz31) → new_enforceWHNF0(new_quot2(vuz40, vuz300, vuz34), new_quot1(vuz33, vuz40, vuz300, vuz34), new_quot2(vuz40, vuz300, vuz34), new_quot1(vuz33, vuz40, vuz300, vuz34), vuz31)
The graph contains the following edges 7 >= 5, 9 >= 5
new_seq(:%(vuz40, Pos(vuz410)), :%(vuz300, Pos(vuz3010)), vuz5, vuz31) → new_enforceWHNF(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
The graph contains the following edges 1 > 1, 2 > 2, 4 >= 9
new_seq(:%(vuz40, Neg(vuz410)), :%(vuz300, Neg(vuz3010)), vuz5, vuz31) → new_enforceWHNF(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
The graph contains the following edges 1 > 1, 2 > 2, 4 >= 9
new_seq(:%(vuz40, Neg(vuz410)), :%(vuz300, Pos(vuz3010)), vuz5, vuz31) → new_enforceWHNF1(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
The graph contains the following edges 1 > 1, 2 > 2, 4 >= 9
new_seq(:%(vuz40, Pos(vuz410)), :%(vuz300, Neg(vuz3010)), vuz5, vuz31) → new_enforceWHNF1(vuz40, vuz300, new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), new_primMulNat0(vuz410, vuz3010), vuz31)
The graph contains the following edges 1 > 1, 2 > 2, 4 >= 9

Haskell To QDPs

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                      ↳ Narrow

                        ↳ QDP

                          ↳ PisEmptyProof

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

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