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

YES 0.852 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule FiniteMap

((foldFM_GE :: (Ordering -> b -> a -> a) -> a -> Ordering -> FiniteMap Ordering b -> a) :: (Ordering -> b -> a -> a) -> a -> Ordering -> FiniteMap Ordering b -> a)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)

instance (Eq a, Eq b) => Eq (FiniteMap a b) where

foldFM_GE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c

foldFM_GE

k z fr EmptyFM

foldFM_GE

k z fr (Branch key elt _ fm_l fm_r)

key >= fr

foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l

otherwise

foldFM_GE k z fr fm_r

module Maybe where

import qualified FiniteMap
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule FiniteMap

((foldFM_GE :: (Ordering -> a -> b -> b) -> b -> Ordering -> FiniteMap Ordering a -> b) :: (Ordering -> a -> b -> b) -> b -> Ordering -> FiniteMap Ordering a -> b)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)

instance (Eq a, Eq b) => Eq (FiniteMap b a) where

foldFM_GE :: Ord c => (c -> b -> a -> a) -> a -> c -> FiniteMap c b -> a

foldFM_GE

k z fr EmptyFM

foldFM_GE

k z fr (Branch key elt vw fm_l fm_r)

key >= fr

foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l

otherwise

foldFM_GE k z fr fm_r

module Maybe where

import qualified FiniteMap
import qualified Prelude

Cond Reductions:
The following Function with conditions

foldFM_GE k z fr EmptyFM = z

foldFM_GE k z fr (Branch key elt vw fm_l fm_r)

| key >= fr

= foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l

| otherwise

= foldFM_GE k z fr fm_r

is transformed to

foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM

foldFM_GE k z fr (Branch key elt vw fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vw fm_l fm_r)

foldFM_GE1 k z fr key elt vw fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l

foldFM_GE1 k z fr key elt vw fm_l fm_r False = foldFM_GE0 k z fr key elt vw fm_l fm_r otherwise

foldFM_GE0 k z fr key elt vw fm_l fm_r True = foldFM_GE k z fr fm_r

foldFM_GE2 k z fr (Branch key elt vw fm_l fm_r) = foldFM_GE1 k z fr key elt vw fm_l fm_r (key >= fr)

foldFM_GE3 k z fr EmptyFM = z

foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy

The following Function with conditions

compare x y

| x == y

= EQ

| x <= y

= LT

| otherwise

= GT

is transformed to

compare x y = compare3 x y

compare2 x y True = EQ

compare2 x y False = compare1 x y (x <= y)

compare0 x y True = GT

compare1 x y True = LT

compare1 x y False = compare0 x y otherwise

compare3 x y = compare2 x y (x == y)

The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule FiniteMap

(foldFM_GE :: (Ordering -> b -> a -> a) -> a -> Ordering -> FiniteMap Ordering b -> a)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a)

instance (Eq a, Eq b) => Eq (FiniteMap a b) where

foldFM_GE :: Ord a => (a -> b -> c -> c) -> c -> a -> FiniteMap a b -> c

foldFM_GE	k z fr EmptyFM	=	foldFM_GE3 k z fr EmptyFM
foldFM_GE	k z fr (Branch key elt vw fm_l fm_r)	=	foldFM_GE2 k z fr (Branch key elt vw fm_l fm_r)

foldFM_GE0

k z fr key elt vw fm_l fm_r True

foldFM_GE k z fr fm_r

foldFM_GE1	k z fr key elt vw fm_l fm_r True	=	foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1	k z fr key elt vw fm_l fm_r False	=	foldFM_GE0 k z fr key elt vw fm_l fm_r otherwise

foldFM_GE2

k z fr (Branch key elt vw fm_l fm_r)

foldFM_GE1 k z fr key elt vw fm_l fm_r (key >= fr)

foldFM_GE3	k z fr EmptyFM	=	z
foldFM_GE3	wv ww wx wy	=	foldFM_GE2 wv ww wx wy

module Maybe where

import qualified FiniteMap
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="foldFM_GE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="foldFM_GE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="foldFM_GE wz3 wz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
5[label="foldFM_GE wz3 wz4 wz5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="foldFM_GE wz3 wz4 wz5 wz6",fontsize=16,color="burlywood",shape="triangle"];152[label="wz6/EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 152[label="",style="solid", color="burlywood", weight=9];
152 -> 7[label="",style="solid", color="burlywood", weight=3];
153[label="wz6/Branch wz60 wz61 wz62 wz63 wz64",fontsize=10,color="white",style="solid",shape="box"];6 -> 153[label="",style="solid", color="burlywood", weight=9];
153 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="foldFM_GE wz3 wz4 wz5 EmptyFM",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="foldFM_GE wz3 wz4 wz5 (Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="foldFM_GE3 wz3 wz4 wz5 EmptyFM",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="foldFM_GE2 wz3 wz4 wz5 (Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="wz4",fontsize=16,color="green",shape="box"];12[label="foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (wz60 >= wz5)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (compare wz60 wz5 /= LT)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare wz60 wz5 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare3 wz60 wz5 == LT))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
16[label="foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare2 wz60 wz5 (wz60 == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];154[label="wz60/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 154[label="",style="solid", color="burlywood", weight=9];
154 -> 17[label="",style="solid", color="burlywood", weight=3];
155[label="wz60/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 155[label="",style="solid", color="burlywood", weight=9];
155 -> 18[label="",style="solid", color="burlywood", weight=3];
156[label="wz60/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 156[label="",style="solid", color="burlywood", weight=9];
156 -> 19[label="",style="solid", color="burlywood", weight=3];
17[label="foldFM_GE1 wz3 wz4 wz5 LT wz61 wz62 wz63 wz64 (not (compare2 LT wz5 (LT == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];157[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];17 -> 157[label="",style="solid", color="burlywood", weight=9];
157 -> 20[label="",style="solid", color="burlywood", weight=3];
158[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];17 -> 158[label="",style="solid", color="burlywood", weight=9];
158 -> 21[label="",style="solid", color="burlywood", weight=3];
159[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];17 -> 159[label="",style="solid", color="burlywood", weight=9];
159 -> 22[label="",style="solid", color="burlywood", weight=3];
18[label="foldFM_GE1 wz3 wz4 wz5 EQ wz61 wz62 wz63 wz64 (not (compare2 EQ wz5 (EQ == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];160[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];18 -> 160[label="",style="solid", color="burlywood", weight=9];
160 -> 23[label="",style="solid", color="burlywood", weight=3];
161[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];18 -> 161[label="",style="solid", color="burlywood", weight=9];
161 -> 24[label="",style="solid", color="burlywood", weight=3];
162[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];18 -> 162[label="",style="solid", color="burlywood", weight=9];
162 -> 25[label="",style="solid", color="burlywood", weight=3];
19[label="foldFM_GE1 wz3 wz4 wz5 GT wz61 wz62 wz63 wz64 (not (compare2 GT wz5 (GT == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];163[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 163[label="",style="solid", color="burlywood", weight=9];
163 -> 26[label="",style="solid", color="burlywood", weight=3];
164[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 164[label="",style="solid", color="burlywood", weight=9];
164 -> 27[label="",style="solid", color="burlywood", weight=3];
165[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 165[label="",style="solid", color="burlywood", weight=9];
165 -> 28[label="",style="solid", color="burlywood", weight=3];
20[label="foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (compare2 LT LT (LT == LT) == LT))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
21[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare2 LT EQ (LT == EQ) == LT))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
22[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare2 LT GT (LT == GT) == LT))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
23[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ LT (EQ == LT) == LT))",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
24[label="foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (compare2 EQ EQ (EQ == EQ) == LT))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
25[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ GT (EQ == GT) == LT))",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
26[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare2 GT LT (GT == LT) == LT))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
27[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare2 GT EQ (GT == EQ) == LT))",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
28[label="foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (compare2 GT GT (GT == GT) == LT))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
29[label="foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (compare2 LT LT True == LT))",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
30[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare2 LT EQ False == LT))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
31[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare2 LT GT False == LT))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
32[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ LT False == LT))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
33[label="foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (compare2 EQ EQ True == LT))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
34[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ GT False == LT))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
35[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare2 GT LT False == LT))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
36[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare2 GT EQ False == LT))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
37[label="foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (compare2 GT GT True == LT))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
38[label="foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
39[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare1 LT EQ (LT <= EQ) == LT))",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
40[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare1 LT GT (LT <= GT) == LT))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
41[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ LT (EQ <= LT) == LT))",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
42[label="foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
43[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ GT (EQ <= GT) == LT))",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
44[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare1 GT LT (GT <= LT) == LT))",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
45[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare1 GT EQ (GT <= EQ) == LT))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
46[label="foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
47[label="foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
48[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare1 LT EQ True == LT))",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
49[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare1 LT GT True == LT))",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
50[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ LT False == LT))",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
51[label="foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];51 -> 60[label="",style="solid", color="black", weight=3];
52[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ GT True == LT))",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
53[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare1 GT LT False == LT))",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
54[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare1 GT EQ False == LT))",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
55[label="foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
56[label="foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
57[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
58[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
59[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare0 EQ LT otherwise == LT))",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
60[label="foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];60 -> 69[label="",style="solid", color="black", weight=3];
61[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
62[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare0 GT LT otherwise == LT))",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
63[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare0 GT EQ otherwise == LT))",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
64[label="foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
65 -> 6[label="",style="dashed", color="red", weight=0];
65[label="foldFM_GE wz3 (wz3 LT wz61 (foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];65 -> 74[label="",style="dashed", color="magenta", weight=3];
65 -> 75[label="",style="dashed", color="magenta", weight=3];
65 -> 76[label="",style="dashed", color="magenta", weight=3];
66[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];66 -> 77[label="",style="solid", color="black", weight=3];
67[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];67 -> 78[label="",style="solid", color="black", weight=3];
68[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare0 EQ LT True == LT))",fontsize=16,color="black",shape="box"];68 -> 79[label="",style="solid", color="black", weight=3];
69 -> 6[label="",style="dashed", color="red", weight=0];
69[label="foldFM_GE wz3 (wz3 EQ wz61 (foldFM_GE wz3 wz4 EQ wz64)) EQ wz63",fontsize=16,color="magenta"];69 -> 80[label="",style="dashed", color="magenta", weight=3];
69 -> 81[label="",style="dashed", color="magenta", weight=3];
69 -> 82[label="",style="dashed", color="magenta", weight=3];
70[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];70 -> 83[label="",style="solid", color="black", weight=3];
71[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare0 GT LT True == LT))",fontsize=16,color="black",shape="box"];71 -> 84[label="",style="solid", color="black", weight=3];
72[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare0 GT EQ True == LT))",fontsize=16,color="black",shape="box"];72 -> 85[label="",style="solid", color="black", weight=3];
73 -> 6[label="",style="dashed", color="red", weight=0];
73[label="foldFM_GE wz3 (wz3 GT wz61 (foldFM_GE wz3 wz4 GT wz64)) GT wz63",fontsize=16,color="magenta"];73 -> 86[label="",style="dashed", color="magenta", weight=3];
73 -> 87[label="",style="dashed", color="magenta", weight=3];
73 -> 88[label="",style="dashed", color="magenta", weight=3];
74[label="wz63",fontsize=16,color="green",shape="box"];75[label="LT",fontsize=16,color="green",shape="box"];76[label="wz3 LT wz61 (foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];76 -> 89[label="",style="dashed", color="green", weight=3];
76 -> 90[label="",style="dashed", color="green", weight=3];
76 -> 91[label="",style="dashed", color="green", weight=3];
77[label="foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];77 -> 92[label="",style="solid", color="black", weight=3];
78[label="foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];78 -> 93[label="",style="solid", color="black", weight=3];
79[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];79 -> 94[label="",style="solid", color="black", weight=3];
80[label="wz63",fontsize=16,color="green",shape="box"];81[label="EQ",fontsize=16,color="green",shape="box"];82[label="wz3 EQ wz61 (foldFM_GE wz3 wz4 EQ wz64)",fontsize=16,color="green",shape="box"];82 -> 95[label="",style="dashed", color="green", weight=3];
82 -> 96[label="",style="dashed", color="green", weight=3];
82 -> 97[label="",style="dashed", color="green", weight=3];
83[label="foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];83 -> 98[label="",style="solid", color="black", weight=3];
84[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];84 -> 99[label="",style="solid", color="black", weight=3];
85[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];85 -> 100[label="",style="solid", color="black", weight=3];
86[label="wz63",fontsize=16,color="green",shape="box"];87[label="GT",fontsize=16,color="green",shape="box"];88[label="wz3 GT wz61 (foldFM_GE wz3 wz4 GT wz64)",fontsize=16,color="green",shape="box"];88 -> 101[label="",style="dashed", color="green", weight=3];
88 -> 102[label="",style="dashed", color="green", weight=3];
88 -> 103[label="",style="dashed", color="green", weight=3];
89[label="LT",fontsize=16,color="green",shape="box"];90[label="wz61",fontsize=16,color="green",shape="box"];91 -> 6[label="",style="dashed", color="red", weight=0];
91[label="foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];91 -> 104[label="",style="dashed", color="magenta", weight=3];
91 -> 105[label="",style="dashed", color="magenta", weight=3];
92[label="foldFM_GE0 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];92 -> 106[label="",style="solid", color="black", weight=3];
93[label="foldFM_GE0 wz3 wz4 GT LT wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];93 -> 107[label="",style="solid", color="black", weight=3];
94[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];94 -> 108[label="",style="solid", color="black", weight=3];
95[label="EQ",fontsize=16,color="green",shape="box"];96[label="wz61",fontsize=16,color="green",shape="box"];97 -> 6[label="",style="dashed", color="red", weight=0];
97[label="foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];97 -> 109[label="",style="dashed", color="magenta", weight=3];
97 -> 110[label="",style="dashed", color="magenta", weight=3];
98[label="foldFM_GE0 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];98 -> 111[label="",style="solid", color="black", weight=3];
99[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];99 -> 112[label="",style="solid", color="black", weight=3];
100[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];100 -> 113[label="",style="solid", color="black", weight=3];
101[label="GT",fontsize=16,color="green",shape="box"];102[label="wz61",fontsize=16,color="green",shape="box"];103 -> 6[label="",style="dashed", color="red", weight=0];
103[label="foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];103 -> 114[label="",style="dashed", color="magenta", weight=3];
103 -> 115[label="",style="dashed", color="magenta", weight=3];
104[label="wz64",fontsize=16,color="green",shape="box"];105[label="LT",fontsize=16,color="green",shape="box"];106[label="foldFM_GE0 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];106 -> 116[label="",style="solid", color="black", weight=3];
107[label="foldFM_GE0 wz3 wz4 GT LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];107 -> 117[label="",style="solid", color="black", weight=3];
108[label="foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];108 -> 118[label="",style="solid", color="black", weight=3];
109[label="wz64",fontsize=16,color="green",shape="box"];110[label="EQ",fontsize=16,color="green",shape="box"];111[label="foldFM_GE0 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];111 -> 119[label="",style="solid", color="black", weight=3];
112[label="foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];112 -> 120[label="",style="solid", color="black", weight=3];
113[label="foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];113 -> 121[label="",style="solid", color="black", weight=3];
114[label="wz64",fontsize=16,color="green",shape="box"];115[label="GT",fontsize=16,color="green",shape="box"];116 -> 6[label="",style="dashed", color="red", weight=0];
116[label="foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];116 -> 122[label="",style="dashed", color="magenta", weight=3];
116 -> 123[label="",style="dashed", color="magenta", weight=3];
117 -> 6[label="",style="dashed", color="red", weight=0];
117[label="foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];117 -> 124[label="",style="dashed", color="magenta", weight=3];
117 -> 125[label="",style="dashed", color="magenta", weight=3];
118 -> 6[label="",style="dashed", color="red", weight=0];
118[label="foldFM_GE wz3 (wz3 EQ wz61 (foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];118 -> 126[label="",style="dashed", color="magenta", weight=3];
118 -> 127[label="",style="dashed", color="magenta", weight=3];
118 -> 128[label="",style="dashed", color="magenta", weight=3];
119 -> 6[label="",style="dashed", color="red", weight=0];
119[label="foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];119 -> 129[label="",style="dashed", color="magenta", weight=3];
119 -> 130[label="",style="dashed", color="magenta", weight=3];
120 -> 6[label="",style="dashed", color="red", weight=0];
120[label="foldFM_GE wz3 (wz3 GT wz61 (foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];120 -> 131[label="",style="dashed", color="magenta", weight=3];
120 -> 132[label="",style="dashed", color="magenta", weight=3];
120 -> 133[label="",style="dashed", color="magenta", weight=3];
121 -> 6[label="",style="dashed", color="red", weight=0];
121[label="foldFM_GE wz3 (wz3 GT wz61 (foldFM_GE wz3 wz4 EQ wz64)) EQ wz63",fontsize=16,color="magenta"];121 -> 134[label="",style="dashed", color="magenta", weight=3];
121 -> 135[label="",style="dashed", color="magenta", weight=3];
121 -> 136[label="",style="dashed", color="magenta", weight=3];
122[label="wz64",fontsize=16,color="green",shape="box"];123[label="EQ",fontsize=16,color="green",shape="box"];124[label="wz64",fontsize=16,color="green",shape="box"];125[label="GT",fontsize=16,color="green",shape="box"];126[label="wz63",fontsize=16,color="green",shape="box"];127[label="LT",fontsize=16,color="green",shape="box"];128[label="wz3 EQ wz61 (foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];128 -> 137[label="",style="dashed", color="green", weight=3];
128 -> 138[label="",style="dashed", color="green", weight=3];
128 -> 139[label="",style="dashed", color="green", weight=3];
129[label="wz64",fontsize=16,color="green",shape="box"];130[label="GT",fontsize=16,color="green",shape="box"];131[label="wz63",fontsize=16,color="green",shape="box"];132[label="LT",fontsize=16,color="green",shape="box"];133[label="wz3 GT wz61 (foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];133 -> 140[label="",style="dashed", color="green", weight=3];
133 -> 141[label="",style="dashed", color="green", weight=3];
133 -> 142[label="",style="dashed", color="green", weight=3];
134[label="wz63",fontsize=16,color="green",shape="box"];135[label="EQ",fontsize=16,color="green",shape="box"];136[label="wz3 GT wz61 (foldFM_GE wz3 wz4 EQ wz64)",fontsize=16,color="green",shape="box"];136 -> 143[label="",style="dashed", color="green", weight=3];
136 -> 144[label="",style="dashed", color="green", weight=3];
136 -> 145[label="",style="dashed", color="green", weight=3];
137[label="EQ",fontsize=16,color="green",shape="box"];138[label="wz61",fontsize=16,color="green",shape="box"];139 -> 6[label="",style="dashed", color="red", weight=0];
139[label="foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];139 -> 146[label="",style="dashed", color="magenta", weight=3];
139 -> 147[label="",style="dashed", color="magenta", weight=3];
140[label="GT",fontsize=16,color="green",shape="box"];141[label="wz61",fontsize=16,color="green",shape="box"];142 -> 6[label="",style="dashed", color="red", weight=0];
142[label="foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];142 -> 148[label="",style="dashed", color="magenta", weight=3];
142 -> 149[label="",style="dashed", color="magenta", weight=3];
143[label="GT",fontsize=16,color="green",shape="box"];144[label="wz61",fontsize=16,color="green",shape="box"];145 -> 6[label="",style="dashed", color="red", weight=0];
145[label="foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];145 -> 150[label="",style="dashed", color="magenta", weight=3];
145 -> 151[label="",style="dashed", color="magenta", weight=3];
146[label="wz64",fontsize=16,color="green",shape="box"];147[label="LT",fontsize=16,color="green",shape="box"];148[label="wz64",fontsize=16,color="green",shape="box"];149[label="LT",fontsize=16,color="green",shape="box"];150[label="wz64",fontsize=16,color="green",shape="box"];151[label="EQ",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

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

new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz63, h, ba)
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 3 SCCs.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz63, h, ba)

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_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, GT, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)

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

new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, EQ, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)

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

new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz63, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) → new_foldFM_GE(wz3, LT, wz64, h, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5

foldFM_GE	k z fr EmptyFM	= foldFM_GE3 k z fr EmptyFM
foldFM_GE	k z fr (Branch key elt vw fm_l fm_r)	= foldFM_GE2 k z fr (Branch key elt vw fm_l fm_r)

foldFM_GE1	k z fr key elt vw fm_l fm_r True	= foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
foldFM_GE1	k z fr key elt vw fm_l fm_r False	= foldFM_GE0 k z fr key elt vw fm_l fm_r otherwise

compare2	x y True	= EQ
compare2	x y False	= compare1 x y (x <= y)

compare1	x y True	= LT
compare1	x y False	= compare0 x y otherwise