/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could not be shown:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 16 ms]
(4) HASKELL
(5) LetRed [EQUIVALENT, 0 ms]
(6) HASKELL


----------------------------------------

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
nub :: Eq a => [a]  ->  [a];
nub l = nub' l [] where { 
nub' [] _ = [];
nub' (x : xs) ls  | x `elem` ls = nub' xs ls
 | otherwise = x : nub' xs (x : ls);
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
nub :: Eq a => [a]  ->  [a];
nub l = nub' l [] where { 
nub' [] wu = [];
nub' (x : xs) ls  | x `elem` ls = nub' xs ls
 | otherwise = x : nub' xs (x : ls);
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"nub' [] wu = [];
nub' (x : xs) ls|x `elem` lsnub' xs ls|otherwisex : nub' xs (x : ls);
"
is transformed to
"nub' [] wu = nub'3 [] wu;
nub' (x : xs) ls = nub'2 (x : xs) ls;
"
"nub'1 x xs ls True = nub' xs ls;
nub'1 x xs ls False = nub'0 x xs ls otherwise;
"
"nub'0 x xs ls True = x : nub' xs (x : ls);
"
"nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
"
"nub'3 [] wu = [];
nub'3 wx wy = nub'2 wx wy;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
nub :: Eq a => [a]  ->  [a];
nub l = nub' l [] where { 
nub' [] wu = nub'3 [] wu;
nub' (x : xs) ls = nub'2 (x : xs) ls;
nub'0 x xs ls True = x : nub' xs (x : ls);
nub'1 x xs ls True = nub' xs ls;
nub'1 x xs ls False = nub'0 x xs ls otherwise;
nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
nub'3 [] wu = [];
nub'3 wx wy = nub'2 wx wy;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

----------------------------------------

(5) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"nub' l [] where {
nub' [] wu = nub'3 [] wu;
nub' (x : xs) ls = nub'2 (x : xs) ls;
;
nub'0 x xs ls True = x : nub' xs (x : ls);
;
nub'1 x xs ls True = nub' xs ls;
nub'1 x xs ls False = nub'0 x xs ls otherwise;
;
nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
;
nub'3 [] wu = [];
nub'3 wx wy = nub'2 wx wy;
} 
"
are unpacked to the following functions on top level
"nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
"
"nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
"
"nubNub' [] wu = nubNub'3 [] wu;
nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
"
"nubNub'3 [] wu = [];
nubNub'3 wx wy = nubNub'2 wx wy;
"
"nubNub'1 x xs ls True = nubNub' xs ls;
nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
"

----------------------------------------

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
nub :: Eq a => [a]  ->  [a];
nub l = nubNub' l [];

nubNub' [] wu = nubNub'3 [] wu;
nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;

nubNub'0 x xs ls True = x : nubNub' xs (x : ls);

nubNub'1 x xs ls True = nubNub' xs ls;
nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;

nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);

nubNub'3 [] wu = [];
nubNub'3 wx wy = nubNub'2 wx wy;

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}