/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) IPR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) COR [EQUIVALENT, 0 ms]
(8) HASKELL


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
mapAndUnzipM :: Monad c => (a  ->  c (b,d))  ->  [a]  ->  c ([b],[d]);
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;

}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\(a,b)~(as,bs)->(a : as,b : bs)"
is transformed to
"unzip0 (a,b) ~(as,bs) = (a : as,b : bs);
"
The following Lambda expression
"\xs->return (x : xs)"
is transformed to
"sequence0 x xs = return (x : xs);
"
The following Lambda expression
"\x->sequence cs >>= sequence0 x"
is transformed to
"sequence1 cs x = sequence cs >>= sequence0 x;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
mapAndUnzipM :: Monad b => (a  ->  b (d,c))  ->  [a]  ->  b ([d],[c]);
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;

}

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

(3) IPR (EQUIVALENT)
IrrPat Reductions:
The variables of the following irrefutable Pattern
"~(as,bs)"
are replaced by calls to these functions
"unzip00 (as,bs) = as;
"
"unzip01 (as,bs) = bs;
"

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

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
mapAndUnzipM :: Monad c => (b  ->  c (a,d))  ->  [b]  ->  c ([a],[d]);
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;

}

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

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

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
mapAndUnzipM :: Monad d => (a  ->  d (c,b))  ->  [a]  ->  d ([c],[b]);
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;

}

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

(7) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

(8)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
mapAndUnzipM :: Monad d => (c  ->  d (a,b))  ->  [c]  ->  d ([a],[b]);
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;

}