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

MAYBE 2.128 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/Monad.hs
H-Termination of the given Haskell-Program with start terms could not be shown:

↳ HASKELL

  ↳ LR

mainModule Monad

((mapAndUnzipM :: (a -> [(b,c)]) -> [a] -> [([b],[c])]) :: (a -> [(b,c)]) -> [a] -> [([b],[c])])

module Monad where

import qualified Maybe
import qualified Prelude

mapAndUnzipM :: Monad b => (a -> b (d,c)) -> [a] -> b ([d],[c])

mapAndUnzipM

f xs

sequence (map f xs) >>= return . unzip

module Maybe where

import qualified Monad
import qualified Prelude

Lambda Reductions:
The following Lambda expression

\(a,b)~(as,bs)→(a : as,b : bs)

is transformed to

unzip0 (a,b) ~(as,bs) = (a : as,b : bs)

The following Lambda expression

\xs→return (x : xs)

is transformed to

sequence0 x xs = return (x : xs)

The following Lambda expression

\x→sequence cs >>= sequence0 x

is transformed to

sequence1 cs x = sequence cs >>= sequence0 x

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

mainModule Monad

((mapAndUnzipM :: (c -> [(b,a)]) -> [c] -> [([b],[a])]) :: (c -> [(b,a)]) -> [c] -> [([b],[a])])

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

mapAndUnzipM :: Monad b => (d -> b (a,c)) -> [d] -> b ([a],[c])

mapAndUnzipM

f xs

sequence (map f xs) >>= return . unzip

IrrPat Reductions:
The variables of the following irrefutable Pattern

~(as,bs)

are replaced by calls to these functions

unzip00 (as,bs) = as

unzip01 (as,bs) = bs

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

mainModule Monad

((mapAndUnzipM :: (a -> [(c,b)]) -> [a] -> [([c],[b])]) :: (a -> [(c,b)]) -> [a] -> [([c],[b])])

module Monad where

import qualified Maybe
import qualified Prelude

mapAndUnzipM :: Monad c => (d -> c (a,b)) -> [d] -> c ([a],[b])

mapAndUnzipM

f xs

sequence (map f xs) >>= return . unzip

module Maybe where

import qualified Monad
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

mainModule Monad

((mapAndUnzipM :: (c -> [(b,a)]) -> [c] -> [([b],[a])]) :: (c -> [(b,a)]) -> [c] -> [([b],[a])])

module Maybe where

import qualified Monad
import qualified Prelude

module Monad where

import qualified Maybe
import qualified Prelude

mapAndUnzipM :: Monad c => (a -> c (b,d)) -> [a] -> c ([b],[d])

mapAndUnzipM

f xs

sequence (map f xs) >>= return . unzip

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                  ↳ Narrow

mainModule Monad

(mapAndUnzipM :: (a -> [(c,b)]) -> [a] -> [([c],[b])])

module Monad where

import qualified Maybe
import qualified Prelude

mapAndUnzipM :: Monad c => (b -> c (d,a)) -> [b] -> c ([d],[a])

mapAndUnzipM

f xs

sequence (map f xs) >>= return . unzip

module Maybe where

import qualified Monad
import qualified Prelude

Haskell To QDPs

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314 -> 6[label="",style="solid", color="burlywood", weight=3];
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315 -> 7[label="",style="solid", color="burlywood", weight=3];
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11[label="return [] >>= return . unzip",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
13[label="vz3 vz40",fontsize=16,color="green",shape="box"];13 -> 18[label="",style="dashed", color="green", weight=3];
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317 -> 16[label="",style="solid", color="burlywood", weight=3];
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318 -> 17[label="",style="solid", color="burlywood", weight=3];
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21[label="[] >>= return . unzip",fontsize=16,color="black",shape="triangle"];21 -> 24[label="",style="solid", color="black", weight=3];
130[label="[]",fontsize=16,color="green",shape="box"];131 -> 21[label="",style="dashed", color="red", weight=0];
131[label="[] >>= return . unzip",fontsize=16,color="magenta"];129[label="return . unzip ++ vz22",fontsize=16,color="black",shape="triangle"];129 -> 135[label="",style="solid", color="black", weight=3];
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321 -> 27[label="",style="solid", color="burlywood", weight=3];
322[label="vz41/[]",fontsize=10,color="white",style="solid",shape="box"];23 -> 322[label="",style="solid", color="burlywood", weight=9];
322 -> 28[label="",style="solid", color="burlywood", weight=3];
24[label="[]",fontsize=16,color="green",shape="box"];135[label="return (unzip vz90) ++ vz22",fontsize=16,color="black",shape="box"];135 -> 145[label="",style="solid", color="black", weight=3];
27[label="(sequence (map vz3 (vz410 : vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 (map vz3 (vz410 : vz411))) >>= return . unzip",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
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145[label="(unzip vz90 : []) ++ vz22",fontsize=16,color="black",shape="box"];145 -> 156[label="",style="solid", color="black", weight=3];
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33 -> 37[label="",style="dashed", color="red", weight=0];
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38[label="vz3 vz410",fontsize=16,color="green",shape="box"];38 -> 45[label="",style="dashed", color="green", weight=3];
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324 -> 43[label="",style="solid", color="burlywood", weight=3];
325[label="vz7/[]",fontsize=10,color="white",style="solid",shape="box"];37 -> 325[label="",style="solid", color="burlywood", weight=9];
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179[label="foldr unzip0 ([],[]) vz90",fontsize=16,color="burlywood",shape="triangle"];326[label="vz90/vz900 : vz901",fontsize=10,color="white",style="solid",shape="box"];179 -> 326[label="",style="solid", color="burlywood", weight=9];
326 -> 187[label="",style="solid", color="burlywood", weight=3];
327[label="vz90/[]",fontsize=10,color="white",style="solid",shape="box"];179 -> 327[label="",style="solid", color="burlywood", weight=9];
327 -> 188[label="",style="solid", color="burlywood", weight=3];
180[label="vz22",fontsize=16,color="green",shape="box"];45[label="vz410",fontsize=16,color="green",shape="box"];43[label="(vz70 : vz71 >>= sequence1 (map vz3 vz411) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];43 -> 48[label="",style="solid", color="black", weight=3];
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188[label="foldr unzip0 ([],[]) []",fontsize=16,color="black",shape="box"];188 -> 208[label="",style="solid", color="black", weight=3];
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207 -> 220[label="",style="dashed", color="red", weight=0];
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208[label="([],[])",fontsize=16,color="green",shape="box"];51[label="((sequence (map vz3 vz411) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 vz411)) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 vz411)) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];329[label="vz411/vz4110 : vz4111",fontsize=10,color="white",style="solid",shape="box"];51 -> 329[label="",style="solid", color="burlywood", weight=9];
329 -> 54[label="",style="solid", color="burlywood", weight=3];
330[label="vz411/[]",fontsize=10,color="white",style="solid",shape="box"];51 -> 330[label="",style="solid", color="burlywood", weight=9];
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221 -> 179[label="",style="dashed", color="red", weight=0];
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332 -> 223[label="",style="solid", color="burlywood", weight=3];
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55[label="((sequence (map vz3 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (map vz3 [])) >>= sequence0 vz50) ++ (vz51 >>= sequence1 ((vz70 : vz71) : map vz3 [])) >>= return . unzip",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
56[label="vz51 >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];333[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];56 -> 333[label="",style="solid", color="burlywood", weight=9];
333 -> 60[label="",style="solid", color="burlywood", weight=3];
334[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];56 -> 334[label="",style="solid", color="burlywood", weight=9];
334 -> 61[label="",style="solid", color="burlywood", weight=3];
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222[label="vz901",fontsize=16,color="green",shape="box"];223[label="unzip0 (vz9000,vz9001) vz25",fontsize=16,color="black",shape="box"];223 -> 226[label="",style="solid", color="black", weight=3];
58 -> 68[label="",style="dashed", color="red", weight=0];
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58 -> 73[label="",style="dashed", color="magenta", weight=3];
58 -> 74[label="",style="dashed", color="magenta", weight=3];
58 -> 75[label="",style="dashed", color="magenta", weight=3];
59 -> 103[label="",style="dashed", color="red", weight=0];
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59 -> 105[label="",style="dashed", color="magenta", weight=3];
59 -> 106[label="",style="dashed", color="magenta", weight=3];
59 -> 107[label="",style="dashed", color="magenta", weight=3];
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61[label="[] >>= sequence1 ([] : map vz3 vz411) >>= return . unzip",fontsize=16,color="black",shape="box"];61 -> 66[label="",style="solid", color="black", weight=3];
62[label="(vz50 : []) : ([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3];
226[label="(vz9000 : unzip00 vz25,vz9001 : unzip01 vz25)",fontsize=16,color="green",shape="box"];226 -> 243[label="",style="dashed", color="green", weight=3];
226 -> 244[label="",style="dashed", color="green", weight=3];
69[label="vz70",fontsize=16,color="green",shape="box"];70[label="vz4111",fontsize=16,color="green",shape="box"];71[label="vz71",fontsize=16,color="green",shape="box"];72[label="(sequence (vz3 vz4110 : map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];72 -> 83[label="",style="solid", color="black", weight=3];
73[label="vz51",fontsize=16,color="green",shape="box"];74[label="vz4110",fontsize=16,color="green",shape="box"];75[label="vz3",fontsize=16,color="green",shape="box"];68[label="vz9 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];337[label="vz9/vz90 : vz91",fontsize=10,color="white",style="solid",shape="box"];68 -> 337[label="",style="solid", color="burlywood", weight=9];
337 -> 84[label="",style="solid", color="burlywood", weight=3];
338[label="vz9/[]",fontsize=10,color="white",style="solid",shape="box"];68 -> 338[label="",style="solid", color="burlywood", weight=9];
338 -> 85[label="",style="solid", color="burlywood", weight=3];
104[label="(sequence [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];104 -> 120[label="",style="solid", color="black", weight=3];
105[label="vz51",fontsize=16,color="green",shape="box"];106[label="vz70",fontsize=16,color="green",shape="box"];107[label="vz71",fontsize=16,color="green",shape="box"];103[label="vz18 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="burlywood",shape="triangle"];339[label="vz18/vz180 : vz181",fontsize=10,color="white",style="solid",shape="box"];103 -> 339[label="",style="solid", color="burlywood", weight=9];
339 -> 121[label="",style="solid", color="burlywood", weight=3];
340[label="vz18/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 340[label="",style="solid", color="burlywood", weight=9];
340 -> 122[label="",style="solid", color="burlywood", weight=3];
65[label="sequence1 ([] : map vz3 vz411) vz510 ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];65 -> 87[label="",style="solid", color="black", weight=3];
66 -> 21[label="",style="dashed", color="red", weight=0];
66[label="[] >>= return . unzip",fontsize=16,color="magenta"];67 -> 129[label="",style="dashed", color="red", weight=0];
67[label="return . unzip ++ (([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip)",fontsize=16,color="magenta"];67 -> 132[label="",style="dashed", color="magenta", weight=3];
67 -> 133[label="",style="dashed", color="magenta", weight=3];
243[label="unzip00 vz25",fontsize=16,color="burlywood",shape="box"];343[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];243 -> 343[label="",style="solid", color="burlywood", weight=9];
343 -> 260[label="",style="solid", color="burlywood", weight=3];
244[label="unzip01 vz25",fontsize=16,color="burlywood",shape="box"];344[label="vz25/(vz250,vz251)",fontsize=10,color="white",style="solid",shape="box"];244 -> 344[label="",style="solid", color="burlywood", weight=9];
344 -> 261[label="",style="solid", color="burlywood", weight=3];
83 -> 89[label="",style="dashed", color="red", weight=0];
83[label="(vz3 vz4110 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz3 vz4110 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];83 -> 90[label="",style="dashed", color="magenta", weight=3];
84[label="(vz90 : vz91) ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];84 -> 91[label="",style="solid", color="black", weight=3];
85[label="[] ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3];
120[label="(return [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];120 -> 136[label="",style="solid", color="black", weight=3];
121[label="(vz180 : vz181) ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];121 -> 137[label="",style="solid", color="black", weight=3];
122[label="[] ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];122 -> 138[label="",style="solid", color="black", weight=3];
87[label="(sequence ([] : map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="black",shape="box"];87 -> 94[label="",style="solid", color="black", weight=3];
132[label="vz50 : []",fontsize=16,color="green",shape="box"];133[label="([] ++ ([] >>= sequence0 vz50)) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3];
260[label="unzip00 (vz250,vz251)",fontsize=16,color="black",shape="box"];260 -> 264[label="",style="solid", color="black", weight=3];
261[label="unzip01 (vz250,vz251)",fontsize=16,color="black",shape="box"];261 -> 265[label="",style="solid", color="black", weight=3];
90[label="vz3 vz4110",fontsize=16,color="green",shape="box"];90 -> 99[label="",style="dashed", color="green", weight=3];
89[label="(vz16 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 (vz16 : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];346[label="vz16/vz160 : vz161",fontsize=10,color="white",style="solid",shape="box"];89 -> 346[label="",style="solid", color="burlywood", weight=9];
346 -> 97[label="",style="solid", color="burlywood", weight=3];
347[label="vz16/[]",fontsize=10,color="white",style="solid",shape="box"];89 -> 347[label="",style="solid", color="burlywood", weight=9];
347 -> 98[label="",style="solid", color="burlywood", weight=3];
91[label="vz90 : vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="black",shape="box"];91 -> 100[label="",style="solid", color="black", weight=3];
92[label="vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];348[label="vz10/vz100 : vz101",fontsize=10,color="white",style="solid",shape="box"];92 -> 348[label="",style="solid", color="burlywood", weight=9];
348 -> 101[label="",style="solid", color="burlywood", weight=3];
349[label="vz10/[]",fontsize=10,color="white",style="solid",shape="box"];92 -> 349[label="",style="solid", color="burlywood", weight=9];
349 -> 102[label="",style="solid", color="burlywood", weight=3];
136[label="([] : [] >>= sequence0 vz70) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];136 -> 146[label="",style="solid", color="black", weight=3];
137[label="vz180 : vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3];
138[label="vz19 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="burlywood",shape="box"];350[label="vz19/vz190 : vz191",fontsize=10,color="white",style="solid",shape="box"];138 -> 350[label="",style="solid", color="burlywood", weight=9];
350 -> 148[label="",style="solid", color="burlywood", weight=3];
351[label="vz19/[]",fontsize=10,color="white",style="solid",shape="box"];138 -> 351[label="",style="solid", color="burlywood", weight=9];
351 -> 149[label="",style="solid", color="burlywood", weight=3];
94 -> 37[label="",style="dashed", color="red", weight=0];
94[label="([] >>= sequence1 (map vz3 vz411) >>= sequence0 vz510) ++ (vz511 >>= sequence1 ([] : map vz3 vz411)) >>= return . unzip",fontsize=16,color="magenta"];94 -> 123[label="",style="dashed", color="magenta", weight=3];
94 -> 124[label="",style="dashed", color="magenta", weight=3];
94 -> 125[label="",style="dashed", color="magenta", weight=3];
139[label="([] >>= sequence0 vz50) ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];139 -> 150[label="",style="solid", color="black", weight=3];
264[label="vz250",fontsize=16,color="green",shape="box"];265[label="vz251",fontsize=16,color="green",shape="box"];99[label="vz4110",fontsize=16,color="green",shape="box"];97[label="(vz160 : vz161 >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];97 -> 127[label="",style="solid", color="black", weight=3];
98[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];98 -> 128[label="",style="solid", color="black", weight=3];
100 -> 129[label="",style="dashed", color="red", weight=0];
100[label="return . unzip ++ (vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip)",fontsize=16,color="magenta"];100 -> 134[label="",style="dashed", color="magenta", weight=3];
101[label="vz100 : vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];101 -> 140[label="",style="solid", color="black", weight=3];
102[label="[] >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= return . unzip",fontsize=16,color="black",shape="box"];102 -> 141[label="",style="solid", color="black", weight=3];
146[label="(sequence0 vz70 [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];146 -> 157[label="",style="solid", color="black", weight=3];
147 -> 129[label="",style="dashed", color="red", weight=0];
147[label="return . unzip ++ (vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip)",fontsize=16,color="magenta"];147 -> 158[label="",style="dashed", color="magenta", weight=3];
147 -> 159[label="",style="dashed", color="magenta", weight=3];
148[label="vz190 : vz191 >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];148 -> 160[label="",style="solid", color="black", weight=3];
149[label="[] >>= sequence1 ((vz20 : vz21) : []) >>= return . unzip",fontsize=16,color="black",shape="box"];149 -> 161[label="",style="solid", color="black", weight=3];
123[label="[]",fontsize=16,color="green",shape="box"];124[label="vz510",fontsize=16,color="green",shape="box"];125[label="vz511",fontsize=16,color="green",shape="box"];150[label="[] ++ (vz51 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];150 -> 162[label="",style="solid", color="black", weight=3];
127[label="(sequence1 (map vz3 vz4111) vz160 ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];127 -> 142[label="",style="solid", color="black", weight=3];
128[label="([] >>= sequence0 vz70) ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];128 -> 143[label="",style="solid", color="black", weight=3];
134 -> 68[label="",style="dashed", color="red", weight=0];
134[label="vz91 ++ (vz10 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];134 -> 144[label="",style="dashed", color="magenta", weight=3];
140 -> 68[label="",style="dashed", color="red", weight=0];
140[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100 ++ (vz101 >>= sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15)) >>= return . unzip",fontsize=16,color="magenta"];140 -> 151[label="",style="dashed", color="magenta", weight=3];
140 -> 152[label="",style="dashed", color="magenta", weight=3];
141 -> 21[label="",style="dashed", color="red", weight=0];
141[label="[] >>= return . unzip",fontsize=16,color="magenta"];157[label="(return (vz70 : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];157 -> 170[label="",style="solid", color="black", weight=3];
158[label="vz180",fontsize=16,color="green",shape="box"];159 -> 103[label="",style="dashed", color="red", weight=0];
159[label="vz181 ++ (vz19 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];159 -> 171[label="",style="dashed", color="magenta", weight=3];
160 -> 103[label="",style="dashed", color="red", weight=0];
160[label="sequence1 ((vz20 : vz21) : []) vz190 ++ (vz191 >>= sequence1 ((vz20 : vz21) : [])) >>= return . unzip",fontsize=16,color="magenta"];160 -> 172[label="",style="dashed", color="magenta", weight=3];
160 -> 173[label="",style="dashed", color="magenta", weight=3];
161 -> 21[label="",style="dashed", color="red", weight=0];
161[label="[] >>= return . unzip",fontsize=16,color="magenta"];162[label="vz51 >>= sequence1 [] >>= return . unzip",fontsize=16,color="burlywood",shape="box"];361[label="vz51/vz510 : vz511",fontsize=10,color="white",style="solid",shape="box"];162 -> 361[label="",style="solid", color="burlywood", weight=9];
361 -> 174[label="",style="solid", color="burlywood", weight=3];
362[label="vz51/[]",fontsize=10,color="white",style="solid",shape="box"];162 -> 362[label="",style="solid", color="burlywood", weight=9];
362 -> 175[label="",style="solid", color="burlywood", weight=3];
142[label="((sequence (map vz3 vz4111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 vz4111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];363[label="vz4111/vz41110 : vz41111",fontsize=10,color="white",style="solid",shape="box"];142 -> 363[label="",style="solid", color="burlywood", weight=9];
363 -> 153[label="",style="solid", color="burlywood", weight=3];
364[label="vz4111/[]",fontsize=10,color="white",style="solid",shape="box"];142 -> 364[label="",style="solid", color="burlywood", weight=9];
364 -> 154[label="",style="solid", color="burlywood", weight=3];
143[label="[] ++ (vz71 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];143 -> 155[label="",style="solid", color="black", weight=3];
144[label="vz91",fontsize=16,color="green",shape="box"];151[label="sequence1 ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) vz100",fontsize=16,color="black",shape="triangle"];151 -> 163[label="",style="solid", color="black", weight=3];
152[label="vz101",fontsize=16,color="green",shape="box"];170[label="(((vz70 : []) : []) ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];170 -> 181[label="",style="solid", color="black", weight=3];
171[label="vz181",fontsize=16,color="green",shape="box"];172[label="sequence1 ((vz20 : vz21) : []) vz190",fontsize=16,color="black",shape="triangle"];172 -> 182[label="",style="solid", color="black", weight=3];
173[label="vz191",fontsize=16,color="green",shape="box"];174[label="vz510 : vz511 >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];174 -> 183[label="",style="solid", color="black", weight=3];
175[label="[] >>= sequence1 [] >>= return . unzip",fontsize=16,color="black",shape="box"];175 -> 184[label="",style="solid", color="black", weight=3];
153[label="((sequence (map vz3 (vz41110 : vz41111)) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 (vz41110 : vz41111))) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 (vz41110 : vz41111))) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];153 -> 164[label="",style="solid", color="black", weight=3];
154[label="((sequence (map vz3 []) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (map vz3 [])) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : map vz3 [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];154 -> 165[label="",style="solid", color="black", weight=3];
155[label="vz71 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];365[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];155 -> 365[label="",style="solid", color="burlywood", weight=9];
365 -> 166[label="",style="solid", color="burlywood", weight=3];
366[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];155 -> 366[label="",style="solid", color="burlywood", weight=9];
366 -> 167[label="",style="solid", color="burlywood", weight=3];
163[label="sequence ((vz11 : vz12) : vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];163 -> 176[label="",style="solid", color="black", weight=3];
181[label="((vz70 : []) : [] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];181 -> 189[label="",style="solid", color="black", weight=3];
182[label="sequence ((vz20 : vz21) : []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];182 -> 190[label="",style="solid", color="black", weight=3];
183[label="sequence1 [] vz510 ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="black",shape="box"];183 -> 191[label="",style="solid", color="black", weight=3];
184 -> 21[label="",style="dashed", color="red", weight=0];
184[label="[] >>= return . unzip",fontsize=16,color="magenta"];164 -> 177[label="",style="dashed", color="red", weight=0];
164[label="((sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];164 -> 178[label="",style="dashed", color="magenta", weight=3];
165 -> 185[label="",style="dashed", color="red", weight=0];
165[label="((sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];165 -> 186[label="",style="dashed", color="magenta", weight=3];
166[label="vz710 : vz711 >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];166 -> 192[label="",style="solid", color="black", weight=3];
167[label="[] >>= sequence1 ([] : map vz3 vz4111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];167 -> 193[label="",style="solid", color="black", weight=3];
176[label="vz11 : vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];176 -> 194[label="",style="solid", color="black", weight=3];
189[label="(vz70 : []) : ([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];189 -> 209[label="",style="solid", color="black", weight=3];
190[label="vz20 : vz21 >>= sequence1 [] >>= sequence0 vz190",fontsize=16,color="black",shape="box"];190 -> 210[label="",style="solid", color="black", weight=3];
191 -> 31[label="",style="dashed", color="red", weight=0];
191[label="(sequence [] >>= sequence0 vz510) ++ (vz511 >>= sequence1 []) >>= return . unzip",fontsize=16,color="magenta"];191 -> 211[label="",style="dashed", color="magenta", weight=3];
191 -> 212[label="",style="dashed", color="magenta", weight=3];
178 -> 72[label="",style="dashed", color="red", weight=0];
178[label="(sequence (vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz160) ++ (vz161 >>= sequence1 (vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz70",fontsize=16,color="magenta"];178 -> 195[label="",style="dashed", color="magenta", weight=3];
178 -> 196[label="",style="dashed", color="magenta", weight=3];
178 -> 197[label="",style="dashed", color="magenta", weight=3];
178 -> 198[label="",style="dashed", color="magenta", weight=3];
178 -> 199[label="",style="dashed", color="magenta", weight=3];
177[label="vz23 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];372[label="vz23/vz230 : vz231",fontsize=10,color="white",style="solid",shape="box"];177 -> 372[label="",style="solid", color="burlywood", weight=9];
372 -> 200[label="",style="solid", color="burlywood", weight=3];
373[label="vz23/[]",fontsize=10,color="white",style="solid",shape="box"];177 -> 373[label="",style="solid", color="burlywood", weight=9];
373 -> 201[label="",style="solid", color="burlywood", weight=3];
186 -> 104[label="",style="dashed", color="red", weight=0];
186[label="(sequence [] >>= sequence0 vz160) ++ (vz161 >>= sequence1 []) >>= sequence0 vz70",fontsize=16,color="magenta"];186 -> 202[label="",style="dashed", color="magenta", weight=3];
186 -> 203[label="",style="dashed", color="magenta", weight=3];
186 -> 204[label="",style="dashed", color="magenta", weight=3];
185[label="vz24 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];375[label="vz24/vz240 : vz241",fontsize=10,color="white",style="solid",shape="box"];185 -> 375[label="",style="solid", color="burlywood", weight=9];
375 -> 205[label="",style="solid", color="burlywood", weight=3];
376[label="vz24/[]",fontsize=10,color="white",style="solid",shape="box"];185 -> 376[label="",style="solid", color="burlywood", weight=9];
376 -> 206[label="",style="solid", color="burlywood", weight=3];
192[label="sequence1 ([] : map vz3 vz4111) vz710 ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];192 -> 213[label="",style="solid", color="black", weight=3];
193[label="[] >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];193 -> 214[label="",style="solid", color="black", weight=3];
194[label="sequence1 (vz13 vz14 : map vz13 vz15) vz11 ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="black",shape="box"];194 -> 215[label="",style="solid", color="black", weight=3];
209 -> 252[label="",style="dashed", color="red", weight=0];
209[label="sequence0 vz50 (vz70 : []) ++ (([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];209 -> 253[label="",style="dashed", color="magenta", weight=3];
209 -> 254[label="",style="dashed", color="magenta", weight=3];
210[label="sequence1 [] vz20 ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="black",shape="box"];210 -> 227[label="",style="solid", color="black", weight=3];
211[label="vz510",fontsize=16,color="green",shape="box"];212[label="vz511",fontsize=16,color="green",shape="box"];195[label="vz70",fontsize=16,color="green",shape="box"];196[label="vz161",fontsize=16,color="green",shape="box"];197[label="vz41110",fontsize=16,color="green",shape="box"];198[label="vz160",fontsize=16,color="green",shape="box"];199[label="vz41111",fontsize=16,color="green",shape="box"];200[label="(vz230 : vz231) ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];200 -> 216[label="",style="solid", color="black", weight=3];
201[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];201 -> 217[label="",style="solid", color="black", weight=3];
202[label="vz70",fontsize=16,color="green",shape="box"];203[label="vz161",fontsize=16,color="green",shape="box"];204[label="vz160",fontsize=16,color="green",shape="box"];205[label="(vz240 : vz241) ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];205 -> 218[label="",style="solid", color="black", weight=3];
206[label="[] ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];206 -> 219[label="",style="solid", color="black", weight=3];
213[label="(sequence ([] : map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];213 -> 228[label="",style="solid", color="black", weight=3];
214[label="[]",fontsize=16,color="green",shape="box"];215 -> 72[label="",style="dashed", color="red", weight=0];
215[label="(sequence (vz13 vz14 : map vz13 vz15) >>= sequence0 vz11) ++ (vz12 >>= sequence1 (vz13 vz14 : map vz13 vz15)) >>= sequence0 vz100",fontsize=16,color="magenta"];215 -> 229[label="",style="dashed", color="magenta", weight=3];
215 -> 230[label="",style="dashed", color="magenta", weight=3];
215 -> 231[label="",style="dashed", color="magenta", weight=3];
215 -> 232[label="",style="dashed", color="magenta", weight=3];
215 -> 233[label="",style="dashed", color="magenta", weight=3];
215 -> 234[label="",style="dashed", color="magenta", weight=3];
253 -> 262[label="",style="dashed", color="red", weight=0];
253[label="([] ++ ([] >>= sequence0 vz70)) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];253 -> 263[label="",style="dashed", color="magenta", weight=3];
254[label="vz70 : []",fontsize=16,color="green",shape="box"];252[label="sequence0 vz50 vz230 ++ vz27",fontsize=16,color="black",shape="triangle"];252 -> 266[label="",style="solid", color="black", weight=3];
227 -> 104[label="",style="dashed", color="red", weight=0];
227[label="(sequence [] >>= sequence0 vz20) ++ (vz21 >>= sequence1 []) >>= sequence0 vz190",fontsize=16,color="magenta"];227 -> 245[label="",style="dashed", color="magenta", weight=3];
227 -> 246[label="",style="dashed", color="magenta", weight=3];
227 -> 247[label="",style="dashed", color="magenta", weight=3];
216[label="vz230 : vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];216 -> 237[label="",style="solid", color="black", weight=3];
217[label="vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];381[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];217 -> 381[label="",style="solid", color="burlywood", weight=9];
381 -> 238[label="",style="solid", color="burlywood", weight=3];
382[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];217 -> 382[label="",style="solid", color="burlywood", weight=9];
382 -> 239[label="",style="solid", color="burlywood", weight=3];
218[label="vz240 : vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];218 -> 240[label="",style="solid", color="black", weight=3];
219[label="vz71 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];383[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];219 -> 383[label="",style="solid", color="burlywood", weight=9];
383 -> 241[label="",style="solid", color="burlywood", weight=3];
384[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];219 -> 384[label="",style="solid", color="burlywood", weight=9];
384 -> 242[label="",style="solid", color="burlywood", weight=3];
228 -> 89[label="",style="dashed", color="red", weight=0];
228[label="([] >>= sequence1 (map vz3 vz4111) >>= sequence0 vz710) ++ (vz711 >>= sequence1 ([] : map vz3 vz4111)) >>= sequence0 vz50",fontsize=16,color="magenta"];228 -> 248[label="",style="dashed", color="magenta", weight=3];
228 -> 249[label="",style="dashed", color="magenta", weight=3];
228 -> 250[label="",style="dashed", color="magenta", weight=3];
229[label="vz100",fontsize=16,color="green",shape="box"];230[label="vz12",fontsize=16,color="green",shape="box"];231[label="vz14",fontsize=16,color="green",shape="box"];232[label="vz11",fontsize=16,color="green",shape="box"];233[label="vz13",fontsize=16,color="green",shape="box"];234[label="vz15",fontsize=16,color="green",shape="box"];263 -> 193[label="",style="dashed", color="red", weight=0];
263[label="[] >>= sequence0 vz70",fontsize=16,color="magenta"];263 -> 267[label="",style="dashed", color="magenta", weight=3];
262[label="([] ++ vz28) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="triangle"];262 -> 268[label="",style="solid", color="black", weight=3];
266[label="return (vz50 : vz230) ++ vz27",fontsize=16,color="black",shape="box"];266 -> 275[label="",style="solid", color="black", weight=3];
245[label="vz190",fontsize=16,color="green",shape="box"];246[label="vz21",fontsize=16,color="green",shape="box"];247[label="vz20",fontsize=16,color="green",shape="box"];237 -> 252[label="",style="dashed", color="red", weight=0];
237[label="sequence0 vz50 vz230 ++ (vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50)",fontsize=16,color="magenta"];237 -> 257[label="",style="dashed", color="magenta", weight=3];
238[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];238 -> 269[label="",style="solid", color="black", weight=3];
239[label="[] >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];239 -> 270[label="",style="solid", color="black", weight=3];
240 -> 252[label="",style="dashed", color="red", weight=0];
240[label="sequence0 vz50 vz240 ++ (vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50)",fontsize=16,color="magenta"];240 -> 258[label="",style="dashed", color="magenta", weight=3];
240 -> 259[label="",style="dashed", color="magenta", weight=3];
241[label="vz710 : vz711 >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];241 -> 271[label="",style="solid", color="black", weight=3];
242[label="[] >>= sequence1 ((vz160 : vz161) : []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];242 -> 272[label="",style="solid", color="black", weight=3];
248[label="vz711",fontsize=16,color="green",shape="box"];249[label="vz710",fontsize=16,color="green",shape="box"];250[label="[]",fontsize=16,color="green",shape="box"];267[label="vz70",fontsize=16,color="green",shape="box"];268[label="vz28 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="burlywood",shape="triangle"];389[label="vz28/vz280 : vz281",fontsize=10,color="white",style="solid",shape="box"];268 -> 389[label="",style="solid", color="burlywood", weight=9];
389 -> 276[label="",style="solid", color="burlywood", weight=3];
390[label="vz28/[]",fontsize=10,color="white",style="solid",shape="box"];268 -> 390[label="",style="solid", color="burlywood", weight=9];
390 -> 277[label="",style="solid", color="burlywood", weight=3];
275[label="((vz50 : vz230) : []) ++ vz27",fontsize=16,color="black",shape="box"];275 -> 282[label="",style="solid", color="black", weight=3];
257 -> 177[label="",style="dashed", color="red", weight=0];
257[label="vz231 ++ (vz71 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];257 -> 273[label="",style="dashed", color="magenta", weight=3];
269 -> 177[label="",style="dashed", color="red", weight=0];
269[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111)) >>= sequence0 vz50",fontsize=16,color="magenta"];269 -> 278[label="",style="dashed", color="magenta", weight=3];
269 -> 279[label="",style="dashed", color="magenta", weight=3];
270 -> 193[label="",style="dashed", color="red", weight=0];
270[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];258 -> 185[label="",style="dashed", color="red", weight=0];
258[label="vz241 ++ (vz71 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];258 -> 274[label="",style="dashed", color="magenta", weight=3];
259[label="vz240",fontsize=16,color="green",shape="box"];271 -> 185[label="",style="dashed", color="red", weight=0];
271[label="sequence1 ((vz160 : vz161) : []) vz710 ++ (vz711 >>= sequence1 ((vz160 : vz161) : [])) >>= sequence0 vz50",fontsize=16,color="magenta"];271 -> 280[label="",style="dashed", color="magenta", weight=3];
271 -> 281[label="",style="dashed", color="magenta", weight=3];
272 -> 193[label="",style="dashed", color="red", weight=0];
272[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];276[label="(vz280 : vz281) ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];276 -> 283[label="",style="solid", color="black", weight=3];
277[label="[] ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];277 -> 284[label="",style="solid", color="black", weight=3];
282[label="(vz50 : vz230) : [] ++ vz27",fontsize=16,color="green",shape="box"];282 -> 294[label="",style="dashed", color="green", weight=3];
273[label="vz231",fontsize=16,color="green",shape="box"];278[label="vz711",fontsize=16,color="green",shape="box"];279 -> 151[label="",style="dashed", color="red", weight=0];
279[label="sequence1 ((vz160 : vz161) : vz3 vz41110 : map vz3 vz41111) vz710",fontsize=16,color="magenta"];279 -> 285[label="",style="dashed", color="magenta", weight=3];
279 -> 286[label="",style="dashed", color="magenta", weight=3];
279 -> 287[label="",style="dashed", color="magenta", weight=3];
279 -> 288[label="",style="dashed", color="magenta", weight=3];
279 -> 289[label="",style="dashed", color="magenta", weight=3];
279 -> 290[label="",style="dashed", color="magenta", weight=3];
274[label="vz241",fontsize=16,color="green",shape="box"];280[label="vz711",fontsize=16,color="green",shape="box"];281 -> 172[label="",style="dashed", color="red", weight=0];
281[label="sequence1 ((vz160 : vz161) : []) vz710",fontsize=16,color="magenta"];281 -> 291[label="",style="dashed", color="magenta", weight=3];
281 -> 292[label="",style="dashed", color="magenta", weight=3];
281 -> 293[label="",style="dashed", color="magenta", weight=3];
283[label="vz280 : vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="black",shape="box"];283 -> 295[label="",style="solid", color="black", weight=3];
284[label="vz71 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="burlywood",shape="box"];399[label="vz71/vz710 : vz711",fontsize=10,color="white",style="solid",shape="box"];284 -> 399[label="",style="solid", color="burlywood", weight=9];
399 -> 296[label="",style="solid", color="burlywood", weight=3];
400[label="vz71/[]",fontsize=10,color="white",style="solid",shape="box"];284 -> 400[label="",style="solid", color="burlywood", weight=9];
400 -> 297[label="",style="solid", color="burlywood", weight=3];
294[label="[] ++ vz27",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3];
285[label="vz160",fontsize=16,color="green",shape="box"];286[label="vz710",fontsize=16,color="green",shape="box"];287[label="vz41111",fontsize=16,color="green",shape="box"];288[label="vz161",fontsize=16,color="green",shape="box"];289[label="vz41110",fontsize=16,color="green",shape="box"];290[label="vz3",fontsize=16,color="green",shape="box"];291[label="vz710",fontsize=16,color="green",shape="box"];292[label="vz160",fontsize=16,color="green",shape="box"];293[label="vz161",fontsize=16,color="green",shape="box"];295 -> 252[label="",style="dashed", color="red", weight=0];
295[label="sequence0 vz50 vz280 ++ (vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50)",fontsize=16,color="magenta"];295 -> 299[label="",style="dashed", color="magenta", weight=3];
295 -> 300[label="",style="dashed", color="magenta", weight=3];
296[label="vz710 : vz711 >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];296 -> 301[label="",style="solid", color="black", weight=3];
297[label="[] >>= sequence1 [] >>= sequence0 vz50",fontsize=16,color="black",shape="box"];297 -> 302[label="",style="solid", color="black", weight=3];
298[label="vz27",fontsize=16,color="green",shape="box"];299 -> 268[label="",style="dashed", color="red", weight=0];
299[label="vz281 ++ (vz71 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];299 -> 303[label="",style="dashed", color="magenta", weight=3];
300[label="vz280",fontsize=16,color="green",shape="box"];301 -> 268[label="",style="dashed", color="red", weight=0];
301[label="sequence1 [] vz710 ++ (vz711 >>= sequence1 []) >>= sequence0 vz50",fontsize=16,color="magenta"];301 -> 304[label="",style="dashed", color="magenta", weight=3];
301 -> 305[label="",style="dashed", color="magenta", weight=3];
302 -> 193[label="",style="dashed", color="red", weight=0];
302[label="[] >>= sequence0 vz50",fontsize=16,color="magenta"];303[label="vz281",fontsize=16,color="green",shape="box"];304[label="sequence1 [] vz710",fontsize=16,color="black",shape="box"];304 -> 306[label="",style="solid", color="black", weight=3];
305[label="vz711",fontsize=16,color="green",shape="box"];306[label="sequence [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];306 -> 307[label="",style="solid", color="black", weight=3];
307[label="return [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];307 -> 308[label="",style="solid", color="black", weight=3];
308[label="[] : [] >>= sequence0 vz710",fontsize=16,color="black",shape="box"];308 -> 309[label="",style="solid", color="black", weight=3];
309 -> 252[label="",style="dashed", color="red", weight=0];
309[label="sequence0 vz710 [] ++ ([] >>= sequence0 vz710)",fontsize=16,color="magenta"];309 -> 310[label="",style="dashed", color="magenta", weight=3];
309 -> 311[label="",style="dashed", color="magenta", weight=3];
309 -> 312[label="",style="dashed", color="magenta", weight=3];
310[label="vz710",fontsize=16,color="green",shape="box"];311 -> 193[label="",style="dashed", color="red", weight=0];
311[label="[] >>= sequence0 vz710",fontsize=16,color="magenta"];311 -> 313[label="",style="dashed", color="magenta", weight=3];
312[label="[]",fontsize=16,color="green",shape="box"];313[label="vz710",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) → new_gtGtEs(vz281, vz71, vz50, h, ba)
new_gtGtEs([], :(vz710, vz711), vz50, h, ba) → new_gtGtEs(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba)

The TRS R consists of the following rules:

new_gtGtEs0(vz50, h, ba) → []
new_psPs(vz50, vz230, vz27, h, ba) → :(:(vz50, vz230), vz27)

The set Q consists of the following terms:

new_gtGtEs0(x0, x1, x2)
new_psPs(x0, x1, x2, x3, x4)

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_gtGtEs(:(vz280, vz281), vz71, vz50, h, ba) → new_gtGtEs(vz281, vz71, vz50, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
new_gtGtEs([], :(vz710, vz711), vz50, h, ba) → new_gtGtEs(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba)
The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) → new_gtGtEs1(new_sequence1(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba)
new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) → new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba)

The TRS R consists of the following rules:

new_gtGtEs4([], [], vz50, h, ba) → new_gtGtEs0(vz50, h, ba)
new_sequence1(vz20, vz21, vz190, bb, bc) → new_gtGtEs2(vz20, vz21, vz190, bb, bc)
new_gtGtEs2(vz70, vz71, vz50, h, ba) → new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, h, ba), vz71, vz50, h, ba), h, ba)
new_gtGtEs0(vz50, h, ba) → []
new_gtGtEs3(vz28, vz71, vz50, h, ba) → new_gtGtEs4(vz28, vz71, vz50, h, ba)
new_gtGtEs4(:(vz280, vz281), vz71, vz50, h, ba) → new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, h, ba), h, ba)
new_psPs(vz50, vz230, vz27, h, ba) → :(:(vz50, vz230), vz27)
new_gtGtEs4([], :(vz710, vz711), vz50, h, ba) → new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, h, ba), h, ba), vz711, vz50, h, ba)

The set Q consists of the following terms:

new_gtGtEs2(x0, x1, x2, x3, x4)
new_gtGtEs0(x0, x1, x2)
new_gtGtEs3(x0, x1, x2, x3, x4)
new_sequence1(x0, x1, x2, x3, x4)
new_psPs(x0, x1, x2, x3, x4)
new_gtGtEs4([], [], x0, x1, x2)
new_gtGtEs4([], :(x0, x1), x2, x3, x4)
new_gtGtEs4(:(x0, x1), x2, x3, x4, x5)

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_gtGtEs1([], :(vz710, vz711), vz160, vz161, vz50, h, ba) → new_gtGtEs1(new_sequence1(vz160, vz161, vz710, h, ba), vz711, vz160, vz161, vz50, h, ba)
The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7
new_gtGtEs1(:(vz240, vz241), vz71, vz160, vz161, vz50, h, ba) → new_gtGtEs1(vz241, vz71, vz160, vz161, vz50, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_sequence11(vz13, vz14, vz15, bc, bd, be) → new_gtGtEs5(vz13, vz14, vz15, bc, bd, be)
new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_sequence11(vz3, vz41110, vz41111, h, ba, bb)

The TRS R consists of the following rules:

new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, bc, bd, be) → new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, bc, bd, be)

The set Q consists of the following terms:

new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

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

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                          ↳ QDP

                            ↳ QReductionProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_sequence11(vz13, vz14, vz15, bc, bd, be) → new_gtGtEs5(vz13, vz14, vz15, bc, bd, be)
new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_sequence11(vz3, vz41110, vz41111, h, ba, bb)

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

new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

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_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                          ↳ QDP

                            ↳ QReductionProof

                              ↳ QDP

                                ↳ UsableRulesReductionPairsProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_sequence11(vz13, vz14, vz15, bc, bd, be) → new_gtGtEs5(vz13, vz14, vz15, bc, bd, be)
new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_sequence11(vz3, vz41110, vz41111, h, ba, bb)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the usable rules with reduction pair processor [15] with a polynomial ordering [25], all dependency pairs and the corresponding usable rules [17] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well.

The following dependency pairs can be deleted:

new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs5(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, :(vz41110, vz41111), h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_sequence11(vz3, vz41110, vz41111, h, ba, bb)

No rules are removed from R.

Used ordering: POLO with Polynomial interpretation [25]:

POL(:(x₁, x₂)) = 1 + 2·x₁ + x₂
POL(new_gtGtEs5(x₁, x₂, x₃, x₄, x₅, x₆)) = x₁ + x₂ + 2·x₃ + x₄ + x₅ + x₆
POL(new_gtGtEs6(x₁, x₂, x₃, x₄, x₅)) = x₁ + 2·x₂ + x₃ + x₄ + x₅
POL(new_gtGtEs7(x₁, x₂, x₃, x₄, x₅, x₆)) = 1 + x₁ + 2·x₂ + 2·x₃ + x₄ + x₅ + x₆
POL(new_sequence11(x₁, x₂, x₃, x₄, x₅, x₆)) = x₁ + 2·x₂ + 2·x₃ + x₄ + x₅ + x₆

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                          ↳ QDP

                            ↳ QReductionProof

                              ↳ QDP

                                ↳ UsableRulesReductionPairsProof

                                  ↳ QDP

                                    ↳ DependencyGraphProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)
new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)
new_sequence11(vz13, vz14, vz15, bc, bd, be) → new_gtGtEs5(vz13, vz14, vz15, bc, bd, be)
new_gtGtEs5(vz3, vz4110, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                          ↳ QDP

                            ↳ QReductionProof

                              ↳ QDP

                                ↳ UsableRulesReductionPairsProof

                                  ↳ QDP

                                    ↳ DependencyGraphProof

                                      ↳ AND

                                        ↳ QDP

                                          ↳ NonTerminationProof

                                        ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)

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

The TRS P consists of the following rules:

new_gtGtEs6(vz3, vz4111, h, ba, bb) → new_gtGtEs6(vz3, vz4111, h, ba, bb)

The TRS R consists of the following rules:none

s = new_gtGtEs6(vz3, vz4111, h, ba, bb) evaluates to t =new_gtGtEs6(vz3, vz4111, h, ba, bb)

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

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_gtGtEs6(vz3, vz4111, h, ba, bb) to new_gtGtEs6(vz3, vz4111, h, ba, bb).

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ UsableRulesProof

                          ↳ QDP

                            ↳ QReductionProof

                              ↳ QDP

                                ↳ UsableRulesReductionPairsProof

                                  ↳ QDP

                                    ↳ DependencyGraphProof

                                      ↳ AND

                                        ↳ QDP

                                        ↳ QDP

                                          ↳ NonTerminationProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) → new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)

The TRS R consists of the following rules:none

s = new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) evaluates to t =new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb)

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

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb) to new_gtGtEs7(vz3, vz41110, vz41111, h, ba, bb).

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_foldr(:(vz900, vz901), h, ba) → new_foldr(vz901, 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_foldr(:(vz900, vz901), h, ba) → new_foldr(vz901, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs9(vz50, :(vz510, vz511), h, ba) → new_gtGtEs9(vz510, vz511, h, ba)

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

new_gtGtEs9(vz50, :(vz510, vz511), h, ba) → new_gtGtEs9(vz510, vz511, h, ba)
The graph contains the following edges 2 > 1, 2 > 2, 3 >= 3, 4 >= 4

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) → new_gtGtEs10(new_sequence1(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba)
new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) → new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba)

The TRS R consists of the following rules:

new_gtGtEs4([], [], vz50, bb, bc) → new_gtGtEs0(vz50, bb, bc)
new_sequence1(vz20, vz21, vz190, h, ba) → new_gtGtEs2(vz20, vz21, vz190, h, ba)
new_gtGtEs2(vz70, vz71, vz50, bb, bc) → new_psPs(vz50, :(vz70, []), new_gtGtEs3(new_gtGtEs0(vz70, bb, bc), vz71, vz50, bb, bc), bb, bc)
new_gtGtEs0(vz50, bb, bc) → []
new_gtGtEs3(vz28, vz71, vz50, bb, bc) → new_gtGtEs4(vz28, vz71, vz50, bb, bc)
new_gtGtEs4(:(vz280, vz281), vz71, vz50, bb, bc) → new_psPs(vz50, vz280, new_gtGtEs4(vz281, vz71, vz50, bb, bc), bb, bc)
new_psPs(vz50, vz230, vz27, bb, bc) → :(:(vz50, vz230), vz27)
new_gtGtEs4([], :(vz710, vz711), vz50, bb, bc) → new_gtGtEs4(new_psPs(vz710, [], new_gtGtEs0(vz710, bb, bc), bb, bc), vz711, vz50, bb, bc)

The set Q consists of the following terms:

new_gtGtEs2(x0, x1, x2, x3, x4)
new_gtGtEs3(x0, x1, x2, x3, x4)
new_gtGtEs4(:(x0, x1), x2, x3, x4, x5)
new_gtGtEs0(x0, x1, x2)
new_sequence1(x0, x1, x2, x3, x4)
new_gtGtEs4([], :(x0, x1), x2, x3, x4)
new_psPs(x0, x1, x2, x3, x4)
new_gtGtEs4([], [], x0, 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_gtGtEs10([], :(vz190, vz191), vz20, vz21, h, ba) → new_gtGtEs10(new_sequence1(vz20, vz21, vz190, h, ba), vz191, vz20, vz21, h, ba)
The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6
new_gtGtEs10(:(vz180, vz181), vz19, vz20, vz21, h, ba) → new_gtGtEs10(vz181, vz19, vz20, vz21, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ DependencyGraphProof

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb)
new_gtGtEs11([], :(vz100, vz101), vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb), vz101, vz11, vz12, vz13, vz14, vz15, h, ba, bb)

The TRS R consists of the following rules:

new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb) → new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, h, ba, bb)

The set Q consists of the following terms:

new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

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

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ QDP

                            ↳ UsableRulesProof

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb)

The TRS R consists of the following rules:

new_sequence10(vz11, vz12, vz13, vz14, vz15, vz100, h, ba, bb) → new_gtGtEs8(vz13, vz14, vz15, vz11, vz12, vz100, h, ba, bb)

The set Q consists of the following terms:

new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ QDP

                            ↳ UsableRulesProof

                              ↳ QDP

                                ↳ QReductionProof

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb)

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

new_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

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_sequence10(x0, x1, x2, x3, x4, x5, x6, x7, x8)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ QDP

                            ↳ UsableRulesProof

                              ↳ QDP

                                ↳ QReductionProof

                                  ↳ QDP

                                    ↳ QDPSizeChangeProof

                      ↳ QDP

                  ↳ Narrow

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

new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb)

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

new_gtGtEs11(:(vz90, vz91), vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb) → new_gtGtEs11(vz91, vz10, vz11, vz12, vz13, vz14, vz15, h, ba, bb)
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

      ↳ IPR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                  ↳ Narrow

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

new_gtGtEs12([], vz3, vz411, vz50, :(vz510, vz511), h, ba, bb) → new_gtGtEs12([], vz3, vz411, vz510, vz511, h, ba, bb)

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

new_gtGtEs12([], vz3, vz411, vz50, :(vz510, vz511), h, ba, bb) → new_gtGtEs12([], vz3, vz411, vz510, vz511, h, ba, bb)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7, 8 >= 8

Haskell To QDPs