Funct Progr 77531 pair #381920391

details

property	value
status	complete
benchmark	lookup_2.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	basic_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.01132583618 seconds
cpu usage	9.611033309
max memory	5.85060352E8

stage attributes

key	value
output-size	12040
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

data Main.Maybe a = Nothing  | Just a ;

data MyBool = MyTrue  | MyFalse ;

data Tup2 b a = Tup2 b a ;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

lookup k Nil = lookup3 k Nil;
lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);

lookup0 k x y xys MyTrue = lookup k xys;

lookup1 k x y xys MyTrue = Main.Just y;
lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;

lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsMyBool k x);

lookup3 k Nil = Main.Nothing;
lookup3 vy vz = lookup2 vy vz;

otherwise :: MyBool;
otherwise = MyTrue;

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data List a = Cons a (List a)  | Nil ;

data Main.Maybe a = Nothing  | Just a ;

data MyBool = MyTrue  | MyFalse ;

data Tup2 a b = Tup2 a b ;

esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
esEsMyBool MyFalse MyFalse = MyTrue;
esEsMyBool MyFalse MyTrue = MyFalse;
esEsMyBool MyTrue MyFalse = MyFalse;
esEsMyBool MyTrue MyTrue = MyTrue;

lookup k Nil = lookup3 k Nil;
lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);

lookup0 k x y xys MyTrue = lookup k xys;

lookup1 k x y xys MyTrue = Main.Just y;

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