YES 0.836
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/Monad.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule Monad
| ((liftM5 :: Monad g => (b -> c -> e -> d -> a -> f) -> g b -> g c -> g e -> g d -> g a -> g f) :: Monad g => (b -> c -> e -> d -> a -> f) -> g b -> g c -> g e -> g d -> g a -> g f) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad f => (b -> e -> a -> d -> c -> g) -> f b -> f e -> f a -> f d -> f c -> f g
liftM5 | f m1 m2 m3 m4 m5 | = | m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->m5 >>= (\x5 ->return (f x1 x2 x3 x4 x5)))))) |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\x5→return (f x1 x2 x3 x4 x5)
is transformed to
liftM50 | f x1 x2 x3 x4 x5 | = return (f x1 x2 x3 x4 x5) |
The following Lambda expression
\x4→m5 >>= liftM50 f x1 x2 x3 x4
is transformed to
liftM51 | m5 f x1 x2 x3 x4 | = m5 >>= liftM50 f x1 x2 x3 x4 |
The following Lambda expression
\x3→m4 >>= liftM51 m5 f x1 x2 x3
is transformed to
liftM52 | m4 m5 f x1 x2 x3 | = m4 >>= liftM51 m5 f x1 x2 x3 |
The following Lambda expression
\x2→m3 >>= liftM52 m4 m5 f x1 x2
is transformed to
liftM53 | m3 m4 m5 f x1 x2 | = m3 >>= liftM52 m4 m5 f x1 x2 |
The following Lambda expression
\x1→m2 >>= liftM53 m3 m4 m5 f x1
is transformed to
liftM54 | m2 m3 m4 m5 f x1 | = m2 >>= liftM53 m3 m4 m5 f x1 |
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
mainModule Monad
| ((liftM5 :: Monad f => (d -> e -> g -> c -> b -> a) -> f d -> f e -> f g -> f c -> f b -> f a) :: Monad f => (d -> e -> g -> c -> b -> a) -> f d -> f e -> f g -> f c -> f b -> f a) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad b => (a -> g -> d -> e -> f -> c) -> b a -> b g -> b d -> b e -> b f -> b c
liftM5 | f m1 m2 m3 m4 m5 | = | m1 >>= liftM54 m2 m3 m4 m5 f |
|
|
liftM50 | f x1 x2 x3 x4 x5 | = | return (f x1 x2 x3 x4 x5) |
|
|
liftM51 | m5 f x1 x2 x3 x4 | = | m5 >>= liftM50 f x1 x2 x3 x4 |
|
|
liftM52 | m4 m5 f x1 x2 x3 | = | m4 >>= liftM51 m5 f x1 x2 x3 |
|
|
liftM53 | m3 m4 m5 f x1 x2 | = | m3 >>= liftM52 m4 m5 f x1 x2 |
|
|
liftM54 | m2 m3 m4 m5 f x1 | = | m2 >>= liftM53 m3 m4 m5 f x1 |
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Monad
| ((liftM5 :: Monad e => (a -> d -> f -> g -> c -> b) -> e a -> e d -> e f -> e g -> e c -> e b) :: Monad e => (a -> d -> f -> g -> c -> b) -> e a -> e d -> e f -> e g -> e c -> e b) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad d => (f -> a -> c -> e -> g -> b) -> d f -> d a -> d c -> d e -> d g -> d b
liftM5 | f m1 m2 m3 m4 m5 | = | m1 >>= liftM54 m2 m3 m4 m5 f |
|
|
liftM50 | f x1 x2 x3 x4 x5 | = | return (f x1 x2 x3 x4 x5) |
|
|
liftM51 | m5 f x1 x2 x3 x4 | = | m5 >>= liftM50 f x1 x2 x3 x4 |
|
|
liftM52 | m4 m5 f x1 x2 x3 | = | m4 >>= liftM51 m5 f x1 x2 x3 |
|
|
liftM53 | m3 m4 m5 f x1 x2 | = | m3 >>= liftM52 m4 m5 f x1 x2 |
|
|
liftM54 | m2 m3 m4 m5 f x1 | = | m2 >>= liftM53 m3 m4 m5 f x1 |
|
module Maybe where
| import qualified Monad import qualified Prelude
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Monad
| (liftM5 :: Monad f => (c -> a -> e -> d -> g -> b) -> f c -> f a -> f e -> f d -> f g -> f b) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad e => (d -> b -> a -> f -> c -> g) -> e d -> e b -> e a -> e f -> e c -> e g
liftM5 | f m1 m2 m3 m4 m5 | = | m1 >>= liftM54 m2 m3 m4 m5 f |
|
|
liftM50 | f x1 x2 x3 x4 x5 | = | return (f x1 x2 x3 x4 x5) |
|
|
liftM51 | m5 f x1 x2 x3 x4 | = | m5 >>= liftM50 f x1 x2 x3 x4 |
|
|
liftM52 | m4 m5 f x1 x2 x3 | = | m4 >>= liftM51 m5 f x1 x2 x3 |
|
|
liftM53 | m3 m4 m5 f x1 x2 | = | m3 >>= liftM52 m4 m5 f x1 x2 |
|
|
liftM54 | m2 m3 m4 m5 f x1 | = | m2 >>= liftM53 m3 m4 m5 f x1 |
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_psPs(:(vy110, vy111), vy9, h) → new_psPs(vy111, vy9, h)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_psPs(:(vy110, vy111), vy9, h) → new_psPs(vy111, vy9, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) → new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)
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_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) → new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)
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, 11 >= 11, 12 >= 12
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) → new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)
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_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) → new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)
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, 11 >= 11, 12 >= 12
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) → new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)
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_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) → new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)
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, 11 >= 11, 12 >= 12
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) → new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)
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_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) → new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)
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, 11 >= 11, 12 >= 12
↳ HASKELL
↳ LR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) → new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)
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_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) → new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)
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, 11 >= 11, 12 >= 12