/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 14 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;
liftM5 :: Monad c => (g  ->  d  ->  b  ->  a  ->  f  ->  e)  ->  c g  ->  c d  ->  c b  ->  c a  ->  c f  ->  c e;
liftM5 f m1 m2 m3 m4 m5 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->m5 >>= (\x5 ->return (f x1 x2 x3 x4 x5))))));

}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\x5->return (f x1 x2 x3 x4 x5)"
is transformed to
"liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
"
The following Lambda expression
"\x4->m5 >>= liftM50 f x1 x2 x3 x4"
is transformed to
"liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
"
The following Lambda expression
"\x3->m4 >>= liftM51 m5 f x1 x2 x3"
is transformed to
"liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
"
The following Lambda expression
"\x2->m3 >>= liftM52 m4 m5 f x1 x2"
is transformed to
"liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
"
The following Lambda expression
"\x1->m2 >>= liftM53 m3 m4 m5 f x1"
is transformed to
"liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 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;
liftM5 :: Monad c => (f  ->  e  ->  a  ->  d  ->  b  ->  g)  ->  c f  ->  c e  ->  c a  ->  c d  ->  c b  ->  c g;
liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;

liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);

liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;

liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;

liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;

liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 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;
liftM5 :: Monad c => (g  ->  a  ->  b  ->  d  ->  f  ->  e)  ->  c g  ->  c a  ->  c b  ->  c d  ->  c f  ->  c e;
liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;

liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);

liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;

liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;

liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;

liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 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;
liftM5 :: Monad b => (f  ->  c  ->  e  ->  d  ->  g  ->  a)  ->  b f  ->  b c  ->  b e  ->  b d  ->  b g  ->  b a;
liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;

liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);

liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;

liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;

liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;

liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;

}

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Monad.liftM5",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Monad.liftM5 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="Monad.liftM5 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
5[label="Monad.liftM5 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
6[label="Monad.liftM5 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
7[label="Monad.liftM5 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="grey",shape="box"];7 -> 8[label="",style="dashed", color="grey", weight=3];
8[label="Monad.liftM5 vy3 vy4 vy5 vy6 vy7 vy8",fontsize=16,color="black",shape="triangle"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="burlywood",shape="box"];42[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];9 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 10[label="",style="solid", color="burlywood", weight=3];
43[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 43[label="",style="solid", color="burlywood", weight=9];
43 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="Nothing >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="Just vy40 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="Nothing",fontsize=16,color="green",shape="box"];13[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="box"];44[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];14 -> 44[label="",style="solid", color="burlywood", weight=9];
44 -> 15[label="",style="solid", color="burlywood", weight=3];
45[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];14 -> 45[label="",style="solid", color="burlywood", weight=9];
45 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="Nothing >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="Just vy50 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="Nothing",fontsize=16,color="green",shape="box"];18[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
19[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];46[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];19 -> 46[label="",style="solid", color="burlywood", weight=9];
46 -> 20[label="",style="solid", color="burlywood", weight=3];
47[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];19 -> 47[label="",style="solid", color="burlywood", weight=9];
47 -> 21[label="",style="solid", color="burlywood", weight=3];
20[label="Nothing >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
21[label="Just vy60 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
22[label="Nothing",fontsize=16,color="green",shape="box"];23[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
24[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];48[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];24 -> 48[label="",style="solid", color="burlywood", weight=9];
48 -> 25[label="",style="solid", color="burlywood", weight=3];
49[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];24 -> 49[label="",style="solid", color="burlywood", weight=9];
49 -> 26[label="",style="solid", color="burlywood", weight=3];
25[label="Nothing >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="Just vy70 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="Nothing",fontsize=16,color="green",shape="box"];28[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
29[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="box"];50[label="vy8/Nothing",fontsize=10,color="white",style="solid",shape="box"];29 -> 50[label="",style="solid", color="burlywood", weight=9];
50 -> 30[label="",style="solid", color="burlywood", weight=3];
51[label="vy8/Just vy80",fontsize=10,color="white",style="solid",shape="box"];29 -> 51[label="",style="solid", color="burlywood", weight=9];
51 -> 31[label="",style="solid", color="burlywood", weight=3];
30[label="Nothing >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
31[label="Just vy80 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
32[label="Nothing",fontsize=16,color="green",shape="box"];33[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3];
34[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
35[label="Just (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="green",shape="box"];35 -> 36[label="",style="dashed", color="green", weight=3];
36[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];36 -> 37[label="",style="dashed", color="green", weight=3];
36 -> 38[label="",style="dashed", color="green", weight=3];
36 -> 39[label="",style="dashed", color="green", weight=3];
36 -> 40[label="",style="dashed", color="green", weight=3];
36 -> 41[label="",style="dashed", color="green", weight=3];
37[label="vy40",fontsize=16,color="green",shape="box"];38[label="vy50",fontsize=16,color="green",shape="box"];39[label="vy60",fontsize=16,color="green",shape="box"];40[label="vy70",fontsize=16,color="green",shape="box"];41[label="vy80",fontsize=16,color="green",shape="box"];}

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

(8)
YES