YES 0.8290000000000001
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
| ((minimum :: [Ordering] -> Ordering) :: [Ordering] -> Ordering) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| ((minimum :: [Ordering] -> Ordering) :: [Ordering] -> Ordering) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
min1 | x y True | = x |
min1 | x y False | = min0 x y otherwise |
min2 | x y | = min1 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
| (minimum :: [Ordering] -> Ordering) |
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_min1(vx30, vx310), vx311)
The TRS R consists of the following rules:
new_min1(LT, EQ) → LT
new_min1(EQ, LT) → LT
new_min1(EQ, GT) → EQ
new_min1(GT, EQ) → EQ
new_min1(EQ, EQ) → EQ
new_min1(LT, LT) → LT
new_min1(LT, GT) → LT
new_min1(GT, LT) → LT
new_min1(GT, GT) → GT
The set Q consists of the following terms:
new_min1(LT, GT)
new_min1(GT, LT)
new_min1(EQ, GT)
new_min1(GT, EQ)
new_min1(LT, EQ)
new_min1(EQ, LT)
new_min1(GT, GT)
new_min1(EQ, EQ)
new_min1(LT, LT)
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_min1(vx30, vx310), vx311)
The graph contains the following edges 2 > 2