Funct Progr 77531 pair #381920713

details

property	value
status	complete
benchmark	notElem_4.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.45265197754 seconds
cpu usage	10.922777711
max memory	5.64764672E8

stage attributes

key	value
output-size	60497
starexec-result	YES

output

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


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


YES
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (12) YES
    (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Float = Float MyInt MyInt ;

data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

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

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

all :: (a  ->  MyBool)  ->  List a  ->  MyBool;
all p = pt and (map p);

and :: List MyBool  ->  MyBool;
and = foldr asAs MyTrue;

asAs :: MyBool  ->  MyBool  ->  MyBool;
asAs MyFalse x = MyFalse;
asAs MyTrue x = x;

esEsFloat :: Float  ->  Float  ->  MyBool;
esEsFloat = primEqFloat;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

foldr :: (b  ->  a  ->  a)  ->  a  ->  List b  ->  a;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

fsEsFloat :: Float  ->  Float  ->  MyBool;
fsEsFloat x y = not (esEsFloat x y);

map :: (b  ->  a)  ->  List b  ->  List a;
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

notElemFloat :: Float  ->  List Float  ->  MyBool;
notElemFloat = pt all fsEsFloat;

primEqFloat :: Float  ->  Float  ->  MyBool;
primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

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

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