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


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


MAYBE
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 not be shown:

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) IFR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) COR [EQUIVALENT, 0 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) AND
    (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) AND
            (14) QDP
                (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (16) YES
            (17) QDP
                (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (19) YES
            (20) QDP
                (21) QDPOrderProof [EQUIVALENT, 37 ms]
                (22) QDP
                (23) DependencyGraphProof [EQUIVALENT, 0 ms]
                (24) QDP
                (25) MNOCProof [EQUIVALENT, 0 ms]
                (26) QDP
                (27) NonTerminationLoopProof [COMPLETE, 0 ms]
                (28) NO
    (29) QDP
        (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
(35) Narrow [COMPLETE, 0 ms]
(36) TRUE


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

(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;
filterM :: Monad a => (b  ->  a Bool)  ->  [b]  ->  a [b];
filterM _ [] = return [];
filterM p (x : xs) = p x >>= (\flg ->filterM p xs >>= (\ys ->return ( if flg then x : ys else ys)));

}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\ys->return (if flg then x : ys else ys)"
is transformed to
"filterM0 flg x ys = return (if flg then x : ys else ys);
"
The following Lambda expression
"\flg->filterM p xs >>= filterM0 flg x"
is transformed to
"filterM1 p xs x flg = filterM p xs >>= filterM0 flg x;
"

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

(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;
filterM :: Monad a => (b  ->  a Bool)  ->  [b]  ->  a [b];
filterM _ [] = return [];
filterM p (x : xs) = p x >>= filterM1 p xs x;

filterM0 flg x ys = return ( if flg then x : ys else ys);

filterM1 p xs x flg = filterM p xs >>= filterM0 flg x;

}

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

(3) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if flg then x : ys else ys"
is transformed to
"filterM00 x ys True = x : ys;
filterM00 x ys False = ys;
"

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

(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;
filterM :: Monad a => (b  ->  a Bool)  ->  [b]  ->  a [b];
filterM _ [] = return [];
filterM p (x : xs) = p x >>= filterM1 p xs x;

filterM0 flg x ys = return (filterM00 x ys flg);

filterM00 x ys True = x : ys;
filterM00 x ys False = ys;

filterM1 p xs x flg = filterM p xs >>= filterM0 flg x;

}

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

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

(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;
filterM :: Monad a => (b  ->  a Bool)  ->  [b]  ->  a [b];
filterM vy [] = return [];
filterM p (x : xs) = p x >>= filterM1 p xs x;

filterM0 flg x ys = return (filterM00 x ys flg);

filterM00 x ys True = x : ys;
filterM00 x ys False = ys;

filterM1 p xs x flg = filterM p xs >>= filterM0 flg x;

}

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

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

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

(8)
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;
filterM :: Monad a => (b  ->  a Bool)  ->  [b]  ->  a [b];
filterM vy [] = return [];
filterM p (x : xs) = p x >>= filterM1 p xs x;

filterM0 flg x ys = return (filterM00 x ys flg);

filterM00 x ys True = x : ys;
filterM00 x ys False = ys;

filterM1 p xs x flg = filterM p xs >>= filterM0 flg x;

}

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

(9) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Monad.filterM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Monad.filterM vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
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126 -> 5[label="",style="solid", color="burlywood", weight=3];
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127 -> 6[label="",style="solid", color="burlywood", weight=3];
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6[label="Monad.filterM vz3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="vz3 vz40 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="blue",shape="box"];128[label=">>= :: (IO Bool) -> (Bool -> IO ([] a)) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 128[label="",style="solid", color="blue", weight=9];
128 -> 9[label="",style="solid", color="blue", weight=3];
129[label=">>= :: (Maybe Bool) -> (Bool -> Maybe ([] a)) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 129[label="",style="solid", color="blue", weight=9];
129 -> 10[label="",style="solid", color="blue", weight=3];
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132 -> 13[label="",style="solid", color="blue", weight=3];
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133 -> 14[label="",style="solid", color="blue", weight=3];
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11 -> 18[label="",style="dashed", color="red", weight=0];
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17[label="vz3 vz40",fontsize=16,color="green",shape="box"];17 -> 25[label="",style="dashed", color="green", weight=3];
16[label="vz5 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="burlywood",shape="triangle"];134[label="vz5/Nothing",fontsize=10,color="white",style="solid",shape="box"];16 -> 134[label="",style="solid", color="burlywood", weight=9];
134 -> 26[label="",style="solid", color="burlywood", weight=3];
135[label="vz5/Just vz50",fontsize=10,color="white",style="solid",shape="box"];16 -> 135[label="",style="solid", color="burlywood", weight=9];
135 -> 27[label="",style="solid", color="burlywood", weight=3];
19[label="vz3 vz40",fontsize=16,color="green",shape="box"];19 -> 28[label="",style="dashed", color="green", weight=3];
18[label="vz6 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="burlywood",shape="triangle"];136[label="vz6/vz60 : vz61",fontsize=10,color="white",style="solid",shape="box"];18 -> 136[label="",style="solid", color="burlywood", weight=9];
136 -> 29[label="",style="solid", color="burlywood", weight=3];
137[label="vz6/[]",fontsize=10,color="white",style="solid",shape="box"];18 -> 137[label="",style="solid", color="burlywood", weight=9];
137 -> 30[label="",style="solid", color="burlywood", weight=3];
20 -> 90[label="",style="dashed", color="red", weight=0];
20[label="primretIO []",fontsize=16,color="magenta"];20 -> 91[label="",style="dashed", color="magenta", weight=3];
21[label="Just []",fontsize=16,color="green",shape="box"];120[label="[]",fontsize=16,color="green",shape="box"];119[label="return vz15",fontsize=16,color="black",shape="triangle"];119 -> 122[label="",style="solid", color="black", weight=3];
24[label="vz3 vz40",fontsize=16,color="green",shape="box"];24 -> 37[label="",style="dashed", color="green", weight=3];
23[label="primbindIO vz7 (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="burlywood",shape="triangle"];138[label="vz7/IO vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 138[label="",style="solid", color="burlywood", weight=9];
138 -> 33[label="",style="solid", color="burlywood", weight=3];
139[label="vz7/AProVE_IO vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 139[label="",style="solid", color="burlywood", weight=9];
139 -> 34[label="",style="solid", color="burlywood", weight=3];
140[label="vz7/AProVE_Exception vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 140[label="",style="solid", color="burlywood", weight=9];
140 -> 35[label="",style="solid", color="burlywood", weight=3];
141[label="vz7/AProVE_Error vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 141[label="",style="solid", color="burlywood", weight=9];
141 -> 36[label="",style="solid", color="burlywood", weight=3];
25[label="vz40",fontsize=16,color="green",shape="box"];26[label="Nothing >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];26 -> 38[label="",style="solid", color="black", weight=3];
27[label="Just vz50 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];27 -> 39[label="",style="solid", color="black", weight=3];
28[label="vz40",fontsize=16,color="green",shape="box"];29[label="vz60 : vz61 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];29 -> 40[label="",style="solid", color="black", weight=3];
30[label="[] >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];30 -> 41[label="",style="solid", color="black", weight=3];
91[label="[]",fontsize=16,color="green",shape="box"];90[label="primretIO vz13",fontsize=16,color="black",shape="triangle"];90 -> 93[label="",style="solid", color="black", weight=3];
122[label="vz15 : []",fontsize=16,color="green",shape="box"];37[label="vz40",fontsize=16,color="green",shape="box"];33[label="primbindIO (IO vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
34[label="primbindIO (AProVE_IO vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
35[label="primbindIO (AProVE_Exception vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
36[label="primbindIO (AProVE_Error vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
38[label="Nothing",fontsize=16,color="green",shape="box"];39[label="Monad.filterM1 vz3 vz41 vz40 vz50",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
40 -> 47[label="",style="dashed", color="red", weight=0];
40[label="Monad.filterM1 vz3 vz41 vz40 vz60 ++ (vz61 >>= Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="magenta"];40 -> 48[label="",style="dashed", color="magenta", weight=3];
41[label="[]",fontsize=16,color="green",shape="box"];93[label="AProVE_IO vz13",fontsize=16,color="green",shape="box"];42[label="error []",fontsize=16,color="red",shape="box"];43[label="Monad.filterM1 vz3 vz41 vz40 vz70",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
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48 -> 18[label="",style="dashed", color="red", weight=0];
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49 -> 54[label="",style="dashed", color="red", weight=0];
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51 -> 4[label="",style="dashed", color="red", weight=0];
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142 -> 57[label="",style="solid", color="burlywood", weight=3];
143[label="vz9/Just vz90",fontsize=10,color="white",style="solid",shape="box"];50 -> 143[label="",style="solid", color="burlywood", weight=9];
143 -> 58[label="",style="solid", color="burlywood", weight=3];
52[label="vz61",fontsize=16,color="green",shape="box"];53 -> 59[label="",style="dashed", color="red", weight=0];
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55 -> 4[label="",style="dashed", color="red", weight=0];
55[label="Monad.filterM vz3 vz41",fontsize=16,color="magenta"];55 -> 61[label="",style="dashed", color="magenta", weight=3];
54[label="vz10 >>= Monad.filterM0 vz70 vz40",fontsize=16,color="black",shape="triangle"];54 -> 62[label="",style="solid", color="black", weight=3];
56[label="vz41",fontsize=16,color="green",shape="box"];57[label="Nothing >>= Monad.filterM0 vz50 vz40",fontsize=16,color="black",shape="box"];57 -> 63[label="",style="solid", color="black", weight=3];
58[label="Just vz90 >>= Monad.filterM0 vz50 vz40",fontsize=16,color="black",shape="box"];58 -> 64[label="",style="solid", color="black", weight=3];
60 -> 4[label="",style="dashed", color="red", weight=0];
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59[label="(vz11 >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="burlywood",shape="triangle"];144[label="vz11/vz110 : vz111",fontsize=10,color="white",style="solid",shape="box"];59 -> 144[label="",style="solid", color="burlywood", weight=9];
144 -> 66[label="",style="solid", color="burlywood", weight=3];
145[label="vz11/[]",fontsize=10,color="white",style="solid",shape="box"];59 -> 145[label="",style="solid", color="burlywood", weight=9];
145 -> 67[label="",style="solid", color="burlywood", weight=3];
61[label="vz41",fontsize=16,color="green",shape="box"];62[label="primbindIO vz10 (Monad.filterM0 vz70 vz40)",fontsize=16,color="burlywood",shape="box"];146[label="vz10/IO vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 146[label="",style="solid", color="burlywood", weight=9];
146 -> 68[label="",style="solid", color="burlywood", weight=3];
147[label="vz10/AProVE_IO vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 147[label="",style="solid", color="burlywood", weight=9];
147 -> 69[label="",style="solid", color="burlywood", weight=3];
148[label="vz10/AProVE_Exception vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 148[label="",style="solid", color="burlywood", weight=9];
148 -> 70[label="",style="solid", color="burlywood", weight=3];
149[label="vz10/AProVE_Error vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 149[label="",style="solid", color="burlywood", weight=9];
149 -> 71[label="",style="solid", color="burlywood", weight=3];
63[label="Nothing",fontsize=16,color="green",shape="box"];64[label="Monad.filterM0 vz50 vz40 vz90",fontsize=16,color="black",shape="box"];64 -> 72[label="",style="solid", color="black", weight=3];
65[label="vz41",fontsize=16,color="green",shape="box"];66[label="(vz110 : vz111 >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="black",shape="box"];66 -> 73[label="",style="solid", color="black", weight=3];
67[label="([] >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
68[label="primbindIO (IO vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];68 -> 75[label="",style="solid", color="black", weight=3];
69[label="primbindIO (AProVE_IO vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];69 -> 76[label="",style="solid", color="black", weight=3];
70[label="primbindIO (AProVE_Exception vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3];
71[label="primbindIO (AProVE_Error vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3];
72[label="return (Monad.filterM00 vz40 vz90 vz50)",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3];
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74[label="[] ++ vz8",fontsize=16,color="black",shape="triangle"];74 -> 81[label="",style="solid", color="black", weight=3];
75[label="error []",fontsize=16,color="red",shape="box"];76[label="Monad.filterM0 vz70 vz40 vz100",fontsize=16,color="black",shape="box"];76 -> 82[label="",style="solid", color="black", weight=3];
77[label="AProVE_Exception vz100",fontsize=16,color="green",shape="box"];78[label="AProVE_Error vz100",fontsize=16,color="green",shape="box"];79[label="Just (Monad.filterM00 vz40 vz90 vz50)",fontsize=16,color="green",shape="box"];79 -> 83[label="",style="dashed", color="green", weight=3];
80[label="(return (Monad.filterM00 vz40 vz110 vz60) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3];
81[label="vz8",fontsize=16,color="green",shape="box"];82[label="return (Monad.filterM00 vz40 vz100 vz70)",fontsize=16,color="black",shape="box"];82 -> 85[label="",style="solid", color="black", weight=3];
83[label="Monad.filterM00 vz40 vz90 vz50",fontsize=16,color="burlywood",shape="triangle"];150[label="vz50/False",fontsize=10,color="white",style="solid",shape="box"];83 -> 150[label="",style="solid", color="burlywood", weight=9];
150 -> 86[label="",style="solid", color="burlywood", weight=3];
151[label="vz50/True",fontsize=10,color="white",style="solid",shape="box"];83 -> 151[label="",style="solid", color="burlywood", weight=9];
151 -> 87[label="",style="solid", color="burlywood", weight=3];
84 -> 88[label="",style="dashed", color="red", weight=0];
84[label="((Monad.filterM00 vz40 vz110 vz60 : []) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="magenta"];84 -> 89[label="",style="dashed", color="magenta", weight=3];
85 -> 90[label="",style="dashed", color="red", weight=0];
85[label="primretIO (Monad.filterM00 vz40 vz100 vz70)",fontsize=16,color="magenta"];85 -> 92[label="",style="dashed", color="magenta", weight=3];
86[label="Monad.filterM00 vz40 vz90 False",fontsize=16,color="black",shape="box"];86 -> 94[label="",style="solid", color="black", weight=3];
87[label="Monad.filterM00 vz40 vz90 True",fontsize=16,color="black",shape="box"];87 -> 95[label="",style="solid", color="black", weight=3];
89 -> 83[label="",style="dashed", color="red", weight=0];
89[label="Monad.filterM00 vz40 vz110 vz60",fontsize=16,color="magenta"];89 -> 96[label="",style="dashed", color="magenta", weight=3];
89 -> 97[label="",style="dashed", color="magenta", weight=3];
88[label="((vz12 : []) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="black",shape="triangle"];88 -> 98[label="",style="solid", color="black", weight=3];
92 -> 83[label="",style="dashed", color="red", weight=0];
92[label="Monad.filterM00 vz40 vz100 vz70",fontsize=16,color="magenta"];92 -> 99[label="",style="dashed", color="magenta", weight=3];
92 -> 100[label="",style="dashed", color="magenta", weight=3];
94[label="vz90",fontsize=16,color="green",shape="box"];95[label="vz40 : vz90",fontsize=16,color="green",shape="box"];96[label="vz60",fontsize=16,color="green",shape="box"];97[label="vz110",fontsize=16,color="green",shape="box"];98 -> 101[label="",style="dashed", color="red", weight=0];
98[label="(vz12 : [] ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="magenta"];98 -> 102[label="",style="dashed", color="magenta", weight=3];
99[label="vz70",fontsize=16,color="green",shape="box"];100[label="vz100",fontsize=16,color="green",shape="box"];102 -> 74[label="",style="dashed", color="red", weight=0];
102[label="[] ++ (vz111 >>= Monad.filterM0 vz60 vz40)",fontsize=16,color="magenta"];102 -> 103[label="",style="dashed", color="magenta", weight=3];
101[label="(vz12 : vz14) ++ vz8",fontsize=16,color="black",shape="triangle"];101 -> 104[label="",style="solid", color="black", weight=3];
103[label="vz111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="burlywood",shape="triangle"];152[label="vz111/vz1110 : vz1111",fontsize=10,color="white",style="solid",shape="box"];103 -> 152[label="",style="solid", color="burlywood", weight=9];
152 -> 105[label="",style="solid", color="burlywood", weight=3];
153[label="vz111/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 153[label="",style="solid", color="burlywood", weight=9];
153 -> 106[label="",style="solid", color="burlywood", weight=3];
104[label="vz12 : vz14 ++ vz8",fontsize=16,color="green",shape="box"];104 -> 107[label="",style="dashed", color="green", weight=3];
105[label="vz1110 : vz1111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="black",shape="box"];105 -> 108[label="",style="solid", color="black", weight=3];
106[label="[] >>= Monad.filterM0 vz60 vz40",fontsize=16,color="black",shape="box"];106 -> 109[label="",style="solid", color="black", weight=3];
107[label="vz14 ++ vz8",fontsize=16,color="burlywood",shape="triangle"];154[label="vz14/vz140 : vz141",fontsize=10,color="white",style="solid",shape="box"];107 -> 154[label="",style="solid", color="burlywood", weight=9];
154 -> 110[label="",style="solid", color="burlywood", weight=3];
155[label="vz14/[]",fontsize=10,color="white",style="solid",shape="box"];107 -> 155[label="",style="solid", color="burlywood", weight=9];
155 -> 111[label="",style="solid", color="burlywood", weight=3];
108 -> 107[label="",style="dashed", color="red", weight=0];
108[label="Monad.filterM0 vz60 vz40 vz1110 ++ (vz1111 >>= Monad.filterM0 vz60 vz40)",fontsize=16,color="magenta"];108 -> 112[label="",style="dashed", color="magenta", weight=3];
108 -> 113[label="",style="dashed", color="magenta", weight=3];
109[label="[]",fontsize=16,color="green",shape="box"];110[label="(vz140 : vz141) ++ vz8",fontsize=16,color="black",shape="box"];110 -> 114[label="",style="solid", color="black", weight=3];
111[label="[] ++ vz8",fontsize=16,color="black",shape="box"];111 -> 115[label="",style="solid", color="black", weight=3];
112 -> 103[label="",style="dashed", color="red", weight=0];
112[label="vz1111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="magenta"];112 -> 116[label="",style="dashed", color="magenta", weight=3];
113[label="Monad.filterM0 vz60 vz40 vz1110",fontsize=16,color="black",shape="box"];113 -> 117[label="",style="solid", color="black", weight=3];
114[label="vz140 : vz141 ++ vz8",fontsize=16,color="green",shape="box"];114 -> 118[label="",style="dashed", color="green", weight=3];
115[label="vz8",fontsize=16,color="green",shape="box"];116[label="vz1111",fontsize=16,color="green",shape="box"];117 -> 119[label="",style="dashed", color="red", weight=0];
117[label="return (Monad.filterM00 vz40 vz1110 vz60)",fontsize=16,color="magenta"];117 -> 121[label="",style="dashed", color="magenta", weight=3];
118 -> 107[label="",style="dashed", color="red", weight=0];
118[label="vz141 ++ vz8",fontsize=16,color="magenta"];118 -> 123[label="",style="dashed", color="magenta", weight=3];
121 -> 83[label="",style="dashed", color="red", weight=0];
121[label="Monad.filterM00 vz40 vz1110 vz60",fontsize=16,color="magenta"];121 -> 124[label="",style="dashed", color="magenta", weight=3];
121 -> 125[label="",style="dashed", color="magenta", weight=3];
123[label="vz141",fontsize=16,color="green",shape="box"];124[label="vz60",fontsize=16,color="green",shape="box"];125[label="vz1110",fontsize=16,color="green",shape="box"];}

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

(10)
Complex Obligation (AND)

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

(11)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_psPs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_[], h)
   new_primbindIO(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_IO, h)
   new_filterM(vz3, :(vz40, vz41), ty_Maybe, h) -> new_gtGtEs0(vz3, vz41, vz40, h)
   new_gtGtEs1(vz3, vz41, vz40, h) -> new_psPs0(vz3, vz41, vz40, h)
   new_filterM(vz3, :(vz40, vz41), ty_IO, h) -> new_primbindIO(vz3, vz41, vz40, h)
   new_gtGtEs1(vz3, vz41, vz40, h) -> new_gtGtEs1(vz3, vz41, vz40, h)
   new_filterM(vz3, :(vz40, vz41), ty_[], h) -> new_gtGtEs1(vz3, vz41, vz40, h)
   new_gtGtEs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_Maybe, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(12) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
----------------------------------------

(13)
Complex Obligation (AND)

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

(14)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_Maybe, h)
   new_filterM(vz3, :(vz40, vz41), ty_Maybe, h) -> new_gtGtEs0(vz3, vz41, vz40, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(15) 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_filterM(vz3, :(vz40, vz41), ty_Maybe, h) -> new_gtGtEs0(vz3, vz41, vz40, h)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 4 >= 4


*new_gtGtEs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_Maybe, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4


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

(16)
YES

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

(17)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_filterM(vz3, :(vz40, vz41), ty_IO, h) -> new_primbindIO(vz3, vz41, vz40, h)
   new_primbindIO(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_IO, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(18) 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_primbindIO(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_IO, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 >= 4


*new_filterM(vz3, :(vz40, vz41), ty_IO, h) -> new_primbindIO(vz3, vz41, vz40, h)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 4 >= 4


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

(19)
YES

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

(20)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_filterM(vz3, :(vz40, vz41), ty_[], h) -> new_gtGtEs1(vz3, vz41, vz40, h)
   new_gtGtEs1(vz3, vz41, vz40, h) -> new_psPs0(vz3, vz41, vz40, h)
   new_psPs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_[], h)
   new_gtGtEs1(vz3, vz41, vz40, h) -> new_gtGtEs1(vz3, vz41, vz40, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(21) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   new_filterM(vz3, :(vz40, vz41), ty_[], h) -> new_gtGtEs1(vz3, vz41, vz40, h)
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(:(x_1, x_2)) = 1 + x_1 + x_2
   POL(new_filterM(x_1, x_2, x_3, x_4)) = 1 + x_2 + x_3
   POL(new_gtGtEs1(x_1, x_2, x_3, x_4)) = 1 + x_2 + x_3
   POL(new_psPs0(x_1, x_2, x_3, x_4)) = 1 + x_2 + x_3
   POL(ty_[]) = 0

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none


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

(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs1(vz3, vz41, vz40, h) -> new_psPs0(vz3, vz41, vz40, h)
   new_psPs0(vz3, vz41, vz40, h) -> new_filterM(vz3, vz41, ty_[], h)
   new_gtGtEs1(vz3, vz41, vz40, h) -> new_gtGtEs1(vz3, vz41, vz40, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(23) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
----------------------------------------

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

   new_gtGtEs1(vz3, vz41, vz40, h) -> new_gtGtEs1(vz3, vz41, vz40, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

The set Q consists of the following terms:

   new_filterM00(x0, x1, True, x2)
   new_psPs4(x0, x1, x2, x3)
   new_psPs1(x0, x1, x2, x3, x4, x5)
   new_psPs2(:(x0, x1), x2, x3, x4, x5)
   new_gtGtEs3(:(x0, x1), x2, x3, x4)
   new_filterM00(x0, x1, False, x2)
   new_psPs2([], x0, x1, x2, x3)
   new_return(x0, x1)
   new_gtGtEs2([], x0, x1, x2, x3)
   new_gtGtEs3([], x0, x1, x2)
   new_gtGtEs2(:(x0, x1), x2, x3, x4, x5)
   new_psPs5(x0, x1)
   new_psPs6([], x0, x1)
   new_psPs6(:(x0, x1), x2, x3)
   new_psPs3(x0, x1, x2, x3, x4, x5)

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

(25) MNOCProof (EQUIVALENT)
We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
----------------------------------------

(26)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs1(vz3, vz41, vz40, h) -> new_gtGtEs1(vz3, vz41, vz40, h)

The TRS R consists of the following rules:

   new_gtGtEs3([], vz60, vz40, h) -> []
   new_psPs6(:(vz140, vz141), vz8, h) -> :(vz140, new_psPs6(vz141, vz8, h))
   new_psPs2(:(vz110, vz111), vz60, vz40, vz8, h) -> new_psPs3(new_filterM00(vz40, vz110, vz60, h), vz111, vz60, vz40, vz8, h)
   new_gtGtEs2(:(vz60, vz61), vz3, vz41, vz40, h) -> new_psPs1(vz3, vz41, vz40, vz60, new_gtGtEs2(vz61, vz3, vz41, vz40, h), h)
   new_psPs3(vz12, vz111, vz60, vz40, vz8, h) -> new_psPs4(vz12, new_psPs5(new_gtGtEs3(vz111, vz60, vz40, h), h), vz8, h)
   new_psPs4(vz12, vz14, vz8, h) -> :(vz12, new_psPs6(vz14, vz8, h))
   new_gtGtEs3(:(vz1110, vz1111), vz60, vz40, h) -> new_psPs6(new_return(new_filterM00(vz40, vz1110, vz60, h), h), new_gtGtEs3(vz1111, vz60, vz40, h), h)
   new_filterM00(vz40, vz90, False, h) -> vz90
   new_psPs6([], vz8, h) -> vz8
   new_gtGtEs2([], vz3, vz41, vz40, h) -> []
   new_return(vz15, h) -> :(vz15, [])
   new_psPs2([], vz60, vz40, vz8, h) -> new_psPs5(vz8, h)
   new_psPs1(vz3, vz41, vz40, vz60, vz8, h) -> new_psPs2(new_filterM0(vz3, vz41, ty_[], h), vz60, vz40, vz8, h)
   new_psPs5(vz8, h) -> vz8
   new_filterM00(vz40, vz90, True, h) -> :(vz40, vz90)

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

(27) NonTerminationLoopProof (COMPLETE)
We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = new_gtGtEs1(vz3, vz41, vz40, h) evaluates to  t =new_gtGtEs1(vz3, vz41, vz40, h)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
* Matcher: [ ]
* Semiunifier: [ ]

--------------------------------------------------------------------------------
Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_gtGtEs1(vz3, vz41, vz40, h) to new_gtGtEs1(vz3, vz41, vz40, h).




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

(28)
NO

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

(29)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_gtGtEs(:(vz1110, vz1111), vz60, vz40, h) -> new_gtGtEs(vz1111, vz60, vz40, h)

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

(30) 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(:(vz1110, vz1111), vz60, vz40, h) -> new_gtGtEs(vz1111, vz60, vz40, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4


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

(31)
YES

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

(32)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_psPs(:(vz140, vz141), vz8, h) -> new_psPs(vz141, vz8, h)

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

(33) 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(:(vz140, vz141), vz8, h) -> new_psPs(vz141, vz8, h)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(34)
YES

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

(35) Narrow (COMPLETE)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Monad.filterM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Monad.filterM vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="Monad.filterM vz3 vz4",fontsize=16,color="burlywood",shape="triangle"];126[label="vz4/vz40 : vz41",fontsize=10,color="white",style="solid",shape="box"];4 -> 126[label="",style="solid", color="burlywood", weight=9];
126 -> 5[label="",style="solid", color="burlywood", weight=3];
127[label="vz4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 127[label="",style="solid", color="burlywood", weight=9];
127 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="Monad.filterM vz3 (vz40 : vz41)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="Monad.filterM vz3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="vz3 vz40 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="blue",shape="box"];128[label=">>= :: (IO Bool) -> (Bool -> IO ([] a)) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 128[label="",style="solid", color="blue", weight=9];
128 -> 9[label="",style="solid", color="blue", weight=3];
129[label=">>= :: (Maybe Bool) -> (Bool -> Maybe ([] a)) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 129[label="",style="solid", color="blue", weight=9];
129 -> 10[label="",style="solid", color="blue", weight=3];
130[label=">>= :: ([] Bool) -> (Bool -> [] ([] a)) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 130[label="",style="solid", color="blue", weight=9];
130 -> 11[label="",style="solid", color="blue", weight=3];
8[label="return []",fontsize=16,color="blue",shape="box"];131[label="return :: ([] a) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];8 -> 131[label="",style="solid", color="blue", weight=9];
131 -> 12[label="",style="solid", color="blue", weight=3];
132[label="return :: ([] a) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];8 -> 132[label="",style="solid", color="blue", weight=9];
132 -> 13[label="",style="solid", color="blue", weight=3];
133[label="return :: ([] a) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];8 -> 133[label="",style="solid", color="blue", weight=9];
133 -> 14[label="",style="solid", color="blue", weight=3];
9[label="vz3 vz40 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];9 -> 15[label="",style="solid", color="black", weight=3];
10 -> 16[label="",style="dashed", color="red", weight=0];
10[label="vz3 vz40 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="magenta"];10 -> 17[label="",style="dashed", color="magenta", weight=3];
11 -> 18[label="",style="dashed", color="red", weight=0];
11[label="vz3 vz40 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="magenta"];11 -> 19[label="",style="dashed", color="magenta", weight=3];
12[label="return []",fontsize=16,color="black",shape="box"];12 -> 20[label="",style="solid", color="black", weight=3];
13[label="return []",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3];
14 -> 119[label="",style="dashed", color="red", weight=0];
14[label="return []",fontsize=16,color="magenta"];14 -> 120[label="",style="dashed", color="magenta", weight=3];
15 -> 23[label="",style="dashed", color="red", weight=0];
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17[label="vz3 vz40",fontsize=16,color="green",shape="box"];17 -> 25[label="",style="dashed", color="green", weight=3];
16[label="vz5 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="burlywood",shape="triangle"];134[label="vz5/Nothing",fontsize=10,color="white",style="solid",shape="box"];16 -> 134[label="",style="solid", color="burlywood", weight=9];
134 -> 26[label="",style="solid", color="burlywood", weight=3];
135[label="vz5/Just vz50",fontsize=10,color="white",style="solid",shape="box"];16 -> 135[label="",style="solid", color="burlywood", weight=9];
135 -> 27[label="",style="solid", color="burlywood", weight=3];
19[label="vz3 vz40",fontsize=16,color="green",shape="box"];19 -> 28[label="",style="dashed", color="green", weight=3];
18[label="vz6 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="burlywood",shape="triangle"];136[label="vz6/vz60 : vz61",fontsize=10,color="white",style="solid",shape="box"];18 -> 136[label="",style="solid", color="burlywood", weight=9];
136 -> 29[label="",style="solid", color="burlywood", weight=3];
137[label="vz6/[]",fontsize=10,color="white",style="solid",shape="box"];18 -> 137[label="",style="solid", color="burlywood", weight=9];
137 -> 30[label="",style="solid", color="burlywood", weight=3];
20 -> 90[label="",style="dashed", color="red", weight=0];
20[label="primretIO []",fontsize=16,color="magenta"];20 -> 91[label="",style="dashed", color="magenta", weight=3];
21[label="Just []",fontsize=16,color="green",shape="box"];120[label="[]",fontsize=16,color="green",shape="box"];119[label="return vz15",fontsize=16,color="black",shape="triangle"];119 -> 122[label="",style="solid", color="black", weight=3];
24[label="vz3 vz40",fontsize=16,color="green",shape="box"];24 -> 37[label="",style="dashed", color="green", weight=3];
23[label="primbindIO vz7 (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="burlywood",shape="triangle"];138[label="vz7/IO vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 138[label="",style="solid", color="burlywood", weight=9];
138 -> 33[label="",style="solid", color="burlywood", weight=3];
139[label="vz7/AProVE_IO vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 139[label="",style="solid", color="burlywood", weight=9];
139 -> 34[label="",style="solid", color="burlywood", weight=3];
140[label="vz7/AProVE_Exception vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 140[label="",style="solid", color="burlywood", weight=9];
140 -> 35[label="",style="solid", color="burlywood", weight=3];
141[label="vz7/AProVE_Error vz70",fontsize=10,color="white",style="solid",shape="box"];23 -> 141[label="",style="solid", color="burlywood", weight=9];
141 -> 36[label="",style="solid", color="burlywood", weight=3];
25[label="vz40",fontsize=16,color="green",shape="box"];26[label="Nothing >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];26 -> 38[label="",style="solid", color="black", weight=3];
27[label="Just vz50 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];27 -> 39[label="",style="solid", color="black", weight=3];
28[label="vz40",fontsize=16,color="green",shape="box"];29[label="vz60 : vz61 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];29 -> 40[label="",style="solid", color="black", weight=3];
30[label="[] >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="black",shape="box"];30 -> 41[label="",style="solid", color="black", weight=3];
91[label="[]",fontsize=16,color="green",shape="box"];90[label="primretIO vz13",fontsize=16,color="black",shape="triangle"];90 -> 93[label="",style="solid", color="black", weight=3];
122[label="vz15 : []",fontsize=16,color="green",shape="box"];37[label="vz40",fontsize=16,color="green",shape="box"];33[label="primbindIO (IO vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
34[label="primbindIO (AProVE_IO vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
35[label="primbindIO (AProVE_Exception vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
36[label="primbindIO (AProVE_Error vz70) (Monad.filterM1 vz3 vz41 vz40)",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
38[label="Nothing",fontsize=16,color="green",shape="box"];39[label="Monad.filterM1 vz3 vz41 vz40 vz50",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
40 -> 47[label="",style="dashed", color="red", weight=0];
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41[label="[]",fontsize=16,color="green",shape="box"];93[label="AProVE_IO vz13",fontsize=16,color="green",shape="box"];42[label="error []",fontsize=16,color="red",shape="box"];43[label="Monad.filterM1 vz3 vz41 vz40 vz70",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
44[label="AProVE_Exception vz70",fontsize=16,color="green",shape="box"];45[label="AProVE_Error vz70",fontsize=16,color="green",shape="box"];46 -> 50[label="",style="dashed", color="red", weight=0];
46[label="Monad.filterM vz3 vz41 >>= Monad.filterM0 vz50 vz40",fontsize=16,color="magenta"];46 -> 51[label="",style="dashed", color="magenta", weight=3];
48 -> 18[label="",style="dashed", color="red", weight=0];
48[label="vz61 >>= Monad.filterM1 vz3 vz41 vz40",fontsize=16,color="magenta"];48 -> 52[label="",style="dashed", color="magenta", weight=3];
47[label="Monad.filterM1 vz3 vz41 vz40 vz60 ++ vz8",fontsize=16,color="black",shape="triangle"];47 -> 53[label="",style="solid", color="black", weight=3];
49 -> 54[label="",style="dashed", color="red", weight=0];
49[label="Monad.filterM vz3 vz41 >>= Monad.filterM0 vz70 vz40",fontsize=16,color="magenta"];49 -> 55[label="",style="dashed", color="magenta", weight=3];
51 -> 4[label="",style="dashed", color="red", weight=0];
51[label="Monad.filterM vz3 vz41",fontsize=16,color="magenta"];51 -> 56[label="",style="dashed", color="magenta", weight=3];
50[label="vz9 >>= Monad.filterM0 vz50 vz40",fontsize=16,color="burlywood",shape="triangle"];142[label="vz9/Nothing",fontsize=10,color="white",style="solid",shape="box"];50 -> 142[label="",style="solid", color="burlywood", weight=9];
142 -> 57[label="",style="solid", color="burlywood", weight=3];
143[label="vz9/Just vz90",fontsize=10,color="white",style="solid",shape="box"];50 -> 143[label="",style="solid", color="burlywood", weight=9];
143 -> 58[label="",style="solid", color="burlywood", weight=3];
52[label="vz61",fontsize=16,color="green",shape="box"];53 -> 59[label="",style="dashed", color="red", weight=0];
53[label="(Monad.filterM vz3 vz41 >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="magenta"];53 -> 60[label="",style="dashed", color="magenta", weight=3];
55 -> 4[label="",style="dashed", color="red", weight=0];
55[label="Monad.filterM vz3 vz41",fontsize=16,color="magenta"];55 -> 61[label="",style="dashed", color="magenta", weight=3];
54[label="vz10 >>= Monad.filterM0 vz70 vz40",fontsize=16,color="black",shape="triangle"];54 -> 62[label="",style="solid", color="black", weight=3];
56[label="vz41",fontsize=16,color="green",shape="box"];57[label="Nothing >>= Monad.filterM0 vz50 vz40",fontsize=16,color="black",shape="box"];57 -> 63[label="",style="solid", color="black", weight=3];
58[label="Just vz90 >>= Monad.filterM0 vz50 vz40",fontsize=16,color="black",shape="box"];58 -> 64[label="",style="solid", color="black", weight=3];
60 -> 4[label="",style="dashed", color="red", weight=0];
60[label="Monad.filterM vz3 vz41",fontsize=16,color="magenta"];60 -> 65[label="",style="dashed", color="magenta", weight=3];
59[label="(vz11 >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="burlywood",shape="triangle"];144[label="vz11/vz110 : vz111",fontsize=10,color="white",style="solid",shape="box"];59 -> 144[label="",style="solid", color="burlywood", weight=9];
144 -> 66[label="",style="solid", color="burlywood", weight=3];
145[label="vz11/[]",fontsize=10,color="white",style="solid",shape="box"];59 -> 145[label="",style="solid", color="burlywood", weight=9];
145 -> 67[label="",style="solid", color="burlywood", weight=3];
61[label="vz41",fontsize=16,color="green",shape="box"];62[label="primbindIO vz10 (Monad.filterM0 vz70 vz40)",fontsize=16,color="burlywood",shape="box"];146[label="vz10/IO vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 146[label="",style="solid", color="burlywood", weight=9];
146 -> 68[label="",style="solid", color="burlywood", weight=3];
147[label="vz10/AProVE_IO vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 147[label="",style="solid", color="burlywood", weight=9];
147 -> 69[label="",style="solid", color="burlywood", weight=3];
148[label="vz10/AProVE_Exception vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 148[label="",style="solid", color="burlywood", weight=9];
148 -> 70[label="",style="solid", color="burlywood", weight=3];
149[label="vz10/AProVE_Error vz100",fontsize=10,color="white",style="solid",shape="box"];62 -> 149[label="",style="solid", color="burlywood", weight=9];
149 -> 71[label="",style="solid", color="burlywood", weight=3];
63[label="Nothing",fontsize=16,color="green",shape="box"];64[label="Monad.filterM0 vz50 vz40 vz90",fontsize=16,color="black",shape="box"];64 -> 72[label="",style="solid", color="black", weight=3];
65[label="vz41",fontsize=16,color="green",shape="box"];66[label="(vz110 : vz111 >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="black",shape="box"];66 -> 73[label="",style="solid", color="black", weight=3];
67[label="([] >>= Monad.filterM0 vz60 vz40) ++ vz8",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
68[label="primbindIO (IO vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];68 -> 75[label="",style="solid", color="black", weight=3];
69[label="primbindIO (AProVE_IO vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];69 -> 76[label="",style="solid", color="black", weight=3];
70[label="primbindIO (AProVE_Exception vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3];
71[label="primbindIO (AProVE_Error vz100) (Monad.filterM0 vz70 vz40)",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3];
72[label="return (Monad.filterM00 vz40 vz90 vz50)",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3];
73[label="(Monad.filterM0 vz60 vz40 vz110 ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="black",shape="box"];73 -> 80[label="",style="solid", color="black", weight=3];
74[label="[] ++ vz8",fontsize=16,color="black",shape="triangle"];74 -> 81[label="",style="solid", color="black", weight=3];
75[label="error []",fontsize=16,color="red",shape="box"];76[label="Monad.filterM0 vz70 vz40 vz100",fontsize=16,color="black",shape="box"];76 -> 82[label="",style="solid", color="black", weight=3];
77[label="AProVE_Exception vz100",fontsize=16,color="green",shape="box"];78[label="AProVE_Error vz100",fontsize=16,color="green",shape="box"];79[label="Just (Monad.filterM00 vz40 vz90 vz50)",fontsize=16,color="green",shape="box"];79 -> 83[label="",style="dashed", color="green", weight=3];
80[label="(return (Monad.filterM00 vz40 vz110 vz60) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3];
81[label="vz8",fontsize=16,color="green",shape="box"];82[label="return (Monad.filterM00 vz40 vz100 vz70)",fontsize=16,color="black",shape="box"];82 -> 85[label="",style="solid", color="black", weight=3];
83[label="Monad.filterM00 vz40 vz90 vz50",fontsize=16,color="burlywood",shape="triangle"];150[label="vz50/False",fontsize=10,color="white",style="solid",shape="box"];83 -> 150[label="",style="solid", color="burlywood", weight=9];
150 -> 86[label="",style="solid", color="burlywood", weight=3];
151[label="vz50/True",fontsize=10,color="white",style="solid",shape="box"];83 -> 151[label="",style="solid", color="burlywood", weight=9];
151 -> 87[label="",style="solid", color="burlywood", weight=3];
84 -> 88[label="",style="dashed", color="red", weight=0];
84[label="((Monad.filterM00 vz40 vz110 vz60 : []) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="magenta"];84 -> 89[label="",style="dashed", color="magenta", weight=3];
85 -> 90[label="",style="dashed", color="red", weight=0];
85[label="primretIO (Monad.filterM00 vz40 vz100 vz70)",fontsize=16,color="magenta"];85 -> 92[label="",style="dashed", color="magenta", weight=3];
86[label="Monad.filterM00 vz40 vz90 False",fontsize=16,color="black",shape="box"];86 -> 94[label="",style="solid", color="black", weight=3];
87[label="Monad.filterM00 vz40 vz90 True",fontsize=16,color="black",shape="box"];87 -> 95[label="",style="solid", color="black", weight=3];
89 -> 83[label="",style="dashed", color="red", weight=0];
89[label="Monad.filterM00 vz40 vz110 vz60",fontsize=16,color="magenta"];89 -> 96[label="",style="dashed", color="magenta", weight=3];
89 -> 97[label="",style="dashed", color="magenta", weight=3];
88[label="((vz12 : []) ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="black",shape="triangle"];88 -> 98[label="",style="solid", color="black", weight=3];
92 -> 83[label="",style="dashed", color="red", weight=0];
92[label="Monad.filterM00 vz40 vz100 vz70",fontsize=16,color="magenta"];92 -> 99[label="",style="dashed", color="magenta", weight=3];
92 -> 100[label="",style="dashed", color="magenta", weight=3];
94[label="vz90",fontsize=16,color="green",shape="box"];95[label="vz40 : vz90",fontsize=16,color="green",shape="box"];96[label="vz60",fontsize=16,color="green",shape="box"];97[label="vz110",fontsize=16,color="green",shape="box"];98 -> 101[label="",style="dashed", color="red", weight=0];
98[label="(vz12 : [] ++ (vz111 >>= Monad.filterM0 vz60 vz40)) ++ vz8",fontsize=16,color="magenta"];98 -> 102[label="",style="dashed", color="magenta", weight=3];
99[label="vz70",fontsize=16,color="green",shape="box"];100[label="vz100",fontsize=16,color="green",shape="box"];102 -> 74[label="",style="dashed", color="red", weight=0];
102[label="[] ++ (vz111 >>= Monad.filterM0 vz60 vz40)",fontsize=16,color="magenta"];102 -> 103[label="",style="dashed", color="magenta", weight=3];
101[label="(vz12 : vz14) ++ vz8",fontsize=16,color="black",shape="triangle"];101 -> 104[label="",style="solid", color="black", weight=3];
103[label="vz111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="burlywood",shape="triangle"];152[label="vz111/vz1110 : vz1111",fontsize=10,color="white",style="solid",shape="box"];103 -> 152[label="",style="solid", color="burlywood", weight=9];
152 -> 105[label="",style="solid", color="burlywood", weight=3];
153[label="vz111/[]",fontsize=10,color="white",style="solid",shape="box"];103 -> 153[label="",style="solid", color="burlywood", weight=9];
153 -> 106[label="",style="solid", color="burlywood", weight=3];
104[label="vz12 : vz14 ++ vz8",fontsize=16,color="green",shape="box"];104 -> 107[label="",style="dashed", color="green", weight=3];
105[label="vz1110 : vz1111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="black",shape="box"];105 -> 108[label="",style="solid", color="black", weight=3];
106[label="[] >>= Monad.filterM0 vz60 vz40",fontsize=16,color="black",shape="box"];106 -> 109[label="",style="solid", color="black", weight=3];
107[label="vz14 ++ vz8",fontsize=16,color="burlywood",shape="triangle"];154[label="vz14/vz140 : vz141",fontsize=10,color="white",style="solid",shape="box"];107 -> 154[label="",style="solid", color="burlywood", weight=9];
154 -> 110[label="",style="solid", color="burlywood", weight=3];
155[label="vz14/[]",fontsize=10,color="white",style="solid",shape="box"];107 -> 155[label="",style="solid", color="burlywood", weight=9];
155 -> 111[label="",style="solid", color="burlywood", weight=3];
108 -> 107[label="",style="dashed", color="red", weight=0];
108[label="Monad.filterM0 vz60 vz40 vz1110 ++ (vz1111 >>= Monad.filterM0 vz60 vz40)",fontsize=16,color="magenta"];108 -> 112[label="",style="dashed", color="magenta", weight=3];
108 -> 113[label="",style="dashed", color="magenta", weight=3];
109[label="[]",fontsize=16,color="green",shape="box"];110[label="(vz140 : vz141) ++ vz8",fontsize=16,color="black",shape="box"];110 -> 114[label="",style="solid", color="black", weight=3];
111[label="[] ++ vz8",fontsize=16,color="black",shape="box"];111 -> 115[label="",style="solid", color="black", weight=3];
112 -> 103[label="",style="dashed", color="red", weight=0];
112[label="vz1111 >>= Monad.filterM0 vz60 vz40",fontsize=16,color="magenta"];112 -> 116[label="",style="dashed", color="magenta", weight=3];
113[label="Monad.filterM0 vz60 vz40 vz1110",fontsize=16,color="black",shape="box"];113 -> 117[label="",style="solid", color="black", weight=3];
114[label="vz140 : vz141 ++ vz8",fontsize=16,color="green",shape="box"];114 -> 118[label="",style="dashed", color="green", weight=3];
115[label="vz8",fontsize=16,color="green",shape="box"];116[label="vz1111",fontsize=16,color="green",shape="box"];117 -> 119[label="",style="dashed", color="red", weight=0];
117[label="return (Monad.filterM00 vz40 vz1110 vz60)",fontsize=16,color="magenta"];117 -> 121[label="",style="dashed", color="magenta", weight=3];
118 -> 107[label="",style="dashed", color="red", weight=0];
118[label="vz141 ++ vz8",fontsize=16,color="magenta"];118 -> 123[label="",style="dashed", color="magenta", weight=3];
121 -> 83[label="",style="dashed", color="red", weight=0];
121[label="Monad.filterM00 vz40 vz1110 vz60",fontsize=16,color="magenta"];121 -> 124[label="",style="dashed", color="magenta", weight=3];
121 -> 125[label="",style="dashed", color="magenta", weight=3];
123[label="vz141",fontsize=16,color="green",shape="box"];124[label="vz60",fontsize=16,color="green",shape="box"];125[label="vz1110",fontsize=16,color="green",shape="box"];}

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

(36)
TRUE