YES 0.763
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 :: (b -> d -> e -> c -> f -> a) -> [b] -> [d] -> [e] -> [c] -> [f] -> [a]) :: (b -> d -> e -> c -> f -> a) -> [b] -> [d] -> [e] -> [c] -> [f] -> [a]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad d => (g -> b -> c -> a -> e -> f) -> d g -> d b -> d c -> d a -> d e -> d f
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 :: (d -> f -> c -> a -> b -> e) -> [d] -> [f] -> [c] -> [a] -> [b] -> [e]) :: (d -> f -> c -> a -> b -> e) -> [d] -> [f] -> [c] -> [a] -> [b] -> [e]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad f => (e -> b -> c -> g -> d -> a) -> f e -> f b -> f c -> f g -> f d -> f a
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 :: (b -> d -> c -> e -> a -> f) -> [b] -> [d] -> [c] -> [e] -> [a] -> [f]) :: (b -> d -> c -> e -> a -> f) -> [b] -> [d] -> [c] -> [e] -> [a] -> [f]) |
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad a => (g -> e -> c -> d -> f -> b) -> a g -> a e -> a c -> a d -> a f -> a 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 :: (c -> f -> b -> d -> a -> e) -> [c] -> [f] -> [b] -> [d] -> [a] -> [e]) |
module Maybe where
| import qualified Monad import qualified Prelude
|
module Monad where
| import qualified Maybe import qualified Prelude
|
| liftM5 :: Monad b => (f -> d -> g -> c -> a -> e) -> b f -> b d -> b g -> b c -> b a -> b e
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(:(vy100, vy101), vy9, h) → new_psPs(vy101, 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(:(vy100, vy101), vy9, h) → new_psPs(vy101, 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