/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 b => (a  ->  g  ->  d  ->  e  ->  c  ->  f)  ->  b a  ->  b g  ->  b d  ->  b e  ->  b c  ->  b 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 b => (e  ->  f  ->  g  ->  a  ->  c  ->  d)  ->  b e  ->  b f  ->  b g  ->  b a  ->  b c  ->  b d;
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 a => (g  ->  d  ->  e  ->  b  ->  f  ->  c)  ->  a g  ->  a d  ->  a e  ->  a b  ->  a f  ->  a c;
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 a => (d  ->  c  ->  e  ->  g  ->  f  ->  b)  ->  a d  ->  a c  ->  a e  ->  a g  ->  a f  ->  a b;
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="burlywood",shape="triangle"];87[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 87[label="",style="solid", color="burlywood", weight=9];
87 -> 10[label="",style="solid", color="burlywood", weight=3];
88[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 88[label="",style="solid", color="burlywood", weight=9];
88 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="vy40 : vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="[] >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12 -> 29[label="",style="dashed", color="red", weight=0];
12[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40 ++ (vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="magenta"];12 -> 30[label="",style="dashed", color="magenta", weight=3];
12 -> 31[label="",style="dashed", color="magenta", weight=3];
13[label="[]",fontsize=16,color="green",shape="box"];30[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];30 -> 40[label="",style="solid", color="black", weight=3];
31 -> 9[label="",style="dashed", color="red", weight=0];
31[label="vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="magenta"];31 -> 41[label="",style="dashed", color="magenta", weight=3];
29[label="vy10 ++ vy9",fontsize=16,color="burlywood",shape="triangle"];89[label="vy10/vy100 : vy101",fontsize=10,color="white",style="solid",shape="box"];29 -> 89[label="",style="solid", color="burlywood", weight=9];
89 -> 42[label="",style="solid", color="burlywood", weight=3];
90[label="vy10/[]",fontsize=10,color="white",style="solid",shape="box"];29 -> 90[label="",style="solid", color="burlywood", weight=9];
90 -> 43[label="",style="solid", color="burlywood", weight=3];
40[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];91[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];40 -> 91[label="",style="solid", color="burlywood", weight=9];
91 -> 44[label="",style="solid", color="burlywood", weight=3];
92[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];40 -> 92[label="",style="solid", color="burlywood", weight=9];
92 -> 45[label="",style="solid", color="burlywood", weight=3];
41[label="vy41",fontsize=16,color="green",shape="box"];42[label="(vy100 : vy101) ++ vy9",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
43[label="[] ++ vy9",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
44[label="vy50 : vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3];
45[label="[] >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
46[label="vy100 : vy101 ++ vy9",fontsize=16,color="green",shape="box"];46 -> 50[label="",style="dashed", color="green", weight=3];
47[label="vy9",fontsize=16,color="green",shape="box"];48 -> 29[label="",style="dashed", color="red", weight=0];
48[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="magenta"];48 -> 51[label="",style="dashed", color="magenta", weight=3];
48 -> 52[label="",style="dashed", color="magenta", weight=3];
49[label="[]",fontsize=16,color="green",shape="box"];50 -> 29[label="",style="dashed", color="red", weight=0];
50[label="vy101 ++ vy9",fontsize=16,color="magenta"];50 -> 53[label="",style="dashed", color="magenta", weight=3];
51[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
52 -> 40[label="",style="dashed", color="red", weight=0];
52[label="vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="magenta"];52 -> 55[label="",style="dashed", color="magenta", weight=3];
53[label="vy101",fontsize=16,color="green",shape="box"];54[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];93[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];54 -> 93[label="",style="solid", color="burlywood", weight=9];
93 -> 56[label="",style="solid", color="burlywood", weight=3];
94[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];54 -> 94[label="",style="solid", color="burlywood", weight=9];
94 -> 57[label="",style="solid", color="burlywood", weight=3];
55[label="vy51",fontsize=16,color="green",shape="box"];56[label="vy60 : vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];56 -> 58[label="",style="solid", color="black", weight=3];
57[label="[] >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];57 -> 59[label="",style="solid", color="black", weight=3];
58 -> 29[label="",style="dashed", color="red", weight=0];
58[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="magenta"];58 -> 60[label="",style="dashed", color="magenta", weight=3];
58 -> 61[label="",style="dashed", color="magenta", weight=3];
59[label="[]",fontsize=16,color="green",shape="box"];60[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
61 -> 54[label="",style="dashed", color="red", weight=0];
61[label="vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="magenta"];61 -> 63[label="",style="dashed", color="magenta", weight=3];
62[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];95[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];62 -> 95[label="",style="solid", color="burlywood", weight=9];
95 -> 64[label="",style="solid", color="burlywood", weight=3];
96[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];62 -> 96[label="",style="solid", color="burlywood", weight=9];
96 -> 65[label="",style="solid", color="burlywood", weight=3];
63[label="vy61",fontsize=16,color="green",shape="box"];64[label="vy70 : vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3];
65[label="[] >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3];
66 -> 29[label="",style="dashed", color="red", weight=0];
66[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];66 -> 68[label="",style="dashed", color="magenta", weight=3];
66 -> 69[label="",style="dashed", color="magenta", weight=3];
67[label="[]",fontsize=16,color="green",shape="box"];68[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];68 -> 70[label="",style="solid", color="black", weight=3];
69 -> 62[label="",style="dashed", color="red", weight=0];
69[label="vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];69 -> 71[label="",style="dashed", color="magenta", weight=3];
70[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="triangle"];97[label="vy8/vy80 : vy81",fontsize=10,color="white",style="solid",shape="box"];70 -> 97[label="",style="solid", color="burlywood", weight=9];
97 -> 72[label="",style="solid", color="burlywood", weight=3];
98[label="vy8/[]",fontsize=10,color="white",style="solid",shape="box"];70 -> 98[label="",style="solid", color="burlywood", weight=9];
98 -> 73[label="",style="solid", color="burlywood", weight=3];
71[label="vy71",fontsize=16,color="green",shape="box"];72[label="vy80 : vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];72 -> 74[label="",style="solid", color="black", weight=3];
73[label="[] >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];73 -> 75[label="",style="solid", color="black", weight=3];
74 -> 29[label="",style="dashed", color="red", weight=0];
74[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80 ++ (vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="magenta"];74 -> 76[label="",style="dashed", color="magenta", weight=3];
74 -> 77[label="",style="dashed", color="magenta", weight=3];
75[label="[]",fontsize=16,color="green",shape="box"];76[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];76 -> 78[label="",style="solid", color="black", weight=3];
77 -> 70[label="",style="dashed", color="red", weight=0];
77[label="vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="magenta"];77 -> 79[label="",style="dashed", color="magenta", weight=3];
78[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
79[label="vy81",fontsize=16,color="green",shape="box"];80[label="vy3 vy40 vy50 vy60 vy70 vy80 : []",fontsize=16,color="green",shape="box"];80 -> 81[label="",style="dashed", color="green", weight=3];
81[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];81 -> 82[label="",style="dashed", color="green", weight=3];
81 -> 83[label="",style="dashed", color="green", weight=3];
81 -> 84[label="",style="dashed", color="green", weight=3];
81 -> 85[label="",style="dashed", color="green", weight=3];
81 -> 86[label="",style="dashed", color="green", weight=3];
82[label="vy40",fontsize=16,color="green",shape="box"];83[label="vy50",fontsize=16,color="green",shape="box"];84[label="vy60",fontsize=16,color="green",shape="box"];85[label="vy70",fontsize=16,color="green",shape="box"];86[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.
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(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


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(23)
YES

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(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.
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(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


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(26)
YES