YES 0.795
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
↳ BR
mainModule Main
| ((maximum :: [()] -> ()) :: [()] -> ()) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| ((maximum :: [()] -> ()) :: [()] -> ()) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
max1 | x y True | = y |
max1 | x y False | = max0 x y otherwise |
max2 | x y | = max1 x y (x <= y) |
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Main
module Main where
Haskell To QDPs
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_foldl(vx30, :(vx310, vx311)) → new_foldl(new_max1(vx30, vx310), vx311)
The TRS R consists of the following rules:
new_max1(@0, @0) → @0
The set Q consists of the following terms:
new_max1(@0, @0)
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_foldl(vx30, :(vx310, vx311)) → new_foldl(new_max1(vx30, vx310), vx311)
The graph contains the following edges 2 > 2