YES 0.644
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule Main
| ((unzip :: [(b,a)] -> ([b],[a])) :: [(b,a)] -> ([b],[a])) |
module Main where
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) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ IPR
mainModule Main
| ((unzip :: [(a,b)] -> ([a],[b])) :: [(a,b)] -> ([a],[b])) |
module Main where
IrrPat Reductions:
The variables of the following irrefutable Pattern
~(as,bs)
are replaced by calls to these functions
↳ HASKELL
↳ LR
↳ HASKELL
↳ IPR
↳ HASKELL
↳ BR
mainModule Main
| ((unzip :: [(b,a)] -> ([b],[a])) :: [(b,a)] -> ([b],[a])) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ IPR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| ((unzip :: [(b,a)] -> ([b],[a])) :: [(b,a)] -> ([b],[a])) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ LR
↳ HASKELL
↳ IPR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Main
| (unzip :: [(a,b)] -> ([a],[b])) |
module Main where
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ IPR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldr(:(vy30, vy31), ba, bb) → new_foldr(vy31, ba, bb)
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(:(vy30, vy31), ba, bb) → new_foldr(vy31, ba, bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3