YES 122.354
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
| ((nub :: [Char] -> [Char]) :: [Char] -> [Char]) |
module List where
| import qualified Maybe import qualified Prelude
|
| nub :: Eq a => [a] -> [a]
nub | l | = |
nub' l [] | where |
nub' | [] _ | = | [] |
nub' | (x : xs) ls | |
| | x `elem` ls | = |
|
| | otherwise | = |
|
|
|
|
|
|
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
| ((nub :: [Char] -> [Char]) :: [Char] -> [Char]) |
module List where
| import qualified Maybe import qualified Prelude
|
| nub :: Eq a => [a] -> [a]
nub | l | = |
nub' l [] | where |
nub' | [] vw | = | [] |
nub' | (x : xs) ls | |
| | x `elem` ls | = |
|
| | otherwise | = |
|
|
|
|
|
|
module Maybe where
| import qualified List import qualified Prelude
|
Cond Reductions:
The following Function with conditions
nub' | [] vw | = [] |
nub' | (x : xs) ls |
| | x `elem` ls | |
| | otherwise | |
|
is transformed to
nub' | [] vw | = nub'3 [] vw |
nub' | (x : xs) ls | = nub'2 (x : xs) ls |
nub'0 | x xs ls True | = x : nub' xs (x : ls) |
nub'1 | x xs ls True | = nub' xs ls |
nub'1 | x xs ls False | = nub'0 x xs ls otherwise |
nub'2 | (x : xs) ls | = nub'1 x xs ls (x `elem` ls) |
nub'3 | [] vw | = [] |
nub'3 | wv ww | = nub'2 wv ww |
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule List
| ((nub :: [Char] -> [Char]) :: [Char] -> [Char]) |
module List where
| import qualified Maybe import qualified Prelude
|
| nub :: Eq a => [a] -> [a]
nub | l | = |
nub' l [] | where |
nub' | [] vw | = | nub'3 [] vw |
nub' | (x : xs) ls | = | nub'2 (x : xs) ls |
|
nub'0 | x xs ls True | = | x : nub' xs (x : ls) |
|
nub'1 | x xs ls True | = | nub' xs ls |
nub'1 | x xs ls False | = | nub'0 x xs ls otherwise |
|
nub'2 | (x : xs) ls | = | nub'1 x xs ls (x `elem` ls) |
|
nub'3 | [] vw | = | [] |
nub'3 | wv ww | = | nub'2 wv ww |
|
|
|
|
module Maybe where
| import qualified List import qualified Prelude
|
Let/Where Reductions:
The bindings of the following Let/Where expression
nub' l [] |
where |
nub' | [] vw | = nub'3 [] vw |
nub' | (x : xs) ls | = nub'2 (x : xs) ls |
|
|
nub'0 | x xs ls True | = x : nub' xs (x : ls) |
|
|
nub'1 | x xs ls True | = nub' xs ls |
nub'1 | x xs ls False | = nub'0 x xs ls otherwise |
|
|
nub'2 | (x : xs) ls | = nub'1 x xs ls (x `elem` ls) |
|
|
nub'3 | [] vw | = [] |
nub'3 | wv ww | = nub'2 wv ww |
|
are unpacked to the following functions on top level
nubNub'3 | [] vw | = [] |
nubNub'3 | wv ww | = nubNub'2 wv ww |
nubNub' | [] vw | = nubNub'3 [] vw |
nubNub' | (x : xs) ls | = nubNub'2 (x : xs) ls |
nubNub'0 | x xs ls True | = x : nubNub' xs (x : ls) |
nubNub'1 | x xs ls True | = nubNub' xs ls |
nubNub'1 | x xs ls False | = nubNub'0 x xs ls otherwise |
nubNub'2 | (x : xs) ls | = nubNub'1 x xs ls (x `elem` ls) |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
mainModule List
| (nub :: [Char] -> [Char]) |
module List where
| import qualified Maybe import qualified Prelude
|
| nub :: Eq a => [a] -> [a]
|
|
nubNub' | [] vw | = | nubNub'3 [] vw |
nubNub' | (x : xs) ls | = | nubNub'2 (x : xs) ls |
|
|
nubNub'0 | x xs ls True | = | x : nubNub' xs (x : ls) |
|
|
nubNub'1 | x xs ls True | = | nubNub' xs ls |
nubNub'1 | x xs ls False | = | nubNub'0 x xs ls otherwise |
|
|
nubNub'2 | (x : xs) ls | = | nubNub'1 x xs ls (x `elem` ls) |
|
|
nubNub'3 | [] vw | = | [] |
nubNub'3 | wv ww | = | nubNub'2 wv ww |
|
module Maybe where
| import qualified List import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_nubNub'14(Char(Succ(wx320800)), wx3209, :(wx32100, wx32101)) → new_nubNub'15(wx320800, wx3209, :(wx32100, wx32101), wx32100, wx32101)
new_nubNub'17(wx3497, wx3498, wx3499, Zero, Zero, wx3502) → new_nubNub'0(wx3498, wx3499)
new_nubNub'0(:(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
new_nubNub'16(wx31000, :(wx3110, wx3111)) → new_nubNub'11(wx3110, wx3111, wx31000, :(Char(Zero), []))
new_nubNub'13(:(wx3110, wx3111), wx3000) → new_nubNub'14(wx3110, wx3111, :(Char(Succ(wx3000)), []))
new_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Succ(wx35010), wx3502) → new_nubNub'17(wx3497, wx3498, wx3499, wx35000, wx35010, wx3502)
new_nubNub'4(:(wx3110, wx3111), wx3000) → new_nubNub'14(wx3110, wx3111, :(Char(Succ(wx3000)), []))
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Succ(wx37530), wx3754) → new_nubNub'10(wx3748, wx3749, wx3750, wx3751, wx3754)
new_nubNub'18(wx3497, :(wx34980, wx34981), wx3499, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
new_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Zero, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
new_nubNub'14(Char(Zero), :(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
new_nubNub'10(wx3748, wx3749, wx3750, wx3751, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
new_nubNub'(:(wx36090, wx36091), wx3610, wx3611) → new_nubNub'11(wx36090, wx36091, wx3610, wx3611)
new_nubNub'11(Char(Zero), wx3548, wx3549, []) → new_nubNub'13(wx3548, wx3549)
new_nubNub'18(wx3497, wx3498, wx3499, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
new_nubNub'2(:(wx34980, wx34981), wx3497, wx3499) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
new_nubNub'10(wx3748, wx3749, wx3750, wx3751, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
new_nubNub'11(Char(Zero), wx3548, wx3549, :(wx35500, wx35501)) → new_nubNub'12(wx3548, wx3549, :(wx35500, wx35501), wx35500, wx35501)
new_nubNub'15(wx3442, wx3443, wx3444, Char(wx34450), wx3446) → new_nubNub'17(wx3442, wx3443, wx3444, Succ(wx3442), wx34450, wx3446)
new_nubNub'17(wx3497, :(wx34980, wx34981), wx3499, Succ(wx35000), Zero, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
new_nubNub'17(wx3497, wx3498, wx3499, Zero, Succ(wx35010), wx3502) → new_nubNub'18(wx3497, wx3498, wx3499, wx3502)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
new_nubNub'14(Char(Succ(wx320800)), wx3209, []) → new_nubNub'16(wx320800, wx3209)
new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), []) → new_nubNub'0(wx3615, :(Char(Succ(wx3616)), wx3617))
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Succ(wx37530), wx3754) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, wx37520, wx37530, wx3754)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
new_nubNub'12(wx3615, wx3616, wx3617, Char(Zero), wx3619) → new_nubNub'(wx3615, wx3616, wx3617)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Zero, wx3754) → new_nubNub'(wx3749, wx3750, wx3751)
new_nubNub'3(:(wx3110, wx3111), wx31000) → new_nubNub'11(wx3110, wx3111, wx31000, :(Char(Zero), []))
new_nubNub'11(Char(Succ(wx354700)), wx3548, wx3549, wx3550) → new_nubNub'1(wx354700, wx3548, wx3549, wx3550, wx354700, wx3549, wx3550)
new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), :(wx36190, wx36191)) → new_nubNub'12(wx3615, wx3616, wx3617, wx36190, wx36191)
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 1 SCC with 3 less nodes.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_nubNub'14(Char(Succ(wx320800)), wx3209, :(wx32100, wx32101)) → new_nubNub'15(wx320800, wx3209, :(wx32100, wx32101), wx32100, wx32101)
new_nubNub'17(wx3497, wx3498, wx3499, Zero, Zero, wx3502) → new_nubNub'0(wx3498, wx3499)
new_nubNub'16(wx31000, :(wx3110, wx3111)) → new_nubNub'11(wx3110, wx3111, wx31000, :(Char(Zero), []))
new_nubNub'0(:(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
new_nubNub'13(:(wx3110, wx3111), wx3000) → new_nubNub'14(wx3110, wx3111, :(Char(Succ(wx3000)), []))
new_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Succ(wx35010), wx3502) → new_nubNub'17(wx3497, wx3498, wx3499, wx35000, wx35010, wx3502)
new_nubNub'18(wx3497, :(wx34980, wx34981), wx3499, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Succ(wx37530), wx3754) → new_nubNub'10(wx3748, wx3749, wx3750, wx3751, wx3754)
new_nubNub'14(Char(Zero), :(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
new_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Zero, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
new_nubNub'10(wx3748, wx3749, wx3750, wx3751, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
new_nubNub'(:(wx36090, wx36091), wx3610, wx3611) → new_nubNub'11(wx36090, wx36091, wx3610, wx3611)
new_nubNub'11(Char(Zero), wx3548, wx3549, []) → new_nubNub'13(wx3548, wx3549)
new_nubNub'18(wx3497, wx3498, wx3499, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
new_nubNub'10(wx3748, wx3749, wx3750, wx3751, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
new_nubNub'11(Char(Zero), wx3548, wx3549, :(wx35500, wx35501)) → new_nubNub'12(wx3548, wx3549, :(wx35500, wx35501), wx35500, wx35501)
new_nubNub'15(wx3442, wx3443, wx3444, Char(wx34450), wx3446) → new_nubNub'17(wx3442, wx3443, wx3444, Succ(wx3442), wx34450, wx3446)
new_nubNub'17(wx3497, :(wx34980, wx34981), wx3499, Succ(wx35000), Zero, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
new_nubNub'17(wx3497, wx3498, wx3499, Zero, Succ(wx35010), wx3502) → new_nubNub'18(wx3497, wx3498, wx3499, wx3502)
new_nubNub'14(Char(Succ(wx320800)), wx3209, []) → new_nubNub'16(wx320800, wx3209)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), []) → new_nubNub'0(wx3615, :(Char(Succ(wx3616)), wx3617))
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Succ(wx37530), wx3754) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, wx37520, wx37530, wx3754)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
new_nubNub'12(wx3615, wx3616, wx3617, Char(Zero), wx3619) → new_nubNub'(wx3615, wx3616, wx3617)
new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Zero, wx3754) → new_nubNub'(wx3749, wx3750, wx3751)
new_nubNub'11(Char(Succ(wx354700)), wx3548, wx3549, wx3550) → new_nubNub'1(wx354700, wx3548, wx3549, wx3550, wx354700, wx3549, wx3550)
new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), :(wx36190, wx36191)) → new_nubNub'12(wx3615, wx3616, wx3617, wx36190, wx36191)
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_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Zero, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 6 > 4, 6 > 5
- new_nubNub'17(wx3497, wx3498, wx3499, Succ(wx35000), Succ(wx35010), wx3502) → new_nubNub'17(wx3497, wx3498, wx3499, wx35000, wx35010, wx3502)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 > 5, 6 >= 6
- new_nubNub'17(wx3497, :(wx34980, wx34981), wx3499, Succ(wx35000), Zero, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3
- new_nubNub'15(wx3442, wx3443, wx3444, Char(wx34450), wx3446) → new_nubNub'17(wx3442, wx3443, wx3444, Succ(wx3442), wx34450, wx3446)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 5, 5 >= 6
- new_nubNub'0(:(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3
- new_nubNub'14(Char(Succ(wx320800)), wx3209, :(wx32100, wx32101)) → new_nubNub'15(wx320800, wx3209, :(wx32100, wx32101), wx32100, wx32101)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 3 > 4, 3 > 5
- new_nubNub'18(wx3497, wx3498, wx3499, :(wx35020, wx35021)) → new_nubNub'15(wx3497, wx3498, wx3499, wx35020, wx35021)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 4 > 5
- new_nubNub'17(wx3497, wx3498, wx3499, Zero, Zero, wx3502) → new_nubNub'0(wx3498, wx3499)
The graph contains the following edges 2 >= 1, 3 >= 2
- new_nubNub'17(wx3497, wx3498, wx3499, Zero, Succ(wx35010), wx3502) → new_nubNub'18(wx3497, wx3498, wx3499, wx3502)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 6 >= 4
- new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), []) → new_nubNub'0(wx3615, :(Char(Succ(wx3616)), wx3617))
The graph contains the following edges 1 >= 1
- new_nubNub'14(Char(Zero), :(wx32090, wx32091), wx3210) → new_nubNub'14(wx32090, wx32091, wx3210)
The graph contains the following edges 2 > 1, 2 > 2, 3 >= 3
- new_nubNub'14(Char(Succ(wx320800)), wx3209, []) → new_nubNub'16(wx320800, wx3209)
The graph contains the following edges 1 > 1, 2 >= 2
- new_nubNub'13(:(wx3110, wx3111), wx3000) → new_nubNub'14(wx3110, wx3111, :(Char(Succ(wx3000)), []))
The graph contains the following edges 1 > 1, 1 > 2
- new_nubNub'16(wx31000, :(wx3110, wx3111)) → new_nubNub'11(wx3110, wx3111, wx31000, :(Char(Zero), []))
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3
- new_nubNub'11(Char(Zero), wx3548, wx3549, :(wx35500, wx35501)) → new_nubNub'12(wx3548, wx3549, :(wx35500, wx35501), wx35500, wx35501)
The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 4 > 4, 4 > 5
- new_nubNub'11(Char(Succ(wx354700)), wx3548, wx3549, wx3550) → new_nubNub'1(wx354700, wx3548, wx3549, wx3550, wx354700, wx3549, wx3550)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 1 > 5, 3 >= 6, 4 >= 7
- new_nubNub'12(wx3615, wx3616, wx3617, Char(Succ(wx361800)), :(wx36190, wx36191)) → new_nubNub'12(wx3615, wx3616, wx3617, wx36190, wx36191)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 5 > 4, 5 > 5
- new_nubNub'12(wx3615, wx3616, wx3617, Char(Zero), wx3619) → new_nubNub'(wx3615, wx3616, wx3617)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
- new_nubNub'(:(wx36090, wx36091), wx3610, wx3611) → new_nubNub'11(wx36090, wx36091, wx3610, wx3611)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4
- new_nubNub'18(wx3497, :(wx34980, wx34981), wx3499, []) → new_nubNub'11(wx34980, wx34981, wx3497, :(Char(Zero), wx3499))
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3
- new_nubNub'11(Char(Zero), wx3548, wx3549, []) → new_nubNub'13(wx3548, wx3549)
The graph contains the following edges 2 >= 1, 3 >= 2
- new_nubNub'10(wx3748, wx3749, wx3750, wx3751, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
The graph contains the following edges 2 >= 1, 1 >= 2
- new_nubNub'10(wx3748, wx3749, wx3750, wx3751, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 6, 5 > 7
- new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Succ(wx37530), wx3754) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, wx37520, wx37530, wx3754)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
- new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Succ(wx37530), wx3754) → new_nubNub'10(wx3748, wx3749, wx3750, wx3751, wx3754)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
- new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, :(Char(wx375400), wx37541)) → new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx3748), wx375400, wx37541)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 > 6, 7 > 7
- new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Succ(wx37520), Zero, []) → new_nubNub'(wx3749, wx3748, :(Char(Succ(wx3750)), wx3751))
The graph contains the following edges 2 >= 1, 1 >= 2
- new_nubNub'1(wx3748, wx3749, wx3750, wx3751, Zero, Zero, wx3754) → new_nubNub'(wx3749, wx3750, wx3751)
The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_nubNub'5(:(Char(Zero), wx311), Char(Zero)) → new_nubNub'5(wx311, Char(Zero))
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_nubNub'5(:(Char(Zero), wx311), Char(Zero)) → new_nubNub'5(wx311, Char(Zero))
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2