/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) HASKELL
(1) IFR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 26 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) NumRed [SOUND, 0 ms]
(10) HASKELL


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

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

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

(1) IFR (EQUIVALENT)
If Reductions:
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;
"

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

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

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

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

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

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"absReal x|x >= 0x|otherwise`negate` x;
"
is transformed to
"absReal x = absReal2 x;
"
"absReal1 x True = x;
absReal1 x False = absReal0 x otherwise;
"
"absReal0 x True = `negate` x;
"
"absReal2 x = absReal1 x (x >= 0);
"
The following Function with conditions
"gcd' x 0 = x;
gcd' x y = gcd' y (x `rem` y);
"
is transformed to
"gcd' x xz = gcd'2 x xz;
gcd' x y = gcd'0 x y;
"
"gcd'0 x y = gcd' y (x `rem` y);
"
"gcd'1 True x xz = x;
gcd'1 yu yv yw = gcd'0 yv yw;
"
"gcd'2 x xz = gcd'1 (xz == 0) x xz;
gcd'2 yx yy = gcd'0 yx yy;
"
The following Function with conditions
"gcd 0 0 = error [];
gcd x y = gcd' (abs x) (abs y) where {
gcd' x 0 = x;
gcd' x y = gcd' y (x `rem` y);
} 
;
"
is transformed to
"gcd yz zu = gcd3 yz zu;
gcd x y = gcd0 x y;
"
"gcd0 x y = gcd' (abs x) (abs y) where {
gcd' x xz = gcd'2 x xz;
gcd' x y = gcd'0 x y;
;
gcd'0 x y = gcd' y (x `rem` y);
;
gcd'1 True x xz = x;
gcd'1 yu yv yw = gcd'0 yv yw;
;
gcd'2 x xz = gcd'1 (xz == 0) x xz;
gcd'2 yx yy = gcd'0 yx yy;
} 
;
"
"gcd1 True yz zu = error [];
gcd1 zv zw zx = gcd0 zw zx;
"
"gcd2 True yz zu = gcd1 (zu == 0) yz zu;
gcd2 zy zz vuu = gcd0 zz vuu;
"
"gcd3 yz zu = gcd2 (yz == 0) yz zu;
gcd3 vuv vuw = gcd0 vuv vuw;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where {
d  = gcd x y;
} 
;
"
is transformed to
"reduce x y = reduce2 x y;
"
"reduce2 x y = reduce1 x y (y == 0) where {
d  = gcd x y;
;
reduce0 x y True = x `quot` d :% (y `quot` d);
;
reduce1 x y True = error [];
reduce1 x y False = reduce0 x y otherwise;
} 
;
"

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

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

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

(7) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"gcd' (abs x) (abs y) where {
gcd' x xz = gcd'2 x xz;
gcd' x y = gcd'0 x y;
;
gcd'0 x y = gcd' y (x `rem` y);
;
gcd'1 True x xz = x;
gcd'1 yu yv yw = gcd'0 yv yw;
;
gcd'2 x xz = gcd'1 (xz == 0) x xz;
gcd'2 yx yy = gcd'0 yx yy;
} 
"
are unpacked to the following functions on top level
"gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y);
"
"gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz;
gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy;
"
"gcd0Gcd'1 True x xz = x;
gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw;
"
"gcd0Gcd' x xz = gcd0Gcd'2 x xz;
gcd0Gcd' x y = gcd0Gcd'0 x y;
"
The bindings of the following Let/Where expression
"reduce1 x y (y == 0) where {
d  = gcd x y;
;
reduce0 x y True = x `quot` d :% (y `quot` d);
;
reduce1 x y True = error [];
reduce1 x y False = reduce0 x y otherwise;
} 
"
are unpacked to the following functions on top level
"reduce2D vux vuy = gcd vux vuy;
"
"reduce2Reduce1 vux vuy x y True = error [];
reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise;
"
"reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy);
"

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

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

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

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

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