Haskell pair #487599612

details

property	value
status	complete
benchmark	List_minimumBy_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.10907316208 seconds
cpu usage	12.796999027
max memory	6.88791552E8

stage attributes

key	value
output-size	9913
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) CR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) QDP
(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(12) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
minimumBy :: (a  ->  a  ->  Ordering)  ->  [a]  ->  a;
minimumBy _ [] = error [];
minimumBy cmp xs = foldl1 min xs where { 
min x y = case cmp x y of { 
GT-> y; 
_-> x; 
 } ;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case cmp x y of {
GT  -> y;
_  -> x}
"
is transformed to
"min0 y x GT = y;
min0 y x _ = x;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
minimumBy :: (a  ->  a  ->  Ordering)  ->  [a]  ->  a;
minimumBy _ [] = error [];
minimumBy cmp xs = foldl1 min xs where { 
min x y = min0 y x (cmp x y);
min0 y x GT = y;
min0 y x _ = x;
 };

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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