Haskell pair #487598439

details

property	value
status	complete
benchmark	fromEnum_2.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.53325796127 seconds
cpu usage	10.966082297
max memory	5.93915904E8

stage attributes

key	value
output-size	42505
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) AND
    (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) DependencyGraphProof [EQUIVALENT, 0 ms]
        (12) AND
            (13) QDP
                (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (15) YES
            (16) QDP
                (17) MRRProof [EQUIVALENT, 9 ms]
                (18) QDP
                (19) PisEmptyProof [EQUIVALENT, 0 ms]
                (20) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

data Tup2 b a = Tup2 b a ;

error :: a;
error = stop MyTrue;

fromEnumRatio :: Ratio MyInt  ->  MyInt;
fromEnumRatio = truncateRatio;

fromIntMyInt :: MyInt  ->  MyInt;
fromIntMyInt x = x;

primDivNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primDivNatS Main.Zero Main.Zero = Main.error;
primDivNatS (Main.Succ x) Main.Zero = Main.error;
primDivNatS (Main.Succ x) (Main.Succ y) = primDivNatS0 x y (primGEqNatS x y);
primDivNatS Main.Zero (Main.Succ x) = Main.Zero;

primDivNatS0 x y MyTrue = Main.Succ (primDivNatS (primMinusNatS x y) (Main.Succ y));
primDivNatS0 x y MyFalse = Main.Zero;

primGEqNatS :: Main.Nat  ->  Main.Nat  ->  MyBool;
primGEqNatS (Main.Succ x) Main.Zero = MyTrue;
primGEqNatS (Main.Succ x) (Main.Succ y) = primGEqNatS x y;
primGEqNatS Main.Zero (Main.Succ x) = MyFalse;
primGEqNatS Main.Zero Main.Zero = MyTrue;

primMinusNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primMinusNatS (Main.Succ x) (Main.Succ y) = primMinusNatS x y;
primMinusNatS Main.Zero (Main.Succ y) = Main.Zero;
primMinusNatS x Main.Zero = x;

primModNatS :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primModNatS Main.Zero Main.Zero = Main.error;
primModNatS Main.Zero (Main.Succ x) = Main.Zero;
primModNatS (Main.Succ x) Main.Zero = Main.error;
primModNatS (Main.Succ x) (Main.Succ Main.Zero) = Main.Zero;
primModNatS (Main.Succ x) (Main.Succ (Main.Succ y)) = primModNatS0 x y (primGEqNatS x (Main.Succ y));

primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Main.Succ y)) (Main.Succ (Main.Succ y));
primModNatS0 x y MyFalse = Main.Succ x;

primQrmInt :: MyInt  ->  MyInt  ->  Tup2 MyInt MyInt;
primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y);

primQuotInt :: MyInt  ->  MyInt  ->  MyInt;
primQuotInt (Main.Pos x) (Main.Pos (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));
primQuotInt (Main.Pos x) (Main.Neg (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
primQuotInt (Main.Neg x) (Main.Pos (Main.Succ y)) = Main.Neg (primDivNatS x (Main.Succ y));
primQuotInt (Main.Neg x) (Main.Neg (Main.Succ y)) = Main.Pos (primDivNatS x (Main.Succ y));

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