/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 6 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 e => (d  ->  b  ->  c  ->  f  ->  a)  ->  e d  ->  e b  ->  e c  ->  e f  ->  e a;
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 a => (f  ->  b  ->  c  ->  d  ->  e)  ->  a f  ->  a b  ->  a c  ->  a d  ->  a 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;

}

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

(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 f => (b  ->  c  ->  e  ->  a  ->  d)  ->  f b  ->  f c  ->  f e  ->  f a  ->  f d;
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 a => (e  ->  d  ->  b  ->  c  ->  f)  ->  a e  ->  a d  ->  a b  ->  a c  ->  a f;
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="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="primbindIO vy4 (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="burlywood",shape="box"];56[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 56[label="",style="solid", color="burlywood", weight=9];
56 -> 10[label="",style="solid", color="burlywood", weight=3];
57[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 57[label="",style="solid", color="burlywood", weight=9];
57 -> 11[label="",style="solid", color="burlywood", weight=3];
58[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 58[label="",style="solid", color="burlywood", weight=9];
58 -> 12[label="",style="solid", color="burlywood", weight=3];
59[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 59[label="",style="solid", color="burlywood", weight=9];
59 -> 13[label="",style="solid", color="burlywood", weight=3];
10[label="primbindIO (IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="primbindIO (AProVE_IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="primbindIO (AProVE_Exception vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="primbindIO (AProVE_Error vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="error []",fontsize=16,color="red",shape="box"];15[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
16[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];17[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];18[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
19[label="primbindIO vy5 (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];60[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 60[label="",style="solid", color="burlywood", weight=9];
60 -> 20[label="",style="solid", color="burlywood", weight=3];
61[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 61[label="",style="solid", color="burlywood", weight=9];
61 -> 21[label="",style="solid", color="burlywood", weight=3];
62[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 62[label="",style="solid", color="burlywood", weight=9];
62 -> 22[label="",style="solid", color="burlywood", weight=3];
63[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 63[label="",style="solid", color="burlywood", weight=9];
63 -> 23[label="",style="solid", color="burlywood", weight=3];
20[label="primbindIO (IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="primbindIO (AProVE_IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="primbindIO (AProVE_Exception vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="primbindIO (AProVE_Error vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="error []",fontsize=16,color="red",shape="box"];25[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
26[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];28[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
29[label="primbindIO vy6 (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];64[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 64[label="",style="solid", color="burlywood", weight=9];
64 -> 30[label="",style="solid", color="burlywood", weight=3];
65[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 65[label="",style="solid", color="burlywood", weight=9];
65 -> 31[label="",style="solid", color="burlywood", weight=3];
66[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 66[label="",style="solid", color="burlywood", weight=9];
66 -> 32[label="",style="solid", color="burlywood", weight=3];
67[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 67[label="",style="solid", color="burlywood", weight=9];
67 -> 33[label="",style="solid", color="burlywood", weight=3];
30[label="primbindIO (IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="primbindIO (AProVE_IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32[label="primbindIO (AProVE_Exception vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
33[label="primbindIO (AProVE_Error vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
34[label="error []",fontsize=16,color="red",shape="box"];35[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];35 -> 38[label="",style="solid", color="black", weight=3];
36[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];37[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];38[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
39[label="primbindIO vy7 (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="burlywood",shape="box"];68[label="vy7/IO vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 68[label="",style="solid", color="burlywood", weight=9];
68 -> 40[label="",style="solid", color="burlywood", weight=3];
69[label="vy7/AProVE_IO vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 69[label="",style="solid", color="burlywood", weight=9];
69 -> 41[label="",style="solid", color="burlywood", weight=3];
70[label="vy7/AProVE_Exception vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 70[label="",style="solid", color="burlywood", weight=9];
70 -> 42[label="",style="solid", color="burlywood", weight=3];
71[label="vy7/AProVE_Error vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 71[label="",style="solid", color="burlywood", weight=9];
71 -> 43[label="",style="solid", color="burlywood", weight=3];
40[label="primbindIO (IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
41[label="primbindIO (AProVE_IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
42[label="primbindIO (AProVE_Exception vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
43[label="primbindIO (AProVE_Error vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
44[label="error []",fontsize=16,color="red",shape="box"];45[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];45 -> 48[label="",style="solid", color="black", weight=3];
46[label="AProVE_Exception vy70",fontsize=16,color="green",shape="box"];47[label="AProVE_Error vy70",fontsize=16,color="green",shape="box"];48[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
49[label="primretIO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];49 -> 50[label="",style="solid", color="black", weight=3];
50[label="AProVE_IO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];50 -> 51[label="",style="dashed", color="green", weight=3];
51[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];51 -> 52[label="",style="dashed", color="green", weight=3];
51 -> 53[label="",style="dashed", color="green", weight=3];
51 -> 54[label="",style="dashed", color="green", weight=3];
51 -> 55[label="",style="dashed", color="green", weight=3];
52[label="vy40",fontsize=16,color="green",shape="box"];53[label="vy50",fontsize=16,color="green",shape="box"];54[label="vy60",fontsize=16,color="green",shape="box"];55[label="vy70",fontsize=16,color="green",shape="box"];}

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

(8)
YES