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

YES 1.2530000000000001 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule List

((isSuffixOf :: [Char] -> [Char] -> Bool) :: [Char] -> [Char] -> Bool)

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] _	=	True
isPrefixOf	_ []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule List

((isSuffixOf :: [Char] -> [Char] -> Bool) :: [Char] -> [Char] -> Bool)

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
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

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule List

(isSuffixOf :: [Char] -> [Char] -> Bool)

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

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291 -> 285[label="",style="dashed", color="red", weight=0];
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294[label="wu1711\n  Eq a",fontsize=16,color="green",shape="box"];295[label="isPrefixOf ((:) wu15 wu14) (wu180 : wu181)\n  Eq a",fontsize=16,color="black",shape="box"];295 -> 299[label="",style="solid", color="black", weight=3];
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421[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];302 -> 421[label="",style="solid", color="blue", weight=9];
421 -> 308[label="",style="solid", color="blue", weight=3];
422[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];302 -> 422[label="",style="solid", color="blue", weight=9];
422 -> 309[label="",style="solid", color="blue", weight=3];
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428 -> 315[label="",style="solid", color="blue", weight=3];
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311[label="wu15 == wu180\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];311 -> 327[label="",style="solid", color="black", weight=3];
312[label="wu15 == wu180",fontsize=16,color="black",shape="triangle"];312 -> 328[label="",style="solid", color="black", weight=3];
313[label="wu15 == wu180",fontsize=16,color="black",shape="triangle"];313 -> 329[label="",style="solid", color="black", weight=3];
314[label="wu15 == wu180",fontsize=16,color="black",shape="triangle"];314 -> 330[label="",style="solid", color="black", weight=3];
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316[label="wu15 == wu180",fontsize=16,color="black",shape="triangle"];316 -> 332[label="",style="solid", color="black", weight=3];
317[label="wu15 == wu180\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];317 -> 333[label="",style="solid", color="black", weight=3];
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320[label="True && isPrefixOf wu24 wu25\n  Eq a",fontsize=16,color="black",shape="box"];320 -> 336[label="",style="solid", color="black", weight=3];
321[label="error []",fontsize=16,color="red",shape="box"];322[label="error []",fontsize=16,color="red",shape="box"];323[label="error []",fontsize=16,color="red",shape="box"];324[label="error []",fontsize=16,color="red",shape="box"];325[label="error []",fontsize=16,color="red",shape="box"];326[label="primEqChar wu15 wu180",fontsize=16,color="burlywood",shape="box"];434[label="wu15/Char wu150",fontsize=10,color="white",style="solid",shape="box"];326 -> 434[label="",style="solid", color="burlywood", weight=9];
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438 -> 341[label="",style="solid", color="burlywood", weight=3];
439[label="wu25/[]",fontsize=10,color="white",style="solid",shape="box"];338 -> 439[label="",style="solid", color="burlywood", weight=9];
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441 -> 348[label="",style="solid", color="burlywood", weight=3];
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345 -> 350[label="",style="dashed", color="magenta", weight=3];
345 -> 351[label="",style="dashed", color="magenta", weight=3];
346[label="False",fontsize=16,color="green",shape="box"];347[label="primEqNat (Succ wu1500) wu1800",fontsize=16,color="burlywood",shape="box"];443[label="wu1800/Succ wu18000",fontsize=10,color="white",style="solid",shape="box"];347 -> 443[label="",style="solid", color="burlywood", weight=9];
443 -> 352[label="",style="solid", color="burlywood", weight=3];
444[label="wu1800/Zero",fontsize=10,color="white",style="solid",shape="box"];347 -> 444[label="",style="solid", color="burlywood", weight=9];
444 -> 353[label="",style="solid", color="burlywood", weight=3];
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445 -> 354[label="",style="solid", color="burlywood", weight=3];
446[label="wu1800/Zero",fontsize=10,color="white",style="solid",shape="box"];348 -> 446[label="",style="solid", color="burlywood", weight=9];
446 -> 355[label="",style="solid", color="burlywood", weight=3];
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448[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 448[label="",style="solid", color="blue", weight=9];
448 -> 357[label="",style="solid", color="blue", weight=3];
449[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 449[label="",style="solid", color="blue", weight=9];
449 -> 358[label="",style="solid", color="blue", weight=3];
450[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 450[label="",style="solid", color="blue", weight=9];
450 -> 359[label="",style="solid", color="blue", weight=3];
451[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 451[label="",style="solid", color="blue", weight=9];
451 -> 360[label="",style="solid", color="blue", weight=3];
452[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 452[label="",style="solid", color="blue", weight=9];
452 -> 361[label="",style="solid", color="blue", weight=3];
453[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 453[label="",style="solid", color="blue", weight=9];
453 -> 362[label="",style="solid", color="blue", weight=3];
454[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 454[label="",style="solid", color="blue", weight=9];
454 -> 363[label="",style="solid", color="blue", weight=3];
455[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 455[label="",style="solid", color="blue", weight=9];
455 -> 364[label="",style="solid", color="blue", weight=3];
456[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 456[label="",style="solid", color="blue", weight=9];
456 -> 365[label="",style="solid", color="blue", weight=3];
457[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 457[label="",style="solid", color="blue", weight=9];
457 -> 366[label="",style="solid", color="blue", weight=3];
458[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 458[label="",style="solid", color="blue", weight=9];
458 -> 367[label="",style="solid", color="blue", weight=3];
459[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 459[label="",style="solid", color="blue", weight=9];
459 -> 368[label="",style="solid", color="blue", weight=3];
460[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];349 -> 460[label="",style="solid", color="blue", weight=9];
460 -> 369[label="",style="solid", color="blue", weight=3];
350[label="wu241\n  Eq a",fontsize=16,color="green",shape="box"];351[label="wu251\n  Eq a",fontsize=16,color="green",shape="box"];352[label="primEqNat (Succ wu1500) (Succ wu18000)",fontsize=16,color="black",shape="box"];352 -> 370[label="",style="solid", color="black", weight=3];
353[label="primEqNat (Succ wu1500) Zero",fontsize=16,color="black",shape="box"];353 -> 371[label="",style="solid", color="black", weight=3];
354[label="primEqNat Zero (Succ wu18000)",fontsize=16,color="black",shape="box"];354 -> 372[label="",style="solid", color="black", weight=3];
355[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];355 -> 373[label="",style="solid", color="black", weight=3];
356 -> 305[label="",style="dashed", color="red", weight=0];
356[label="wu240 == wu250",fontsize=16,color="magenta"];356 -> 374[label="",style="dashed", color="magenta", weight=3];
356 -> 375[label="",style="dashed", color="magenta", weight=3];
357 -> 306[label="",style="dashed", color="red", weight=0];
357[label="wu240 == wu250",fontsize=16,color="magenta"];357 -> 376[label="",style="dashed", color="magenta", weight=3];
357 -> 377[label="",style="dashed", color="magenta", weight=3];
358 -> 307[label="",style="dashed", color="red", weight=0];
358[label="wu240 == wu250\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];358 -> 378[label="",style="dashed", color="magenta", weight=3];
358 -> 379[label="",style="dashed", color="magenta", weight=3];
359 -> 308[label="",style="dashed", color="red", weight=0];
359[label="wu240 == wu250\n  Eq a",fontsize=16,color="magenta"];359 -> 380[label="",style="dashed", color="magenta", weight=3];
359 -> 381[label="",style="dashed", color="magenta", weight=3];
360 -> 309[label="",style="dashed", color="red", weight=0];
360[label="wu240 == wu250\n  Integral a",fontsize=16,color="magenta"];360 -> 382[label="",style="dashed", color="magenta", weight=3];
360 -> 383[label="",style="dashed", color="magenta", weight=3];
361 -> 310[label="",style="dashed", color="red", weight=0];
361[label="wu240 == wu250",fontsize=16,color="magenta"];361 -> 384[label="",style="dashed", color="magenta", weight=3];
361 -> 385[label="",style="dashed", color="magenta", weight=3];
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362[label="wu240 == wu250\n  Eq a  Eq b",fontsize=16,color="magenta"];362 -> 386[label="",style="dashed", color="magenta", weight=3];
362 -> 387[label="",style="dashed", color="magenta", weight=3];
363 -> 312[label="",style="dashed", color="red", weight=0];
363[label="wu240 == wu250",fontsize=16,color="magenta"];363 -> 388[label="",style="dashed", color="magenta", weight=3];
363 -> 389[label="",style="dashed", color="magenta", weight=3];
364 -> 313[label="",style="dashed", color="red", weight=0];
364[label="wu240 == wu250",fontsize=16,color="magenta"];364 -> 390[label="",style="dashed", color="magenta", weight=3];
364 -> 391[label="",style="dashed", color="magenta", weight=3];
365 -> 314[label="",style="dashed", color="red", weight=0];
365[label="wu240 == wu250",fontsize=16,color="magenta"];365 -> 392[label="",style="dashed", color="magenta", weight=3];
365 -> 393[label="",style="dashed", color="magenta", weight=3];
366 -> 315[label="",style="dashed", color="red", weight=0];
366[label="wu240 == wu250",fontsize=16,color="magenta"];366 -> 394[label="",style="dashed", color="magenta", weight=3];
366 -> 395[label="",style="dashed", color="magenta", weight=3];
367 -> 316[label="",style="dashed", color="red", weight=0];
367[label="wu240 == wu250",fontsize=16,color="magenta"];367 -> 396[label="",style="dashed", color="magenta", weight=3];
367 -> 397[label="",style="dashed", color="magenta", weight=3];
368 -> 317[label="",style="dashed", color="red", weight=0];
368[label="wu240 == wu250\n  Eq a  Eq b",fontsize=16,color="magenta"];368 -> 398[label="",style="dashed", color="magenta", weight=3];
368 -> 399[label="",style="dashed", color="magenta", weight=3];
369 -> 318[label="",style="dashed", color="red", weight=0];
369[label="wu240 == wu250\n  Eq a",fontsize=16,color="magenta"];369 -> 400[label="",style="dashed", color="magenta", weight=3];
369 -> 401[label="",style="dashed", color="magenta", weight=3];
370 -> 344[label="",style="dashed", color="red", weight=0];
370[label="primEqNat wu1500 wu18000",fontsize=16,color="magenta"];370 -> 402[label="",style="dashed", color="magenta", weight=3];
370 -> 403[label="",style="dashed", color="magenta", weight=3];
371[label="False",fontsize=16,color="green",shape="box"];372[label="False",fontsize=16,color="green",shape="box"];373[label="True",fontsize=16,color="green",shape="box"];374[label="wu250",fontsize=16,color="green",shape="box"];375[label="wu240",fontsize=16,color="green",shape="box"];376[label="wu250",fontsize=16,color="green",shape="box"];377[label="wu240",fontsize=16,color="green",shape="box"];378[label="wu250\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];379[label="wu240\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];380[label="wu250\n  Eq a",fontsize=16,color="green",shape="box"];381[label="wu240\n  Eq a",fontsize=16,color="green",shape="box"];382[label="wu250\n  Integral a",fontsize=16,color="green",shape="box"];383[label="wu240\n  Integral a",fontsize=16,color="green",shape="box"];384[label="wu250",fontsize=16,color="green",shape="box"];385[label="wu240",fontsize=16,color="green",shape="box"];386[label="wu250\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];387[label="wu240\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];388[label="wu250",fontsize=16,color="green",shape="box"];389[label="wu240",fontsize=16,color="green",shape="box"];390[label="wu250",fontsize=16,color="green",shape="box"];391[label="wu240",fontsize=16,color="green",shape="box"];392[label="wu250",fontsize=16,color="green",shape="box"];393[label="wu240",fontsize=16,color="green",shape="box"];394[label="wu250",fontsize=16,color="green",shape="box"];395[label="wu240",fontsize=16,color="green",shape="box"];396[label="wu250",fontsize=16,color="green",shape="box"];397[label="wu240",fontsize=16,color="green",shape="box"];398[label="wu250\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];399[label="wu240\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];400[label="wu250\n  Eq a",fontsize=16,color="green",shape="box"];401[label="wu240\n  Eq a",fontsize=16,color="green",shape="box"];402[label="wu1500",fontsize=16,color="green",shape="box"];403[label="wu18000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(wu1500), Succ(wu18000)) → new_primEqNat(wu1500, wu18000)

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_primEqNat(Succ(wu1500), Succ(wu18000)) → new_primEqNat(wu1500, wu18000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_asAs(True, :(wu240, wu241), :(wu250, wu251), ba) → new_asAs(new_esEs(wu240, wu250, ba), wu241, wu251, ba)

The TRS R consists of the following rules:

new_esEs7(wu15, wu180) → error([])
new_esEs2(wu15, wu180, db, dc, dd) → error([])
new_primEqNat0(Succ(wu1500), Succ(wu18000)) → new_primEqNat0(wu1500, wu18000)
new_primEqNat0(Zero, Zero) → True
new_esEs3(wu15, wu180, cd) → error([])
new_esEs(wu240, wu250, ty_Double) → new_esEs10(wu240, wu250)
new_esEs13(wu15, wu180, cg) → error([])
new_esEs(wu240, wu250, ty_Int) → new_esEs7(wu240, wu250)
new_esEs(wu240, wu250, ty_Float) → new_esEs11(wu240, wu250)
new_esEs8(wu15, wu180) → error([])
new_esEs(wu240, wu250, ty_Bool) → new_esEs1(wu240, wu250)
new_primEqNat0(Succ(wu1500), Zero) → False
new_primEqNat0(Zero, Succ(wu18000)) → False
new_esEs(wu240, wu250, app(app(ty_@2, ca), cb)) → new_esEs12(wu240, wu250, ca, cb)
new_esEs6(wu15, wu180, ce, cf) → error([])
new_esEs(wu240, wu250, ty_Ordering) → new_esEs8(wu240, wu250)
new_esEs5(Char(wu150), Char(wu1800)) → new_primEqNat0(wu150, wu1800)
new_esEs4(wu15, wu180, da) → error([])
new_esEs(wu240, wu250, app(app(ty_Either, bg), bh)) → new_esEs6(wu240, wu250, bg, bh)
new_esEs9(wu15, wu180) → error([])
new_esEs(wu240, wu250, app(ty_[], be)) → new_esEs3(wu240, wu250, be)
new_esEs1(wu15, wu180) → error([])
new_esEs(wu240, wu250, ty_@0) → new_esEs0(wu240, wu250)
new_esEs12(wu15, wu180, de, df) → error([])
new_esEs11(wu15, wu180) → error([])
new_esEs(wu240, wu250, app(app(app(ty_@3, bb), bc), bd)) → new_esEs2(wu240, wu250, bb, bc, bd)
new_esEs10(wu15, wu180) → error([])
new_esEs(wu240, wu250, app(ty_Maybe, cc)) → new_esEs13(wu240, wu250, cc)
new_esEs0(wu15, wu180) → error([])
new_esEs(wu240, wu250, ty_Char) → new_esEs5(wu240, wu250)
new_esEs(wu240, wu250, ty_Integer) → new_esEs9(wu240, wu250)
new_esEs(wu240, wu250, app(ty_Ratio, bf)) → new_esEs4(wu240, wu250, bf)

The set Q consists of the following terms:

new_esEs6(x0, x1, x2, x3)
new_esEs(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1)
new_esEs(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_esEs(x0, x1, ty_Int)
new_esEs(x0, x1, app(app(ty_Either, x2), x3))
new_esEs(x0, x1, ty_Bool)
new_esEs(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs(x0, x1, ty_Integer)
new_esEs7(x0, x1)
new_esEs10(x0, x1)
new_esEs12(x0, x1, x2, x3)
new_esEs9(x0, x1)
new_esEs(x0, x1, app(app(ty_@2, x2), x3))
new_esEs(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_primEqNat0(Zero, Zero)
new_esEs(x0, x1, ty_Double)
new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13(x0, x1, x2)
new_esEs5(Char(x0), Char(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs1(x0, x1)
new_esEs4(x0, x1, x2)
new_esEs3(x0, x1, x2)
new_esEs(x0, x1, ty_Float)
new_esEs2(x0, x1, x2, x3, x4)
new_esEs0(x0, x1)
new_esEs(x0, x1, app(ty_Maybe, x2))
new_esEs(x0, x1, ty_Ordering)

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_asAs(True, :(wu240, wu241), :(wu250, wu251), ba) → new_asAs(new_esEs(wu240, wu250, ba), wu241, wu251, ba)
The graph contains the following edges 2 > 2, 3 > 3, 4 >= 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_isPrefixOf(wu15, wu14, wu18, :(wu1710, wu1711), ba) → new_isPrefixOf(wu15, wu14, new_flip(wu18, wu1710, ba), wu1711, ba)

The TRS R consists of the following rules:

new_flip(wu14, wu15, ba) → :(wu15, wu14)

The set Q consists of the following terms:

new_flip(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_isPrefixOf(wu15, wu14, wu18, :(wu1710, wu1711), ba) → new_isPrefixOf(wu15, wu14, new_flip(wu18, wu1710, ba), wu1711, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_isPrefixOf0(wu14, wu15, :(wu160, wu161), wu17, ba) → new_isPrefixOf0(new_flip(wu14, wu15, ba), wu160, wu161, wu17, ba)

The TRS R consists of the following rules:

new_flip(wu14, wu15, ba) → :(wu15, wu14)

The set Q consists of the following terms:

new_flip(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_isPrefixOf0(wu14, wu15, :(wu160, wu161), wu17, ba) → new_isPrefixOf0(new_flip(wu14, wu15, ba), wu160, wu161, wu17, ba)
The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5