YES 0.9380000000000001
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
| (((>) :: Ratio Int -> Ratio Int -> Bool) :: Ratio Int -> Ratio Int -> Bool) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| (((>) :: Ratio Int -> Ratio Int -> Bool) :: Ratio Int -> Ratio Int -> Bool) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
mainModule Main
| ((>) :: Ratio Int -> Ratio Int -> Bool) |
module Main where
Haskell To QDPs
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(vx1400), Succ(vx41000)) → new_primPlusNat(vx1400, vx41000)
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_primPlusNat(Succ(vx1400), Succ(vx41000)) → new_primPlusNat(vx1400, vx41000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(vx3000), Succ(vx4100)) → new_primMulNat(vx3000, Succ(vx4100))
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_primMulNat(Succ(vx3000), Succ(vx4100)) → new_primMulNat(vx3000, Succ(vx4100))
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_esEs(Succ(vx1000), Succ(vx1600)) → new_esEs(vx1000, vx1600)
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_esEs(Succ(vx1000), Succ(vx1600)) → new_esEs(vx1000, vx1600)
The graph contains the following edges 1 > 1, 2 > 2