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

YES 0.847 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

((liftM4 :: Monad a => (d -> b -> e -> c -> f) -> a d -> a b -> a e -> a c -> a f) :: Monad a => (d -> b -> e -> c -> f) -> a d -> a b -> a e -> a c -> a f)

module Monad where

import qualified Maybe
import qualified Prelude

liftM4 :: Monad c => (d -> f -> e -> a -> b) -> c d -> c f -> c e -> c a -> c b

liftM4

f m1 m2 m3 m4

m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4)))))

module Maybe where

import qualified Monad
import qualified Prelude

Lambda Reductions:
The following Lambda expression

\x4→return (f x1 x2 x3 x4)

is transformed to

liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4)

The following Lambda expression

\x3→m4 >>= liftM40 f x1 x2 x3

is transformed to

liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3

The following Lambda expression

\x2→m3 >>= liftM41 m4 f x1 x2

is transformed to

liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2

The following Lambda expression

\x1→m2 >>= liftM42 m3 m4 f x1

is transformed to

liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

mainModule Monad

((liftM4 :: Monad f => (a -> d -> b -> c -> e) -> f a -> f d -> f b -> f c -> f e) :: Monad f => (a -> d -> b -> c -> e) -> f a -> f d -> f b -> f c -> f e)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM4 :: Monad f => (e -> a -> c -> b -> d) -> f e -> f a -> f c -> f b -> f d

liftM4

f m1 m2 m3 m4

m1 >>= liftM43 m2 m3 m4 f

liftM40

f x1 x2 x3 x4

return (f x1 x2 x3 x4)

liftM41

m4 f x1 x2 x3

m4 >>= liftM40 f x1 x2 x3

liftM42

m3 m4 f x1 x2

m3 >>= liftM41 m4 f x1 x2

liftM43

m2 m3 m4 f x1

m2 >>= liftM42 m3 m4 f x1

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Monad

((liftM4 :: Monad e => (d -> a -> c -> b -> f) -> e d -> e a -> e c -> e b -> e f) :: Monad e => (d -> a -> c -> b -> f) -> e d -> e a -> e c -> e b -> e f)

module Monad where

import qualified Maybe
import qualified Prelude

liftM4 :: Monad a => (b -> e -> c -> d -> f) -> a b -> a e -> a c -> a d -> a f

liftM4

f m1 m2 m3 m4

m1 >>= liftM43 m2 m3 m4 f

liftM40

f x1 x2 x3 x4

return (f x1 x2 x3 x4)

liftM41

m4 f x1 x2 x3

m4 >>= liftM40 f x1 x2 x3

liftM42

m3 m4 f x1 x2

m3 >>= liftM41 m4 f x1 x2

liftM43

m2 m3 m4 f x1

m2 >>= liftM42 m3 m4 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

(liftM4 :: Monad c => (d -> f -> b -> e -> a) -> c d -> c f -> c b -> c e -> c a)

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

liftM4 :: Monad f => (b -> e -> c -> a -> d) -> f b -> f e -> f c -> f a -> f d

liftM4

f m1 m2 m3 m4

m1 >>= liftM43 m2 m3 m4 f

liftM40

f x1 x2 x3 x4

return (f x1 x2 x3 x4)

liftM41

m4 f x1 x2 x3

m4 >>= liftM40 f x1 x2 x3

liftM42

m3 m4 f x1 x2

m3 >>= liftM41 m4 f x1 x2

liftM43

m2 m3 m4 f x1

m2 >>= liftM42 m3 m4 f x1

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="liftM4\n  Monad a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="liftM4 vy3\n  Monad a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="liftM4 vy3 vy4\n  Monad a",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
5[label="liftM4 vy3 vy4 vy5\n  Monad a",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="liftM4 vy3 vy4 vy5 vy6\n  Monad a",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
7[label="liftM4 vy3 vy4 vy5 vy6 vy7\n  Monad a",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="vy4 >>= liftM43 vy5 vy6 vy7 vy3\n  Monad a",fontsize=16,color="blue",shape="box"];142[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];8 -> 142[label="",style="solid", color="blue", weight=9];
142 -> 9[label="",style="solid", color="blue", weight=3];
143[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];8 -> 143[label="",style="solid", color="blue", weight=9];
143 -> 10[label="",style="solid", color="blue", weight=3];
144[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];8 -> 144[label="",style="solid", color="blue", weight=9];
144 -> 11[label="",style="solid", color="blue", weight=3];
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10[label="vy4 >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="triangle"];145[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];10 -> 145[label="",style="solid", color="burlywood", weight=9];
145 -> 13[label="",style="solid", color="burlywood", weight=3];
146[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 146[label="",style="solid", color="burlywood", weight=9];
146 -> 14[label="",style="solid", color="burlywood", weight=3];
11[label="vy4 >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="box"];147[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];11 -> 147[label="",style="solid", color="burlywood", weight=9];
147 -> 15[label="",style="solid", color="burlywood", weight=3];
148[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 148[label="",style="solid", color="burlywood", weight=9];
148 -> 16[label="",style="solid", color="burlywood", weight=3];
12[label="primbindIO vy4 (liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
13[label="vy40 : vy41 >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3];
14[label="[] >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3];
15[label="Nothing >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];15 -> 20[label="",style="solid", color="black", weight=3];
16[label="Just vy40 >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];16 -> 21[label="",style="solid", color="black", weight=3];
17[label="terminator vy4 (liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];17 -> 22[label="",style="solid", color="black", weight=3];
18 -> 58[label="",style="dashed", color="red", weight=0];
18[label="liftM43 vy5 vy6 vy7 vy3 vy40 ++ (vy41 >>= liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="magenta"];18 -> 59[label="",style="dashed", color="magenta", weight=3];
18 -> 60[label="",style="dashed", color="magenta", weight=3];
19[label="[]",fontsize=16,color="green",shape="box"];20[label="Nothing",fontsize=16,color="green",shape="box"];21[label="liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="ter0m vy4 (liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="green",shape="box"];22 -> 26[label="",style="dashed", color="green", weight=3];
22 -> 27[label="",style="dashed", color="green", weight=3];
59[label="liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];59 -> 69[label="",style="solid", color="black", weight=3];
60 -> 10[label="",style="dashed", color="red", weight=0];
60[label="vy41 >>= liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="magenta"];60 -> 70[label="",style="dashed", color="magenta", weight=3];
58[label="vy10 ++ vy8",fontsize=16,color="burlywood",shape="triangle"];151[label="vy10/vy100 : vy101",fontsize=10,color="white",style="solid",shape="box"];58 -> 151[label="",style="solid", color="burlywood", weight=9];
151 -> 71[label="",style="solid", color="burlywood", weight=3];
152[label="vy10/[]",fontsize=10,color="white",style="solid",shape="box"];58 -> 152[label="",style="solid", color="burlywood", weight=9];
152 -> 72[label="",style="solid", color="burlywood", weight=3];
25[label="vy5 >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="box"];153[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];25 -> 153[label="",style="solid", color="burlywood", weight=9];
153 -> 30[label="",style="solid", color="burlywood", weight=3];
154[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];25 -> 154[label="",style="solid", color="burlywood", weight=9];
154 -> 31[label="",style="solid", color="burlywood", weight=3];
26[label="vy4",fontsize=16,color="green",shape="box"];27[label="liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="grey",shape="box"];27 -> 32[label="",style="dashed", color="grey", weight=3];
69[label="vy5 >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];155[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];69 -> 155[label="",style="solid", color="burlywood", weight=9];
155 -> 76[label="",style="solid", color="burlywood", weight=3];
156[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];69 -> 156[label="",style="solid", color="burlywood", weight=9];
156 -> 77[label="",style="solid", color="burlywood", weight=3];
70[label="vy41",fontsize=16,color="green",shape="box"];71[label="(vy100 : vy101) ++ vy8",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3];
72[label="[] ++ vy8",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3];
30[label="Nothing >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];30 -> 35[label="",style="solid", color="black", weight=3];
31[label="Just vy50 >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];31 -> 36[label="",style="solid", color="black", weight=3];
32[label="liftM43 vy5 vy6 vy7 vy3 vy9",fontsize=16,color="black",shape="triangle"];32 -> 37[label="",style="solid", color="black", weight=3];
76[label="vy50 : vy51 >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3];
77[label="[] >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3];
78[label="vy100 : vy101 ++ vy8",fontsize=16,color="green",shape="box"];78 -> 85[label="",style="dashed", color="green", weight=3];
79[label="vy8",fontsize=16,color="green",shape="box"];35[label="Nothing",fontsize=16,color="green",shape="box"];36[label="liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3];
37[label="vy5 >>= liftM42 vy6 vy7 vy3 vy9",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
83 -> 58[label="",style="dashed", color="red", weight=0];
83[label="liftM42 vy6 vy7 vy3 vy40 vy50 ++ (vy51 >>= liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="magenta"];83 -> 88[label="",style="dashed", color="magenta", weight=3];
83 -> 89[label="",style="dashed", color="magenta", weight=3];
84[label="[]",fontsize=16,color="green",shape="box"];85 -> 58[label="",style="dashed", color="red", weight=0];
85[label="vy101 ++ vy8",fontsize=16,color="magenta"];85 -> 90[label="",style="dashed", color="magenta", weight=3];
40[label="vy6 >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];159[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];40 -> 159[label="",style="solid", color="burlywood", weight=9];
159 -> 44[label="",style="solid", color="burlywood", weight=3];
160[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];40 -> 160[label="",style="solid", color="burlywood", weight=9];
160 -> 45[label="",style="solid", color="burlywood", weight=3];
41[label="primbindIO vy5 (liftM42 vy6 vy7 vy3 vy9)",fontsize=16,color="black",shape="box"];41 -> 46[label="",style="solid", color="black", weight=3];
88[label="liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];88 -> 93[label="",style="solid", color="black", weight=3];
89 -> 69[label="",style="dashed", color="red", weight=0];
89[label="vy51 >>= liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="magenta"];89 -> 94[label="",style="dashed", color="magenta", weight=3];
90[label="vy101",fontsize=16,color="green",shape="box"];44[label="Nothing >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];44 -> 49[label="",style="solid", color="black", weight=3];
45[label="Just vy60 >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];45 -> 50[label="",style="solid", color="black", weight=3];
46[label="terminator vy5 (liftM42 vy6 vy7 vy3 vy9)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
93[label="vy6 >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];162[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];93 -> 162[label="",style="solid", color="burlywood", weight=9];
162 -> 97[label="",style="solid", color="burlywood", weight=3];
163[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];93 -> 163[label="",style="solid", color="burlywood", weight=9];
163 -> 98[label="",style="solid", color="burlywood", weight=3];
94[label="vy51",fontsize=16,color="green",shape="box"];49[label="Nothing",fontsize=16,color="green",shape="box"];50[label="liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
51[label="ter1m vy5 (liftM42 vy6 vy7 vy3 vy9)",fontsize=16,color="green",shape="box"];51 -> 55[label="",style="dashed", color="green", weight=3];
51 -> 56[label="",style="dashed", color="green", weight=3];
97[label="vy60 : vy61 >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];97 -> 105[label="",style="solid", color="black", weight=3];
98[label="[] >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];98 -> 106[label="",style="solid", color="black", weight=3];
54[label="vy7 >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];164[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];54 -> 164[label="",style="solid", color="burlywood", weight=9];
164 -> 73[label="",style="solid", color="burlywood", weight=3];
165[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];54 -> 165[label="",style="solid", color="burlywood", weight=9];
165 -> 74[label="",style="solid", color="burlywood", weight=3];
55[label="vy5",fontsize=16,color="green",shape="box"];56[label="liftM42 vy6 vy7 vy3 vy9",fontsize=16,color="grey",shape="box"];56 -> 75[label="",style="dashed", color="grey", weight=3];
105 -> 58[label="",style="dashed", color="red", weight=0];
105[label="liftM41 vy7 vy3 vy40 vy50 vy60 ++ (vy61 >>= liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="magenta"];105 -> 108[label="",style="dashed", color="magenta", weight=3];
105 -> 109[label="",style="dashed", color="magenta", weight=3];
106[label="[]",fontsize=16,color="green",shape="box"];73[label="Nothing >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];73 -> 80[label="",style="solid", color="black", weight=3];
74[label="Just vy70 >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];74 -> 81[label="",style="solid", color="black", weight=3];
75[label="liftM42 vy6 vy7 vy3 vy9 vy11",fontsize=16,color="black",shape="triangle"];75 -> 82[label="",style="solid", color="black", weight=3];
108[label="liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];108 -> 111[label="",style="solid", color="black", weight=3];
109 -> 93[label="",style="dashed", color="red", weight=0];
109[label="vy61 >>= liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="magenta"];109 -> 112[label="",style="dashed", color="magenta", weight=3];
80[label="Nothing",fontsize=16,color="green",shape="box"];81[label="liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];81 -> 86[label="",style="solid", color="black", weight=3];
82[label="vy6 >>= liftM41 vy7 vy3 vy9 vy11",fontsize=16,color="black",shape="box"];82 -> 87[label="",style="solid", color="black", weight=3];
111[label="vy7 >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];168[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];111 -> 168[label="",style="solid", color="burlywood", weight=9];
168 -> 114[label="",style="solid", color="burlywood", weight=3];
169[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];111 -> 169[label="",style="solid", color="burlywood", weight=9];
169 -> 115[label="",style="solid", color="burlywood", weight=3];
112[label="vy61",fontsize=16,color="green",shape="box"];86[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];86 -> 91[label="",style="solid", color="black", weight=3];
87[label="primbindIO vy6 (liftM41 vy7 vy3 vy9 vy11)",fontsize=16,color="black",shape="box"];87 -> 92[label="",style="solid", color="black", weight=3];
114[label="vy70 : vy71 >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];114 -> 117[label="",style="solid", color="black", weight=3];
115[label="[] >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];115 -> 118[label="",style="solid", color="black", weight=3];
91[label="Just (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];91 -> 95[label="",style="dashed", color="green", weight=3];
92[label="terminator vy6 (liftM41 vy7 vy3 vy9 vy11)",fontsize=16,color="black",shape="box"];92 -> 96[label="",style="solid", color="black", weight=3];
117 -> 58[label="",style="dashed", color="red", weight=0];
117[label="liftM40 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];117 -> 120[label="",style="dashed", color="magenta", weight=3];
117 -> 121[label="",style="dashed", color="magenta", weight=3];
118[label="[]",fontsize=16,color="green",shape="box"];95[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];95 -> 99[label="",style="dashed", color="green", weight=3];
95 -> 100[label="",style="dashed", color="green", weight=3];
95 -> 101[label="",style="dashed", color="green", weight=3];
95 -> 102[label="",style="dashed", color="green", weight=3];
96[label="ter2m vy6 (liftM41 vy7 vy3 vy9 vy11)",fontsize=16,color="green",shape="box"];96 -> 103[label="",style="dashed", color="green", weight=3];
96 -> 104[label="",style="dashed", color="green", weight=3];
120[label="liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];120 -> 124[label="",style="solid", color="black", weight=3];
121 -> 111[label="",style="dashed", color="red", weight=0];
121[label="vy71 >>= liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];121 -> 125[label="",style="dashed", color="magenta", weight=3];
99[label="vy40",fontsize=16,color="green",shape="box"];100[label="vy50",fontsize=16,color="green",shape="box"];101[label="vy60",fontsize=16,color="green",shape="box"];102[label="vy70",fontsize=16,color="green",shape="box"];103[label="vy6",fontsize=16,color="green",shape="box"];104[label="liftM41 vy7 vy3 vy9 vy11",fontsize=16,color="grey",shape="box"];104 -> 107[label="",style="dashed", color="grey", weight=3];
124[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];124 -> 127[label="",style="solid", color="black", weight=3];
125[label="vy71",fontsize=16,color="green",shape="box"];107[label="liftM41 vy7 vy3 vy9 vy11 vy12",fontsize=16,color="black",shape="triangle"];107 -> 110[label="",style="solid", color="black", weight=3];
127[label="vy3 vy40 vy50 vy60 vy70 : []",fontsize=16,color="green",shape="box"];127 -> 129[label="",style="dashed", color="green", weight=3];
110[label="vy7 >>= liftM40 vy3 vy9 vy11 vy12",fontsize=16,color="black",shape="box"];110 -> 113[label="",style="solid", color="black", weight=3];
129[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];129 -> 131[label="",style="dashed", color="green", weight=3];
129 -> 132[label="",style="dashed", color="green", weight=3];
129 -> 133[label="",style="dashed", color="green", weight=3];
129 -> 134[label="",style="dashed", color="green", weight=3];
113[label="primbindIO vy7 (liftM40 vy3 vy9 vy11 vy12)",fontsize=16,color="black",shape="box"];113 -> 116[label="",style="solid", color="black", weight=3];
131[label="vy40",fontsize=16,color="green",shape="box"];132[label="vy50",fontsize=16,color="green",shape="box"];133[label="vy60",fontsize=16,color="green",shape="box"];134[label="vy70",fontsize=16,color="green",shape="box"];116[label="terminator vy7 (liftM40 vy3 vy9 vy11 vy12)",fontsize=16,color="black",shape="box"];116 -> 119[label="",style="solid", color="black", weight=3];
119[label="ter3m vy7 (liftM40 vy3 vy9 vy11 vy12)",fontsize=16,color="green",shape="box"];119 -> 122[label="",style="dashed", color="green", weight=3];
119 -> 123[label="",style="dashed", color="green", weight=3];
122[label="vy7",fontsize=16,color="green",shape="box"];123[label="liftM40 vy3 vy9 vy11 vy12",fontsize=16,color="grey",shape="box"];123 -> 126[label="",style="dashed", color="grey", weight=3];
126[label="liftM40 vy3 vy9 vy11 vy12 vy13",fontsize=16,color="black",shape="triangle"];126 -> 128[label="",style="solid", color="black", weight=3];
128[label="return (vy3 vy9 vy11 vy12 vy13)",fontsize=16,color="black",shape="box"];128 -> 130[label="",style="solid", color="black", weight=3];
130[label="primretIO (vy3 vy9 vy11 vy12 vy13)",fontsize=16,color="black",shape="box"];130 -> 135[label="",style="solid", color="black", weight=3];
135[label="terminator (vy3 vy9 vy11 vy12 vy13)",fontsize=16,color="black",shape="box"];135 -> 136[label="",style="solid", color="black", weight=3];
136[label="ter4m (vy3 vy9 vy11 vy12 vy13)",fontsize=16,color="green",shape="box"];136 -> 137[label="",style="dashed", color="green", weight=3];
137[label="vy3 vy9 vy11 vy12 vy13",fontsize=16,color="green",shape="box"];137 -> 138[label="",style="dashed", color="green", weight=3];
137 -> 139[label="",style="dashed", color="green", weight=3];
137 -> 140[label="",style="dashed", color="green", weight=3];
137 -> 141[label="",style="dashed", color="green", weight=3];
138[label="vy9",fontsize=16,color="green",shape="box"];139[label="vy11",fontsize=16,color="green",shape="box"];140[label="vy12",fontsize=16,color="green",shape="box"];141[label="vy13",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_psPs(:(vy100, vy101), vy8, h) → new_psPs(vy101, vy8, 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(:(vy100, vy101), vy8, h) → new_psPs(vy101, vy8, 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

                  ↳ QDP

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

new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) → new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd)

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

new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) → new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) → new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd)

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

new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) → new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) → new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd)

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

new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) → new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) → new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd)

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

new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) → new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10