Funct Progr 77531 pair #381921030

details

property	value
status	complete
benchmark	Monad_liftM4_3.hs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	full_haskell

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.39079809189 seconds
cpu usage	11.111389798
max memory	6.55396864E8

stage attributes

key	value
output-size	10213
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 12 ms]
(8) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
liftM4 :: Monad f => (c  ->  d  ->  a  ->  e  ->  b)  ->  f c  ->  f d  ->  f a  ->  f e  ->  f b;
liftM4 f m1 m2 m3 m4 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4)))));

}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\x4->return (f x1 x2 x3 x4)"
is transformed to
"liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
"
The following Lambda expression
"\x3->m4 >>= liftM40 f x1 x2 x3"
is transformed to
"liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
"
The following Lambda expression
"\x2->m3 >>= liftM41 m4 f x1 x2"
is transformed to
"liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
"
The following Lambda expression
"\x1->m2 >>= liftM42 m3 m4 f x1"
is transformed to
"liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
liftM4 :: Monad f => (a  ->  b  ->  d  ->  e  ->  c)  ->  f a  ->  f b  ->  f d  ->  f e  ->  f c;
liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;

liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);

liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;

liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;

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