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


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


MAYBE
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) IFR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) BR [EQUIVALENT, 8 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 0 ms]
(12) HASKELL
(13) NumRed [SOUND, 0 ms]
(14) HASKELL


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\vu54->case vu54 of {
(ch,''' : t)  -> if ch /= ''' : [] then (''' : ch ++ ''' : [],t) : [] else [];
_  -> []}
"
is transformed to
"lex0 vu54 = case vu54 of {
(ch,''' : t)  -> if ch /= ''' : [] then (''' : ch ++ ''' : [],t) : [] else [];
_  -> []}
;
"
The following Lambda expression
"\vu56->case vu56 of {
(str,u)  -> (ch ++ str,u) : [];
_  -> []}
"
is transformed to
"lexString0 ch vu56 = case vu56 of {
(str,u)  -> (ch ++ str,u) : [];
_  -> []}
;
"
The following Lambda expression
"\vu57->case vu57 of {
(ch,t)  -> concatMap (lexString0 ch) (lexString t);
_  -> []}
"
is transformed to
"lexString1 vu57 = case vu57 of {
(ch,t)  -> concatMap (lexString0 ch) (lexString t);
_  -> []}
;
"
The following Lambda expression
"\vu58->case vu58 of {
'\' : t  -> ([],t) : [];
_  -> []}
"
is transformed to
"lexStrItem0 vu58 = case vu58 of {
'\' : t  -> ([],t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu55->case vu55 of {
(str,t)  -> ('"' : str,t) : [];
_  -> []}
"
is transformed to
"lex1 vu55 = case vu55 of {
(str,t)  -> ('"' : str,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu63->case vu63 of {
(e,u)  -> ('.' : ds ++ e,u) : [];
_  -> []}
"
is transformed to
"lexFracExp0 ds vu63 = case vu63 of {
(e,u)  -> ('.' : ds ++ e,u) : [];
_  -> []}
;
"
The following Lambda expression
"\vu64->case vu64 of {
(ds,t)  -> concatMap (lexFracExp0 ds) (lexExp t);
_  -> []}
"
is transformed to
"lexFracExp1 vu64 = case vu64 of {
(ds,t)  -> concatMap (lexFracExp0 ds) (lexExp t);
_  -> []}
;
"
The following Lambda expression
"\vu65->case vu65 of {
(ds,u)  -> (e : c : ds,u) : [];
_  -> []}
"
is transformed to
"lexExp0 e c vu65 = case vu65 of {
(ds,u)  -> (e : c : ds,u) : [];
_  -> []}
;
"
The following Lambda expression
"\vu66->case vu66 of {
c : t  -> if c `elem` '+' : '-' : [] then concatMap (lexExp0 e c) (lexDigits t) else [];
_  -> []}
"
is transformed to
"lexExp1 e vu66 = case vu66 of {
c : t  -> if c `elem` '+' : '-' : [] then concatMap (lexExp0 e c) (lexDigits t) else [];
_  -> []}
;
"
The following Lambda expression
"\vu67->case vu67 of {
(ds,t)  -> (e : ds,t) : [];
_  -> []}
"
is transformed to
"lexExp2 e vu67 = case vu67 of {
(ds,t)  -> (e : ds,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu59->case vu59 of {
(sym,t)  -> (c : sym,t) : [];
_  -> []}
"
is transformed to
"lex2 c vu59 = case vu59 of {
(sym,t)  -> (c : sym,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu60->case vu60 of {
(nam,t)  -> (c : nam,t) : [];
_  -> []}
"
is transformed to
"lex3 c vu60 = case vu60 of {
(nam,t)  -> (c : nam,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu61->case vu61 of {
(fe,t)  -> (c : ds ++ fe,t) : [];
_  -> []}
"
is transformed to
"lex4 c ds vu61 = case vu61 of {
(fe,t)  -> (c : ds ++ fe,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu62->case vu62 of {
(ds,s)  -> concatMap (lex4 c ds) (lexFracExp s);
_  -> []}
"
is transformed to
"lex5 c vu62 = case vu62 of {
(ds,s)  -> concatMap (lex4 c ds) (lexFracExp s);
_  -> []}
;
"
The following Lambda expression
"\ab->(a,b)"
is transformed to
"zip0 a b = (a,b);
"
The following Lambda expression
"\vu68->case vu68 of {
(cs@(_ : _),t)  -> (cs,t) : [];
_  -> []}
"
is transformed to
"nonnull0 vu68 = case vu68 of {
(cs@(_ : _),t)  -> (cs,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu69->case vu69 of {
([],s')  -> (mne,s') : [];
_  -> []}
"
is transformed to
"lexEsc0 mne vu69 = case vu69 of {
([],s')  -> (mne,s') : [];
_  -> []}
;
"
The following Lambda expression
"\vu70->case vu70 of {
(c,mne)  -> concatMap (lexEsc0 mne) (lexmatch mne s : []);
_  -> []}
"
is transformed to
"lexEsc1 s vu70 = case vu70 of {
(c,mne)  -> concatMap (lexEsc0 mne) (lexmatch mne s : []);
_  -> []}
;
"
The following Lambda expression
"\(_,zs)->zs"
is transformed to
"zs0 (_,zs) = zs;
"
The following Lambda expression
"\(ys,_)->ys"
is transformed to
"ys0 (ys,_) = ys;
"

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(3) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case vu55 of {
(str,t)  -> ('"' : str,t) : [];
_  -> []}
"
is transformed to
"lex10 (str,t) = ('"' : str,t) : [];
lex10 _ = [];
"
The following Case expression
"case vu57 of {
(ch,t)  -> concatMap (lexString0 ch) (lexString t);
_  -> []}
"
is transformed to
"lexString10 (ch,t) = concatMap (lexString0 ch) (lexString t);
lexString10 _ = [];
"
The following Case expression
"case vu56 of {
(str,u)  -> (ch ++ str,u) : [];
_  -> []}
"
is transformed to
"lexString00 ch (str,u) = (ch ++ str,u) : [];
lexString00 ch _ = [];
"
The following Case expression
"case vu58 of {
'\' : t  -> ([],t) : [];
_  -> []}
"
is transformed to
"lexStrItem00 ('\' : t) = ([],t) : [];
lexStrItem00 _ = [];
"
The following Case expression
"case vu59 of {
(sym,t)  -> (c : sym,t) : [];
_  -> []}
"
is transformed to
"lex20 c (sym,t) = (c : sym,t) : [];
lex20 c _ = [];
"
The following Case expression
"case vu67 of {
(ds,t)  -> (e : ds,t) : [];
_  -> []}
"
is transformed to
"lexExp20 e (ds,t) = (e : ds,t) : [];
lexExp20 e _ = [];
"
The following Case expression
"case vu65 of {
(ds,u)  -> (e : c : ds,u) : [];
_  -> []}
"
is transformed to
"lexExp00 e c (ds,u) = (e : c : ds,u) : [];
lexExp00 e c _ = [];
"
The following Case expression
"case vu62 of {
(ds,s)  -> concatMap (lex4 c ds) (lexFracExp s);
_  -> []}
"
is transformed to
"lex50 c (ds,s) = concatMap (lex4 c ds) (lexFracExp s);
lex50 c _ = [];
"
The following Case expression
"case vu66 of {
c : t  -> if c `elem` '+' : '-' : [] then concatMap (lexExp0 e c) (lexDigits t) else [];
_  -> []}
"
is transformed to
"lexExp10 e (c : t) = if c `elem` '+' : '-' : [] then concatMap (lexExp0 e c) (lexDigits t) else [];
lexExp10 e _ = [];
"
The following Case expression
"case vu60 of {
(nam,t)  -> (c : nam,t) : [];
_  -> []}
"
is transformed to
"lex30 c (nam,t) = (c : nam,t) : [];
lex30 c _ = [];
"
The following Case expression
"case vu61 of {
(fe,t)  -> (c : ds ++ fe,t) : [];
_  -> []}
"
is transformed to
"lex40 c ds (fe,t) = (c : ds ++ fe,t) : [];
lex40 c ds _ = [];
"
The following Case expression
"case vu63 of {
(e,u)  -> ('.' : ds ++ e,u) : [];
_  -> []}
"
is transformed to
"lexFracExp00 ds (e,u) = ('.' : ds ++ e,u) : [];
lexFracExp00 ds _ = [];
"
The following Case expression
"case vu64 of {
(ds,t)  -> concatMap (lexFracExp0 ds) (lexExp t);
_  -> []}
"
is transformed to
"lexFracExp10 (ds,t) = concatMap (lexFracExp0 ds) (lexExp t);
lexFracExp10 _ = [];
"
The following Case expression
"case vu54 of {
(ch,''' : t)  -> if ch /= ''' : [] then (''' : ch ++ ''' : [],t) : [] else [];
_  -> []}
"
is transformed to
"lex00 (ch,''' : t) = if ch /= ''' : [] then (''' : ch ++ ''' : [],t) : [] else [];
lex00 _ = [];
"
The following Case expression
"case vu68 of {
(cs@(_ : _),t)  -> (cs,t) : [];
_  -> []}
"
is transformed to
"nonnull00 (cs@(_ : _),t) = (cs,t) : [];
nonnull00 _ = [];
"
The following Case expression
"case concatMap (lexEsc1 s) table of {
pr : _  -> pr : [];
[]  -> []}
"
is transformed to
"lexEsc2 (pr : _) = pr : [];
lexEsc2 [] = [];
"
The following Case expression
"case vu69 of {
([],s')  -> (mne,s') : [];
_  -> []}
"
is transformed to
"lexEsc00 mne ([],s') = (mne,s') : [];
lexEsc00 mne _ = [];
"
The following Case expression
"case vu70 of {
(c,mne)  -> concatMap (lexEsc0 mne) (lexmatch mne s : []);
_  -> []}
"
is transformed to
"lexEsc10 s (c,mne) = concatMap (lexEsc0 mne) (lexmatch mne s : []);
lexEsc10 s _ = [];
"

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

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(5) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if c `elem` '+' : '-' : [] then concatMap (lexExp0 e c) (lexDigits t) else []"
is transformed to
"lexExp100 e c t True = concatMap (lexExp0 e c) (lexDigits t);
lexExp100 e c t False = [];
"
The following If expression
"if ch /= ''' : [] then (''' : ch ++ ''' : [],t) : [] else []"
is transformed to
"lex000 ch t True = (''' : ch ++ ''' : [],t) : [];
lex000 ch t False = [];
"

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

(6)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

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

Binding Reductions:
The bind variable of the following binding Pattern
"cs@(wu : wv)"
is replaced by the following term
"wu : wv"
The bind variable of the following binding Pattern
"xs@(zw : zx)"
is replaced by the following term
"zw : zx"
The bind variable of the following binding Pattern
"s@(vuu : vuv)"
is replaced by the following term
"vuu : vuv"
The bind variable of the following binding Pattern
"xs@(vvu : vvv)"
is replaced by the following term
"vvu : vvv"

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

(8)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(9) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"takeWhile p [] = [];
takeWhile p (x : xs)|p xx : takeWhile p xs|otherwise[];
"
is transformed to
"takeWhile p [] = takeWhile3 p [];
takeWhile p (x : xs) = takeWhile2 p (x : xs);
"
"takeWhile0 p x xs True = [];
"
"takeWhile1 p x xs True = x : takeWhile p xs;
takeWhile1 p x xs False = takeWhile0 p x xs otherwise;
"
"takeWhile2 p (x : xs) = takeWhile1 p x xs (p x);
"
"takeWhile3 p [] = [];
takeWhile3 vwu vwv = takeWhile2 vwu vwv;
"
The following Function with conditions
"lexString ('"' : s) = ('"' : [],s) : [];
lexString s = concatMap lexString1 (lexStrItem s);
"
is transformed to
"lexString (vwx : s) = lexString4 (vwx : s);
lexString s = lexString2 s;
"
"lexString2 s = concatMap lexString1 (lexStrItem s);
"
"lexString3 True (vwx : s) = ('"' : [],s) : [];
lexString3 vwy vwz = lexString2 vwz;
"
"lexString4 (vwx : s) = lexString3 (vwx == '"') (vwx : s);
lexString4 vxu = lexString2 vxu;
"
The following Function with conditions
"lexStrItem ('\' : '&' : s) = ('\' : '&' : [],s) : [];
lexStrItem ('\' : c : s)|isSpace cconcatMap lexStrItem0 (dropWhile isSpace s : []);
lexStrItem s = lexLitChar s;
"
is transformed to
"lexStrItem (vyy : vzw) = lexStrItem7 (vyy : vzw);
lexStrItem (vxw : vxz) = lexStrItem4 (vxw : vxz);
lexStrItem s = lexStrItem1 s;
"
"lexStrItem1 s = lexLitChar s;
"
"lexStrItem2 vxw c s True = concatMap lexStrItem0 (dropWhile isSpace s : []);
lexStrItem2 vxw c s False = lexStrItem1 (vxw : c : s);
"
"lexStrItem3 True (vxw : c : s) = lexStrItem2 vxw c s (isSpace c);
lexStrItem3 vyu vyv = lexStrItem1 vyv;
"
"lexStrItem4 (vxw : vxz) = lexStrItem3 (vxw == '\') (vxw : vxz);
lexStrItem4 vyw = lexStrItem1 vyw;
"
"lexStrItem5 True (vyy : vzu : s) = ('\' : '&' : [],s) : [];
lexStrItem5 vzx vzy = lexStrItem4 vzy;
"
"lexStrItem6 True (vyy : vzu : s) = lexStrItem5 (vzu == '&') (vyy : vzu : s);
lexStrItem6 vzz wuu = lexStrItem4 wuu;
"
"lexStrItem7 (vyy : vzw) = lexStrItem6 (vyy == '\') (vyy : vzw);
lexStrItem7 wuv = lexStrItem4 wuv;
"
The following Function with conditions
"lexStrItem00 ('\' : t) = ([],t) : [];
lexStrItem00 wz = [];
"
is transformed to
"lexStrItem00 (wux : t) = lexStrItem002 (wux : t);
lexStrItem00 wz = lexStrItem000 wz;
"
"lexStrItem000 wz = [];
"
"lexStrItem001 True (wux : t) = ([],t) : [];
lexStrItem001 wuy wuz = lexStrItem000 wuz;
"
"lexStrItem002 (wux : t) = lexStrItem001 (wux == '\') (wux : t);
lexStrItem002 wvu = lexStrItem000 wvu;
"
The following Function with conditions
"lexExp (e : s)|e `elem` 'e' : 'E' : []concatMap (lexExp1 e) (s : []) ++ concatMap (lexExp2 e) (lexDigits s);
lexExp s = ([],s) : [];
"
is transformed to
"lexExp (e : s) = lexExp5 (e : s);
lexExp s = lexExp3 s;
"
"lexExp3 s = ([],s) : [];
"
"lexExp4 e s True = concatMap (lexExp1 e) (s : []) ++ concatMap (lexExp2 e) (lexDigits s);
lexExp4 e s False = lexExp3 (e : s);
"
"lexExp5 (e : s) = lexExp4 e s (e `elem` 'e' : 'E' : []);
lexExp5 wvw = lexExp3 wvw;
"
The following Function with conditions
"lexFracExp ('.' : c : cs)|isDigit cconcatMap lexFracExp1 (lexDigits (c : cs));
lexFracExp s = lexExp s;
"
is transformed to
"lexFracExp (wvy : wwv) = lexFracExp5 (wvy : wwv);
lexFracExp s = lexFracExp2 s;
"
"lexFracExp2 s = lexExp s;
"
"lexFracExp3 wvy c cs True = concatMap lexFracExp1 (lexDigits (c : cs));
lexFracExp3 wvy c cs False = lexFracExp2 (wvy : c : cs);
"
"lexFracExp4 True (wvy : c : cs) = lexFracExp3 wvy c cs (isDigit c);
lexFracExp4 www wwx = lexFracExp2 wwx;
"
"lexFracExp5 (wvy : wwv) = lexFracExp4 (wvy == '.') (wvy : wwv);
lexFracExp5 wwy = lexFracExp2 wwy;
"
The following Function with conditions
"lex [] = ([],[]) : [];
lex (c : s)|isSpace clex (dropWhile isSpace s);
lex (''' : s) = concatMap lex0 (lexLitChar s);
lex ('"' : s) = concatMap lex1 (lexString s) where {
lex1 vu55 = lex10 vu55;
;
lex10 (str,t) = ('"' : str,t) : [];
lex10 xu = [];
;
lexStrItem ('\' : '&' : s) = ('\' : '&' : [],s) : [];
lexStrItem ('\' : c : s)|isSpace cconcatMap lexStrItem0 (dropWhile isSpace s : []);
lexStrItem s = lexLitChar s;
;
lexStrItem0 vu58 = lexStrItem00 vu58;
;
lexStrItem00 ('\' : t) = ([],t) : [];
lexStrItem00 wz = [];
;
lexString ('"' : s) = ('"' : [],s) : [];
lexString s = concatMap lexString1 (lexStrItem s);
;
lexString0 ch vu56 = lexString00 ch vu56;
;
lexString00 ch (str,u) = (ch ++ str,u) : [];
lexString00 ch wx = [];
;
lexString1 vu57 = lexString10 vu57;
;
lexString10 (ch,t) = concatMap (lexString0 ch) (lexString t);
lexString10 wy = [];
} 
;
lex (c : s)|isSingle c(c : [],s) : []|isSym cconcatMap (lex2 c) (span isSym s : [])|isAlpha cconcatMap (lex3 c) (span isIdChar s : [])|isDigit cconcatMap (lex5 c) (span isDigit s : [])|otherwise[] where {
isIdChar c = isAlphaNum c || c `elem` '_' : ''' : [];
;
isSingle c = c `elem` ',' : ';' : '(' : ')' : '[' : ']' : '{' : '}' : '_' : '`' : [];
;
isSym c = c `elem` '!' : '@' : '#' : '$' : '%' : '&' : '*' : '+' : '.' : '/' : '<' : '=' : '>' : '?' : '\' : '^' : '|' : ':' : '-' : '~' : [];
;
lex2 c vu59 = lex20 c vu59;
;
lex20 c (sym,t) = (c : sym,t) : [];
lex20 c yw = [];
;
lex3 c vu60 = lex30 c vu60;
;
lex30 c (nam,t) = (c : nam,t) : [];
lex30 c yx = [];
;
lex4 c ds vu61 = lex40 c ds vu61;
;
lex40 c ds (fe,t) = (c : ds ++ fe,t) : [];
lex40 c ds yu = [];
;
lex5 c vu62 = lex50 c vu62;
;
lex50 c (ds,s) = concatMap (lex4 c ds) (lexFracExp s);
lex50 c yv = [];
;
lexExp (e : s)|e `elem` 'e' : 'E' : []concatMap (lexExp1 e) (s : []) ++ concatMap (lexExp2 e) (lexDigits s);
lexExp s = ([],s) : [];
;
lexExp0 e c vu65 = lexExp00 e c vu65;
;
lexExp00 e c (ds,u) = (e : c : ds,u) : [];
lexExp00 e c xv = [];
;
lexExp1 e vu66 = lexExp10 e vu66;
;
lexExp10 e (c : t) = lexExp100 e c t (c `elem` '+' : '-' : []);
lexExp10 e xx = [];
;
lexExp100 e c t True = concatMap (lexExp0 e c) (lexDigits t);
lexExp100 e c t False = [];
;
lexExp2 e vu67 = lexExp20 e vu67;
;
lexExp20 e (ds,t) = (e : ds,t) : [];
lexExp20 e xw = [];
;
lexFracExp ('.' : c : cs)|isDigit cconcatMap lexFracExp1 (lexDigits (c : cs));
lexFracExp s = lexExp s;
;
lexFracExp0 ds vu63 = lexFracExp00 ds vu63;
;
lexFracExp00 ds (e,u) = ('.' : ds ++ e,u) : [];
lexFracExp00 ds xz = [];
;
lexFracExp1 vu64 = lexFracExp10 vu64;
;
lexFracExp10 (ds,t) = concatMap (lexFracExp0 ds) (lexExp t);
lexFracExp10 xy = [];
} 
;
"
is transformed to
"lex [] = lex19 [];
lex (c : s) = lex18 (c : s);
lex (wyu : s) = lex16 (wyu : s);
lex (wxv : s) = lex14 (wxv : s);
lex (c : s) = lex12 (c : s);
"
"lex12 (c : s) = lex11 c s (isSingle c) where {
isIdChar c = isAlphaNum c || c `elem` '_' : ''' : [];
;
isSingle c = c `elem` ',' : ';' : '(' : ')' : '[' : ']' : '{' : '}' : '_' : '`' : [];
;
isSym c = c `elem` '!' : '@' : '#' : '$' : '%' : '&' : '*' : '+' : '.' : '/' : '<' : '=' : '>' : '?' : '\' : '^' : '|' : ':' : '-' : '~' : [];
;
lex11 c s True = (c : [],s) : [];
lex11 c s False = lex9 c s (isSym c);
;
lex2 c vu59 = lex20 c vu59;
;
lex20 c (sym,t) = (c : sym,t) : [];
lex20 c yw = [];
;
lex3 c vu60 = lex30 c vu60;
;
lex30 c (nam,t) = (c : nam,t) : [];
lex30 c yx = [];
;
lex4 c ds vu61 = lex40 c ds vu61;
;
lex40 c ds (fe,t) = (c : ds ++ fe,t) : [];
lex40 c ds yu = [];
;
lex5 c vu62 = lex50 c vu62;
;
lex50 c (ds,s) = concatMap (lex4 c ds) (lexFracExp s);
lex50 c yv = [];
;
lex6 c s True = [];
;
lex7 c s True = concatMap (lex5 c) (span isDigit s : []);
lex7 c s False = lex6 c s otherwise;
;
lex8 c s True = concatMap (lex3 c) (span isIdChar s : []);
lex8 c s False = lex7 c s (isDigit c);
;
lex9 c s True = concatMap (lex2 c) (span isSym s : []);
lex9 c s False = lex8 c s (isAlpha c);
;
lexExp (e : s) = lexExp5 (e : s);
lexExp s = lexExp3 s;
;
lexExp0 e c vu65 = lexExp00 e c vu65;
;
lexExp00 e c (ds,u) = (e : c : ds,u) : [];
lexExp00 e c xv = [];
;
lexExp1 e vu66 = lexExp10 e vu66;
;
lexExp10 e (c : t) = lexExp100 e c t (c `elem` '+' : '-' : []);
lexExp10 e xx = [];
;
lexExp100 e c t True = concatMap (lexExp0 e c) (lexDigits t);
lexExp100 e c t False = [];
;
lexExp2 e vu67 = lexExp20 e vu67;
;
lexExp20 e (ds,t) = (e : ds,t) : [];
lexExp20 e xw = [];
;
lexExp3 s = ([],s) : [];
;
lexExp4 e s True = concatMap (lexExp1 e) (s : []) ++ concatMap (lexExp2 e) (lexDigits s);
lexExp4 e s False = lexExp3 (e : s);
;
lexExp5 (e : s) = lexExp4 e s (e `elem` 'e' : 'E' : []);
lexExp5 wvw = lexExp3 wvw;
;
lexFracExp (wvy : wwv) = lexFracExp5 (wvy : wwv);
lexFracExp s = lexFracExp2 s;
;
lexFracExp0 ds vu63 = lexFracExp00 ds vu63;
;
lexFracExp00 ds (e,u) = ('.' : ds ++ e,u) : [];
lexFracExp00 ds xz = [];
;
lexFracExp1 vu64 = lexFracExp10 vu64;
;
lexFracExp10 (ds,t) = concatMap (lexFracExp0 ds) (lexExp t);
lexFracExp10 xy = [];
;
lexFracExp2 s = lexExp s;
;
lexFracExp3 wvy c cs True = concatMap lexFracExp1 (lexDigits (c : cs));
lexFracExp3 wvy c cs False = lexFracExp2 (wvy : c : cs);
;
lexFracExp4 True (wvy : c : cs) = lexFracExp3 wvy c cs (isDigit c);
lexFracExp4 www wwx = lexFracExp2 wwx;
;
lexFracExp5 (wvy : wwv) = lexFracExp4 (wvy == '.') (wvy : wwv);
lexFracExp5 wwy = lexFracExp2 wwy;
} 
;
"
"lex13 True (wxv : s) = concatMap lex1 (lexString s) where {
lex1 vu55 = lex10 vu55;
;
lex10 (str,t) = ('"' : str,t) : [];
lex10 xu = [];
;
lexStrItem (vyy : vzw) = lexStrItem7 (vyy : vzw);
lexStrItem (vxw : vxz) = lexStrItem4 (vxw : vxz);
lexStrItem s = lexStrItem1 s;
;
lexStrItem0 vu58 = lexStrItem00 vu58;
;
lexStrItem00 (wux : t) = lexStrItem002 (wux : t);
lexStrItem00 wz = lexStrItem000 wz;
;
lexStrItem000 wz = [];
;
lexStrItem001 True (wux : t) = ([],t) : [];
lexStrItem001 wuy wuz = lexStrItem000 wuz;
;
lexStrItem002 (wux : t) = lexStrItem001 (wux == '\') (wux : t);
lexStrItem002 wvu = lexStrItem000 wvu;
;
lexStrItem1 s = lexLitChar s;
;
lexStrItem2 vxw c s True = concatMap lexStrItem0 (dropWhile isSpace s : []);
lexStrItem2 vxw c s False = lexStrItem1 (vxw : c : s);
;
lexStrItem3 True (vxw : c : s) = lexStrItem2 vxw c s (isSpace c);
lexStrItem3 vyu vyv = lexStrItem1 vyv;
;
lexStrItem4 (vxw : vxz) = lexStrItem3 (vxw == '\') (vxw : vxz);
lexStrItem4 vyw = lexStrItem1 vyw;
;
lexStrItem5 True (vyy : vzu : s) = ('\' : '&' : [],s) : [];
lexStrItem5 vzx vzy = lexStrItem4 vzy;
;
lexStrItem6 True (vyy : vzu : s) = lexStrItem5 (vzu == '&') (vyy : vzu : s);
lexStrItem6 vzz wuu = lexStrItem4 wuu;
;
lexStrItem7 (vyy : vzw) = lexStrItem6 (vyy == '\') (vyy : vzw);
lexStrItem7 wuv = lexStrItem4 wuv;
;
lexString (vwx : s) = lexString4 (vwx : s);
lexString s = lexString2 s;
;
lexString0 ch vu56 = lexString00 ch vu56;
;
lexString00 ch (str,u) = (ch ++ str,u) : [];
lexString00 ch wx = [];
;
lexString1 vu57 = lexString10 vu57;
;
lexString10 (ch,t) = concatMap (lexString0 ch) (lexString t);
lexString10 wy = [];
;
lexString2 s = concatMap lexString1 (lexStrItem s);
;
lexString3 True (vwx : s) = ('"' : [],s) : [];
lexString3 vwy vwz = lexString2 vwz;
;
lexString4 (vwx : s) = lexString3 (vwx == '"') (vwx : s);
lexString4 vxu = lexString2 vxu;
} 
;
lex13 wxw wxx = lex12 wxx;
"
"lex14 (wxv : s) = lex13 (wxv == '"') (wxv : s);
lex14 wxy = lex12 wxy;
"
"lex15 True (wyu : s) = concatMap lex0 (lexLitChar s);
lex15 wyv wyw = lex14 wyw;
"
"lex16 (wyu : s) = lex15 (wyu == ''') (wyu : s);
lex16 wyx = lex14 wyx;
"
"lex17 c s True = lex (dropWhile isSpace s);
lex17 c s False = lex16 (c : s);
"
"lex18 (c : s) = lex17 c s (isSpace c);
lex18 wyz = lex16 wyz;
"
"lex19 [] = ([],[]) : [];
lex19 wzv = lex18 wzv;
"
The following Function with conditions
"lexmatch (x : xs) (y : ys)|x == ylexmatch xs ys;
lexmatch xs ys = (xs,ys);
"
is transformed to
"lexmatch (x : xs) (y : ys) = lexmatch2 (x : xs) (y : ys);
lexmatch xs ys = lexmatch0 xs ys;
"
"lexmatch0 xs ys = (xs,ys);
"
"lexmatch1 x xs y ys True = lexmatch xs ys;
lexmatch1 x xs y ys False = lexmatch0 (x : xs) (y : ys);
"
"lexmatch2 (x : xs) (y : ys) = lexmatch1 x xs y ys (x == y);
lexmatch2 wzy wzz = lexmatch0 wzy wzz;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"dropWhile p [] = [];
dropWhile p (zw : zx)|p zwdropWhile p zx|otherwisezw : zx;
"
is transformed to
"dropWhile p [] = dropWhile3 p [];
dropWhile p (zw : zx) = dropWhile2 p (zw : zx);
"
"dropWhile0 p zw zx True = zw : zx;
"
"dropWhile1 p zw zx True = dropWhile p zx;
dropWhile1 p zw zx False = dropWhile0 p zw zx otherwise;
"
"dropWhile2 p (zw : zx) = dropWhile1 p zw zx (p zw);
"
"dropWhile3 p [] = [];
dropWhile3 xuw xux = dropWhile2 xuw xux;
"
The following Function with conditions
"lex00 (ch,''' : t) = lex000 ch t (ch /= ''' : []);
lex00 zy = [];
"
is transformed to
"lex00 (ch,xvu : t) = lex003 (ch,xvu : t);
lex00 zy = lex001 zy;
"
"lex001 zy = [];
"
"lex002 True (ch,xvu : t) = lex000 ch t (ch /= ''' : []);
lex002 xvv xvw = lex001 xvw;
"
"lex003 (ch,xvu : t) = lex002 (xvu == ''') (ch,xvu : t);
lex003 xvx = lex001 xvx;
"
The following Function with conditions
"lexEsc (c : s)|c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : [](c : [],s) : [];
lexEsc ('^' : c : s)|c >= '@' && c <= '_'('^' : c : [],s) : [];
lexEsc ('o' : s) = prefix 'o' (span isOctDigit s) : [];
lexEsc ('x' : s) = prefix 'x' (span isHexDigit s) : [];
lexEsc (vuu : vuv)|isDigit vuuspan isDigit (vuu : vuv) : []|isUpper vuulexEsc2 (concatMap (lexEsc1 (vuu : vuv)) table);
lexEsc vuw = [];
"
is transformed to
"lexEsc (c : s) = lexEsc16 (c : s);
lexEsc (xxz : xyw) = lexEsc14 (xxz : xyw);
lexEsc (xxu : s) = lexEsc11 (xxu : s);
lexEsc (xwv : s) = lexEsc8 (xwv : s);
lexEsc (vuu : vuv) = lexEsc6 (vuu : vuv);
lexEsc vuw = lexEsc3 vuw;
"
"lexEsc3 vuw = [];
"
"lexEsc5 vuu vuv True = span isDigit (vuu : vuv) : [];
lexEsc5 vuu vuv False = lexEsc4 vuu vuv (isUpper vuu);
"
"lexEsc4 vuu vuv True = lexEsc2 (concatMap (lexEsc1 (vuu : vuv)) table);
lexEsc4 vuu vuv False = lexEsc3 (vuu : vuv);
"
"lexEsc6 (vuu : vuv) = lexEsc5 vuu vuv (isDigit vuu);
lexEsc6 xvz = lexEsc3 xvz;
"
"lexEsc7 True (xwv : s) = prefix 'x' (span isHexDigit s) : [];
lexEsc7 xww xwx = lexEsc6 xwx;
"
"lexEsc8 (xwv : s) = lexEsc7 (xwv == 'x') (xwv : s);
lexEsc8 xwy = lexEsc6 xwy;
"
"lexEsc9 True (xxu : s) = prefix 'o' (span isOctDigit s) : [];
lexEsc9 xxv xxw = lexEsc8 xxw;
"
"lexEsc11 (xxu : s) = lexEsc9 (xxu == 'o') (xxu : s);
lexEsc11 xxx = lexEsc8 xxx;
"
"lexEsc12 xxz c s True = ('^' : c : [],s) : [];
lexEsc12 xxz c s False = lexEsc11 (xxz : c : s);
"
"lexEsc13 True (xxz : c : s) = lexEsc12 xxz c s (c >= '@' && c <= '_');
lexEsc13 xyx xyy = lexEsc11 xyy;
"
"lexEsc14 (xxz : xyw) = lexEsc13 (xxz == '^') (xxz : xyw);
lexEsc14 xyz = lexEsc11 xyz;
"
"lexEsc15 c s True = (c : [],s) : [];
lexEsc15 c s False = lexEsc14 (c : s);
"
"lexEsc16 (c : s) = lexEsc15 c s (c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : []);
lexEsc16 xzv = lexEsc14 xzv;
"
The following Function with conditions
"lexLitChar [] = [];
lexLitChar (c : s)|c /= '\'(c : [],s) : []|otherwisemap (prefix '\') (lexEsc s) where {
lexEsc (c : s)|c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : [](c : [],s) : [];
lexEsc ('^' : c : s)|c >= '@' && c <= '_'('^' : c : [],s) : [];
lexEsc ('o' : s) = prefix 'o' (span isOctDigit s) : [];
lexEsc ('x' : s) = prefix 'x' (span isHexDigit s) : [];
lexEsc (vuu : vuv)|isDigit vuuspan isDigit (vuu : vuv) : []|isUpper vuulexEsc2 (concatMap (lexEsc1 (vuu : vuv)) table);
lexEsc vuw = [];
;
lexEsc0 mne vu69 = lexEsc00 mne vu69;
;
lexEsc00 mne ([],s') = (mne,s') : [];
lexEsc00 mne vuy = [];
;
lexEsc1 s vu70 = lexEsc10 s vu70;
;
lexEsc10 s (c,mne) = concatMap (lexEsc0 mne) (lexmatch mne s : []);
lexEsc10 s vuz = [];
;
lexEsc2 (pr : vux) = pr : [];
lexEsc2 [] = [];
;
prefix c (t,s) = (c : t,s);
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} 
;
"
is transformed to
"lexLitChar [] = lexLitChar3 [];
lexLitChar (c : s) = lexLitChar2 (c : s);
"
"lexLitChar2 (c : s) = lexLitChar1 c s (c /= '\') where {
lexEsc (c : s) = lexEsc16 (c : s);
lexEsc (xxz : xyw) = lexEsc14 (xxz : xyw);
lexEsc (xxu : s) = lexEsc11 (xxu : s);
lexEsc (xwv : s) = lexEsc8 (xwv : s);
lexEsc (vuu : vuv) = lexEsc6 (vuu : vuv);
lexEsc vuw = lexEsc3 vuw;
;
lexEsc0 mne vu69 = lexEsc00 mne vu69;
;
lexEsc00 mne ([],s') = (mne,s') : [];
lexEsc00 mne vuy = [];
;
lexEsc1 s vu70 = lexEsc10 s vu70;
;
lexEsc10 s (c,mne) = concatMap (lexEsc0 mne) (lexmatch mne s : []);
lexEsc10 s vuz = [];
;
lexEsc11 (xxu : s) = lexEsc9 (xxu == 'o') (xxu : s);
lexEsc11 xxx = lexEsc8 xxx;
;
lexEsc12 xxz c s True = ('^' : c : [],s) : [];
lexEsc12 xxz c s False = lexEsc11 (xxz : c : s);
;
lexEsc13 True (xxz : c : s) = lexEsc12 xxz c s (c >= '@' && c <= '_');
lexEsc13 xyx xyy = lexEsc11 xyy;
;
lexEsc14 (xxz : xyw) = lexEsc13 (xxz == '^') (xxz : xyw);
lexEsc14 xyz = lexEsc11 xyz;
;
lexEsc15 c s True = (c : [],s) : [];
lexEsc15 c s False = lexEsc14 (c : s);
;
lexEsc16 (c : s) = lexEsc15 c s (c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : []);
lexEsc16 xzv = lexEsc14 xzv;
;
lexEsc2 (pr : vux) = pr : [];
lexEsc2 [] = [];
;
lexEsc3 vuw = [];
;
lexEsc4 vuu vuv True = lexEsc2 (concatMap (lexEsc1 (vuu : vuv)) table);
lexEsc4 vuu vuv False = lexEsc3 (vuu : vuv);
;
lexEsc5 vuu vuv True = span isDigit (vuu : vuv) : [];
lexEsc5 vuu vuv False = lexEsc4 vuu vuv (isUpper vuu);
;
lexEsc6 (vuu : vuv) = lexEsc5 vuu vuv (isDigit vuu);
lexEsc6 xvz = lexEsc3 xvz;
;
lexEsc7 True (xwv : s) = prefix 'x' (span isHexDigit s) : [];
lexEsc7 xww xwx = lexEsc6 xwx;
;
lexEsc8 (xwv : s) = lexEsc7 (xwv == 'x') (xwv : s);
lexEsc8 xwy = lexEsc6 xwy;
;
lexEsc9 True (xxu : s) = prefix 'o' (span isOctDigit s) : [];
lexEsc9 xxv xxw = lexEsc8 xxw;
;
lexLitChar0 c s True = map (prefix '\') (lexEsc s);
;
lexLitChar1 c s True = (c : [],s) : [];
lexLitChar1 c s False = lexLitChar0 c s otherwise;
;
prefix c (t,s) = (c : t,s);
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} 
;
"
"lexLitChar3 [] = [];
lexLitChar3 xzy = lexLitChar2 xzy;
"
The following Function with conditions
"span p [] = ([],[]);
span p (vvu : vvv)|p vvu(vvu : ys,zs)|otherwise([],vvu : vvv) where {
vu43  = span p vvv;
;
ys  = ys0 vu43;
;
ys0 (ys,vvx) = ys;
;
zs  = zs0 vu43;
;
zs0 (vvw,zs) = zs;
} 
;
"
is transformed to
"span p [] = span3 p [];
span p (vvu : vvv) = span2 p (vvu : vvv);
"
"span2 p (vvu : vvv) = span1 p vvu vvv (p vvu) where {
span0 p vvu vvv True = ([],vvu : vvv);
;
span1 p vvu vvv True = (vvu : ys,zs);
span1 p vvu vvv False = span0 p vvu vvv otherwise;
;
vu43  = span p vvv;
;
ys  = ys0 vu43;
;
ys0 (ys,vvx) = ys;
;
zs  = zs0 vu43;
;
zs0 (vvw,zs) = zs;
} 
;
"
"span3 p [] = ([],[]);
span3 yuv yuw = span2 yuv yuw;
"

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

(10)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(11) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"concatMap lex1 (lexString s) where {
lex1 vu55 = lex10 vu55;
;
lex10 (str,t) = ('"' : str,t) : [];
lex10 xu = [];
;
lexStrItem (vyy : vzw) = lexStrItem7 (vyy : vzw);
lexStrItem (vxw : vxz) = lexStrItem4 (vxw : vxz);
lexStrItem s = lexStrItem1 s;
;
lexStrItem0 vu58 = lexStrItem00 vu58;
;
lexStrItem00 (wux : t) = lexStrItem002 (wux : t);
lexStrItem00 wz = lexStrItem000 wz;
;
lexStrItem000 wz = [];
;
lexStrItem001 True (wux : t) = ([],t) : [];
lexStrItem001 wuy wuz = lexStrItem000 wuz;
;
lexStrItem002 (wux : t) = lexStrItem001 (wux == '\') (wux : t);
lexStrItem002 wvu = lexStrItem000 wvu;
;
lexStrItem1 s = lexLitChar s;
;
lexStrItem2 vxw c s True = concatMap lexStrItem0 (dropWhile isSpace s : []);
lexStrItem2 vxw c s False = lexStrItem1 (vxw : c : s);
;
lexStrItem3 True (vxw : c : s) = lexStrItem2 vxw c s (isSpace c);
lexStrItem3 vyu vyv = lexStrItem1 vyv;
;
lexStrItem4 (vxw : vxz) = lexStrItem3 (vxw == '\') (vxw : vxz);
lexStrItem4 vyw = lexStrItem1 vyw;
;
lexStrItem5 True (vyy : vzu : s) = ('\' : '&' : [],s) : [];
lexStrItem5 vzx vzy = lexStrItem4 vzy;
;
lexStrItem6 True (vyy : vzu : s) = lexStrItem5 (vzu == '&') (vyy : vzu : s);
lexStrItem6 vzz wuu = lexStrItem4 wuu;
;
lexStrItem7 (vyy : vzw) = lexStrItem6 (vyy == '\') (vyy : vzw);
lexStrItem7 wuv = lexStrItem4 wuv;
;
lexString (vwx : s) = lexString4 (vwx : s);
lexString s = lexString2 s;
;
lexString0 ch vu56 = lexString00 ch vu56;
;
lexString00 ch (str,u) = (ch ++ str,u) : [];
lexString00 ch wx = [];
;
lexString1 vu57 = lexString10 vu57;
;
lexString10 (ch,t) = concatMap (lexString0 ch) (lexString t);
lexString10 wy = [];
;
lexString2 s = concatMap lexString1 (lexStrItem s);
;
lexString3 True (vwx : s) = ('"' : [],s) : [];
lexString3 vwy vwz = lexString2 vwz;
;
lexString4 (vwx : s) = lexString3 (vwx == '"') (vwx : s);
lexString4 vxu = lexString2 vxu;
} 
"
are unpacked to the following functions on top level
"lex13LexStrItem (vyy : vzw) = lex13LexStrItem7 (vyy : vzw);
lex13LexStrItem (vxw : vxz) = lex13LexStrItem4 (vxw : vxz);
lex13LexStrItem s = lex13LexStrItem1 s;
"
"lex13LexStrItem3 True (vxw : c : s) = lex13LexStrItem2 vxw c s (isSpace c);
lex13LexStrItem3 vyu vyv = lex13LexStrItem1 vyv;
"
"lex13LexString3 True (vwx : s) = ('"' : [],s) : [];
lex13LexString3 vwy vwz = lex13LexString2 vwz;
"
"lex13LexStrItem4 (vxw : vxz) = lex13LexStrItem3 (vxw == '\') (vxw : vxz);
lex13LexStrItem4 vyw = lex13LexStrItem1 vyw;
"
"lex13LexStrItem001 True (wux : t) = ([],t) : [];
lex13LexStrItem001 wuy wuz = lex13LexStrItem000 wuz;
"
"lex13LexStrItem000 wz = [];
"
"lex13LexStrItem00 (wux : t) = lex13LexStrItem002 (wux : t);
lex13LexStrItem00 wz = lex13LexStrItem000 wz;
"
"lex13LexStrItem2 vxw c s True = concatMap lex13LexStrItem0 (dropWhile isSpace s : []);
lex13LexStrItem2 vxw c s False = lex13LexStrItem1 (vxw : c : s);
"
"lex13LexString (vwx : s) = lex13LexString4 (vwx : s);
lex13LexString s = lex13LexString2 s;
"
"lex13LexString1 vu57 = lex13LexString10 vu57;
"
"lex13LexStrItem002 (wux : t) = lex13LexStrItem001 (wux == '\') (wux : t);
lex13LexStrItem002 wvu = lex13LexStrItem000 wvu;
"
"lex13LexStrItem6 True (vyy : vzu : s) = lex13LexStrItem5 (vzu == '&') (vyy : vzu : s);
lex13LexStrItem6 vzz wuu = lex13LexStrItem4 wuu;
"
"lex13LexString10 (ch,t) = concatMap (lex13LexString0 ch) (lex13LexString t);
lex13LexString10 wy = [];
"
"lex13Lex1 vu55 = lex13Lex10 vu55;
"
"lex13LexStrItem1 s = lexLitChar s;
"
"lex13LexString2 s = concatMap lex13LexString1 (lex13LexStrItem s);
"
"lex13LexString00 ch (str,u) = (ch ++ str,u) : [];
lex13LexString00 ch wx = [];
"
"lex13Lex10 (str,t) = ('"' : str,t) : [];
lex13Lex10 xu = [];
"
"lex13LexString4 (vwx : s) = lex13LexString3 (vwx == '"') (vwx : s);
lex13LexString4 vxu = lex13LexString2 vxu;
"
"lex13LexString0 ch vu56 = lex13LexString00 ch vu56;
"
"lex13LexStrItem5 True (vyy : vzu : s) = ('\' : '&' : [],s) : [];
lex13LexStrItem5 vzx vzy = lex13LexStrItem4 vzy;
"
"lex13LexStrItem7 (vyy : vzw) = lex13LexStrItem6 (vyy == '\') (vyy : vzw);
lex13LexStrItem7 wuv = lex13LexStrItem4 wuv;
"
"lex13LexStrItem0 vu58 = lex13LexStrItem00 vu58;
"
The bindings of the following Let/Where expression
"span1 p vvu vvv (p vvu) where {
span0 p vvu vvv True = ([],vvu : vvv);
;
span1 p vvu vvv True = (vvu : ys,zs);
span1 p vvu vvv False = span0 p vvu vvv otherwise;
;
vu43  = span p vvv;
;
ys  = ys0 vu43;
;
ys0 (ys,vvx) = ys;
;
zs  = zs0 vu43;
;
zs0 (vvw,zs) = zs;
} 
"
are unpacked to the following functions on top level
"span2Ys0 yux yuy (ys,vvx) = ys;
"
"span2Ys yux yuy = span2Ys0 yux yuy (span2Vu43 yux yuy);
"
"span2Span0 yux yuy p vvu vvv True = ([],vvu : vvv);
"
"span2Span1 yux yuy p vvu vvv True = (vvu : span2Ys yux yuy,span2Zs yux yuy);
span2Span1 yux yuy p vvu vvv False = span2Span0 yux yuy p vvu vvv otherwise;
"
"span2Zs yux yuy = span2Zs0 yux yuy (span2Vu43 yux yuy);
"
"span2Vu43 yux yuy = span yux yuy;
"
"span2Zs0 yux yuy (vvw,zs) = zs;
"
The bindings of the following Let/Where expression
"lex11 c s (isSingle c) where {
isIdChar c = isAlphaNum c || c `elem` '_' : ''' : [];
;
isSingle c = c `elem` ',' : ';' : '(' : ')' : '[' : ']' : '{' : '}' : '_' : '`' : [];
;
isSym c = c `elem` '!' : '@' : '#' : '$' : '%' : '&' : '*' : '+' : '.' : '/' : '<' : '=' : '>' : '?' : '\' : '^' : '|' : ':' : '-' : '~' : [];
;
lex11 c s True = (c : [],s) : [];
lex11 c s False = lex9 c s (isSym c);
;
lex2 c vu59 = lex20 c vu59;
;
lex20 c (sym,t) = (c : sym,t) : [];
lex20 c yw = [];
;
lex3 c vu60 = lex30 c vu60;
;
lex30 c (nam,t) = (c : nam,t) : [];
lex30 c yx = [];
;
lex4 c ds vu61 = lex40 c ds vu61;
;
lex40 c ds (fe,t) = (c : ds ++ fe,t) : [];
lex40 c ds yu = [];
;
lex5 c vu62 = lex50 c vu62;
;
lex50 c (ds,s) = concatMap (lex4 c ds) (lexFracExp s);
lex50 c yv = [];
;
lex6 c s True = [];
;
lex7 c s True = concatMap (lex5 c) (span isDigit s : []);
lex7 c s False = lex6 c s otherwise;
;
lex8 c s True = concatMap (lex3 c) (span isIdChar s : []);
lex8 c s False = lex7 c s (isDigit c);
;
lex9 c s True = concatMap (lex2 c) (span isSym s : []);
lex9 c s False = lex8 c s (isAlpha c);
;
lexExp (e : s) = lexExp5 (e : s);
lexExp s = lexExp3 s;
;
lexExp0 e c vu65 = lexExp00 e c vu65;
;
lexExp00 e c (ds,u) = (e : c : ds,u) : [];
lexExp00 e c xv = [];
;
lexExp1 e vu66 = lexExp10 e vu66;
;
lexExp10 e (c : t) = lexExp100 e c t (c `elem` '+' : '-' : []);
lexExp10 e xx = [];
;
lexExp100 e c t True = concatMap (lexExp0 e c) (lexDigits t);
lexExp100 e c t False = [];
;
lexExp2 e vu67 = lexExp20 e vu67;
;
lexExp20 e (ds,t) = (e : ds,t) : [];
lexExp20 e xw = [];
;
lexExp3 s = ([],s) : [];
;
lexExp4 e s True = concatMap (lexExp1 e) (s : []) ++ concatMap (lexExp2 e) (lexDigits s);
lexExp4 e s False = lexExp3 (e : s);
;
lexExp5 (e : s) = lexExp4 e s (e `elem` 'e' : 'E' : []);
lexExp5 wvw = lexExp3 wvw;
;
lexFracExp (wvy : wwv) = lexFracExp5 (wvy : wwv);
lexFracExp s = lexFracExp2 s;
;
lexFracExp0 ds vu63 = lexFracExp00 ds vu63;
;
lexFracExp00 ds (e,u) = ('.' : ds ++ e,u) : [];
lexFracExp00 ds xz = [];
;
lexFracExp1 vu64 = lexFracExp10 vu64;
;
lexFracExp10 (ds,t) = concatMap (lexFracExp0 ds) (lexExp t);
lexFracExp10 xy = [];
;
lexFracExp2 s = lexExp s;
;
lexFracExp3 wvy c cs True = concatMap lexFracExp1 (lexDigits (c : cs));
lexFracExp3 wvy c cs False = lexFracExp2 (wvy : c : cs);
;
lexFracExp4 True (wvy : c : cs) = lexFracExp3 wvy c cs (isDigit c);
lexFracExp4 www wwx = lexFracExp2 wwx;
;
lexFracExp5 (wvy : wwv) = lexFracExp4 (wvy == '.') (wvy : wwv);
lexFracExp5 wwy = lexFracExp2 wwy;
} 
"
are unpacked to the following functions on top level
"lex12Lex9 c s True = concatMap (lex12Lex2 c) (span lex12IsSym s : []);
lex12Lex9 c s False = lex12Lex8 c s (isAlpha c);
"
"lex12LexFracExp (wvy : wwv) = lex12LexFracExp5 (wvy : wwv);
lex12LexFracExp s = lex12LexFracExp2 s;
"
"lex12LexFracExp5 (wvy : wwv) = lex12LexFracExp4 (wvy == '.') (wvy : wwv);
lex12LexFracExp5 wwy = lex12LexFracExp2 wwy;
"
"lex12LexFracExp0 ds vu63 = lex12LexFracExp00 ds vu63;
"
"lex12LexFracExp1 vu64 = lex12LexFracExp10 vu64;
"
"lex12LexExp1 e vu66 = lex12LexExp10 e vu66;
"
"lex12LexExp5 (e : s) = lex12LexExp4 e s (e `elem` 'e' : 'E' : []);
lex12LexExp5 wvw = lex12LexExp3 wvw;
"
"lex12LexExp3 s = ([],s) : [];
"
"lex12LexFracExp00 ds (e,u) = ('.' : ds ++ e,u) : [];
lex12LexFracExp00 ds xz = [];
"
"lex12LexExp00 e c (ds,u) = (e : c : ds,u) : [];
lex12LexExp00 e c xv = [];
"
"lex12LexExp0 e c vu65 = lex12LexExp00 e c vu65;
"
"lex12Lex30 c (nam,t) = (c : nam,t) : [];
lex12Lex30 c yx = [];
"
"lex12LexExp100 e c t True = concatMap (lex12LexExp0 e c) (lexDigits t);
lex12LexExp100 e c t False = [];
"
"lex12LexExp20 e (ds,t) = (e : ds,t) : [];
lex12LexExp20 e xw = [];
"
"lex12LexFracExp2 s = lex12LexExp s;
"
"lex12IsSingle c = c `elem` ',' : ';' : '(' : ')' : '[' : ']' : '{' : '}' : '_' : '`' : [];
"
"lex12Lex11 c s True = (c : [],s) : [];
lex12Lex11 c s False = lex12Lex9 c s (lex12IsSym c);
"
"lex12IsSym c = c `elem` '!' : '@' : '#' : '$' : '%' : '&' : '*' : '+' : '.' : '/' : '<' : '=' : '>' : '?' : '\' : '^' : '|' : ':' : '-' : '~' : [];
"
"lex12Lex8 c s True = concatMap (lex12Lex3 c) (span lex12IsIdChar s : []);
lex12Lex8 c s False = lex12Lex7 c s (isDigit c);
"
"lex12LexFracExp4 True (wvy : c : cs) = lex12LexFracExp3 wvy c cs (isDigit c);
lex12LexFracExp4 www wwx = lex12LexFracExp2 wwx;
"
"lex12LexFracExp3 wvy c cs True = concatMap lex12LexFracExp1 (lexDigits (c : cs));
lex12LexFracExp3 wvy c cs False = lex12LexFracExp2 (wvy : c : cs);
"
"lex12LexFracExp10 (ds,t) = concatMap (lex12LexFracExp0 ds) (lex12LexExp t);
lex12LexFracExp10 xy = [];
"
"lex12LexExp (e : s) = lex12LexExp5 (e : s);
lex12LexExp s = lex12LexExp3 s;
"
"lex12LexExp4 e s True = concatMap (lex12LexExp1 e) (s : []) ++ concatMap (lex12LexExp2 e) (lexDigits s);
lex12LexExp4 e s False = lex12LexExp3 (e : s);
"
"lex12Lex50 c (ds,s) = concatMap (lex12Lex4 c ds) (lex12LexFracExp s);
lex12Lex50 c yv = [];
"
"lex12Lex20 c (sym,t) = (c : sym,t) : [];
lex12Lex20 c yw = [];
"
"lex12Lex40 c ds (fe,t) = (c : ds ++ fe,t) : [];
lex12Lex40 c ds yu = [];
"
"lex12Lex5 c vu62 = lex12Lex50 c vu62;
"
"lex12Lex4 c ds vu61 = lex12Lex40 c ds vu61;
"
"lex12IsIdChar c = isAlphaNum c || c `elem` '_' : ''' : [];
"
"lex12Lex6 c s True = [];
"
"lex12LexExp2 e vu67 = lex12LexExp20 e vu67;
"
"lex12Lex3 c vu60 = lex12Lex30 c vu60;
"
"lex12Lex7 c s True = concatMap (lex12Lex5 c) (span isDigit s : []);
lex12Lex7 c s False = lex12Lex6 c s otherwise;
"
"lex12Lex2 c vu59 = lex12Lex20 c vu59;
"
"lex12LexExp10 e (c : t) = lex12LexExp100 e c t (c `elem` '+' : '-' : []);
lex12LexExp10 e xx = [];
"
The bindings of the following Let/Where expression
"lexLitChar1 c s (c /= '\') where {
lexEsc (c : s) = lexEsc16 (c : s);
lexEsc (xxz : xyw) = lexEsc14 (xxz : xyw);
lexEsc (xxu : s) = lexEsc11 (xxu : s);
lexEsc (xwv : s) = lexEsc8 (xwv : s);
lexEsc (vuu : vuv) = lexEsc6 (vuu : vuv);
lexEsc vuw = lexEsc3 vuw;
;
lexEsc0 mne vu69 = lexEsc00 mne vu69;
;
lexEsc00 mne ([],s') = (mne,s') : [];
lexEsc00 mne vuy = [];
;
lexEsc1 s vu70 = lexEsc10 s vu70;
;
lexEsc10 s (c,mne) = concatMap (lexEsc0 mne) (lexmatch mne s : []);
lexEsc10 s vuz = [];
;
lexEsc11 (xxu : s) = lexEsc9 (xxu == 'o') (xxu : s);
lexEsc11 xxx = lexEsc8 xxx;
;
lexEsc12 xxz c s True = ('^' : c : [],s) : [];
lexEsc12 xxz c s False = lexEsc11 (xxz : c : s);
;
lexEsc13 True (xxz : c : s) = lexEsc12 xxz c s (c >= '@' && c <= '_');
lexEsc13 xyx xyy = lexEsc11 xyy;
;
lexEsc14 (xxz : xyw) = lexEsc13 (xxz == '^') (xxz : xyw);
lexEsc14 xyz = lexEsc11 xyz;
;
lexEsc15 c s True = (c : [],s) : [];
lexEsc15 c s False = lexEsc14 (c : s);
;
lexEsc16 (c : s) = lexEsc15 c s (c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : []);
lexEsc16 xzv = lexEsc14 xzv;
;
lexEsc2 (pr : vux) = pr : [];
lexEsc2 [] = [];
;
lexEsc3 vuw = [];
;
lexEsc4 vuu vuv True = lexEsc2 (concatMap (lexEsc1 (vuu : vuv)) table);
lexEsc4 vuu vuv False = lexEsc3 (vuu : vuv);
;
lexEsc5 vuu vuv True = span isDigit (vuu : vuv) : [];
lexEsc5 vuu vuv False = lexEsc4 vuu vuv (isUpper vuu);
;
lexEsc6 (vuu : vuv) = lexEsc5 vuu vuv (isDigit vuu);
lexEsc6 xvz = lexEsc3 xvz;
;
lexEsc7 True (xwv : s) = prefix 'x' (span isHexDigit s) : [];
lexEsc7 xww xwx = lexEsc6 xwx;
;
lexEsc8 (xwv : s) = lexEsc7 (xwv == 'x') (xwv : s);
lexEsc8 xwy = lexEsc6 xwy;
;
lexEsc9 True (xxu : s) = prefix 'o' (span isOctDigit s) : [];
lexEsc9 xxv xxw = lexEsc8 xxw;
;
lexLitChar0 c s True = map (prefix '\') (lexEsc s);
;
lexLitChar1 c s True = (c : [],s) : [];
lexLitChar1 c s False = lexLitChar0 c s otherwise;
;
prefix c (t,s) = (c : t,s);
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} 
"
are unpacked to the following functions on top level
"lexLitChar2LexEsc5 vuu vuv True = span isDigit (vuu : vuv) : [];
lexLitChar2LexEsc5 vuu vuv False = lexLitChar2LexEsc4 vuu vuv (isUpper vuu);
"
"lexLitChar2LexEsc16 (c : s) = lexLitChar2LexEsc15 c s (c `elem` 'a' : 'b' : 'f' : 'n' : 'r' : 't' : 'v' : '\' : '"' : ''' : []);
lexLitChar2LexEsc16 xzv = lexLitChar2LexEsc14 xzv;
"
"lexLitChar2LexEsc (c : s) = lexLitChar2LexEsc16 (c : s);
lexLitChar2LexEsc (xxz : xyw) = lexLitChar2LexEsc14 (xxz : xyw);
lexLitChar2LexEsc (xxu : s) = lexLitChar2LexEsc11 (xxu : s);
lexLitChar2LexEsc (xwv : s) = lexLitChar2LexEsc8 (xwv : s);
lexLitChar2LexEsc (vuu : vuv) = lexLitChar2LexEsc6 (vuu : vuv);
lexLitChar2LexEsc vuw = lexLitChar2LexEsc3 vuw;
"
"lexLitChar2LexEsc1 s vu70 = lexLitChar2LexEsc10 s vu70;
"
"lexLitChar2LexEsc8 (xwv : s) = lexLitChar2LexEsc7 (xwv == 'x') (xwv : s);
lexLitChar2LexEsc8 xwy = lexLitChar2LexEsc6 xwy;
"
"lexLitChar2LexEsc6 (vuu : vuv) = lexLitChar2LexEsc5 vuu vuv (isDigit vuu);
lexLitChar2LexEsc6 xvz = lexLitChar2LexEsc3 xvz;
"
"lexLitChar2LexEsc15 c s True = (c : [],s) : [];
lexLitChar2LexEsc15 c s False = lexLitChar2LexEsc14 (c : s);
"
"lexLitChar2LexLitChar0 c s True = map (lexLitChar2Prefix '\') (lexLitChar2LexEsc s);
"
"lexLitChar2LexEsc13 True (xxz : c : s) = lexLitChar2LexEsc12 xxz c s (c >= '@' && c <= '_');
lexLitChar2LexEsc13 xyx xyy = lexLitChar2LexEsc11 xyy;
"
"lexLitChar2LexEsc10 s (c,mne) = concatMap (lexLitChar2LexEsc0 mne) (lexmatch mne s : []);
lexLitChar2LexEsc10 s vuz = [];
"
"lexLitChar2LexEsc7 True (xwv : s) = lexLitChar2Prefix 'x' (span isHexDigit s) : [];
lexLitChar2LexEsc7 xww xwx = lexLitChar2LexEsc6 xwx;
"
"lexLitChar2LexEsc14 (xxz : xyw) = lexLitChar2LexEsc13 (xxz == '^') (xxz : xyw);
lexLitChar2LexEsc14 xyz = lexLitChar2LexEsc11 xyz;
"
"lexLitChar2LexEsc4 vuu vuv True = lexLitChar2LexEsc2 (concatMap (lexLitChar2LexEsc1 (vuu : vuv)) lexLitChar2Table);
lexLitChar2LexEsc4 vuu vuv False = lexLitChar2LexEsc3 (vuu : vuv);
"
"lexLitChar2LexEsc2 (pr : vux) = pr : [];
lexLitChar2LexEsc2 [] = [];
"
"lexLitChar2LexEsc00 mne ([],s') = (mne,s') : [];
lexLitChar2LexEsc00 mne vuy = [];
"
"lexLitChar2LexEsc11 (xxu : s) = lexLitChar2LexEsc9 (xxu == 'o') (xxu : s);
lexLitChar2LexEsc11 xxx = lexLitChar2LexEsc8 xxx;
"
"lexLitChar2LexEsc9 True (xxu : s) = lexLitChar2Prefix 'o' (span isOctDigit s) : [];
lexLitChar2LexEsc9 xxv xxw = lexLitChar2LexEsc8 xxw;
"
"lexLitChar2Table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
"
"lexLitChar2LexEsc3 vuw = [];
"
"lexLitChar2LexEsc0 mne vu69 = lexLitChar2LexEsc00 mne vu69;
"
"lexLitChar2Prefix c (t,s) = (c : t,s);
"
"lexLitChar2LexLitChar1 c s True = (c : [],s) : [];
lexLitChar2LexLitChar1 c s False = lexLitChar2LexLitChar0 c s otherwise;
"
"lexLitChar2LexEsc12 xxz c s True = ('^' : c : [],s) : [];
lexLitChar2LexEsc12 xxz c s False = lexLitChar2LexEsc11 (xxz : c : s);
"

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

(12)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(13) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

(14)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}