/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 14 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 2 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
"\nd->n * radix + d"
is transformed to
"readInt0 radix n d = n * radix + d;
"
The following Lambda expression
"\vu77->case vu77 of {
(ds,r)  -> (foldl1 (readInt0 radix) (map (fromIntegral . digToInt) ds),r) : [];
_  -> []}
"
is transformed to
"readInt1 radix digToInt vu77 = case vu77 of {
(ds,r)  -> (foldl1 (readInt0 radix) (map (fromIntegral . digToInt) ds),r) : [];
_  -> []}
;
"
The following Lambda expression
"\ab->(a,b)"
is transformed to
"zip0 a b = (a,b);
"
The following Lambda expression
"\vu71->case vu71 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc0 vu71 = case vu71 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu72->case vu72 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc1 vu72 = case vu72 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu73->case vu73 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc2 vu73 = case vu73 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
;
"
The following Lambda expression
"\vu74->case vu74 of {
([],s')  -> (c,s') : [];
_  -> []}
"
is transformed to
"readEsc3 c vu74 = case vu74 of {
([],s')  -> (c,s') : [];
_  -> []}
;
"
The following Lambda expression
"\vu75->case vu75 of {
(c,mne)  -> concatMap (readEsc3 c) (lexmatch mne s : []);
_  -> []}
"
is transformed to
"readEsc4 s vu75 = case vu75 of {
(c,mne)  -> concatMap (readEsc3 c) (lexmatch mne s : []);
_  -> []}
;
"
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
"\d->fromEnum d - fromEnum_0"
is transformed to
"readOct0 d = fromEnum d - fromEnum_0;
"
The following Lambda expression
"\d->fromEnum d - fromEnum_0"
is transformed to
"readDec0 d = fromEnum d - fromEnum_0;
"
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 vu77 of {
(ds,r)  -> (foldl1 (readInt0 radix) (map (fromIntegral . digToInt) ds),r) : [];
_  -> []}
"
is transformed to
"readInt10 radix digToInt (ds,r) = (foldl1 (readInt0 radix) (map (fromIntegral . digToInt) ds),r) : [];
readInt10 radix digToInt _ = [];
"
The following Case expression
"case vu73 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc20 (n,t) = (toEnum n,t) : [];
readEsc20 _ = [];
"
The following Case expression
"case vu72 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc10 (n,t) = (toEnum n,t) : [];
readEsc10 _ = [];
"
The following Case expression
"case vu71 of {
(n,t)  -> (toEnum n,t) : [];
_  -> []}
"
is transformed to
"readEsc00 (n,t) = (toEnum n,t) : [];
readEsc00 _ = [];
"
The following Case expression
"case vu75 of {
(c,mne)  -> concatMap (readEsc3 c) (lexmatch mne s : []);
_  -> []}
"
is transformed to
"readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s _ = [];
"
The following Case expression
"case vu74 of {
([],s')  -> (c,s') : [];
_  -> []}
"
is transformed to
"readEsc30 c ([],s') = (c,s') : [];
readEsc30 c _ = [];
"
The following Case expression
"case concatMap (readEsc4 s) table of {
pr : _  -> pr : [];
[]  -> []}
"
is transformed to
"readEsc5 (pr : _) = pr : [];
readEsc5 [] = [];
"
The following Case expression
"case vu68 of {
(cs@(_ : _),t)  -> (cs,t) : [];
_  -> []}
"
is transformed to
"nonnull00 (cs@(_ : _),t) = (cs,t) : [];
nonnull00 _ = [];
"

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

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

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

(5) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if isUpper d then 'A' else 'a'"
is transformed to
"hex0 True = 'A';
hex0 False = 'a';
"
The following If expression
"if isDigit d then fromEnum_0 else fromEnum (hex0 (isUpper d)) - 10"
is transformed to
"hex1 d True = fromEnum_0;
hex1 d False = fromEnum (hex0 (isUpper d)) - 10;
"

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

(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@(vy : vz)"
is replaced by the following term
"vy : vz"
The bind variable of the following binding Pattern
"s@(ww : wx)"
is replaced by the following term
"ww : wx"
The bind variable of the following binding Pattern
"s@(wz : xu)"
is replaced by the following term
"wz : xu"
The bind variable of the following binding Pattern
"xs@(zv : zw)"
is replaced by the following term
"zv : zw"

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

(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 vuv vuw = takeWhile2 vuv vuw;
"
The following Function with conditions
"readEsc ('a' : s) = ('\7',s) : [];
readEsc ('b' : s) = ('\8',s) : [];
readEsc ('f' : s) = ('\12',s) : [];
readEsc ('n' : s) = ('\10',s) : [];
readEsc ('r' : s) = ('\13',s) : [];
readEsc ('t' : s) = ('\9',s) : [];
readEsc ('v' : s) = ('\11',s) : [];
readEsc ('\' : s) = ('\',s) : [];
readEsc ('"' : s) = ('"',s) : [];
readEsc (''' : s) = (''',s) : [];
readEsc ('^' : c : s)|c >= '@' && c <= '_'(toEnum (fromEnum c - fromEnum '@'),s) : [];
readEsc (ww : wx)|isDigit wwconcatMap readEsc0 (readDec (ww : wx));
readEsc ('o' : s) = concatMap readEsc1 (readOct s);
readEsc ('x' : s) = concatMap readEsc2 (readHex s);
readEsc (wz : xu)|isUpper wzlet {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table);
readEsc xy = [];
"
is transformed to
"readEsc (wzz : s) = readEsc41 (wzz : s);
readEsc (wzu : s) = readEsc38 (wzu : s);
readEsc (wyv : s) = readEsc36 (wyv : s);
readEsc (wxw : s) = readEsc34 (wxw : s);
readEsc (wwx : s) = readEsc32 (wwx : s);
readEsc (wvy : s) = readEsc29 (wvy : s);
readEsc (wuz : s) = readEsc27 (wuz : s);
readEsc (wuu : s) = readEsc25 (wuu : s);
readEsc (vzv : s) = readEsc23 (vzv : s);
readEsc (vyw : s) = readEsc21 (vyw : s);
readEsc (vxu : vxx) = readEsc18 (vxu : vxx);
readEsc (ww : wx) = readEsc15 (ww : wx);
readEsc (vvz : s) = readEsc13 (vvz : s);
readEsc (vvu : s) = readEsc11 (vvu : s);
readEsc (wz : xu) = readEsc8 (wz : xu);
readEsc xy = readEsc6 xy;
"
"readEsc6 xy = [];
"
"readEsc7 wz xu True = let {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table);
readEsc7 wz xu False = readEsc6 (wz : xu);
"
"readEsc8 (wz : xu) = readEsc7 wz xu (isUpper wz);
readEsc8 vuy = readEsc6 vuy;
"
"readEsc9 True (vvu : s) = concatMap readEsc2 (readHex s);
readEsc9 vvv vvw = readEsc8 vvw;
"
"readEsc11 (vvu : s) = readEsc9 (vvu == 'x') (vvu : s);
readEsc11 vvx = readEsc8 vvx;
"
"readEsc12 True (vvz : s) = concatMap readEsc1 (readOct s);
readEsc12 vwu vwv = readEsc11 vwv;
"
"readEsc13 (vvz : s) = readEsc12 (vvz == 'o') (vvz : s);
readEsc13 vww = readEsc11 vww;
"
"readEsc14 ww wx True = concatMap readEsc0 (readDec (ww : wx));
readEsc14 ww wx False = readEsc13 (ww : wx);
"
"readEsc15 (ww : wx) = readEsc14 ww wx (isDigit ww);
readEsc15 vwy = readEsc13 vwy;
"
"readEsc16 vxu c s True = (toEnum (fromEnum c - fromEnum '@'),s) : [];
readEsc16 vxu c s False = readEsc15 (vxu : c : s);
"
"readEsc17 True (vxu : c : s) = readEsc16 vxu c s (c >= '@' && c <= '_');
readEsc17 vxy vxz = readEsc15 vxz;
"
"readEsc18 (vxu : vxx) = readEsc17 (vxu == '^') (vxu : vxx);
readEsc18 vyu = readEsc15 vyu;
"
"readEsc19 True (vyw : s) = (''',s) : [];
readEsc19 vyx vyy = readEsc18 vyy;
"
"readEsc21 (vyw : s) = readEsc19 (vyw == ''') (vyw : s);
readEsc21 vyz = readEsc18 vyz;
"
"readEsc22 True (vzv : s) = ('"',s) : [];
readEsc22 vzw vzx = readEsc21 vzx;
"
"readEsc23 (vzv : s) = readEsc22 (vzv == '"') (vzv : s);
readEsc23 vzy = readEsc21 vzy;
"
"readEsc24 True (wuu : s) = ('\',s) : [];
readEsc24 wuv wuw = readEsc23 wuw;
"
"readEsc25 (wuu : s) = readEsc24 (wuu == '\') (wuu : s);
readEsc25 wux = readEsc23 wux;
"
"readEsc26 True (wuz : s) = ('\11',s) : [];
readEsc26 wvu wvv = readEsc25 wvv;
"
"readEsc27 (wuz : s) = readEsc26 (wuz == 'v') (wuz : s);
readEsc27 wvw = readEsc25 wvw;
"
"readEsc28 True (wvy : s) = ('\9',s) : [];
readEsc28 wvz wwu = readEsc27 wwu;
"
"readEsc29 (wvy : s) = readEsc28 (wvy == 't') (wvy : s);
readEsc29 wwv = readEsc27 wwv;
"
"readEsc31 True (wwx : s) = ('\13',s) : [];
readEsc31 wwy wwz = readEsc29 wwz;
"
"readEsc32 (wwx : s) = readEsc31 (wwx == 'r') (wwx : s);
readEsc32 wxu = readEsc29 wxu;
"
"readEsc33 True (wxw : s) = ('\10',s) : [];
readEsc33 wxx wxy = readEsc32 wxy;
"
"readEsc34 (wxw : s) = readEsc33 (wxw == 'n') (wxw : s);
readEsc34 wxz = readEsc32 wxz;
"
"readEsc35 True (wyv : s) = ('\12',s) : [];
readEsc35 wyw wyx = readEsc34 wyx;
"
"readEsc36 (wyv : s) = readEsc35 (wyv == 'f') (wyv : s);
readEsc36 wyy = readEsc34 wyy;
"
"readEsc37 True (wzu : s) = ('\8',s) : [];
readEsc37 wzv wzw = readEsc36 wzw;
"
"readEsc38 (wzu : s) = readEsc37 (wzu == 'b') (wzu : s);
readEsc38 wzx = readEsc36 wzx;
"
"readEsc39 True (wzz : s) = ('\7',s) : [];
readEsc39 xuu xuv = readEsc38 xuv;
"
"readEsc41 (wzz : s) = readEsc39 (wzz == 'a') (wzz : s);
readEsc41 xuw = readEsc38 xuw;
"
The following Function with conditions
"readLitChar ('\' : s) = readEsc s where {
readEsc ('a' : s) = ('\7',s) : [];
readEsc ('b' : s) = ('\8',s) : [];
readEsc ('f' : s) = ('\12',s) : [];
readEsc ('n' : s) = ('\10',s) : [];
readEsc ('r' : s) = ('\13',s) : [];
readEsc ('t' : s) = ('\9',s) : [];
readEsc ('v' : s) = ('\11',s) : [];
readEsc ('\' : s) = ('\',s) : [];
readEsc ('"' : s) = ('"',s) : [];
readEsc (''' : s) = (''',s) : [];
readEsc ('^' : c : s)|c >= '@' && c <= '_'(toEnum (fromEnum c - fromEnum '@'),s) : [];
readEsc (ww : wx)|isDigit wwconcatMap readEsc0 (readDec (ww : wx));
readEsc ('o' : s) = concatMap readEsc1 (readOct s);
readEsc ('x' : s) = concatMap readEsc2 (readHex s);
readEsc (wz : xu)|isUpper wzlet {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table);
readEsc xy = [];
;
readEsc0 vu71 = readEsc00 vu71;
;
readEsc00 (n,t) = (toEnum n,t) : [];
readEsc00 xz = [];
;
readEsc1 vu72 = readEsc10 vu72;
;
readEsc10 (n,t) = (toEnum n,t) : [];
readEsc10 yu = [];
;
readEsc2 vu73 = readEsc20 vu73;
;
readEsc20 (n,t) = (toEnum n,t) : [];
readEsc20 yv = [];
} 
;
readLitChar (c : s) = (c,s) : [];
"
is transformed to
"readLitChar (xuz : s) = readLitChar2 (xuz : s);
readLitChar (c : s) = readLitChar0 (c : s);
"
"readLitChar0 (c : s) = (c,s) : [];
"
"readLitChar1 True (xuz : s) = readEsc s where {
readEsc (wzz : s) = readEsc41 (wzz : s);
readEsc (wzu : s) = readEsc38 (wzu : s);
readEsc (wyv : s) = readEsc36 (wyv : s);
readEsc (wxw : s) = readEsc34 (wxw : s);
readEsc (wwx : s) = readEsc32 (wwx : s);
readEsc (wvy : s) = readEsc29 (wvy : s);
readEsc (wuz : s) = readEsc27 (wuz : s);
readEsc (wuu : s) = readEsc25 (wuu : s);
readEsc (vzv : s) = readEsc23 (vzv : s);
readEsc (vyw : s) = readEsc21 (vyw : s);
readEsc (vxu : vxx) = readEsc18 (vxu : vxx);
readEsc (ww : wx) = readEsc15 (ww : wx);
readEsc (vvz : s) = readEsc13 (vvz : s);
readEsc (vvu : s) = readEsc11 (vvu : s);
readEsc (wz : xu) = readEsc8 (wz : xu);
readEsc xy = readEsc6 xy;
;
readEsc0 vu71 = readEsc00 vu71;
;
readEsc00 (n,t) = (toEnum n,t) : [];
readEsc00 xz = [];
;
readEsc1 vu72 = readEsc10 vu72;
;
readEsc10 (n,t) = (toEnum n,t) : [];
readEsc10 yu = [];
;
readEsc11 (vvu : s) = readEsc9 (vvu == 'x') (vvu : s);
readEsc11 vvx = readEsc8 vvx;
;
readEsc12 True (vvz : s) = concatMap readEsc1 (readOct s);
readEsc12 vwu vwv = readEsc11 vwv;
;
readEsc13 (vvz : s) = readEsc12 (vvz == 'o') (vvz : s);
readEsc13 vww = readEsc11 vww;
;
readEsc14 ww wx True = concatMap readEsc0 (readDec (ww : wx));
readEsc14 ww wx False = readEsc13 (ww : wx);
;
readEsc15 (ww : wx) = readEsc14 ww wx (isDigit ww);
readEsc15 vwy = readEsc13 vwy;
;
readEsc16 vxu c s True = (toEnum (fromEnum c - fromEnum '@'),s) : [];
readEsc16 vxu c s False = readEsc15 (vxu : c : s);
;
readEsc17 True (vxu : c : s) = readEsc16 vxu c s (c >= '@' && c <= '_');
readEsc17 vxy vxz = readEsc15 vxz;
;
readEsc18 (vxu : vxx) = readEsc17 (vxu == '^') (vxu : vxx);
readEsc18 vyu = readEsc15 vyu;
;
readEsc19 True (vyw : s) = (''',s) : [];
readEsc19 vyx vyy = readEsc18 vyy;
;
readEsc2 vu73 = readEsc20 vu73;
;
readEsc20 (n,t) = (toEnum n,t) : [];
readEsc20 yv = [];
;
readEsc21 (vyw : s) = readEsc19 (vyw == ''') (vyw : s);
readEsc21 vyz = readEsc18 vyz;
;
readEsc22 True (vzv : s) = ('"',s) : [];
readEsc22 vzw vzx = readEsc21 vzx;
;
readEsc23 (vzv : s) = readEsc22 (vzv == '"') (vzv : s);
readEsc23 vzy = readEsc21 vzy;
;
readEsc24 True (wuu : s) = ('\',s) : [];
readEsc24 wuv wuw = readEsc23 wuw;
;
readEsc25 (wuu : s) = readEsc24 (wuu == '\') (wuu : s);
readEsc25 wux = readEsc23 wux;
;
readEsc26 True (wuz : s) = ('\11',s) : [];
readEsc26 wvu wvv = readEsc25 wvv;
;
readEsc27 (wuz : s) = readEsc26 (wuz == 'v') (wuz : s);
readEsc27 wvw = readEsc25 wvw;
;
readEsc28 True (wvy : s) = ('\9',s) : [];
readEsc28 wvz wwu = readEsc27 wwu;
;
readEsc29 (wvy : s) = readEsc28 (wvy == 't') (wvy : s);
readEsc29 wwv = readEsc27 wwv;
;
readEsc31 True (wwx : s) = ('\13',s) : [];
readEsc31 wwy wwz = readEsc29 wwz;
;
readEsc32 (wwx : s) = readEsc31 (wwx == 'r') (wwx : s);
readEsc32 wxu = readEsc29 wxu;
;
readEsc33 True (wxw : s) = ('\10',s) : [];
readEsc33 wxx wxy = readEsc32 wxy;
;
readEsc34 (wxw : s) = readEsc33 (wxw == 'n') (wxw : s);
readEsc34 wxz = readEsc32 wxz;
;
readEsc35 True (wyv : s) = ('\12',s) : [];
readEsc35 wyw wyx = readEsc34 wyx;
;
readEsc36 (wyv : s) = readEsc35 (wyv == 'f') (wyv : s);
readEsc36 wyy = readEsc34 wyy;
;
readEsc37 True (wzu : s) = ('\8',s) : [];
readEsc37 wzv wzw = readEsc36 wzw;
;
readEsc38 (wzu : s) = readEsc37 (wzu == 'b') (wzu : s);
readEsc38 wzx = readEsc36 wzx;
;
readEsc39 True (wzz : s) = ('\7',s) : [];
readEsc39 xuu xuv = readEsc38 xuv;
;
readEsc41 (wzz : s) = readEsc39 (wzz == 'a') (wzz : s);
readEsc41 xuw = readEsc38 xuw;
;
readEsc6 xy = [];
;
readEsc7 wz xu True = let {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table);
readEsc7 wz xu False = readEsc6 (wz : xu);
;
readEsc8 (wz : xu) = readEsc7 wz xu (isUpper wz);
readEsc8 vuy = readEsc6 vuy;
;
readEsc9 True (vvu : s) = concatMap readEsc2 (readHex s);
readEsc9 vvv vvw = readEsc8 vvw;
} 
;
readLitChar1 xvu xvv = readLitChar0 xvv;
"
"readLitChar2 (xuz : s) = readLitChar1 (xuz == '\') (xuz : s);
readLitChar2 xvw = readLitChar0 xvw;
"
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 xvz xwu = lexmatch0 xvz xwu;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"span p [] = ([],[]);
span p (zv : zw)|p zv(zv : ys,zs)|otherwise([],zv : zw) where {
vu43  = span p zw;
;
ys  = ys0 vu43;
;
ys0 (ys,zy) = ys;
;
zs  = zs0 vu43;
;
zs0 (zx,zs) = zs;
} 
;
"
is transformed to
"span p [] = span3 p [];
span p (zv : zw) = span2 p (zv : zw);
"
"span2 p (zv : zw) = span1 p zv zw (p zv) where {
span0 p zv zw True = ([],zv : zw);
;
span1 p zv zw True = (zv : ys,zs);
span1 p zv zw False = span0 p zv zw otherwise;
;
vu43  = span p zw;
;
ys  = ys0 vu43;
;
ys0 (ys,zy) = ys;
;
zs  = zs0 vu43;
;
zs0 (zx,zs) = zs;
} 
;
"
"span3 p [] = ([],[]);
span3 xwx xwy = span2 xwx xwy;
"

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

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

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

(11) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"span1 p zv zw (p zv) where {
span0 p zv zw True = ([],zv : zw);
;
span1 p zv zw True = (zv : ys,zs);
span1 p zv zw False = span0 p zv zw otherwise;
;
vu43  = span p zw;
;
ys  = ys0 vu43;
;
ys0 (ys,zy) = ys;
;
zs  = zs0 vu43;
;
zs0 (zx,zs) = zs;
} 
"
are unpacked to the following functions on top level
"span2Span0 xwz xxu p zv zw True = ([],zv : zw);
"
"span2Zs xwz xxu = span2Zs0 xwz xxu (span2Vu43 xwz xxu);
"
"span2Zs0 xwz xxu (zx,zs) = zs;
"
"span2Vu43 xwz xxu = span xwz xxu;
"
"span2Ys xwz xxu = span2Ys0 xwz xxu (span2Vu43 xwz xxu);
"
"span2Span1 xwz xxu p zv zw True = (zv : span2Ys xwz xxu,span2Zs xwz xxu);
span2Span1 xwz xxu p zv zw False = span2Span0 xwz xxu p zv zw otherwise;
"
"span2Ys0 xwz xxu (ys,zy) = ys;
"
The bindings of the following Let/Where expression
"readInt 16 isHexDigit hex where {
hex d = fromEnum d - hex1 d (isDigit d);
;
hex0 True = 'A';
hex0 False = 'a';
;
hex1 d True = fromEnum_0;
hex1 d False = fromEnum (hex0 (isUpper d)) - 10;
} 
"
are unpacked to the following functions on top level
"readHexHex0 True = 'A';
readHexHex0 False = 'a';
"
"readHexHex d = fromEnum d - readHexHex1 d (isDigit d);
"
"readHexHex1 d True = fromEnum_0;
readHexHex1 d False = fromEnum (readHexHex0 (isUpper d)) - 10;
"
The bindings of the following Let/Where expression
"readEsc s where {
readEsc (wzz : s) = readEsc41 (wzz : s);
readEsc (wzu : s) = readEsc38 (wzu : s);
readEsc (wyv : s) = readEsc36 (wyv : s);
readEsc (wxw : s) = readEsc34 (wxw : s);
readEsc (wwx : s) = readEsc32 (wwx : s);
readEsc (wvy : s) = readEsc29 (wvy : s);
readEsc (wuz : s) = readEsc27 (wuz : s);
readEsc (wuu : s) = readEsc25 (wuu : s);
readEsc (vzv : s) = readEsc23 (vzv : s);
readEsc (vyw : s) = readEsc21 (vyw : s);
readEsc (vxu : vxx) = readEsc18 (vxu : vxx);
readEsc (ww : wx) = readEsc15 (ww : wx);
readEsc (vvz : s) = readEsc13 (vvz : s);
readEsc (vvu : s) = readEsc11 (vvu : s);
readEsc (wz : xu) = readEsc8 (wz : xu);
readEsc xy = readEsc6 xy;
;
readEsc0 vu71 = readEsc00 vu71;
;
readEsc00 (n,t) = (toEnum n,t) : [];
readEsc00 xz = [];
;
readEsc1 vu72 = readEsc10 vu72;
;
readEsc10 (n,t) = (toEnum n,t) : [];
readEsc10 yu = [];
;
readEsc11 (vvu : s) = readEsc9 (vvu == 'x') (vvu : s);
readEsc11 vvx = readEsc8 vvx;
;
readEsc12 True (vvz : s) = concatMap readEsc1 (readOct s);
readEsc12 vwu vwv = readEsc11 vwv;
;
readEsc13 (vvz : s) = readEsc12 (vvz == 'o') (vvz : s);
readEsc13 vww = readEsc11 vww;
;
readEsc14 ww wx True = concatMap readEsc0 (readDec (ww : wx));
readEsc14 ww wx False = readEsc13 (ww : wx);
;
readEsc15 (ww : wx) = readEsc14 ww wx (isDigit ww);
readEsc15 vwy = readEsc13 vwy;
;
readEsc16 vxu c s True = (toEnum (fromEnum c - fromEnum '@'),s) : [];
readEsc16 vxu c s False = readEsc15 (vxu : c : s);
;
readEsc17 True (vxu : c : s) = readEsc16 vxu c s (c >= '@' && c <= '_');
readEsc17 vxy vxz = readEsc15 vxz;
;
readEsc18 (vxu : vxx) = readEsc17 (vxu == '^') (vxu : vxx);
readEsc18 vyu = readEsc15 vyu;
;
readEsc19 True (vyw : s) = (''',s) : [];
readEsc19 vyx vyy = readEsc18 vyy;
;
readEsc2 vu73 = readEsc20 vu73;
;
readEsc20 (n,t) = (toEnum n,t) : [];
readEsc20 yv = [];
;
readEsc21 (vyw : s) = readEsc19 (vyw == ''') (vyw : s);
readEsc21 vyz = readEsc18 vyz;
;
readEsc22 True (vzv : s) = ('"',s) : [];
readEsc22 vzw vzx = readEsc21 vzx;
;
readEsc23 (vzv : s) = readEsc22 (vzv == '"') (vzv : s);
readEsc23 vzy = readEsc21 vzy;
;
readEsc24 True (wuu : s) = ('\',s) : [];
readEsc24 wuv wuw = readEsc23 wuw;
;
readEsc25 (wuu : s) = readEsc24 (wuu == '\') (wuu : s);
readEsc25 wux = readEsc23 wux;
;
readEsc26 True (wuz : s) = ('\11',s) : [];
readEsc26 wvu wvv = readEsc25 wvv;
;
readEsc27 (wuz : s) = readEsc26 (wuz == 'v') (wuz : s);
readEsc27 wvw = readEsc25 wvw;
;
readEsc28 True (wvy : s) = ('\9',s) : [];
readEsc28 wvz wwu = readEsc27 wwu;
;
readEsc29 (wvy : s) = readEsc28 (wvy == 't') (wvy : s);
readEsc29 wwv = readEsc27 wwv;
;
readEsc31 True (wwx : s) = ('\13',s) : [];
readEsc31 wwy wwz = readEsc29 wwz;
;
readEsc32 (wwx : s) = readEsc31 (wwx == 'r') (wwx : s);
readEsc32 wxu = readEsc29 wxu;
;
readEsc33 True (wxw : s) = ('\10',s) : [];
readEsc33 wxx wxy = readEsc32 wxy;
;
readEsc34 (wxw : s) = readEsc33 (wxw == 'n') (wxw : s);
readEsc34 wxz = readEsc32 wxz;
;
readEsc35 True (wyv : s) = ('\12',s) : [];
readEsc35 wyw wyx = readEsc34 wyx;
;
readEsc36 (wyv : s) = readEsc35 (wyv == 'f') (wyv : s);
readEsc36 wyy = readEsc34 wyy;
;
readEsc37 True (wzu : s) = ('\8',s) : [];
readEsc37 wzv wzw = readEsc36 wzw;
;
readEsc38 (wzu : s) = readEsc37 (wzu == 'b') (wzu : s);
readEsc38 wzx = readEsc36 wzx;
;
readEsc39 True (wzz : s) = ('\7',s) : [];
readEsc39 xuu xuv = readEsc38 xuv;
;
readEsc41 (wzz : s) = readEsc39 (wzz == 'a') (wzz : s);
readEsc41 xuw = readEsc38 xuw;
;
readEsc6 xy = [];
;
readEsc7 wz xu True = let {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table);
readEsc7 wz xu False = readEsc6 (wz : xu);
;
readEsc8 (wz : xu) = readEsc7 wz xu (isUpper wz);
readEsc8 vuy = readEsc6 vuy;
;
readEsc9 True (vvu : s) = concatMap readEsc2 (readHex s);
readEsc9 vvv vvw = readEsc8 vvw;
} 
"
are unpacked to the following functions on top level
"readLitChar1ReadEsc14 ww wx True = concatMap readLitChar1ReadEsc0 (readDec (ww : wx));
readLitChar1ReadEsc14 ww wx False = readLitChar1ReadEsc13 (ww : wx);
"
"readLitChar1ReadEsc2 vu73 = readLitChar1ReadEsc20 vu73;
"
"readLitChar1ReadEsc29 (wvy : s) = readLitChar1ReadEsc28 (wvy == 't') (wvy : s);
readLitChar1ReadEsc29 wwv = readLitChar1ReadEsc27 wwv;
"
"readLitChar1ReadEsc23 (vzv : s) = readLitChar1ReadEsc22 (vzv == '"') (vzv : s);
readLitChar1ReadEsc23 vzy = readLitChar1ReadEsc21 vzy;
"
"readLitChar1ReadEsc1 vu72 = readLitChar1ReadEsc10 vu72;
"
"readLitChar1ReadEsc00 (n,t) = (toEnum n,t) : [];
readLitChar1ReadEsc00 xz = [];
"
"readLitChar1ReadEsc17 True (vxu : c : s) = readLitChar1ReadEsc16 vxu c s (c >= '@' && c <= '_');
readLitChar1ReadEsc17 vxy vxz = readLitChar1ReadEsc15 vxz;
"
"readLitChar1ReadEsc22 True (vzv : s) = ('"',s) : [];
readLitChar1ReadEsc22 vzw vzx = readLitChar1ReadEsc21 vzx;
"
"readLitChar1ReadEsc21 (vyw : s) = readLitChar1ReadEsc19 (vyw == ''') (vyw : s);
readLitChar1ReadEsc21 vyz = readLitChar1ReadEsc18 vyz;
"
"readLitChar1ReadEsc27 (wuz : s) = readLitChar1ReadEsc26 (wuz == 'v') (wuz : s);
readLitChar1ReadEsc27 wvw = readLitChar1ReadEsc25 wvw;
"
"readLitChar1ReadEsc32 (wwx : s) = readLitChar1ReadEsc31 (wwx == 'r') (wwx : s);
readLitChar1ReadEsc32 wxu = readLitChar1ReadEsc29 wxu;
"
"readLitChar1ReadEsc9 True (vvu : s) = concatMap readLitChar1ReadEsc2 (readHex s);
readLitChar1ReadEsc9 vvv vvw = readLitChar1ReadEsc8 vvw;
"
"readLitChar1ReadEsc35 True (wyv : s) = ('\12',s) : [];
readLitChar1ReadEsc35 wyw wyx = readLitChar1ReadEsc34 wyx;
"
"readLitChar1ReadEsc31 True (wwx : s) = ('\13',s) : [];
readLitChar1ReadEsc31 wwy wwz = readLitChar1ReadEsc29 wwz;
"
"readLitChar1ReadEsc11 (vvu : s) = readLitChar1ReadEsc9 (vvu == 'x') (vvu : s);
readLitChar1ReadEsc11 vvx = readLitChar1ReadEsc8 vvx;
"
"readLitChar1ReadEsc (wzz : s) = readLitChar1ReadEsc41 (wzz : s);
readLitChar1ReadEsc (wzu : s) = readLitChar1ReadEsc38 (wzu : s);
readLitChar1ReadEsc (wyv : s) = readLitChar1ReadEsc36 (wyv : s);
readLitChar1ReadEsc (wxw : s) = readLitChar1ReadEsc34 (wxw : s);
readLitChar1ReadEsc (wwx : s) = readLitChar1ReadEsc32 (wwx : s);
readLitChar1ReadEsc (wvy : s) = readLitChar1ReadEsc29 (wvy : s);
readLitChar1ReadEsc (wuz : s) = readLitChar1ReadEsc27 (wuz : s);
readLitChar1ReadEsc (wuu : s) = readLitChar1ReadEsc25 (wuu : s);
readLitChar1ReadEsc (vzv : s) = readLitChar1ReadEsc23 (vzv : s);
readLitChar1ReadEsc (vyw : s) = readLitChar1ReadEsc21 (vyw : s);
readLitChar1ReadEsc (vxu : vxx) = readLitChar1ReadEsc18 (vxu : vxx);
readLitChar1ReadEsc (ww : wx) = readLitChar1ReadEsc15 (ww : wx);
readLitChar1ReadEsc (vvz : s) = readLitChar1ReadEsc13 (vvz : s);
readLitChar1ReadEsc (vvu : s) = readLitChar1ReadEsc11 (vvu : s);
readLitChar1ReadEsc (wz : xu) = readLitChar1ReadEsc8 (wz : xu);
readLitChar1ReadEsc xy = readLitChar1ReadEsc6 xy;
"
"readLitChar1ReadEsc24 True (wuu : s) = ('\',s) : [];
readLitChar1ReadEsc24 wuv wuw = readLitChar1ReadEsc23 wuw;
"
"readLitChar1ReadEsc6 xy = [];
"
"readLitChar1ReadEsc18 (vxu : vxx) = readLitChar1ReadEsc17 (vxu == '^') (vxu : vxx);
readLitChar1ReadEsc18 vyu = readLitChar1ReadEsc15 vyu;
"
"readLitChar1ReadEsc10 (n,t) = (toEnum n,t) : [];
readLitChar1ReadEsc10 yu = [];
"
"readLitChar1ReadEsc37 True (wzu : s) = ('\8',s) : [];
readLitChar1ReadEsc37 wzv wzw = readLitChar1ReadEsc36 wzw;
"
"readLitChar1ReadEsc0 vu71 = readLitChar1ReadEsc00 vu71;
"
"readLitChar1ReadEsc15 (ww : wx) = readLitChar1ReadEsc14 ww wx (isDigit ww);
readLitChar1ReadEsc15 vwy = readLitChar1ReadEsc13 vwy;
"
"readLitChar1ReadEsc34 (wxw : s) = readLitChar1ReadEsc33 (wxw == 'n') (wxw : s);
readLitChar1ReadEsc34 wxz = readLitChar1ReadEsc32 wxz;
"
"readLitChar1ReadEsc36 (wyv : s) = readLitChar1ReadEsc35 (wyv == 'f') (wyv : s);
readLitChar1ReadEsc36 wyy = readLitChar1ReadEsc34 wyy;
"
"readLitChar1ReadEsc26 True (wuz : s) = ('\11',s) : [];
readLitChar1ReadEsc26 wvu wvv = readLitChar1ReadEsc25 wvv;
"
"readLitChar1ReadEsc16 vxu c s True = (toEnum (fromEnum c - fromEnum '@'),s) : [];
readLitChar1ReadEsc16 vxu c s False = readLitChar1ReadEsc15 (vxu : c : s);
"
"readLitChar1ReadEsc20 (n,t) = (toEnum n,t) : [];
readLitChar1ReadEsc20 yv = [];
"
"readLitChar1ReadEsc12 True (vvz : s) = concatMap readLitChar1ReadEsc1 (readOct s);
readLitChar1ReadEsc12 vwu vwv = readLitChar1ReadEsc11 vwv;
"
"readLitChar1ReadEsc38 (wzu : s) = readLitChar1ReadEsc37 (wzu == 'b') (wzu : s);
readLitChar1ReadEsc38 wzx = readLitChar1ReadEsc36 wzx;
"
"readLitChar1ReadEsc33 True (wxw : s) = ('\10',s) : [];
readLitChar1ReadEsc33 wxx wxy = readLitChar1ReadEsc32 wxy;
"
"readLitChar1ReadEsc41 (wzz : s) = readLitChar1ReadEsc39 (wzz == 'a') (wzz : s);
readLitChar1ReadEsc41 xuw = readLitChar1ReadEsc38 xuw;
"
"readLitChar1ReadEsc25 (wuu : s) = readLitChar1ReadEsc24 (wuu == '\') (wuu : s);
readLitChar1ReadEsc25 wux = readLitChar1ReadEsc23 wux;
"
"readLitChar1ReadEsc19 True (vyw : s) = (''',s) : [];
readLitChar1ReadEsc19 vyx vyy = readLitChar1ReadEsc18 vyy;
"
"readLitChar1ReadEsc39 True (wzz : s) = ('\7',s) : [];
readLitChar1ReadEsc39 xuu xuv = readLitChar1ReadEsc38 xuv;
"
"readLitChar1ReadEsc13 (vvz : s) = readLitChar1ReadEsc12 (vvz == 'o') (vvz : s);
readLitChar1ReadEsc13 vww = readLitChar1ReadEsc11 vww;
"
"readLitChar1ReadEsc8 (wz : xu) = readLitChar1ReadEsc7 wz xu (isUpper wz);
readLitChar1ReadEsc8 vuy = readLitChar1ReadEsc6 vuy;
"
"readLitChar1ReadEsc7 wz xu True = readLitChar1ReadEsc7ReadEsc5 (concatMap (readLitChar1ReadEsc7ReadEsc4 (wz : xu)) readLitChar1ReadEsc7Table);
readLitChar1ReadEsc7 wz xu False = readLitChar1ReadEsc6 (wz : xu);
"
"readLitChar1ReadEsc28 True (wvy : s) = ('\9',s) : [];
readLitChar1ReadEsc28 wvz wwu = readLitChar1ReadEsc27 wwu;
"
The bindings of the following Let/Where expression
"let {
readEsc3 c vu74 = readEsc30 c vu74;
;
readEsc30 c ([],s') = (c,s') : [];
readEsc30 c xx = [];
;
readEsc4 s vu75 = readEsc40 s vu75;
;
readEsc40 s (c,mne) = concatMap (readEsc3 c) (lexmatch mne s : []);
readEsc40 s xw = [];
;
readEsc5 (pr : xv) = pr : [];
readEsc5 [] = [];
;
table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
} in readEsc5 (concatMap (readEsc4 (wz : xu)) table)"
are unpacked to the following functions on top level
"readLitChar1ReadEsc7ReadEsc3 c vu74 = readLitChar1ReadEsc7ReadEsc30 c vu74;
"
"readLitChar1ReadEsc7ReadEsc30 c ([],s') = (c,s') : [];
readLitChar1ReadEsc7ReadEsc30 c xx = [];
"
"readLitChar1ReadEsc7ReadEsc4 s vu75 = readLitChar1ReadEsc7ReadEsc40 s vu75;
"
"readLitChar1ReadEsc7ReadEsc5 (pr : xv) = pr : [];
readLitChar1ReadEsc7ReadEsc5 [] = [];
"
"readLitChar1ReadEsc7Table  = ('\127','D' : 'E' : 'L' : []) : asciiTab;
"
"readLitChar1ReadEsc7ReadEsc40 s (c,mne) = concatMap (readLitChar1ReadEsc7ReadEsc3 c) (lexmatch mne s : []);
readLitChar1ReadEsc7ReadEsc40 s xw = [];
"

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

(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;
}