/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (26) 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 e => (d  ->  g  ->  a  ->  b  ->  c  ->  f)  ->  e d  ->  e g  ->  e a  ->  e b  ->  e c  ->  e f;
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 g => (e  ->  b  ->  c  ->  d  ->  f  ->  a)  ->  g e  ->  g b  ->  g c  ->  g d  ->  g f  ->  g 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;

}

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

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

}

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

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

}

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

(7) Narrow (SOUND)
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="blue",shape="box"];180[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];9 -> 180[label="",style="solid", color="blue", weight=9];
180 -> 10[label="",style="solid", color="blue", weight=3];
181[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];9 -> 181[label="",style="solid", color="blue", weight=9];
181 -> 11[label="",style="solid", color="blue", weight=3];
182[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];9 -> 182[label="",style="solid", color="blue", weight=9];
182 -> 12[label="",style="solid", color="blue", weight=3];
10[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
11[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="burlywood",shape="box"];183[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];11 -> 183[label="",style="solid", color="burlywood", weight=9];
183 -> 14[label="",style="solid", color="burlywood", weight=3];
184[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];11 -> 184[label="",style="solid", color="burlywood", weight=9];
184 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="burlywood",shape="triangle"];185[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];12 -> 185[label="",style="solid", color="burlywood", weight=9];
185 -> 16[label="",style="solid", color="burlywood", weight=3];
186[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 186[label="",style="solid", color="burlywood", weight=9];
186 -> 17[label="",style="solid", color="burlywood", weight=3];
13[label="primbindIO vy4 (Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="burlywood",shape="box"];187[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];13 -> 187[label="",style="solid", color="burlywood", weight=9];
187 -> 18[label="",style="solid", color="burlywood", weight=3];
188[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];13 -> 188[label="",style="solid", color="burlywood", weight=9];
188 -> 19[label="",style="solid", color="burlywood", weight=3];
189[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];13 -> 189[label="",style="solid", color="burlywood", weight=9];
189 -> 20[label="",style="solid", color="burlywood", weight=3];
190[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];13 -> 190[label="",style="solid", color="burlywood", weight=9];
190 -> 21[label="",style="solid", color="burlywood", weight=3];
14[label="Nothing >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];14 -> 22[label="",style="solid", color="black", weight=3];
15[label="Just vy40 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];15 -> 23[label="",style="solid", color="black", weight=3];
16[label="vy40 : vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];16 -> 24[label="",style="solid", color="black", weight=3];
17[label="[] >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3];
18[label="primbindIO (IO vy40) (Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3];
19[label="primbindIO (AProVE_IO vy40) (Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="black",shape="box"];19 -> 27[label="",style="solid", color="black", weight=3];
20[label="primbindIO (AProVE_Exception vy40) (Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="black",shape="box"];20 -> 28[label="",style="solid", color="black", weight=3];
21[label="primbindIO (AProVE_Error vy40) (Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="black",shape="box"];21 -> 29[label="",style="solid", color="black", weight=3];
22[label="Nothing",fontsize=16,color="green",shape="box"];23[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];23 -> 30[label="",style="solid", color="black", weight=3];
24 -> 74[label="",style="dashed", color="red", weight=0];
24[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40 ++ (vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="magenta"];24 -> 75[label="",style="dashed", color="magenta", weight=3];
24 -> 76[label="",style="dashed", color="magenta", weight=3];
25[label="[]",fontsize=16,color="green",shape="box"];26[label="error []",fontsize=16,color="red",shape="box"];27[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];27 -> 33[label="",style="solid", color="black", weight=3];
28[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];29[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];30[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="box"];191[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];30 -> 191[label="",style="solid", color="burlywood", weight=9];
191 -> 34[label="",style="solid", color="burlywood", weight=3];
192[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];30 -> 192[label="",style="solid", color="burlywood", weight=9];
192 -> 35[label="",style="solid", color="burlywood", weight=3];
75 -> 12[label="",style="dashed", color="red", weight=0];
75[label="vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="magenta"];75 -> 85[label="",style="dashed", color="magenta", weight=3];
76[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];76 -> 86[label="",style="solid", color="black", weight=3];
74[label="vy10 ++ vy9",fontsize=16,color="burlywood",shape="triangle"];193[label="vy10/vy100 : vy101",fontsize=10,color="white",style="solid",shape="box"];74 -> 193[label="",style="solid", color="burlywood", weight=9];
193 -> 87[label="",style="solid", color="burlywood", weight=3];
194[label="vy10/[]",fontsize=10,color="white",style="solid",shape="box"];74 -> 194[label="",style="solid", color="burlywood", weight=9];
194 -> 88[label="",style="solid", color="burlywood", weight=3];
33[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];33 -> 38[label="",style="solid", color="black", weight=3];
34[label="Nothing >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3];
35[label="Just vy50 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
85[label="vy41",fontsize=16,color="green",shape="box"];86[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];195[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];86 -> 195[label="",style="solid", color="burlywood", weight=9];
195 -> 95[label="",style="solid", color="burlywood", weight=3];
196[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];86 -> 196[label="",style="solid", color="burlywood", weight=9];
196 -> 96[label="",style="solid", color="burlywood", weight=3];
87[label="(vy100 : vy101) ++ vy9",fontsize=16,color="black",shape="box"];87 -> 97[label="",style="solid", color="black", weight=3];
88[label="[] ++ vy9",fontsize=16,color="black",shape="box"];88 -> 98[label="",style="solid", color="black", weight=3];
38[label="primbindIO vy5 (Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];197[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];38 -> 197[label="",style="solid", color="burlywood", weight=9];
197 -> 43[label="",style="solid", color="burlywood", weight=3];
198[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];38 -> 198[label="",style="solid", color="burlywood", weight=9];
198 -> 44[label="",style="solid", color="burlywood", weight=3];
199[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];38 -> 199[label="",style="solid", color="burlywood", weight=9];
199 -> 45[label="",style="solid", color="burlywood", weight=3];
200[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];38 -> 200[label="",style="solid", color="burlywood", weight=9];
200 -> 46[label="",style="solid", color="burlywood", weight=3];
39[label="Nothing",fontsize=16,color="green",shape="box"];40[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3];
95[label="vy50 : vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
96[label="[] >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];96 -> 102[label="",style="solid", color="black", weight=3];
97[label="vy100 : vy101 ++ vy9",fontsize=16,color="green",shape="box"];97 -> 103[label="",style="dashed", color="green", weight=3];
98[label="vy9",fontsize=16,color="green",shape="box"];43[label="primbindIO (IO vy50) (Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
44[label="primbindIO (AProVE_IO vy50) (Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
45[label="primbindIO (AProVE_Exception vy50) (Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3];
46[label="primbindIO (AProVE_Error vy50) (Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="black",shape="box"];46 -> 53[label="",style="solid", color="black", weight=3];
47[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];201[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];47 -> 201[label="",style="solid", color="burlywood", weight=9];
201 -> 54[label="",style="solid", color="burlywood", weight=3];
202[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];47 -> 202[label="",style="solid", color="burlywood", weight=9];
202 -> 55[label="",style="solid", color="burlywood", weight=3];
101 -> 74[label="",style="dashed", color="red", weight=0];
101[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="magenta"];101 -> 107[label="",style="dashed", color="magenta", weight=3];
101 -> 108[label="",style="dashed", color="magenta", weight=3];
102[label="[]",fontsize=16,color="green",shape="box"];103 -> 74[label="",style="dashed", color="red", weight=0];
103[label="vy101 ++ vy9",fontsize=16,color="magenta"];103 -> 109[label="",style="dashed", color="magenta", weight=3];
50[label="error []",fontsize=16,color="red",shape="box"];51[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];51 -> 58[label="",style="solid", color="black", weight=3];
52[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];53[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];54[label="Nothing >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];54 -> 59[label="",style="solid", color="black", weight=3];
55[label="Just vy60 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];55 -> 60[label="",style="solid", color="black", weight=3];
107 -> 86[label="",style="dashed", color="red", weight=0];
107[label="vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="magenta"];107 -> 116[label="",style="dashed", color="magenta", weight=3];
108[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];108 -> 117[label="",style="solid", color="black", weight=3];
109[label="vy101",fontsize=16,color="green",shape="box"];58[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];58 -> 63[label="",style="solid", color="black", weight=3];
59[label="Nothing",fontsize=16,color="green",shape="box"];60[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
116[label="vy51",fontsize=16,color="green",shape="box"];117[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];203[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];117 -> 203[label="",style="solid", color="burlywood", weight=9];
203 -> 123[label="",style="solid", color="burlywood", weight=3];
204[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];117 -> 204[label="",style="solid", color="burlywood", weight=9];
204 -> 124[label="",style="solid", color="burlywood", weight=3];
63[label="primbindIO vy6 (Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];205[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];63 -> 205[label="",style="solid", color="burlywood", weight=9];
205 -> 67[label="",style="solid", color="burlywood", weight=3];
206[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];63 -> 206[label="",style="solid", color="burlywood", weight=9];
206 -> 68[label="",style="solid", color="burlywood", weight=3];
207[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];63 -> 207[label="",style="solid", color="burlywood", weight=9];
207 -> 69[label="",style="solid", color="burlywood", weight=3];
208[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];63 -> 208[label="",style="solid", color="burlywood", weight=9];
208 -> 70[label="",style="solid", color="burlywood", weight=3];
64[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];209[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];64 -> 209[label="",style="solid", color="burlywood", weight=9];
209 -> 71[label="",style="solid", color="burlywood", weight=3];
210[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];64 -> 210[label="",style="solid", color="burlywood", weight=9];
210 -> 72[label="",style="solid", color="burlywood", weight=3];
123[label="vy60 : vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];123 -> 127[label="",style="solid", color="black", weight=3];
124[label="[] >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3];
67[label="primbindIO (IO vy60) (Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];67 -> 89[label="",style="solid", color="black", weight=3];
68[label="primbindIO (AProVE_IO vy60) (Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];68 -> 90[label="",style="solid", color="black", weight=3];
69[label="primbindIO (AProVE_Exception vy60) (Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];69 -> 91[label="",style="solid", color="black", weight=3];
70[label="primbindIO (AProVE_Error vy60) (Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];70 -> 92[label="",style="solid", color="black", weight=3];
71[label="Nothing >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];71 -> 93[label="",style="solid", color="black", weight=3];
72[label="Just vy70 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];72 -> 94[label="",style="solid", color="black", weight=3];
127 -> 74[label="",style="dashed", color="red", weight=0];
127[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="magenta"];127 -> 131[label="",style="dashed", color="magenta", weight=3];
127 -> 132[label="",style="dashed", color="magenta", weight=3];
128[label="[]",fontsize=16,color="green",shape="box"];89[label="error []",fontsize=16,color="red",shape="box"];90[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];90 -> 99[label="",style="solid", color="black", weight=3];
91[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];92[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];93[label="Nothing",fontsize=16,color="green",shape="box"];94[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
131 -> 117[label="",style="dashed", color="red", weight=0];
131[label="vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="magenta"];131 -> 142[label="",style="dashed", color="magenta", weight=3];
132[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];132 -> 143[label="",style="solid", color="black", weight=3];
99[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];99 -> 104[label="",style="solid", color="black", weight=3];
100[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="box"];211[label="vy8/Nothing",fontsize=10,color="white",style="solid",shape="box"];100 -> 211[label="",style="solid", color="burlywood", weight=9];
211 -> 105[label="",style="solid", color="burlywood", weight=3];
212[label="vy8/Just vy80",fontsize=10,color="white",style="solid",shape="box"];100 -> 212[label="",style="solid", color="burlywood", weight=9];
212 -> 106[label="",style="solid", color="burlywood", weight=3];
142[label="vy61",fontsize=16,color="green",shape="box"];143[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];213[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];143 -> 213[label="",style="solid", color="burlywood", weight=9];
213 -> 148[label="",style="solid", color="burlywood", weight=3];
214[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];143 -> 214[label="",style="solid", color="burlywood", weight=9];
214 -> 149[label="",style="solid", color="burlywood", weight=3];
104[label="primbindIO vy7 (Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="burlywood",shape="box"];215[label="vy7/IO vy70",fontsize=10,color="white",style="solid",shape="box"];104 -> 215[label="",style="solid", color="burlywood", weight=9];
215 -> 110[label="",style="solid", color="burlywood", weight=3];
216[label="vy7/AProVE_IO vy70",fontsize=10,color="white",style="solid",shape="box"];104 -> 216[label="",style="solid", color="burlywood", weight=9];
216 -> 111[label="",style="solid", color="burlywood", weight=3];
217[label="vy7/AProVE_Exception vy70",fontsize=10,color="white",style="solid",shape="box"];104 -> 217[label="",style="solid", color="burlywood", weight=9];
217 -> 112[label="",style="solid", color="burlywood", weight=3];
218[label="vy7/AProVE_Error vy70",fontsize=10,color="white",style="solid",shape="box"];104 -> 218[label="",style="solid", color="burlywood", weight=9];
218 -> 113[label="",style="solid", color="burlywood", weight=3];
105[label="Nothing >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];105 -> 114[label="",style="solid", color="black", weight=3];
106[label="Just vy80 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];106 -> 115[label="",style="solid", color="black", weight=3];
148[label="vy70 : vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];148 -> 151[label="",style="solid", color="black", weight=3];
149[label="[] >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];149 -> 152[label="",style="solid", color="black", weight=3];
110[label="primbindIO (IO vy70) (Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];110 -> 118[label="",style="solid", color="black", weight=3];
111[label="primbindIO (AProVE_IO vy70) (Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];111 -> 119[label="",style="solid", color="black", weight=3];
112[label="primbindIO (AProVE_Exception vy70) (Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];112 -> 120[label="",style="solid", color="black", weight=3];
113[label="primbindIO (AProVE_Error vy70) (Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];113 -> 121[label="",style="solid", color="black", weight=3];
114[label="Nothing",fontsize=16,color="green",shape="box"];115[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];115 -> 122[label="",style="solid", color="black", weight=3];
151 -> 74[label="",style="dashed", color="red", weight=0];
151[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];151 -> 154[label="",style="dashed", color="magenta", weight=3];
151 -> 155[label="",style="dashed", color="magenta", weight=3];
152[label="[]",fontsize=16,color="green",shape="box"];118[label="error []",fontsize=16,color="red",shape="box"];119[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
120[label="AProVE_Exception vy70",fontsize=16,color="green",shape="box"];121[label="AProVE_Error vy70",fontsize=16,color="green",shape="box"];122[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];122 -> 126[label="",style="solid", color="black", weight=3];
154 -> 143[label="",style="dashed", color="red", weight=0];
154[label="vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];154 -> 157[label="",style="dashed", color="magenta", weight=3];
155[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];155 -> 158[label="",style="solid", color="black", weight=3];
125[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3];
126[label="Just (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="green",shape="box"];126 -> 130[label="",style="dashed", color="green", weight=3];
157[label="vy71",fontsize=16,color="green",shape="box"];158[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="triangle"];219[label="vy8/vy80 : vy81",fontsize=10,color="white",style="solid",shape="box"];158 -> 219[label="",style="solid", color="burlywood", weight=9];
219 -> 160[label="",style="solid", color="burlywood", weight=3];
220[label="vy8/[]",fontsize=10,color="white",style="solid",shape="box"];158 -> 220[label="",style="solid", color="burlywood", weight=9];
220 -> 161[label="",style="solid", color="burlywood", weight=3];
129[label="primbindIO vy8 (Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="burlywood",shape="box"];221[label="vy8/IO vy80",fontsize=10,color="white",style="solid",shape="box"];129 -> 221[label="",style="solid", color="burlywood", weight=9];
221 -> 133[label="",style="solid", color="burlywood", weight=3];
222[label="vy8/AProVE_IO vy80",fontsize=10,color="white",style="solid",shape="box"];129 -> 222[label="",style="solid", color="burlywood", weight=9];
222 -> 134[label="",style="solid", color="burlywood", weight=3];
223[label="vy8/AProVE_Exception vy80",fontsize=10,color="white",style="solid",shape="box"];129 -> 223[label="",style="solid", color="burlywood", weight=9];
223 -> 135[label="",style="solid", color="burlywood", weight=3];
224[label="vy8/AProVE_Error vy80",fontsize=10,color="white",style="solid",shape="box"];129 -> 224[label="",style="solid", color="burlywood", weight=9];
224 -> 136[label="",style="solid", color="burlywood", weight=3];
130[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];130 -> 137[label="",style="dashed", color="green", weight=3];
130 -> 138[label="",style="dashed", color="green", weight=3];
130 -> 139[label="",style="dashed", color="green", weight=3];
130 -> 140[label="",style="dashed", color="green", weight=3];
130 -> 141[label="",style="dashed", color="green", weight=3];
160[label="vy80 : vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];160 -> 167[label="",style="solid", color="black", weight=3];
161[label="[] >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];161 -> 168[label="",style="solid", color="black", weight=3];
133[label="primbindIO (IO vy80) (Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];133 -> 144[label="",style="solid", color="black", weight=3];
134[label="primbindIO (AProVE_IO vy80) (Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];134 -> 145[label="",style="solid", color="black", weight=3];
135[label="primbindIO (AProVE_Exception vy80) (Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];135 -> 146[label="",style="solid", color="black", weight=3];
136[label="primbindIO (AProVE_Error vy80) (Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];136 -> 147[label="",style="solid", color="black", weight=3];
137[label="vy40",fontsize=16,color="green",shape="box"];138[label="vy50",fontsize=16,color="green",shape="box"];139[label="vy60",fontsize=16,color="green",shape="box"];140[label="vy70",fontsize=16,color="green",shape="box"];141[label="vy80",fontsize=16,color="green",shape="box"];167 -> 74[label="",style="dashed", color="red", weight=0];
167[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80 ++ (vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="magenta"];167 -> 169[label="",style="dashed", color="magenta", weight=3];
167 -> 170[label="",style="dashed", color="magenta", weight=3];
168[label="[]",fontsize=16,color="green",shape="box"];144[label="error []",fontsize=16,color="red",shape="box"];145[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];145 -> 150[label="",style="solid", color="black", weight=3];
146[label="AProVE_Exception vy80",fontsize=16,color="green",shape="box"];147[label="AProVE_Error vy80",fontsize=16,color="green",shape="box"];169 -> 158[label="",style="dashed", color="red", weight=0];
169[label="vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="magenta"];169 -> 171[label="",style="dashed", color="magenta", weight=3];
170[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];170 -> 172[label="",style="solid", color="black", weight=3];
150[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];150 -> 153[label="",style="solid", color="black", weight=3];
171[label="vy81",fontsize=16,color="green",shape="box"];172[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];172 -> 173[label="",style="solid", color="black", weight=3];
153[label="primretIO (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];153 -> 156[label="",style="solid", color="black", weight=3];
173[label="vy3 vy40 vy50 vy60 vy70 vy80 : []",fontsize=16,color="green",shape="box"];173 -> 174[label="",style="dashed", color="green", weight=3];
156[label="AProVE_IO (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="green",shape="box"];156 -> 159[label="",style="dashed", color="green", weight=3];
174[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];174 -> 175[label="",style="dashed", color="green", weight=3];
174 -> 176[label="",style="dashed", color="green", weight=3];
174 -> 177[label="",style="dashed", color="green", weight=3];
174 -> 178[label="",style="dashed", color="green", weight=3];
174 -> 179[label="",style="dashed", color="green", weight=3];
159[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];159 -> 162[label="",style="dashed", color="green", weight=3];
159 -> 163[label="",style="dashed", color="green", weight=3];
159 -> 164[label="",style="dashed", color="green", weight=3];
159 -> 165[label="",style="dashed", color="green", weight=3];
159 -> 166[label="",style="dashed", color="green", weight=3];
175[label="vy40",fontsize=16,color="green",shape="box"];176[label="vy50",fontsize=16,color="green",shape="box"];177[label="vy60",fontsize=16,color="green",shape="box"];178[label="vy70",fontsize=16,color="green",shape="box"];179[label="vy80",fontsize=16,color="green",shape="box"];162[label="vy40",fontsize=16,color="green",shape="box"];163[label="vy50",fontsize=16,color="green",shape="box"];164[label="vy60",fontsize=16,color="green",shape="box"];165[label="vy70",fontsize=16,color="green",shape="box"];166[label="vy80",fontsize=16,color="green",shape="box"];}

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) -> new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(10) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) -> new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12


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

(11)
YES

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

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) -> new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(13) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) -> new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12


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

(14)
YES

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

(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) -> new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(16) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) -> new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12


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

(17)
YES

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

(18)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) -> new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(19) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) -> new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12


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

(20)
YES

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

(21)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) -> new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(22) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) -> new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12


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

(23)
YES

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

(24)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_psPs(:(vy100, vy101), vy9, h) -> new_psPs(vy101, vy9, h)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(25) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_psPs(:(vy100, vy101), vy9, h) -> new_psPs(vy101, vy9, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(26)
YES