MAYBE 20.191
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could not be shown:
↳ HASKELL
↳ LR
mainModule List
| ((intersect :: [Float] -> [Float] -> [Float]) :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (\vv2 ->
case | vv2 of |
| x | -> | if any (eq x) ys then x : [] else [] |
| _ | -> | [] |
) xs |
|
module Maybe where
| import qualified List import qualified Prelude
|
Lambda Reductions:
The following Lambda expression
\vv2→
case | vv2 of |
| x | → if any (eq x) ys then x : [] else [] |
| _ | → [] |
is transformed to
intersectBy0 | eq ys vv2 | =
case | vv2 of | | x | → if any (eq x) ys then x : [] else [] |
| _ | → [] |
|
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
mainModule List
| ((intersect :: [Float] -> [Float] -> [Float]) :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (intersectBy0 eq ys) xs |
|
|
intersectBy0 | eq ys vv2 | = |
case | vv2 of |
| x | -> | if any (eq x) ys then x : [] else [] |
| _ | -> | [] |
|
|
module Maybe where
| import qualified List import qualified Prelude
|
Case Reductions:
The following Case expression
case | vv2 of |
| x | → if any (eq x) ys then x : [] else [] |
| _ | → [] |
is transformed to
intersectBy00 | eq ys x | = if any (eq x) ys then x : [] else [] |
intersectBy00 | eq ys _ | = [] |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
mainModule List
| ((intersect :: [Float] -> [Float] -> [Float]) :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (intersectBy0 eq ys) xs |
|
|
intersectBy0 | eq ys vv2 | = | intersectBy00 eq ys vv2 |
|
|
intersectBy00 | eq ys x | = | if any (eq x) ys then x : [] else [] |
intersectBy00 | eq ys _ | = | [] |
|
module Maybe where
| import qualified List import qualified Prelude
|
If Reductions:
The following If expression
if any (eq x) ys then x : [] else []
is transformed to
intersectBy000 | x True | = x : [] |
intersectBy000 | x False | = [] |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule List
| ((intersect :: [Float] -> [Float] -> [Float]) :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (intersectBy0 eq ys) xs |
|
|
intersectBy0 | eq ys vv2 | = | intersectBy00 eq ys vv2 |
|
|
intersectBy00 | eq ys x | = | intersectBy000 x (any (eq x) ys) |
intersectBy00 | eq ys _ | = | [] |
|
|
intersectBy000 | x True | = | x : [] |
intersectBy000 | x False | = | [] |
|
module Maybe where
| import qualified List import qualified Prelude
|
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule List
| ((intersect :: [Float] -> [Float] -> [Float]) :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (intersectBy0 eq ys) xs |
|
|
intersectBy0 | eq ys vv2 | = | intersectBy00 eq ys vv2 |
|
|
intersectBy00 | eq ys x | = | intersectBy000 x (any (eq x) ys) |
intersectBy00 | eq ys vw | = | [] |
|
|
intersectBy000 | x True | = | x : [] |
intersectBy000 | x False | = | [] |
|
module Maybe where
| import qualified List import qualified Prelude
|
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ Narrow
mainModule List
| (intersect :: [Float] -> [Float] -> [Float]) |
module List where
| import qualified Maybe import qualified Prelude
|
| intersect :: Eq a => [a] -> [a] -> [a]
intersect | | = | intersectBy (==) |
|
| intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
intersectBy | eq xs ys | = | concatMap (intersectBy0 eq ys) xs |
|
|
intersectBy0 | eq ys vv2 | = | intersectBy00 eq ys vv2 |
|
|
intersectBy00 | eq ys x | = | intersectBy000 x (any (eq x) ys) |
intersectBy00 | eq ys vw | = | [] |
|
|
intersectBy000 | x True | = | x : [] |
intersectBy000 | x False | = | [] |
|
module Maybe where
| import qualified List import qualified Prelude
|
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_pePe(Succ(wv32700), Succ(wv33200), wv326) → new_pePe(wv32700, wv33200, wv326)
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_pePe(Succ(wv32700), Succ(wv33200), wv326) → new_pePe(wv32700, wv33200, wv326)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(wv8200), Succ(wv400000)) → new_primPlusNat(wv8200, wv400000)
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(wv8200), Succ(wv400000)) → new_primPlusNat(wv8200, wv400000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_primMulNat(Succ(wv300000), wv40000) → new_primMulNat(wv300000, wv40000)
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(wv300000), wv40000) → new_primMulNat(wv300000, wv40000)
The graph contains the following edges 1 > 1, 2 >= 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_foldr(wv60, wv6100, :(wv650, wv651)) → new_foldr(wv60, wv6100, wv651)
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(wv60, wv6100, :(wv650, wv651)) → new_foldr(wv60, wv6100, wv651)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) → new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00023(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00048(wv173, wv41) → new_intersectBy00088(wv41)
new_intersectBy00085(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy000122(wv74, Succ(wv7500), wv77, Zero, wv79) → new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy00052(wv30100000, Succ(wv1950), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy00078(wv285, wv41) → new_intersectBy000111(wv41)
new_intersectBy00023(wv30000, wv30100000, Succ(wv990), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy00098(wv34, wv3500, Succ(wv1900), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00097(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00037(wv30100000, Succ(wv1390), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00085(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0005(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00067(wv30100000, Succ(wv2510), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy0004(wv74, wv7500, Zero, Succ(Succ(wv10800)), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00041(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00033(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00039(wv147, wv41) → new_intersectBy00091(wv41)
new_intersectBy00083(Succ(wv3120), wv41) → new_intersectBy000113(wv41)
new_intersectBy000116(wv47, wv4800, wv2600, Succ(wv2940), wv52) → new_intersectBy000108(wv47, wv4800, wv2600, wv2940, wv52)
new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000121(wv74, wv750, wv77, wv780, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00025(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00057(wv30100000, Succ(wv2120), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52)
new_intersectBy00064(wv30100000, Succ(wv2300), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy000103(wv60, wv6100, Zero, Succ(Succ(wv23800)), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy000107(wv60, wv6100, Succ(wv2420), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000102(wv60, wv2040, wv65) → new_intersectBy000101(wv60, Zero, wv65)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Neg(Zero), wv52) → new_intersectBy000119(wv47, wv4800, Zero, wv52)
new_intersectBy00030(wv30100000, Succ(wv1210), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00099(wv34, wv3500, Succ(wv1920), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Neg(Zero), wv39) → new_intersectBy00097(wv34, wv3500, Zero, wv39)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00020(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00042(wv34, Pos(wv350), Succ(wv1480), Pos(wv380), wv39) → new_intersectBy0005(wv34, wv350, wv39)
new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Pos(Succ(wv5100)), wv52) → new_intersectBy000118(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00095(wv34, wv1480, wv39) → new_intersectBy0009(wv34, Zero, wv39)
new_intersectBy00020(wv30000, Succ(wv910), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy000(wv30000, wv301, new_primMulNat0(wv30000, wv40000), wv40000, wv401, wv41)
new_intersectBy000109(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00027(wv30100000, Succ(wv1120), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00019(wv30000, wv30100000, Succ(wv860), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000104(wv47, Zero, wv52)
new_intersectBy00026(wv30000, :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy00090(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000110(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00062(wv229, wv41) → new_intersectBy000111(wv41)
new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) → new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
new_intersectBy00041(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00041(wv301, wv401, wv41)
new_intersectBy00071(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy000(wv74, Neg(wv750), Succ(wv760), wv77, Neg(wv780), wv79) → new_intersectBy0003(wv74, wv750, new_primPlusNat0(wv760, wv77), wv780, wv79)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Neg(Zero), wv65) → new_intersectBy000107(wv60, wv6100, Zero, wv65)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Pos(Zero), wv39) → new_intersectBy00096(wv34, wv3500, Zero, wv39)
new_intersectBy000105(wv60, wv2040, wv65) → new_intersectBy000104(wv60, Zero, wv65)
new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00012(wv74, wv7500, Succ(wv770), Succ(wv10800), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
new_intersectBy00085(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00018(wv30000, :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy00082(wv30100000, Succ(wv3070), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy00041(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Zero), wv52) → new_intersectBy000115(wv47, wv2600, wv52)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00042(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy000100(wv74, wv7500, Succ(wv770), Succ(wv11000), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
new_intersectBy00011(wv74, Succ(wv7500), wv77, Zero, wv79) → new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy00077(Succ(wv2820), wv41) → new_intersectBy000110(wv41)
new_intersectBy00055(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00017(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00070(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy000(wv74, Pos(wv750), Succ(wv760), wv77, Pos(wv780), wv79) → new_intersectBy0000(wv74, wv750, new_primPlusNat0(wv760, wv77), wv780, wv79)
new_intersectBy00015(wv30000, Succ(wv3200), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy00072(wv47, Pos(wv480), Succ(wv2600), Neg(wv510), wv52) → new_intersectBy000101(wv47, wv480, wv52)
new_intersectBy00085(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy00074(Succ(wv2730), wv41) → new_intersectBy000110(wv41)
new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00019(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000117(wv47, wv2600, wv52) → new_intersectBy000104(wv47, Zero, wv52)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy00051(wv194, wv41) → new_intersectBy00091(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00029(wv120, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00017(wv30000, Succ(wv830), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Pos(Succ(wv6400)), wv65) → new_intersectBy000106(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
new_intersectBy00053(Succ(wv2000), wv41) → new_intersectBy00090(wv41)
new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) → new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
new_intersectBy00011(wv74, Zero, wv77, Succ(wv7800), wv79) → new_intersectBy0005(wv74, Zero, wv79)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000112(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00085(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy0006(wv74, wv77, wv79) → new_intersectBy0005(wv74, Zero, wv79)
new_intersectBy00071(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Succ(wv10800)), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Pos(Zero), wv52) → new_intersectBy000118(wv47, wv4800, Zero, wv52)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00015(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00026(wv30000, wv41)
new_intersectBy000113(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00014(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Zero), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Pos(Zero), wv65) → new_intersectBy000106(wv60, wv6100, Zero, wv65)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy00071(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy00012(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00012(wv74, wv7500, Zero, Succ(wv10800), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00098(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Neg(Zero), wv39) → new_intersectBy00099(wv34, wv3500, Zero, wv39)
new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0006(wv74, wv77, wv79)
new_intersectBy000100(wv74, wv7500, Zero, Succ(wv11000), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy000100(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy0007(Float(Neg(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00085(wv301, wv401, wv41)
new_intersectBy00031(Succ(wv1260), wv41) → new_intersectBy00087(wv41)
new_intersectBy00081(wv306, wv41) → new_intersectBy000114(wv41)
new_intersectBy00021(wv30000, wv94, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000122(wv74, Zero, wv77, Zero, wv79) → new_intersectBy00010(wv74, wv77, wv79)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00073(wv30100000, Succ(wv2680), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy00042(wv34, Neg(wv350), Succ(wv1480), Neg(wv380), wv39) → new_intersectBy0009(wv34, wv350, wv39)
new_intersectBy00072(wv47, Neg(wv480), Succ(wv2600), Pos(wv510), wv52) → new_intersectBy000104(wv47, wv480, wv52)
new_intersectBy000115(wv47, wv2600, wv52) → new_intersectBy000101(wv47, Zero, wv52)
new_intersectBy00059(wv220, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00025(wv30000, wv107, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00096(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy000(wv74, Pos(wv750), Succ(wv760), wv77, Neg(wv780), wv79) → new_intersectBy0001(wv74, wv750, new_primPlusNat0(wv760, wv77), wv780, wv79)
new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00045(wv164, wv41) → new_intersectBy00088(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00065(Succ(wv2350), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00080(Succ(wv2910), wv41) → new_intersectBy000113(wv41)
new_intersectBy00035(Succ(wv1350), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00055(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy00034(wv30100000, Succ(wv1300), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy000108(wv60, wv6100, Succ(wv20400), Succ(wv23800), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00024(wv30000, Succ(wv1040), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39)
new_intersectBy00069(wv259, wv41) → new_intersectBy000114(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00016(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00088(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00085(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00092(wv34, wv3500, wv1480, Succ(wv1820), wv39) → new_intersectBy00012(wv34, wv3500, wv1480, wv1820, wv39)
new_intersectBy00085(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65)
new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Succ(wv11000)), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
new_intersectBy00049(wv30100000, Succ(wv1740), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Succ(wv23800)), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
new_intersectBy00032(wv129, wv41) → new_intersectBy00088(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(wv610), Succ(wv2040), Neg(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000118(wv47, wv4800, Succ(wv2960), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy00046(wv30100000, Succ(wv1650), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy00050(Succ(wv1790), wv41) → new_intersectBy00090(wv41)
new_intersectBy00022(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy00055(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy0007(Float(Pos(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00055(wv301, wv401, wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy00041(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy000(wv74, Neg(wv750), Zero, wv77, Pos(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy0009(wv34, Zero, wv39)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00011(wv74, Succ(wv7500), wv77, Succ(wv7800), wv79) → new_intersectBy0004(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00054(wv203, wv41) → new_intersectBy00091(wv41)
new_intersectBy000104(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00021(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0009(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy0007(Float(Neg(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00071(wv301, wv401, wv41)
new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy0005(wv34, Zero, wv39)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Neg(Succ(wv5100)), wv52) → new_intersectBy000119(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy000119(wv47, wv4800, Succ(wv2980), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00093(wv34, wv1480, wv39)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00013(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy00091(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00075(wv276, wv41) → new_intersectBy000111(wv41)
new_intersectBy00056(wv60, Pos(wv610), Succ(wv2040), Pos(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Zero), wv65) → new_intersectBy000102(wv60, wv2040, wv65)
new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000117(wv47, wv2600, wv52)
new_intersectBy00055(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy00040(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00044(Succ(wv1610), wv41) → new_intersectBy00087(wv41)
new_intersectBy000122(wv74, Succ(wv7500), wv77, Succ(wv7800), wv79) → new_intersectBy0008(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00018(wv30000, wv41)
new_intersectBy00096(wv34, wv3500, Succ(wv1860), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
new_intersectBy00061(Succ(wv2260), wv41) → new_intersectBy000110(wv41)
new_intersectBy00016(wv30000, wv30100000, Succ(wv3220), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy00084(wv315, wv41) → new_intersectBy000114(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000105(wv60, wv2040, wv65)
new_intersectBy000(wv74, Neg(wv750), Succ(wv760), wv77, Pos(wv780), wv79) → new_intersectBy0002(wv74, wv750, new_primPlusNat0(wv760, wv77), wv780, wv79)
new_intersectBy00071(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00066(wv250, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00094(wv34, wv3500, wv1480, Succ(wv1840), wv39) → new_intersectBy000100(wv34, wv3500, wv1480, wv1840, wv39)
new_intersectBy00087(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy000111(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) → new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
new_intersectBy0008(wv74, wv7500, Zero, Succ(Succ(wv11000)), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00072(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy00011(wv74, Zero, wv77, Zero, wv79) → new_intersectBy0006(wv74, wv77, wv79)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy00056(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy000120(wv74, wv750, wv77, wv780, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy000114(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00071(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00071(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00072(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy00089(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Zero), wv79) → new_intersectBy00010(wv74, wv77, wv79)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00041(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00060(wv30100000, Succ(wv2210), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000104(wv60, Zero, wv65)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00042(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00099(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Pos(Zero), wv39) → new_intersectBy00098(wv34, wv3500, Zero, wv39)
new_intersectBy00041(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0008(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Neg(Succ(wv6400)), wv65) → new_intersectBy000107(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0005(wv74, Zero, wv79)
new_intersectBy00010(wv74, wv77, wv79) → new_intersectBy0009(wv74, Zero, wv79)
new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Zero), wv79) → new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy00055(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00043(wv30100000, Succ(wv1560), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy00036(wv138, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00058(Succ(wv2170), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00063(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000106(wv60, wv6100, Succ(wv2400), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00041(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00028(Succ(wv1170), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00068(Succ(wv2560), wv41) → new_intersectBy000113(wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00024(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00097(wv34, wv3500, Succ(wv1880), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
new_intersectBy00076(wv30100000, Succ(wv2770), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy000(wv74, Pos(wv750), Zero, wv77, Neg(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy000108(wv60, wv6100, Succ(wv20400), Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000108(wv60, wv6100, Zero, Succ(wv23800), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00047(Succ(wv1700), wv41) → new_intersectBy00087(wv41)
new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0004(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00095(wv34, wv1480, wv39)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000101(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
new_intersectBy00038(Succ(wv1440), wv41) → new_intersectBy00090(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Succ(wv6400)), wv65) → new_intersectBy000101(wv60, Zero, wv65)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00056(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00014(wv30000, wv30100000, Succ(wv3160), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00085(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00093(wv34, wv1480, wv39) → new_intersectBy0005(wv34, Zero, wv39)
new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0009(wv74, Zero, wv79)
new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Succ(wv5100)), wv52) → new_intersectBy000101(wv47, Zero, wv52)
new_intersectBy000122(wv74, Zero, wv77, Succ(wv7800), wv79) → new_intersectBy0009(wv74, Zero, wv79)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00079(wv30100000, Succ(wv2860), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy00086(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 8 SCCs with 22 less nodes.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) → new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) → new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
R is empty.
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ NonTerminationProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) → new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.
The TRS P consists of the following rules:
new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) → new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
The TRS R consists of the following rules:none
s = new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) evaluates to t =new_intersectBy0003(wv74, wv750, wv98, wv780, wv79)
Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
- Semiunifier: [ ]
- Matcher: [ ]
Rewriting sequence
The DP semiunifies directly so there is only one rewrite step from new_intersectBy0003(wv74, wv750, wv98, wv780, wv79) to new_intersectBy0003(wv74, wv750, wv98, wv780, wv79).
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) → new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) → new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
R is empty.
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ NonTerminationProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) → new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.
The TRS P consists of the following rules:
new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) → new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
The TRS R consists of the following rules:none
s = new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) evaluates to t =new_intersectBy0001(wv74, wv750, wv96, wv780, wv79)
Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
- Semiunifier: [ ]
- Matcher: [ ]
Rewriting sequence
The DP semiunifies directly so there is only one rewrite step from new_intersectBy0001(wv74, wv750, wv96, wv780, wv79) to new_intersectBy0001(wv74, wv750, wv96, wv780, wv79).
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) → new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) → new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
R is empty.
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ NonTerminationProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) → new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.
The TRS P consists of the following rules:
new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) → new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
The TRS R consists of the following rules:none
s = new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) evaluates to t =new_intersectBy0002(wv74, wv750, wv97, wv780, wv79)
Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
- Semiunifier: [ ]
- Matcher: [ ]
Rewriting sequence
The DP semiunifies directly so there is only one rewrite step from new_intersectBy0002(wv74, wv750, wv97, wv780, wv79) to new_intersectBy0002(wv74, wv750, wv97, wv780, wv79).
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000105(wv60, wv2040, wv65)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Neg(Succ(wv6400)), wv65) → new_intersectBy000107(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
new_intersectBy000105(wv60, wv2040, wv65) → new_intersectBy000104(wv60, Zero, wv65)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
new_intersectBy000106(wv60, wv6100, Succ(wv2400), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Pos(Succ(wv5100)), wv52) → new_intersectBy000118(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy000104(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
new_intersectBy000108(wv60, wv6100, Succ(wv20400), Succ(wv23800), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
new_intersectBy000108(wv60, wv6100, Succ(wv20400), Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000108(wv60, wv6100, Zero, Succ(wv23800), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Zero), wv52) → new_intersectBy000115(wv47, wv2600, wv52)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy00056(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00072(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Neg(Succ(wv5100)), wv52) → new_intersectBy000119(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
new_intersectBy000119(wv47, wv4800, Succ(wv2980), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000104(wv47, Zero, wv52)
new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Zero), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65)
new_intersectBy00072(wv47, Pos(wv480), Succ(wv2600), Neg(wv510), wv52) → new_intersectBy000101(wv47, wv480, wv52)
new_intersectBy000101(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Succ(wv6400)), wv65) → new_intersectBy000101(wv60, Zero, wv65)
new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Succ(wv23800)), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00072(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00056(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy000116(wv47, wv4800, wv2600, Succ(wv2940), wv52) → new_intersectBy000108(wv47, wv4800, wv2600, wv2940, wv52)
new_intersectBy00056(wv60, Pos(wv610), Succ(wv2040), Pos(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Zero), wv65) → new_intersectBy000102(wv60, wv2040, wv65)
new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000117(wv47, wv2600, wv52)
new_intersectBy00056(wv60, Neg(wv610), Succ(wv2040), Neg(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000104(wv60, Zero, wv65)
new_intersectBy000117(wv47, wv2600, wv52) → new_intersectBy000104(wv47, Zero, wv52)
new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Succ(wv5100)), wv52) → new_intersectBy000101(wv47, Zero, wv52)
new_intersectBy000118(wv47, wv4800, Succ(wv2960), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52)
new_intersectBy00072(wv47, Neg(wv480), Succ(wv2600), Pos(wv510), wv52) → new_intersectBy000104(wv47, wv480, wv52)
new_intersectBy000103(wv60, wv6100, Zero, Succ(Succ(wv23800)), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000115(wv47, wv2600, wv52) → new_intersectBy000101(wv47, Zero, wv52)
new_intersectBy000107(wv60, wv6100, Succ(wv2420), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
new_intersectBy000102(wv60, wv2040, wv65) → new_intersectBy000101(wv60, Zero, wv65)
new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Pos(Succ(wv6400)), wv65) → new_intersectBy000106(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
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_intersectBy000108(wv60, wv6100, Succ(wv20400), Succ(wv23800), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy000104(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000104(wv60, Zero, wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy000101(wv60, wv610, :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy000106(wv60, wv6100, Succ(wv2400), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Pos(Succ(wv6400)), wv65) → new_intersectBy000106(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Succ(wv23800)), wv65) → new_intersectBy000108(wv60, wv6100, wv20400, wv23800, wv65)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy000116(wv47, wv4800, wv2600, Succ(wv2940), wv52) → new_intersectBy000108(wv47, wv4800, wv2600, wv2940, wv52)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
- new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy00056(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 4, 3 >= 5
- new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00056(wv30000, wv301, Zero, wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 3, 2 > 4, 3 >= 5
- new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Succ(wv6400)), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 5 >= 5
- new_intersectBy00056(wv60, Neg(Succ(wv6100)), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy000103(wv60, wv6100, wv2040, Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000118(wv47, wv4800, Succ(wv2960), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Pos(Succ(wv5100)), wv52) → new_intersectBy000118(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy00072(wv47, Neg(Succ(wv4800)), Zero, Neg(Succ(wv5100)), wv52) → new_intersectBy000119(wv47, wv4800, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy000119(wv47, wv4800, Succ(wv2980), wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00072(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 4, 3 >= 5
- new_intersectBy0007(Float(Neg(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00072(wv30000, wv301, Zero, wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 3, 2 > 4, 3 >= 5
- new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52) → new_intersectBy000104(wv47, Succ(wv4800), wv52)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, new_primPlusNat0(new_primMulNat0(wv4800, wv5100), Succ(wv5100)), wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 5 >= 5
- new_intersectBy00072(wv47, Neg(Succ(wv4800)), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000116(wv47, wv4800, wv2600, Zero, wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy000115(wv47, wv2600, wv52) → new_intersectBy000101(wv47, Zero, wv52)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy000102(wv60, wv2040, wv65) → new_intersectBy000101(wv60, Zero, wv65)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Zero), wv52) → new_intersectBy000115(wv47, wv2600, wv52)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Succ(wv6400)), wv65) → new_intersectBy000101(wv60, Zero, wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Zero), wv52) → new_intersectBy000117(wv47, wv2600, wv52)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy00056(wv60, Neg(Succ(wv6100)), Zero, Neg(Succ(wv6400)), wv65) → new_intersectBy000107(wv60, wv6100, new_primPlusNat0(new_primMulNat0(wv6100, wv6400), Succ(wv6400)), wv65)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy000107(wv60, wv6100, Succ(wv2420), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy000117(wv47, wv2600, wv52) → new_intersectBy000104(wv47, Zero, wv52)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy000105(wv60, wv2040, wv65) → new_intersectBy000104(wv60, Zero, wv65)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy00056(wv60, Pos(Zero), Succ(wv2040), Neg(Zero), wv65) → new_intersectBy000102(wv60, wv2040, wv65)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy00056(wv60, Neg(Zero), Succ(wv2040), Pos(Zero), wv65) → new_intersectBy000105(wv60, wv2040, wv65)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy000108(wv60, wv6100, Zero, Succ(wv23800), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000108(wv60, wv6100, Succ(wv20400), Zero, wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000103(wv60, wv6100, Zero, Succ(Succ(wv23800)), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000103(wv60, wv6100, Succ(wv20400), Succ(Zero), wv65) → new_intersectBy000104(wv60, Succ(wv6100), wv65)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy00072(wv47, Neg(Zero), Succ(wv2600), Neg(Succ(wv5100)), wv52) → new_intersectBy000104(wv47, Zero, wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00072(wv47, Neg(wv480), Succ(wv2600), Pos(wv510), wv52) → new_intersectBy000104(wv47, wv480, wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00056(wv60, Neg(wv610), Succ(wv2040), Neg(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Neg(wv610)), wv650, wv651)
The graph contains the following edges 5 > 2, 5 > 3
- new_intersectBy00056(wv60, Pos(wv610), Succ(wv2040), Pos(wv640), :(wv650, wv651)) → new_intersectBy0007(Float(Neg(Succ(wv60)), Pos(wv610)), wv650, wv651)
The graph contains the following edges 5 > 2, 5 > 3
- new_intersectBy00072(wv47, Pos(wv480), Succ(wv2600), Neg(wv510), wv52) → new_intersectBy000101(wv47, wv480, wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00072(wv47, Pos(Zero), Succ(wv2600), Pos(Succ(wv5100)), wv52) → new_intersectBy000101(wv47, Zero, wv52)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy00078(wv285, wv41) → new_intersectBy000111(wv41)
new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00065(Succ(wv2350), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00080(Succ(wv2910), wv41) → new_intersectBy000113(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00069(wv259, wv41) → new_intersectBy000114(wv41)
new_intersectBy00067(wv30100000, Succ(wv2510), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy00085(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00083(Succ(wv3120), wv41) → new_intersectBy000113(wv41)
new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00057(wv30100000, Succ(wv2120), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00064(wv30100000, Succ(wv2300), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00071(wv301, wv401, wv41)
new_intersectBy000109(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000110(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00075(wv276, wv41) → new_intersectBy000111(wv41)
new_intersectBy00062(wv229, wv41) → new_intersectBy000111(wv41)
new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00061(Succ(wv2260), wv41) → new_intersectBy000110(wv41)
new_intersectBy00084(wv315, wv41) → new_intersectBy000114(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy00066(wv250, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00085(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
new_intersectBy00082(wv30100000, Succ(wv3070), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy000111(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000114(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00071(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00071(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00077(Succ(wv2820), wv41) → new_intersectBy000110(wv41)
new_intersectBy00070(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00085(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00074(Succ(wv2730), wv41) → new_intersectBy000110(wv41)
new_intersectBy00060(wv30100000, Succ(wv2210), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000112(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00085(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
new_intersectBy00071(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00063(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00058(Succ(wv2170), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00068(Succ(wv2560), wv41) → new_intersectBy000113(wv41)
new_intersectBy00071(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00076(wv30100000, Succ(wv2770), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy000113(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00071(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00085(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Neg(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00085(wv301, wv401, wv41)
new_intersectBy00081(wv306, wv41) → new_intersectBy000114(wv41)
new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00073(wv30100000, Succ(wv2680), wv41) → new_intersectBy000109(wv30100000, wv41)
new_intersectBy00079(wv30100000, Succ(wv2860), wv41) → new_intersectBy000112(wv30100000, wv41)
new_intersectBy00059(wv220, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
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_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3
- new_intersectBy00070(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00071(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00071(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00085(wv301, wv401, wv41)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00071(wv301, wv401, wv41)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_intersectBy00078(wv285, wv41) → new_intersectBy000111(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00085(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy000111(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00078(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00059(wv220, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00071(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00059(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00071(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00065(Succ(wv2350), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00065(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy000113(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00068(Succ(wv2560), wv41) → new_intersectBy000113(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00071(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00068(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00083(Succ(wv3120), wv41) → new_intersectBy000113(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00080(Succ(wv2910), wv41) → new_intersectBy000113(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00083(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00085(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00080(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00064(wv30100000, Succ(wv2300), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00064(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy000112(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00079(wv30100000, Succ(wv2860), wv41) → new_intersectBy000112(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00079(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00067(wv30100000, Succ(wv2510), wv41) → new_intersectBy000112(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00082(wv30100000, Succ(wv3070), wv41) → new_intersectBy000112(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00071(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00067(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00085(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00082(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00057(wv30100000, Succ(wv2120), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00057(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy000109(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00073(wv30100000, Succ(wv2680), wv41) → new_intersectBy000109(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00073(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00060(wv30100000, Succ(wv2210), wv41) → new_intersectBy000109(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00076(wv30100000, Succ(wv2770), wv41) → new_intersectBy000109(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00071(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00060(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00085(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00076(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3
- new_intersectBy00063(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00071(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00069(wv259, wv41) → new_intersectBy000114(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy000114(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00071(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00069(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00066(wv250, :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00081(wv306, wv41) → new_intersectBy000114(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00084(wv315, wv41) → new_intersectBy000114(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00085(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00081(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00071(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00066(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00085(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00084(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00058(Succ(wv2170), :(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy000110(:(wv410, wv411)) → new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00058(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00061(Succ(wv2260), wv41) → new_intersectBy000110(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00071(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00071(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00061(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00074(Succ(wv2730), wv41) → new_intersectBy000110(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00077(Succ(wv2820), wv41) → new_intersectBy000110(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00074(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00085(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00077(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00085(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00062(wv229, wv41) → new_intersectBy000111(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00075(wv276, wv41) → new_intersectBy000111(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00062(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00075(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00085(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00085(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00070(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00085(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00085(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Neg(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00063(wv41)
The graph contains the following edges 3 >= 1
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy00048(wv173, wv41) → new_intersectBy00088(wv41)
new_intersectBy00052(wv30100000, Succ(wv1950), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00045(wv164, wv41) → new_intersectBy00088(wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00035(Succ(wv1350), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00055(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00034(wv30100000, Succ(wv1300), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00037(wv30100000, Succ(wv1390), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00033(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy00041(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00039(wv147, wv41) → new_intersectBy00091(wv41)
new_intersectBy00088(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00049(wv30100000, Succ(wv1740), wv41) → new_intersectBy00089(wv30100000, wv41)
new_intersectBy00032(wv129, wv41) → new_intersectBy00088(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00046(wv30100000, Succ(wv1650), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy00050(Succ(wv1790), wv41) → new_intersectBy00090(wv41)
new_intersectBy00055(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00055(wv301, wv401, wv41)
new_intersectBy00030(wv30100000, Succ(wv1210), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00054(wv203, wv41) → new_intersectBy00091(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00055(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
new_intersectBy00027(wv30100000, Succ(wv1120), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00090(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00091(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy00055(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy00040(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00041(wv301, wv401, wv41)
new_intersectBy00041(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00044(Succ(wv1610), wv41) → new_intersectBy00087(wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00087(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00055(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00089(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00051(wv194, wv41) → new_intersectBy00091(wv41)
new_intersectBy00029(wv120, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
new_intersectBy00053(Succ(wv2000), wv41) → new_intersectBy00090(wv41)
new_intersectBy00043(wv30100000, Succ(wv1560), wv41) → new_intersectBy00086(wv30100000, wv41)
new_intersectBy00055(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00036(wv138, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00041(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
new_intersectBy00028(Succ(wv1170), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
new_intersectBy00055(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00047(Succ(wv1700), wv41) → new_intersectBy00087(wv41)
new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
new_intersectBy00038(Succ(wv1440), wv41) → new_intersectBy00090(wv41)
new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00031(Succ(wv1260), wv41) → new_intersectBy00087(wv41)
new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00086(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
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_intersectBy0007(Float(Pos(Zero), wv301), Float(Pos(Zero), wv401), wv41) → new_intersectBy00041(wv301, wv401, wv41)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_intersectBy00027(wv30100000, Succ(wv1120), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy0007(Float(Pos(Zero), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00055(wv301, wv401, wv41)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
- new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00027(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00086(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00046(wv30100000, Succ(wv1650), wv41) → new_intersectBy00086(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00046(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00030(wv30100000, Succ(wv1210), wv41) → new_intersectBy00086(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00043(wv30100000, Succ(wv1560), wv41) → new_intersectBy00086(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00041(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00030(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00055(Pos(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00043(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00033(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00041(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3
- new_intersectBy00041(Pos(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00041(Neg(Succ(Zero)), Pos(Succ(wv40100)), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00054(wv203, wv41) → new_intersectBy00091(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00091(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00055(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00054(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00036(wv138, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00041(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00036(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00039(wv147, wv41) → new_intersectBy00091(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00051(wv194, wv41) → new_intersectBy00091(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00041(Neg(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00039(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00055(Neg(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00051(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00049(wv30100000, Succ(wv1740), wv41) → new_intersectBy00089(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00089(wv30100000, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00049(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00034(wv30100000, Succ(wv1300), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), wv410, wv411)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00037(wv30100000, Succ(wv1390), wv41) → new_intersectBy00089(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00052(wv30100000, Succ(wv1950), wv41) → new_intersectBy00089(wv30100000, wv41)
The graph contains the following edges 1 >= 1, 3 >= 2
- new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00037(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00055(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Neg(Succ(wv40100)), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00052(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00041(Neg(Succ(Succ(Succ(Succ(wv30100000))))), Pos(Succ(wv40100)), wv41) → new_intersectBy00034(wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00045(wv164, wv41) → new_intersectBy00088(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00088(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00055(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00045(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00040(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00041(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), wv410, wv411)
The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3
- new_intersectBy00047(Succ(wv1700), wv41) → new_intersectBy00087(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00087(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00047(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00028(Succ(wv1170), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00031(Succ(wv1260), wv41) → new_intersectBy00087(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00044(Succ(wv1610), wv41) → new_intersectBy00087(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00031(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00055(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00044(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00041(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00028(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00050(Succ(wv1790), wv41) → new_intersectBy00090(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00090(:(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 1 > 2, 1 > 3
- new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00050(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00035(Succ(wv1350), :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00029(wv120, :(wv410, wv411)) → new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), wv410, wv411)
The graph contains the following edges 2 > 2, 2 > 3
- new_intersectBy00038(Succ(wv1440), wv41) → new_intersectBy00090(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00053(Succ(wv2000), wv41) → new_intersectBy00090(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00038(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00055(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wv40100)), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00055(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00053(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00041(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wv40100)), wv41) → new_intersectBy00035(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00048(wv173, wv41) → new_intersectBy00088(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy00032(wv129, wv41) → new_intersectBy00088(wv41)
The graph contains the following edges 2 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00048(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Succ(Zero)))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00041(Pos(Succ(Succ(Zero))), Pos(Succ(wv40100)), wv41) → new_intersectBy00029(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00041(Pos(Succ(Succ(Zero))), Neg(Succ(wv40100)), wv41) → new_intersectBy00032(new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 3 >= 2
- new_intersectBy00055(Pos(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00055(Pos(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00055(Neg(Succ(Zero)), Neg(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy00055(Neg(Succ(Zero)), Pos(Succ(wv40100)), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Pos(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00033(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Pos(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Pos(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
- new_intersectBy0007(Float(Pos(Zero), Neg(Succ(Zero))), Float(Neg(Succ(wv40000)), Neg(Succ(wv40100))), wv41) → new_intersectBy00040(wv41)
The graph contains the following edges 3 >= 1
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) → new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) → new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
R is empty.
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ UsableRulesProof
↳ QDP
↳ QReductionProof
↳ QDP
↳ NonTerminationProof
↳ QDP
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) → new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.
The TRS P consists of the following rules:
new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) → new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
The TRS R consists of the following rules:none
s = new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) evaluates to t =new_intersectBy0000(wv74, wv750, wv95, wv780, wv79)
Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
- Semiunifier: [ ]
- Matcher: [ ]
Rewriting sequence
The DP semiunifies directly so there is only one rewrite step from new_intersectBy0000(wv74, wv750, wv95, wv780, wv79) to new_intersectBy0000(wv74, wv750, wv95, wv780, wv79).
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_intersectBy00016(wv30000, wv30100000, Succ(wv3220), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00023(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00096(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00023(wv30000, wv30100000, Succ(wv990), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy00098(wv34, wv3500, Succ(wv1900), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00097(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00012(wv74, wv7500, Succ(wv770), Succ(wv10800), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
new_intersectBy00018(wv30000, :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy00094(wv34, wv3500, wv1480, Succ(wv1840), wv39) → new_intersectBy000100(wv34, wv3500, wv1480, wv1840, wv39)
new_intersectBy0008(wv74, wv7500, Zero, Succ(Succ(wv11000)), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00024(wv30000, Succ(wv1040), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00042(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
new_intersectBy0005(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy000100(wv74, wv7500, Succ(wv770), Succ(wv11000), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
new_intersectBy0004(wv74, wv7500, Zero, Succ(Succ(wv10800)), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00016(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00092(wv34, wv3500, wv1480, Succ(wv1820), wv39) → new_intersectBy00012(wv34, wv3500, wv1480, wv1820, wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00017(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Succ(wv11000)), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
new_intersectBy00015(wv30000, Succ(wv3200), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Zero), wv79) → new_intersectBy00010(wv74, wv77, wv79)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00019(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00025(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00042(wv30000, wv301, Zero, wv401, wv41)
new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00017(wv30000, Succ(wv830), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00099(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy00022(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0008(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy0006(wv74, wv77, wv79) → new_intersectBy0005(wv74, Zero, wv79)
new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0005(wv74, Zero, wv79)
new_intersectBy00010(wv74, wv77, wv79) → new_intersectBy0009(wv74, Zero, wv79)
new_intersectBy00099(wv34, wv3500, Succ(wv1920), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Zero), wv79) → new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Succ(wv10800)), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00020(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy000(wv74, Neg(wv750), Zero, wv77, Pos(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy00042(wv34, Pos(wv350), Succ(wv1480), Pos(wv380), wv39) → new_intersectBy0005(wv34, wv350, wv39)
new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy0009(wv34, Zero, wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00015(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00024(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00097(wv34, wv3500, Succ(wv1880), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00021(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
new_intersectBy0009(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
new_intersectBy000(wv74, Pos(wv750), Zero, wv77, Neg(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00026(wv30000, wv41)
new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy0005(wv34, Zero, wv39)
new_intersectBy00095(wv34, wv1480, wv39) → new_intersectBy0009(wv34, Zero, wv39)
new_intersectBy00020(wv30000, Succ(wv910), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy000(wv30000, wv301, new_primMulNat0(wv30000, wv40000), wv40000, wv401, wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00014(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
new_intersectBy00019(wv30000, wv30100000, Succ(wv860), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00093(wv34, wv1480, wv39)
new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0004(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
new_intersectBy00026(wv30000, :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00095(wv34, wv1480, wv39)
new_intersectBy00013(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
new_intersectBy00012(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00012(wv74, wv7500, Zero, Succ(wv10800), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00098(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0006(wv74, wv77, wv79)
new_intersectBy00014(wv30000, wv30100000, Succ(wv3160), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy000100(wv74, wv7500, Zero, Succ(wv11000), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy000100(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
new_intersectBy00093(wv34, wv1480, wv39) → new_intersectBy0005(wv34, Zero, wv39)
new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0009(wv74, Zero, wv79)
new_intersectBy00021(wv30000, wv94, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy00042(wv34, Neg(wv350), Succ(wv1480), Neg(wv380), wv39) → new_intersectBy0009(wv34, wv350, wv39)
new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00018(wv30000, wv41)
new_intersectBy00025(wv30000, wv107, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
new_intersectBy00096(wv34, wv3500, Succ(wv1860), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
The TRS R consists of the following rules:
new_primPlusNat1(Zero, wv40000) → Succ(wv40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wv820), wv40000) → Succ(Succ(new_primPlusNat0(wv820, wv40000)))
new_primMulNat0(Zero, wv40000) → Zero
new_primPlusNat0(Succ(wv8200), Zero) → Succ(wv8200)
new_primPlusNat0(Zero, Succ(wv400000)) → Succ(wv400000)
new_primPlusNat0(Succ(wv8200), Succ(wv400000)) → Succ(Succ(new_primPlusNat0(wv8200, wv400000)))
new_primMulNat0(Succ(wv300000), wv40000) → new_primPlusNat1(new_primMulNat0(wv300000, wv40000), wv40000)
The set Q consists of the following terms:
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Succ(x0), x1)
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_intersectBy00023(wv30000, wv30100000, Succ(wv990), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00023(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 4
- new_intersectBy0009(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00025(wv30000, wv107, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00025(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00020(wv30000, Succ(wv910), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00020(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0009(wv74, Zero, wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 2, 6 >= 3
- new_intersectBy000(wv74, Neg(wv750), Zero, wv77, Pos(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
The graph contains the following edges 6 > 2, 6 > 3
- new_intersectBy00022(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Neg(wv750)), wv790, wv791)
The graph contains the following edges 3 >= 2, 4 >= 3
- new_intersectBy000(wv74, Pos(wv750), Zero, wv77, Neg(wv780), :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
The graph contains the following edges 6 > 2, 6 > 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Pos(Succ(wv40000)), wv401), wv41) → new_intersectBy000(wv30000, wv301, new_primMulNat0(wv30000, wv40000), wv40000, wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 4, 2 > 5, 3 >= 6
- new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0005(wv74, wv750, :(wv790, wv791)) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
The graph contains the following edges 3 > 2, 3 > 3
- new_intersectBy00013(wv74, wv750, wv790, wv791) → new_intersectBy0007(Float(Pos(Succ(wv74)), Pos(wv750)), wv790, wv791)
The graph contains the following edges 3 >= 2, 4 >= 3
- new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0005(wv74, Zero, wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 2, 6 >= 3
- new_intersectBy00097(wv34, wv3500, Succ(wv1880), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00097(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Succ(wv40000)), wv401), wv41) → new_intersectBy00042(wv30000, wv301, new_primPlusNat0(new_primMulNat0(wv30000, wv40000), Succ(wv40000)), wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 4, 3 >= 5
- new_intersectBy0007(Float(Pos(Succ(wv30000)), wv301), Float(Neg(Zero), wv401), wv41) → new_intersectBy00042(wv30000, wv301, Zero, wv401, wv41)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 3, 2 > 4, 3 >= 5
- new_intersectBy00098(wv34, wv3500, Succ(wv1900), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00098(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy00096(wv34, wv3500, Succ(wv1860), wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00042(wv34, Pos(Succ(wv3500)), Zero, Pos(Succ(wv3800)), wv39) → new_intersectBy00096(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0005(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy00093(wv34, wv1480, wv39) → new_intersectBy0005(wv34, Zero, wv39)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00093(wv34, wv1480, wv39)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy00092(wv34, wv3500, wv1480, Succ(wv1820), wv39) → new_intersectBy00012(wv34, wv3500, wv1480, wv1820, wv39)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
- new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 5 >= 5
- new_intersectBy00042(wv34, Pos(Succ(wv3500)), Succ(wv1480), Neg(Zero), wv39) → new_intersectBy00092(wv34, wv3500, wv1480, Zero, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy00012(wv74, wv7500, Succ(wv770), Succ(wv10800), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Succ(wv10800)), wv79) → new_intersectBy00012(wv74, wv7500, wv770, wv10800, wv79)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy00094(wv34, wv3500, wv1480, Succ(wv1840), wv39) → new_intersectBy000100(wv34, wv3500, wv1480, wv1840, wv39)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 >= 5
- new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 5 >= 5
- new_intersectBy00042(wv34, Neg(Succ(wv3500)), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00094(wv34, wv3500, wv1480, Zero, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy000100(wv74, wv7500, Succ(wv770), Succ(wv11000), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Succ(wv11000)), wv79) → new_intersectBy000100(wv74, wv7500, wv770, wv11000, wv79)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4, 5 >= 5
- new_intersectBy00099(wv34, wv3500, Succ(wv1920), wv39) → new_intersectBy0009(wv34, Succ(wv3500), wv39)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy00042(wv34, Neg(Succ(wv3500)), Zero, Neg(Succ(wv3800)), wv39) → new_intersectBy00099(wv34, wv3500, new_primPlusNat0(new_primMulNat0(wv3500, wv3800), Succ(wv3800)), wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 4
- new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Zero), wv39) → new_intersectBy00095(wv34, wv1480, wv39)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
- new_intersectBy00095(wv34, wv1480, wv39) → new_intersectBy0009(wv34, Zero, wv39)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy00017(wv30000, Succ(wv830), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00017(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
The graph contains the following edges 1 > 1, 1 > 2, 3 > 3, 3 > 4
- new_intersectBy00018(wv30000, :(wv410, wv411)) → new_intersectBy00013(wv30000, Succ(Zero), wv410, wv411)
The graph contains the following edges 1 >= 1, 2 > 3, 2 > 4
- new_intersectBy00026(wv30000, :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
The graph contains the following edges 1 >= 1, 2 > 3, 2 > 4
- new_intersectBy00015(wv30000, Succ(wv3200), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Zero))), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00015(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00014(wv30000, wv30100000, Succ(wv3160), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00014(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 4
- new_intersectBy00016(wv30000, wv30100000, Succ(wv3220), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00016(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 4
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00018(wv30000, wv41)
The graph contains the following edges 1 > 1, 3 >= 2
- new_intersectBy0006(wv74, wv77, wv79) → new_intersectBy0005(wv74, Zero, wv79)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy000(wv74, Pos(Zero), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0006(wv74, wv77, wv79)
The graph contains the following edges 1 >= 1, 4 >= 2, 6 >= 3
- new_intersectBy00019(wv30000, wv30100000, Succ(wv860), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Succ(wv30100000)))), wv41)
The graph contains the following edges 1 >= 1, 4 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Succ(wv30100000)))))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00019(wv30000, wv30100000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wv30100000, wv40100), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 4
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00026(wv30000, wv41)
The graph contains the following edges 1 > 1, 3 >= 2
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Zero))), Float(Pos(Zero), Pos(Succ(wv40100))), :(wv410, wv411)) → new_intersectBy00022(wv30000, Succ(Zero), wv410, wv411)
The graph contains the following edges 1 > 1, 1 > 2, 3 > 3, 3 > 4
- new_intersectBy00021(wv30000, wv94, wv41) → new_intersectBy0009(wv30000, Succ(Succ(Zero)), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy00021(wv30000, new_primPlusNat0(wv40100, wv40100), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Neg(Succ(Succ(Succ(Zero))))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy00024(wv30000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wv40100)), Succ(wv40100)), Succ(wv40100)), wv41)
The graph contains the following edges 1 > 1, 3 >= 3
- new_intersectBy00024(wv30000, Succ(wv1040), wv41) → new_intersectBy0009(wv30000, Succ(Succ(Succ(Zero))), wv41)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy00010(wv74, wv77, wv79) → new_intersectBy0009(wv74, Zero, wv79)
The graph contains the following edges 1 >= 1, 3 >= 3
- new_intersectBy000(wv74, Neg(Zero), Zero, wv77, Neg(Zero), wv79) → new_intersectBy00010(wv74, wv77, wv79)
The graph contains the following edges 1 >= 1, 4 >= 2, 6 >= 3
- new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Succ(wv7800)), wv79) → new_intersectBy0008(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 6 >= 5
- new_intersectBy000(wv74, Neg(Succ(wv7500)), Zero, wv77, Neg(Zero), wv79) → new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 3 >= 4, 5 > 4, 6 >= 5
- new_intersectBy0008(wv74, wv7500, wv77, Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Succ(wv7800)), wv79) → new_intersectBy0004(wv74, wv7500, wv77, new_primPlusNat0(new_primMulNat0(wv7500, wv7800), Succ(wv7800)), wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 6 >= 5
- new_intersectBy000(wv74, Pos(Succ(wv7500)), Zero, wv77, Pos(Zero), wv79) → new_intersectBy0004(wv74, wv7500, wv77, Zero, wv79)
The graph contains the following edges 1 >= 1, 2 > 2, 4 >= 3, 3 >= 4, 5 > 4, 6 >= 5
- new_intersectBy00042(wv34, Neg(wv350), Succ(wv1480), Neg(wv380), wv39) → new_intersectBy0009(wv34, wv350, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00042(wv34, Neg(Zero), Succ(wv1480), Pos(Succ(wv3800)), wv39) → new_intersectBy0009(wv34, Zero, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy000100(wv74, wv7500, Zero, Succ(wv11000), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy000100(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0008(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0008(wv74, wv7500, Zero, Succ(Succ(wv11000)), wv79) → new_intersectBy0009(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Neg(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_intersectBy0007(Float(Pos(Succ(wv30000)), Pos(Succ(Succ(Zero)))), Float(Pos(Zero), Pos(Succ(wv40100))), wv41) → new_intersectBy0005(wv30000, Succ(Succ(Zero)), wv41)
The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
- new_intersectBy00042(wv34, Pos(wv350), Succ(wv1480), Pos(wv380), wv39) → new_intersectBy0005(wv34, wv350, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00042(wv34, Pos(Zero), Succ(wv1480), Neg(Succ(wv3800)), wv39) → new_intersectBy0005(wv34, Zero, wv39)
The graph contains the following edges 1 >= 1, 2 > 2, 5 >= 3
- new_intersectBy00012(wv74, wv7500, Succ(wv770), Zero, wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy00012(wv74, wv7500, Zero, Succ(wv10800), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0004(wv74, wv7500, Zero, Succ(Succ(wv10800)), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
- new_intersectBy0004(wv74, wv7500, Succ(wv770), Succ(Zero), wv79) → new_intersectBy0005(wv74, Succ(wv7500), wv79)
The graph contains the following edges 1 >= 1, 5 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_psPs(:(wv200, wv201), wv21, ba) → new_psPs(wv201, wv21, ba)
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(:(wv200, wv201), wv21, ba) → new_psPs(wv201, wv21, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
↳ HASKELL
↳ LR
↳ HASKELL
↳ CR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
↳ Narrow
Q DP problem:
The TRS P consists of the following rules:
new_foldr0(wv4, :(wv30, wv31)) → new_foldr0(wv4, wv31)
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_foldr0(wv4, :(wv30, wv31)) → new_foldr0(wv4, wv31)
The graph contains the following edges 1 >= 1, 2 > 2
Haskell To QDPs