Haskell pair #487599586

details

property	value
status	complete
benchmark	List_insert_1.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n095.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	13.7496569157 seconds
cpu usage	28.439191071
max memory	4.039221248E9

stage attributes

key	value
output-size	747557
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) IFR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) COR [EQUIVALENT, 0 ms]
(8) HASKELL
(9) LetRed [EQUIVALENT, 0 ms]
(10) HASKELL
(11) NumRed [SOUND, 0 ms]
(12) HASKELL
(13) Narrow [SOUND, 0 ms]
(14) AND
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 111 ms]
        (20) YES
    (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (26) YES
    (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (32) YES
    (33) QDP
        (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (35) 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;
insert :: Ord a => a  ->  [a]  ->  [a];
insert e ls = insertBy compare e ls;

insertBy :: (a  ->  a  ->  Ordering)  ->  a  ->  [a]  ->  [a];
insertBy _ x [] = x : [];
insertBy cmp x ys@(y : ys') = case cmp x y of { 
GT-> y : insertBy cmp x ys'; 
_-> x : ys; 
 } ;

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

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

(1) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case compare x y of {
EQ  -> o;
LT  -> LT;
GT  -> GT}
"
is transformed to
"primCompAux0 o EQ = o;
primCompAux0 o LT = LT;
primCompAux0 o GT = GT;
"
The following Case expression
"case cmp x y of {
GT  -> y : insertBy cmp x ys';

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