/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 0 ms]
(10) HASKELL
(11) LetRed [EQUIVALENT, 0 ms]
(12) HASKELL
(13) NumRed [SOUND, 19 ms]
(14) HASKELL


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

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

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\_->q"
is transformed to
"gtGt0 q _ = q;
"
The following Lambda expression
"\ab->(a,b)"
is transformed to
"zip0 a b = (a,b);
"

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

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

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

(3) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case loc of {
[]  -> id;
_  -> (showString ('\10' : 'A' : 'c' : 't' : 'i' : 'o' : 'n' : ':' : '\32' : [])) . showString loc}
"
is transformed to
"showsPrec0 loc [] = id;
showsPrec0 loc _ = (showString ('\10' : 'A' : 'c' : 't' : 'i' : 'o' : 'n' : ':' : '\32' : [])) . showString loc;
"
The following Case expression
"case descr of {
[]  -> id;
_  -> (showString ('\10' : 'R' : 'e' : 'a' : 's' : 'o' : 'n' : ':' : '\32' : [])) . showString descr}
"
is transformed to
"showsPrec1 descr [] = id;
showsPrec1 descr _ = (showString ('\10' : 'R' : 'e' : 'a' : 's' : 'o' : 'n' : ':' : '\32' : [])) . showString descr;
"
The following Case expression
"case mbFile of {
Nothing  -> id;
Just name  -> (showString ('\10' : 'R' : 'e' : 's' : 'o' : 'u' : 'r' : 'c' : 'e' : ':' : '\32' : [])) . showString name}
"
is transformed to
"showsPrec2 Nothing = id;
showsPrec2 (Just name) = (showString ('\10' : 'R' : 'e' : 's' : 'o' : 'u' : 'r' : 'c' : 'e' : ':' : '\32' : [])) . showString name;
"
The following Case expression
"case x of {
IOError_UserError  -> 'U' : 'E' : [];
IOError_IllegalError  -> 'I' : 'O' : [];
IOError_PermDenied  -> 'P' : 'D' : [];
IOError_AlreadyExists  -> 'A' : 'E' : [];
IOError_AlreadyInUse  -> 'R' : 'B' : [];
IOError_DoesNotExist  -> 'D' : 'N' : 'E' : [];
IOError_FullError  -> 'R' : 'E' : [];
IOError_EOF  -> 'E' : 'O' : 'F' : [];
IOError_WriteError  -> 'W' : 'E' : []}
"
is transformed to
"show0 IOError_UserError = 'U' : 'E' : [];
show0 IOError_IllegalError = 'I' : 'O' : [];
show0 IOError_PermDenied = 'P' : 'D' : [];
show0 IOError_AlreadyExists = 'A' : 'E' : [];
show0 IOError_AlreadyInUse = 'R' : 'B' : [];
show0 IOError_DoesNotExist = 'D' : 'N' : 'E' : [];
show0 IOError_FullError = 'R' : 'E' : [];
show0 IOError_EOF = 'E' : 'O' : 'F' : [];
show0 IOError_WriteError = 'W' : 'E' : [];
"

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

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

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

(5) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if b then (showChar '(') . p . showChar ')' else p"
is transformed to
"showParen0 p True = (showChar '(') . p . showChar ')';
showParen0 p False = p;
"
The following If expression
"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
is transformed to
"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
primDivNatS0 x y False = Zero;
"
The following If expression
"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
is transformed to
"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
primModNatS0 x y False = Succ x;
"
The following If expression
"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
is transformed to
"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
primModNatP0 x y False = primMinusNatS y x;
"

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

(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
"s@(wz : xu)"
is replaced by the following term
"wz : xu"

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

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

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

(9) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"showsPrec p ''' = showString (''' : '\' : ''' : ''' : []);
showsPrec p c = (showChar ''') . (showLitChar c) . showChar ''';
"
is transformed to
"showsPrec p zx = showsPrec5 p zx;
showsPrec p c = showsPrec3 p c;
"
"showsPrec3 p c = (showChar ''') . (showLitChar c) . showChar ''';
"
"showsPrec4 True p zx = showString (''' : '\' : ''' : ''' : []);
showsPrec4 zy zz vuu = showsPrec3 zz vuu;
"
"showsPrec5 p zx = showsPrec4 (zx == ''') p zx;
showsPrec5 vuv vuw = showsPrec3 vuv vuw;
"
The following Function with conditions
"showl [] = showChar '"';
showl ('"' : cs) = (showString ('\' : '"' : [])) . showl cs;
showl (c : cs) = (showLitChar c) . showl cs;
"
is transformed to
"showl [] = showl3 [];
showl (vuz : cs) = showl2 (vuz : cs);
showl (c : cs) = showl0 (c : cs);
"
"showl0 (c : cs) = (showLitChar c) . showl cs;
"
"showl1 True (vuz : cs) = (showString ('\' : '"' : [])) . showl cs;
showl1 vvu vvv = showl0 vvv;
"
"showl2 (vuz : cs) = showl1 (vuz == '"') (vuz : cs);
showl2 vvw = showl0 vvw;
"
"showl3 [] = showChar '"';
showl3 vvy = showl2 vvy;
"
The following Function with conditions
"randomSelect (x : []) = x;
randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
"
is transformed to
"randomSelect (x : []) = randomSelect3 (x : []);
randomSelect (x : xs) = randomSelect2 (x : xs);
"
"randomSelect0 x xs True = x;
"
"randomSelect1 x xs True = randomSelect xs;
randomSelect1 x xs False = randomSelect0 x xs otherwise;
"
"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
"
"randomSelect3 (x : []) = x;
randomSelect3 vww = randomSelect2 vww;
"
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 vwz vxu = takeWhile2 vwz vxu;
"
The following Function with conditions
"!! (x : vy) 0 = x;
!! (vz : xs) n|n > 0xs !! (n - 1);
!! (wu : wv) ww = error [];
!! [] wx = error [];
"
is transformed to
"!! (x : vy) vyx = emEm5 (x : vy) vyx;
!! (vz : xs) n = emEm3 (vz : xs) n;
!! (wu : wv) ww = emEm1 (wu : wv) ww;
!! [] wx = emEm0 [] wx;
"
"emEm0 [] wx = error [];
"
"emEm1 (wu : wv) ww = error [];
emEm1 vxx vxy = emEm0 vxx vxy;
"
"emEm2 vz xs n True = xs !! (n - 1);
emEm2 vz xs n False = emEm1 (vz : xs) n;
"
"emEm3 (vz : xs) n = emEm2 vz xs n (n > 0);
emEm3 vyu vyv = emEm1 vyu vyv;
"
"emEm4 True (x : vy) vyx = x;
emEm4 vyy vyz vzu = emEm3 vyz vzu;
"
"emEm5 (x : vy) vyx = emEm4 (vyx == 0) (x : vy) vyx;
emEm5 vzv vzw = emEm3 vzv vzw;
"
The following Function with conditions
"showLitChar c|c > '\127'(showChar '\') . protectEsc isDigit (shows (fromEnum c));
showLitChar '\127' = showString ('\' : 'D' : 'E' : 'L' : []);
showLitChar '\' = showString ('\' : '\' : []);
showLitChar c|c >= '\32'showChar c;
showLitChar '\7' = showString ('\' : 'a' : []);
showLitChar '\8' = showString ('\' : 'b' : []);
showLitChar '\12' = showString ('\' : 'f' : []);
showLitChar '\10' = showString ('\' : 'n' : []);
showLitChar '\13' = showString ('\' : 'r' : []);
showLitChar '\9' = showString ('\' : 't' : []);
showLitChar '\11' = showString ('\' : 'v' : []);
showLitChar '\14' = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
showLitChar c = showString ('\' : snd (asciiTab !! (fromEnum c)));
"
is transformed to
"showLitChar c = showLitChar24 c;
showLitChar wzy = showLitChar22 wzy;
showLitChar wzu = showLitChar20 wzu;
showLitChar c = showLitChar18 c;
showLitChar wyv = showLitChar16 wyv;
showLitChar wxx = showLitChar14 wxx;
showLitChar wwz = showLitChar12 wwz;
showLitChar wwv = showLitChar10 wwv;
showLitChar wvx = showLitChar8 wvx;
showLitChar wuz = showLitChar6 wuz;
showLitChar wuv = showLitChar4 wuv;
showLitChar vzx = showLitChar2 vzx;
showLitChar c = showLitChar0 c;
"
"showLitChar0 c = showString ('\' : snd (asciiTab !! (fromEnum c)));
"
"showLitChar1 True vzx = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
showLitChar1 vzy vzz = showLitChar0 vzz;
"
"showLitChar2 vzx = showLitChar1 (vzx == '\14') vzx;
showLitChar2 wuu = showLitChar0 wuu;
"
"showLitChar3 True wuv = showString ('\' : 'v' : []);
showLitChar3 wuw wux = showLitChar2 wux;
"
"showLitChar4 wuv = showLitChar3 (wuv == '\11') wuv;
showLitChar4 wuy = showLitChar2 wuy;
"
"showLitChar5 True wuz = showString ('\' : 't' : []);
showLitChar5 wvu wvv = showLitChar4 wvv;
"
"showLitChar6 wuz = showLitChar5 (wuz == '\9') wuz;
showLitChar6 wvw = showLitChar4 wvw;
"
"showLitChar7 True wvx = showString ('\' : 'r' : []);
showLitChar7 wvy wvz = showLitChar6 wvz;
"
"showLitChar8 wvx = showLitChar7 (wvx == '\13') wvx;
showLitChar8 wwu = showLitChar6 wwu;
"
"showLitChar9 True wwv = showString ('\' : 'n' : []);
showLitChar9 www wwx = showLitChar8 wwx;
"
"showLitChar10 wwv = showLitChar9 (wwv == '\10') wwv;
showLitChar10 wwy = showLitChar8 wwy;
"
"showLitChar11 True wwz = showString ('\' : 'f' : []);
showLitChar11 wxu wxv = showLitChar10 wxv;
"
"showLitChar12 wwz = showLitChar11 (wwz == '\12') wwz;
showLitChar12 wxw = showLitChar10 wxw;
"
"showLitChar13 True wxx = showString ('\' : 'b' : []);
showLitChar13 wxy wxz = showLitChar12 wxz;
"
"showLitChar14 wxx = showLitChar13 (wxx == '\8') wxx;
showLitChar14 wyu = showLitChar12 wyu;
"
"showLitChar15 True wyv = showString ('\' : 'a' : []);
showLitChar15 wyw wyx = showLitChar14 wyx;
"
"showLitChar16 wyv = showLitChar15 (wyv == '\7') wyv;
showLitChar16 wyy = showLitChar14 wyy;
"
"showLitChar17 c True = showChar c;
showLitChar17 c False = showLitChar16 c;
"
"showLitChar18 c = showLitChar17 c (c >= '\32');
showLitChar18 wyz = showLitChar16 wyz;
"
"showLitChar19 True wzu = showString ('\' : '\' : []);
showLitChar19 wzv wzw = showLitChar18 wzw;
"
"showLitChar20 wzu = showLitChar19 (wzu == '\') wzu;
showLitChar20 wzx = showLitChar18 wzx;
"
"showLitChar21 True wzy = showString ('\' : 'D' : 'E' : 'L' : []);
showLitChar21 wzz xuu = showLitChar20 xuu;
"
"showLitChar22 wzy = showLitChar21 (wzy == '\127') wzy;
showLitChar22 xuv = showLitChar20 xuv;
"
"showLitChar23 c True = (showChar '\') . protectEsc isDigit (shows (fromEnum c));
showLitChar23 c False = showLitChar22 c;
"
"showLitChar24 c = showLitChar23 c (c > '\127');
showLitChar24 xuw = showLitChar22 xuw;
"
The following Function with conditions
"cont (wz : xu)|p wz('\' : '&' : []) ++ wz : xu;
cont s = s;
"
is transformed to
"cont (wz : xu) = cont2 (wz : xu);
cont s = cont0 s;
"
"cont0 s = s;
"
"cont1 wz xu True = ('\' : '&' : []) ++ wz : xu;
cont1 wz xu False = cont0 (wz : xu);
"
"cont2 (wz : xu) = cont1 wz xu (p wz);
cont2 xuy = cont0 xuy;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

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

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

(11) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"(showChar '[') . (shows x) . showl xs where {
showl [] = showChar ']';
showl (x : xs) = (showChar ',') . (shows x) . showl xs;
} 
"
are unpacked to the following functions on top level
"showListShowl [] = showChar ']';
showListShowl (x : xs) = (showChar ',') . (shows x) . showListShowl xs;
"
The bindings of the following Let/Where expression
"(showChar '"') . showl cs where {
showl [] = showl3 [];
showl (vuz : cs) = showl2 (vuz : cs);
showl (c : cs) = showl0 (c : cs);
;
showl0 (c : cs) = (showLitChar c) . showl cs;
;
showl1 True (vuz : cs) = (showString ('\' : '"' : [])) . showl cs;
showl1 vvu vvv = showl0 vvv;
;
showl2 (vuz : cs) = showl1 (vuz == '"') (vuz : cs);
showl2 vvw = showl0 vvw;
;
showl3 [] = showChar '"';
showl3 vvy = showl2 vvy;
} 
"
are unpacked to the following functions on top level
"showListShowl3 [] = showChar '"';
showListShowl3 vvy = showListShowl2 vvy;
"
"showListShowl2 (vuz : cs) = showListShowl1 (vuz == '"') (vuz : cs);
showListShowl2 vvw = showListShowl0 vvw;
"
"showListShowl0 (c : cs) = (showLitChar c) . showListShowl4 cs;
"
"showListShowl1 True (vuz : cs) = (showString ('\' : '"' : [])) . showListShowl4 cs;
showListShowl1 vvu vvv = showListShowl0 vvv;
"
"showListShowl4 [] = showListShowl3 [];
showListShowl4 (vuz : cs) = showListShowl2 (vuz : cs);
showListShowl4 (c : cs) = showListShowl0 (c : cs);
"
The bindings of the following Let/Where expression
"f . cont where {
cont (wz : xu) = cont2 (wz : xu);
cont s = cont0 s;
;
cont0 s = s;
;
cont1 wz xu True = ('\' : '&' : []) ++ wz : xu;
cont1 wz xu False = cont0 (wz : xu);
;
cont2 (wz : xu) = cont1 wz xu (p wz);
cont2 xuy = cont0 xuy;
} 
"
are unpacked to the following functions on top level
"protectEscCont0 xuz s = s;
"
"protectEscCont xuz (wz : xu) = protectEscCont2 xuz (wz : xu);
protectEscCont xuz s = protectEscCont0 xuz s;
"
"protectEscCont1 xuz wz xu True = ('\' : '&' : []) ++ wz : xu;
protectEscCont1 xuz wz xu False = protectEscCont0 xuz (wz : xu);
"
"protectEscCont2 xuz (wz : xu) = protectEscCont1 xuz wz xu (xuz wz);
protectEscCont2 xuz xuy = protectEscCont0 xuz xuy;
"

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

(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;
}