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

YES 0.842 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/Monad.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ LR

mainModule Monad

((liftM3 :: Monad b => (e -> a -> d -> c) -> b e -> b a -> b d -> b c) :: Monad b => (e -> a -> d -> c) -> b e -> b a -> b d -> b c)

module Monad where

import qualified Maybe
import qualified Prelude

liftM3 :: Monad a => (e -> c -> d -> b) -> a e -> a c -> a d -> a b

liftM3

f m1 m2 m3

m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->return (f x1 x2 x3))))

module Maybe where

import qualified Monad
import qualified Prelude

Lambda Reductions:
The following Lambda expression

\x3→return (f x1 x2 x3)

is transformed to

liftM30 f x1 x2 x3 = return (f x1 x2 x3)

The following Lambda expression

\x2→m3 >>= liftM30 f x1 x2

is transformed to

liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2

The following Lambda expression

\x1→m2 >>= liftM31 m3 f x1

is transformed to

liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

mainModule Monad

((liftM3 :: Monad c => (e -> d -> b -> a) -> c e -> c d -> c b -> c a) :: Monad c => (e -> d -> b -> a) -> c e -> c d -> c b -> c a)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM3 :: Monad a => (e -> d -> b -> c) -> a e -> a d -> a b -> a c

liftM3

f m1 m2 m3

m1 >>= liftM32 m2 m3 f

liftM30

f x1 x2 x3

return (f x1 x2 x3)

liftM31

m3 f x1 x2

m3 >>= liftM30 f x1 x2

liftM32

m2 m3 f x1

m2 >>= liftM31 m3 f x1

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Monad

((liftM3 :: Monad b => (c -> e -> d -> a) -> b c -> b e -> b d -> b a) :: Monad b => (c -> e -> d -> a) -> b c -> b e -> b d -> b a)

module Monad where

import qualified Maybe
import qualified Prelude

liftM3 :: Monad c => (d -> b -> a -> e) -> c d -> c b -> c a -> c e

liftM3

f m1 m2 m3

m1 >>= liftM32 m2 m3 f

liftM30

f x1 x2 x3

return (f x1 x2 x3)

liftM31

m3 f x1 x2

m3 >>= liftM30 f x1 x2

liftM32

m2 m3 f x1

m2 >>= liftM31 m3 f x1

module Maybe where

import qualified Monad
import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

mainModule Monad

(liftM3 :: Monad d => (a -> c -> b -> e) -> d a -> d c -> d b -> d e)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM3 :: Monad d => (b -> e -> c -> a) -> d b -> d e -> d c -> d a

liftM3

f m1 m2 m3

m1 >>= liftM32 m2 m3 f

liftM30

f x1 x2 x3

return (f x1 x2 x3)

liftM31

m3 f x1 x2

m3 >>= liftM30 f x1 x2

liftM32

m2 m3 f x1

m2 >>= liftM31 m3 f x1

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="liftM3\n  Monad a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="liftM3 vy3\n  Monad a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="liftM3 vy3 vy4\n  Monad a",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
5[label="liftM3 vy3 vy4 vy5\n  Monad a",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="liftM3 vy3 vy4 vy5 vy6\n  Monad a",fontsize=16,color="black",shape="triangle"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="vy4 >>= liftM32 vy5 vy6 vy3\n  Monad a",fontsize=16,color="blue",shape="box"];118[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];7 -> 118[label="",style="solid", color="blue", weight=9];
118 -> 8[label="",style="solid", color="blue", weight=3];
119[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];7 -> 119[label="",style="solid", color="blue", weight=9];
119 -> 9[label="",style="solid", color="blue", weight=3];
120[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];7 -> 120[label="",style="solid", color="blue", weight=9];
120 -> 10[label="",style="solid", color="blue", weight=3];
8[label="vy4 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="burlywood",shape="box"];121[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];8 -> 121[label="",style="solid", color="burlywood", weight=9];
121 -> 11[label="",style="solid", color="burlywood", weight=3];
122[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 122[label="",style="solid", color="burlywood", weight=9];
122 -> 12[label="",style="solid", color="burlywood", weight=3];
9[label="vy4 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="burlywood",shape="triangle"];123[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 123[label="",style="solid", color="burlywood", weight=9];
123 -> 13[label="",style="solid", color="burlywood", weight=3];
124[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 124[label="",style="solid", color="burlywood", weight=9];
124 -> 14[label="",style="solid", color="burlywood", weight=3];
10[label="vy4 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3];
11[label="Nothing >>= liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3];
12[label="Just vy40 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
13[label="vy40 : vy41 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3];
14[label="[] >>= liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3];
15[label="primbindIO vy4 (liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];15 -> 20[label="",style="solid", color="black", weight=3];
16[label="Nothing",fontsize=16,color="green",shape="box"];17[label="liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18 -> 56[label="",style="dashed", color="red", weight=0];
18[label="liftM32 vy5 vy6 vy3 vy40 ++ (vy41 >>= liftM32 vy5 vy6 vy3)",fontsize=16,color="magenta"];18 -> 57[label="",style="dashed", color="magenta", weight=3];
18 -> 58[label="",style="dashed", color="magenta", weight=3];
19[label="[]",fontsize=16,color="green",shape="box"];20[label="terminator vy4 (liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="vy5 >>= liftM31 vy6 vy3 vy40",fontsize=16,color="burlywood",shape="box"];126[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];21 -> 126[label="",style="solid", color="burlywood", weight=9];
126 -> 25[label="",style="solid", color="burlywood", weight=3];
127[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];21 -> 127[label="",style="solid", color="burlywood", weight=9];
127 -> 26[label="",style="solid", color="burlywood", weight=3];
57 -> 9[label="",style="dashed", color="red", weight=0];
57[label="vy41 >>= liftM32 vy5 vy6 vy3",fontsize=16,color="magenta"];57 -> 67[label="",style="dashed", color="magenta", weight=3];
58[label="liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];58 -> 68[label="",style="solid", color="black", weight=3];
56[label="vy9 ++ vy7",fontsize=16,color="burlywood",shape="triangle"];129[label="vy9/vy90 : vy91",fontsize=10,color="white",style="solid",shape="box"];56 -> 129[label="",style="solid", color="burlywood", weight=9];
129 -> 69[label="",style="solid", color="burlywood", weight=3];
130[label="vy9/[]",fontsize=10,color="white",style="solid",shape="box"];56 -> 130[label="",style="solid", color="burlywood", weight=9];
130 -> 70[label="",style="solid", color="burlywood", weight=3];
24[label="ter0m vy4 (liftM32 vy5 vy6 vy3)",fontsize=16,color="green",shape="box"];24 -> 29[label="",style="dashed", color="green", weight=3];
24 -> 30[label="",style="dashed", color="green", weight=3];
25[label="Nothing >>= liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];25 -> 31[label="",style="solid", color="black", weight=3];
26[label="Just vy50 >>= liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];26 -> 32[label="",style="solid", color="black", weight=3];
67[label="vy41",fontsize=16,color="green",shape="box"];68[label="vy5 >>= liftM31 vy6 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];131[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];68 -> 131[label="",style="solid", color="burlywood", weight=9];
131 -> 74[label="",style="solid", color="burlywood", weight=3];
132[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];68 -> 132[label="",style="solid", color="burlywood", weight=9];
132 -> 75[label="",style="solid", color="burlywood", weight=3];
69[label="(vy90 : vy91) ++ vy7",fontsize=16,color="black",shape="box"];69 -> 76[label="",style="solid", color="black", weight=3];
70[label="[] ++ vy7",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3];
29[label="vy4",fontsize=16,color="green",shape="box"];30[label="liftM32 vy5 vy6 vy3",fontsize=16,color="grey",shape="box"];30 -> 35[label="",style="dashed", color="grey", weight=3];
31[label="Nothing",fontsize=16,color="green",shape="box"];32[label="liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
74[label="vy50 : vy51 >>= liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];74 -> 82[label="",style="solid", color="black", weight=3];
75[label="[] >>= liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];75 -> 83[label="",style="solid", color="black", weight=3];
76[label="vy90 : vy91 ++ vy7",fontsize=16,color="green",shape="box"];76 -> 84[label="",style="dashed", color="green", weight=3];
77[label="vy7",fontsize=16,color="green",shape="box"];35[label="liftM32 vy5 vy6 vy3 vy8",fontsize=16,color="black",shape="triangle"];35 -> 39[label="",style="solid", color="black", weight=3];
36[label="vy6 >>= liftM30 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];133[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];36 -> 133[label="",style="solid", color="burlywood", weight=9];
133 -> 40[label="",style="solid", color="burlywood", weight=3];
134[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];36 -> 134[label="",style="solid", color="burlywood", weight=9];
134 -> 41[label="",style="solid", color="burlywood", weight=3];
82 -> 56[label="",style="dashed", color="red", weight=0];
82[label="liftM31 vy6 vy3 vy40 vy50 ++ (vy51 >>= liftM31 vy6 vy3 vy40)",fontsize=16,color="magenta"];82 -> 86[label="",style="dashed", color="magenta", weight=3];
82 -> 87[label="",style="dashed", color="magenta", weight=3];
83[label="[]",fontsize=16,color="green",shape="box"];84 -> 56[label="",style="dashed", color="red", weight=0];
84[label="vy91 ++ vy7",fontsize=16,color="magenta"];84 -> 88[label="",style="dashed", color="magenta", weight=3];
39[label="vy5 >>= liftM31 vy6 vy3 vy8",fontsize=16,color="black",shape="box"];39 -> 44[label="",style="solid", color="black", weight=3];
40[label="Nothing >>= liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];40 -> 45[label="",style="solid", color="black", weight=3];
41[label="Just vy60 >>= liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];41 -> 46[label="",style="solid", color="black", weight=3];
86 -> 68[label="",style="dashed", color="red", weight=0];
86[label="vy51 >>= liftM31 vy6 vy3 vy40",fontsize=16,color="magenta"];86 -> 90[label="",style="dashed", color="magenta", weight=3];
87[label="liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];87 -> 91[label="",style="solid", color="black", weight=3];
88[label="vy91",fontsize=16,color="green",shape="box"];44[label="primbindIO vy5 (liftM31 vy6 vy3 vy8)",fontsize=16,color="black",shape="box"];44 -> 49[label="",style="solid", color="black", weight=3];
45[label="Nothing",fontsize=16,color="green",shape="box"];46[label="liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3];
90[label="vy51",fontsize=16,color="green",shape="box"];91[label="vy6 >>= liftM30 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];138[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];91 -> 138[label="",style="solid", color="burlywood", weight=9];
138 -> 93[label="",style="solid", color="burlywood", weight=3];
139[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];91 -> 139[label="",style="solid", color="burlywood", weight=9];
139 -> 94[label="",style="solid", color="burlywood", weight=3];
49[label="terminator vy5 (liftM31 vy6 vy3 vy8)",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
50[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
93[label="vy60 : vy61 >>= liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];93 -> 96[label="",style="solid", color="black", weight=3];
94[label="[] >>= liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];94 -> 97[label="",style="solid", color="black", weight=3];
53[label="ter1m vy5 (liftM31 vy6 vy3 vy8)",fontsize=16,color="green",shape="box"];53 -> 71[label="",style="dashed", color="green", weight=3];
53 -> 72[label="",style="dashed", color="green", weight=3];
54[label="Just (vy3 vy40 vy50 vy60)",fontsize=16,color="green",shape="box"];54 -> 73[label="",style="dashed", color="green", weight=3];
96 -> 56[label="",style="dashed", color="red", weight=0];
96[label="liftM30 vy3 vy40 vy50 vy60 ++ (vy61 >>= liftM30 vy3 vy40 vy50)",fontsize=16,color="magenta"];96 -> 100[label="",style="dashed", color="magenta", weight=3];
96 -> 101[label="",style="dashed", color="magenta", weight=3];
97[label="[]",fontsize=16,color="green",shape="box"];71[label="vy5",fontsize=16,color="green",shape="box"];72[label="liftM31 vy6 vy3 vy8",fontsize=16,color="grey",shape="box"];72 -> 78[label="",style="dashed", color="grey", weight=3];
73[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];73 -> 79[label="",style="dashed", color="green", weight=3];
73 -> 80[label="",style="dashed", color="green", weight=3];
73 -> 81[label="",style="dashed", color="green", weight=3];
100 -> 91[label="",style="dashed", color="red", weight=0];
100[label="vy61 >>= liftM30 vy3 vy40 vy50",fontsize=16,color="magenta"];100 -> 103[label="",style="dashed", color="magenta", weight=3];
101[label="liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];101 -> 104[label="",style="solid", color="black", weight=3];
78[label="liftM31 vy6 vy3 vy8 vy10",fontsize=16,color="black",shape="triangle"];78 -> 85[label="",style="solid", color="black", weight=3];
79[label="vy40",fontsize=16,color="green",shape="box"];80[label="vy50",fontsize=16,color="green",shape="box"];81[label="vy60",fontsize=16,color="green",shape="box"];103[label="vy61",fontsize=16,color="green",shape="box"];104[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
85[label="vy6 >>= liftM30 vy3 vy8 vy10",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3];
106[label="vy3 vy40 vy50 vy60 : []",fontsize=16,color="green",shape="box"];106 -> 108[label="",style="dashed", color="green", weight=3];
89[label="primbindIO vy6 (liftM30 vy3 vy8 vy10)",fontsize=16,color="black",shape="box"];89 -> 92[label="",style="solid", color="black", weight=3];
108[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];108 -> 110[label="",style="dashed", color="green", weight=3];
108 -> 111[label="",style="dashed", color="green", weight=3];
108 -> 112[label="",style="dashed", color="green", weight=3];
92[label="terminator vy6 (liftM30 vy3 vy8 vy10)",fontsize=16,color="black",shape="box"];92 -> 95[label="",style="solid", color="black", weight=3];
110[label="vy40",fontsize=16,color="green",shape="box"];111[label="vy50",fontsize=16,color="green",shape="box"];112[label="vy60",fontsize=16,color="green",shape="box"];95[label="ter2m vy6 (liftM30 vy3 vy8 vy10)",fontsize=16,color="green",shape="box"];95 -> 98[label="",style="dashed", color="green", weight=3];
95 -> 99[label="",style="dashed", color="green", weight=3];
98[label="vy6",fontsize=16,color="green",shape="box"];99[label="liftM30 vy3 vy8 vy10",fontsize=16,color="grey",shape="box"];99 -> 102[label="",style="dashed", color="grey", weight=3];
102[label="liftM30 vy3 vy8 vy10 vy11",fontsize=16,color="black",shape="triangle"];102 -> 105[label="",style="solid", color="black", weight=3];
105[label="return (vy3 vy8 vy10 vy11)",fontsize=16,color="black",shape="box"];105 -> 107[label="",style="solid", color="black", weight=3];
107[label="primretIO (vy3 vy8 vy10 vy11)",fontsize=16,color="black",shape="box"];107 -> 109[label="",style="solid", color="black", weight=3];
109[label="terminator (vy3 vy8 vy10 vy11)",fontsize=16,color="black",shape="box"];109 -> 113[label="",style="solid", color="black", weight=3];
113[label="ter3m (vy3 vy8 vy10 vy11)",fontsize=16,color="green",shape="box"];113 -> 114[label="",style="dashed", color="green", weight=3];
114[label="vy3 vy8 vy10 vy11",fontsize=16,color="green",shape="box"];114 -> 115[label="",style="dashed", color="green", weight=3];
114 -> 116[label="",style="dashed", color="green", weight=3];
114 -> 117[label="",style="dashed", color="green", weight=3];
115[label="vy8",fontsize=16,color="green",shape="box"];116[label="vy10",fontsize=16,color="green",shape="box"];117[label="vy11",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_psPs(:(vy90, vy91), vy7, h) → new_psPs(vy91, vy7, h)

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_psPs(:(vy90, vy91), vy7, h) → new_psPs(vy91, vy7, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_gtGtEs(:(vy60, vy61), vy3, vy40, vy50, h, ba, bb, bc) → new_gtGtEs(vy61, vy3, vy40, vy50, h, ba, bb, bc)

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

new_gtGtEs(:(vy60, vy61), vy3, vy40, vy50, h, ba, bb, bc) → new_gtGtEs(vy61, vy3, vy40, vy50, h, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_gtGtEs0(:(vy50, vy51), vy6, vy3, vy40, h, ba, bb, bc) → new_gtGtEs0(vy51, vy6, vy3, vy40, h, ba, bb, bc)

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

new_gtGtEs0(:(vy50, vy51), vy6, vy3, vy40, h, ba, bb, bc) → new_gtGtEs0(vy51, vy6, vy3, vy40, h, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_gtGtEs1(:(vy40, vy41), vy5, vy6, vy3, h, ba, bb, bc) → new_gtGtEs1(vy41, vy5, vy6, vy3, h, ba, bb, bc)

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

new_gtGtEs1(:(vy40, vy41), vy5, vy6, vy3, h, ba, bb, bc) → new_gtGtEs1(vy41, vy5, vy6, vy3, h, ba, bb, bc)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8