/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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;

liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;

}

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

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

(4)
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 d => (f  ->  a  ->  b  ->  c  ->  e)  ->  d f  ->  d a  ->  d b  ->  d c  ->  d e;
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;

liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;

}

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

(6)
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 d => (b  ->  f  ->  e  ->  c  ->  a)  ->  d b  ->  d f  ->  d e  ->  d c  ->  d a;
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;

liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;

}

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Monad.liftM4",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Monad.liftM4 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="Monad.liftM4 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
5[label="Monad.liftM4 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="Monad.liftM4 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
7[label="Monad.liftM4 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="box"];35[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];8 -> 35[label="",style="solid", color="burlywood", weight=9];
35 -> 9[label="",style="solid", color="burlywood", weight=3];
36[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 36[label="",style="solid", color="burlywood", weight=9];
36 -> 10[label="",style="solid", color="burlywood", weight=3];
9[label="Nothing >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Just vy40 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="Nothing",fontsize=16,color="green",shape="box"];12[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="box"];37[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];13 -> 37[label="",style="solid", color="burlywood", weight=9];
37 -> 14[label="",style="solid", color="burlywood", weight=3];
38[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9];
38 -> 15[label="",style="solid", color="burlywood", weight=3];
14[label="Nothing >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="Just vy50 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="Nothing",fontsize=16,color="green",shape="box"];17[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
18[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];39[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];18 -> 39[label="",style="solid", color="burlywood", weight=9];
39 -> 19[label="",style="solid", color="burlywood", weight=3];
40[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];18 -> 40[label="",style="solid", color="burlywood", weight=9];
40 -> 20[label="",style="solid", color="burlywood", weight=3];
19[label="Nothing >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="Just vy60 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
21[label="Nothing",fontsize=16,color="green",shape="box"];22[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
23[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];41[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];23 -> 41[label="",style="solid", color="burlywood", weight=9];
41 -> 24[label="",style="solid", color="burlywood", weight=3];
42[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];23 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 25[label="",style="solid", color="burlywood", weight=3];
24[label="Nothing >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="Just vy70 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="Nothing",fontsize=16,color="green",shape="box"];27[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
28[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
29[label="Just (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];29 -> 30[label="",style="dashed", color="green", weight=3];
30[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];30 -> 31[label="",style="dashed", color="green", weight=3];
30 -> 32[label="",style="dashed", color="green", weight=3];
30 -> 33[label="",style="dashed", color="green", weight=3];
30 -> 34[label="",style="dashed", color="green", weight=3];
31[label="vy40",fontsize=16,color="green",shape="box"];32[label="vy50",fontsize=16,color="green",shape="box"];33[label="vy60",fontsize=16,color="green",shape="box"];34[label="vy70",fontsize=16,color="green",shape="box"];}

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

(8)
YES