9.22/3.98	YES
11.37/4.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.37/4.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.37/4.57	
11.37/4.57	
11.37/4.57	H-Termination with start terms of the given HASKELL could be proven:
11.37/4.57	
11.37/4.57	(0) HASKELL
11.37/4.57	(1) LR [EQUIVALENT, 0 ms]
11.37/4.57	(2) HASKELL
11.37/4.57	(3) BR [EQUIVALENT, 0 ms]
11.37/4.57	(4) HASKELL
11.37/4.57	(5) COR [EQUIVALENT, 0 ms]
11.37/4.57	(6) HASKELL
11.37/4.57	(7) Narrow [SOUND, 0 ms]
11.37/4.57	(8) AND
11.37/4.57	    (9) QDP
11.37/4.57	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.37/4.57	        (11) YES
11.37/4.57	    (12) QDP
11.37/4.57	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.37/4.57	        (14) YES
11.37/4.57	    (15) QDP
11.37/4.57	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.37/4.57	        (17) YES
11.37/4.57	    (18) QDP
11.37/4.57	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.37/4.57	        (20) YES
11.37/4.57	    (21) QDP
11.37/4.57	        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.37/4.57	        (23) YES
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(0)
11.37/4.57	Obligation:
11.37/4.57	mainModule Main 
11.37/4.57	module Maybe where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Main where {
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Monad where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Prelude;
11.37/4.57	liftM4 :: Monad d => (f  ->  e  ->  c  ->  a  ->  b)  ->  d f  ->  d e  ->  d c  ->  d a  ->  d b;
11.37/4.57	liftM4 f m1 m2 m3 m4 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4)))));
11.37/4.57	
11.37/4.57	}
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(1) LR (EQUIVALENT)
11.37/4.57	Lambda Reductions:
11.37/4.57	The following Lambda expression
11.37/4.57	"\x4->return (f x1 x2 x3 x4)"
11.37/4.57	is transformed to
11.37/4.57	"liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.37/4.57	"
11.37/4.57	The following Lambda expression
11.37/4.57	"\x3->m4 >>= liftM40 f x1 x2 x3"
11.37/4.57	is transformed to
11.37/4.57	"liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.37/4.57	"
11.37/4.57	The following Lambda expression
11.37/4.57	"\x2->m3 >>= liftM41 m4 f x1 x2"
11.37/4.57	is transformed to
11.37/4.57	"liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.37/4.57	"
11.37/4.57	The following Lambda expression
11.37/4.57	"\x1->m2 >>= liftM42 m3 m4 f x1"
11.37/4.57	is transformed to
11.37/4.57	"liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.37/4.57	"
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(2)
11.37/4.57	Obligation:
11.37/4.57	mainModule Main 
11.37/4.57	module Maybe where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Main where {
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Monad where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Prelude;
11.37/4.57	liftM4 :: Monad d => (e  ->  c  ->  b  ->  f  ->  a)  ->  d e  ->  d c  ->  d b  ->  d f  ->  d a;
11.37/4.57	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.37/4.57	
11.37/4.57	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.37/4.57	
11.37/4.57	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.37/4.57	
11.37/4.57	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.37/4.57	
11.37/4.57	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.37/4.57	
11.37/4.57	}
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(3) BR (EQUIVALENT)
11.37/4.57	Replaced joker patterns by fresh variables and removed binding patterns.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(4)
11.37/4.57	Obligation:
11.37/4.57	mainModule Main 
11.37/4.57	module Maybe where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Main where {
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Monad where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Prelude;
11.37/4.57	liftM4 :: Monad a => (e  ->  d  ->  c  ->  f  ->  b)  ->  a e  ->  a d  ->  a c  ->  a f  ->  a b;
11.37/4.57	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.37/4.57	
11.37/4.57	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.37/4.57	
11.37/4.57	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.37/4.57	
11.37/4.57	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.37/4.57	
11.37/4.57	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.37/4.57	
11.37/4.57	}
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(5) COR (EQUIVALENT)
11.37/4.57	Cond Reductions:
11.37/4.57	The following Function with conditions
11.37/4.57	"undefined |Falseundefined;
11.37/4.57	"
11.37/4.57	is transformed to
11.37/4.57	"undefined  = undefined1;
11.37/4.57	"
11.37/4.57	"undefined0 True = undefined;
11.37/4.57	"
11.37/4.57	"undefined1  = undefined0 False;
11.37/4.57	"
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(6)
11.37/4.57	Obligation:
11.37/4.57	mainModule Main 
11.37/4.57	module Maybe where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Main where {
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Monad;
11.37/4.57	import qualified Prelude;
11.37/4.57	}
11.37/4.57	module Monad where {
11.37/4.57	import qualified Main;
11.37/4.57	import qualified Maybe;
11.37/4.57	import qualified Prelude;
11.37/4.57	liftM4 :: Monad e => (b  ->  f  ->  a  ->  c  ->  d)  ->  e b  ->  e f  ->  e a  ->  e c  ->  e d;
11.37/4.57	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.37/4.57	
11.37/4.57	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.37/4.57	
11.37/4.57	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.37/4.57	
11.37/4.57	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.37/4.57	
11.37/4.57	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.37/4.57	
11.37/4.57	}
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(7) Narrow (SOUND)
11.37/4.57	Haskell To QDPs
11.37/4.57	
11.37/4.57	digraph dp_graph {
11.37/4.57	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM4",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.37/4.57	3[label="Monad.liftM4 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.37/4.57	4[label="Monad.liftM4 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.37/4.57	5[label="Monad.liftM4 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.37/4.57	6[label="Monad.liftM4 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
11.37/4.57	7[label="Monad.liftM4 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
11.37/4.57	8[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="blue",shape="box"];153[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];8 -> 153[label="",style="solid", color="blue", weight=9];
11.37/4.57	153 -> 9[label="",style="solid", color="blue", weight=3];
11.37/4.57	154[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];8 -> 154[label="",style="solid", color="blue", weight=9];
11.37/4.57	154 -> 10[label="",style="solid", color="blue", weight=3];
11.37/4.57	155[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];8 -> 155[label="",style="solid", color="blue", weight=9];
11.37/4.57	155 -> 11[label="",style="solid", color="blue", weight=3];
11.37/4.57	9[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="triangle"];156[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 156[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	156 -> 12[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	157[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 157[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	157 -> 13[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	10[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="box"];158[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];10 -> 158[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	158 -> 14[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	159[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];10 -> 159[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	159 -> 15[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	11[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3];
11.37/4.57	12[label="vy40 : vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
11.37/4.57	13[label="[] >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3];
11.37/4.57	14[label="Nothing >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3];
11.37/4.57	15[label="Just vy40 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];15 -> 20[label="",style="solid", color="black", weight=3];
11.37/4.57	16[label="primbindIO vy4 (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="burlywood",shape="box"];160[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];16 -> 160[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	160 -> 21[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	161[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];16 -> 161[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	161 -> 22[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	162[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];16 -> 162[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	162 -> 23[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	163[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];16 -> 163[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	163 -> 24[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	17 -> 67[label="",style="dashed", color="red", weight=0];
11.37/4.57	17[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40 ++ (vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="magenta"];17 -> 68[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	17 -> 69[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	18[label="[]",fontsize=16,color="green",shape="box"];19[label="Nothing",fontsize=16,color="green",shape="box"];20[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];20 -> 27[label="",style="solid", color="black", weight=3];
11.37/4.57	21[label="primbindIO (IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];21 -> 28[label="",style="solid", color="black", weight=3];
11.37/4.57	22[label="primbindIO (AProVE_IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];22 -> 29[label="",style="solid", color="black", weight=3];
11.37/4.57	23[label="primbindIO (AProVE_Exception vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];23 -> 30[label="",style="solid", color="black", weight=3];
11.37/4.57	24[label="primbindIO (AProVE_Error vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];24 -> 31[label="",style="solid", color="black", weight=3];
11.37/4.57	68 -> 9[label="",style="dashed", color="red", weight=0];
11.37/4.57	68[label="vy41 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="magenta"];68 -> 78[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	69[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];69 -> 79[label="",style="solid", color="black", weight=3];
11.37/4.57	67[label="vy9 ++ vy8",fontsize=16,color="burlywood",shape="triangle"];164[label="vy9/vy90 : vy91",fontsize=10,color="white",style="solid",shape="box"];67 -> 164[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	164 -> 80[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	165[label="vy9/[]",fontsize=10,color="white",style="solid",shape="box"];67 -> 165[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	165 -> 81[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	27[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="box"];166[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];27 -> 166[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	166 -> 34[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	167[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];27 -> 167[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	167 -> 35[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	28[label="error []",fontsize=16,color="red",shape="box"];29[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];29 -> 36[label="",style="solid", color="black", weight=3];
11.37/4.57	30[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];31[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];78[label="vy41",fontsize=16,color="green",shape="box"];79[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];168[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];79 -> 168[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	168 -> 88[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	169[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];79 -> 169[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	169 -> 89[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	80[label="(vy90 : vy91) ++ vy8",fontsize=16,color="black",shape="box"];80 -> 90[label="",style="solid", color="black", weight=3];
11.37/4.57	81[label="[] ++ vy8",fontsize=16,color="black",shape="box"];81 -> 91[label="",style="solid", color="black", weight=3];
11.37/4.57	34[label="Nothing >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3];
11.37/4.57	35[label="Just vy50 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
11.37/4.57	36[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];36 -> 41[label="",style="solid", color="black", weight=3];
11.37/4.57	88[label="vy50 : vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];88 -> 98[label="",style="solid", color="black", weight=3];
11.37/4.57	89[label="[] >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];89 -> 99[label="",style="solid", color="black", weight=3];
11.37/4.57	90[label="vy90 : vy91 ++ vy8",fontsize=16,color="green",shape="box"];90 -> 100[label="",style="dashed", color="green", weight=3];
11.37/4.57	91[label="vy8",fontsize=16,color="green",shape="box"];39[label="Nothing",fontsize=16,color="green",shape="box"];40[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
11.37/4.57	41[label="primbindIO vy5 (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];170[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];41 -> 170[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	170 -> 45[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	171[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];41 -> 171[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	171 -> 46[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	172[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];41 -> 172[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	172 -> 47[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	173[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];41 -> 173[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	173 -> 48[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	98 -> 67[label="",style="dashed", color="red", weight=0];
11.37/4.57	98[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="magenta"];98 -> 103[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	98 -> 104[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	99[label="[]",fontsize=16,color="green",shape="box"];100 -> 67[label="",style="dashed", color="red", weight=0];
11.37/4.57	100[label="vy91 ++ vy8",fontsize=16,color="magenta"];100 -> 105[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	44[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];174[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];44 -> 174[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	174 -> 51[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	175[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];44 -> 175[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	175 -> 52[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	45[label="primbindIO (IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3];
11.37/4.57	46[label="primbindIO (AProVE_IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];46 -> 54[label="",style="solid", color="black", weight=3];
11.37/4.57	47[label="primbindIO (AProVE_Exception vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];47 -> 55[label="",style="solid", color="black", weight=3];
11.37/4.57	48[label="primbindIO (AProVE_Error vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];48 -> 56[label="",style="solid", color="black", weight=3];
11.37/4.57	103 -> 79[label="",style="dashed", color="red", weight=0];
11.37/4.57	103[label="vy51 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="magenta"];103 -> 108[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	104[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];104 -> 109[label="",style="solid", color="black", weight=3];
11.37/4.57	105[label="vy91",fontsize=16,color="green",shape="box"];51[label="Nothing >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];51 -> 59[label="",style="solid", color="black", weight=3];
11.37/4.57	52[label="Just vy60 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];52 -> 60[label="",style="solid", color="black", weight=3];
11.37/4.57	53[label="error []",fontsize=16,color="red",shape="box"];54[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];54 -> 61[label="",style="solid", color="black", weight=3];
11.37/4.57	55[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];56[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];108[label="vy51",fontsize=16,color="green",shape="box"];109[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];176[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];109 -> 176[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	176 -> 115[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	177[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];109 -> 177[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	177 -> 116[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	59[label="Nothing",fontsize=16,color="green",shape="box"];60[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
11.37/4.57	61[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];61 -> 65[label="",style="solid", color="black", weight=3];
11.37/4.57	115[label="vy60 : vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];115 -> 125[label="",style="solid", color="black", weight=3];
11.37/4.57	116[label="[] >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];116 -> 126[label="",style="solid", color="black", weight=3];
11.37/4.57	64[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];178[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];64 -> 178[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	178 -> 82[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	179[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];64 -> 179[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	179 -> 83[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	65[label="primbindIO vy6 (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];180[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];65 -> 180[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	180 -> 84[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	181[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];65 -> 181[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	181 -> 85[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	182[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];65 -> 182[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	182 -> 86[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	183[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];65 -> 183[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	183 -> 87[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	125 -> 67[label="",style="dashed", color="red", weight=0];
11.37/4.57	125[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="magenta"];125 -> 128[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	125 -> 129[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	126[label="[]",fontsize=16,color="green",shape="box"];82[label="Nothing >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];82 -> 92[label="",style="solid", color="black", weight=3];
11.37/4.57	83[label="Just vy70 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];83 -> 93[label="",style="solid", color="black", weight=3];
11.37/4.57	84[label="primbindIO (IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];84 -> 94[label="",style="solid", color="black", weight=3];
11.37/4.57	85[label="primbindIO (AProVE_IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];85 -> 95[label="",style="solid", color="black", weight=3];
11.37/4.57	86[label="primbindIO (AProVE_Exception vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];86 -> 96[label="",style="solid", color="black", weight=3];
11.37/4.57	87[label="primbindIO (AProVE_Error vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];87 -> 97[label="",style="solid", color="black", weight=3];
11.37/4.57	128 -> 109[label="",style="dashed", color="red", weight=0];
11.37/4.57	128[label="vy61 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="magenta"];128 -> 131[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	129[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];129 -> 132[label="",style="solid", color="black", weight=3];
11.37/4.57	92[label="Nothing",fontsize=16,color="green",shape="box"];93[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];93 -> 101[label="",style="solid", color="black", weight=3];
11.37/4.57	94[label="error []",fontsize=16,color="red",shape="box"];95[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3];
11.37/4.57	96[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];97[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];131[label="vy61",fontsize=16,color="green",shape="box"];132[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];184[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];132 -> 184[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	184 -> 134[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	185[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];132 -> 185[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	185 -> 135[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	101[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];101 -> 106[label="",style="solid", color="black", weight=3];
11.37/4.57	102[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];102 -> 107[label="",style="solid", color="black", weight=3];
11.37/4.57	134[label="vy70 : vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3];
11.37/4.57	135[label="[] >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];135 -> 138[label="",style="solid", color="black", weight=3];
11.37/4.57	106[label="Just (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];106 -> 110[label="",style="dashed", color="green", weight=3];
11.37/4.57	107[label="primbindIO vy7 (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="burlywood",shape="box"];186[label="vy7/IO vy70",fontsize=10,color="white",style="solid",shape="box"];107 -> 186[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	186 -> 111[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	187[label="vy7/AProVE_IO vy70",fontsize=10,color="white",style="solid",shape="box"];107 -> 187[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	187 -> 112[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	188[label="vy7/AProVE_Exception vy70",fontsize=10,color="white",style="solid",shape="box"];107 -> 188[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	188 -> 113[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	189[label="vy7/AProVE_Error vy70",fontsize=10,color="white",style="solid",shape="box"];107 -> 189[label="",style="solid", color="burlywood", weight=9];
11.37/4.57	189 -> 114[label="",style="solid", color="burlywood", weight=3];
11.37/4.57	137 -> 67[label="",style="dashed", color="red", weight=0];
11.37/4.57	137[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];137 -> 143[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	137 -> 144[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	138[label="[]",fontsize=16,color="green",shape="box"];110[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];110 -> 117[label="",style="dashed", color="green", weight=3];
11.37/4.57	110 -> 118[label="",style="dashed", color="green", weight=3];
11.37/4.57	110 -> 119[label="",style="dashed", color="green", weight=3];
11.37/4.57	110 -> 120[label="",style="dashed", color="green", weight=3];
11.37/4.57	111[label="primbindIO (IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];111 -> 121[label="",style="solid", color="black", weight=3];
11.37/4.57	112[label="primbindIO (AProVE_IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];112 -> 122[label="",style="solid", color="black", weight=3];
11.37/4.57	113[label="primbindIO (AProVE_Exception vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];113 -> 123[label="",style="solid", color="black", weight=3];
11.37/4.57	114[label="primbindIO (AProVE_Error vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];114 -> 124[label="",style="solid", color="black", weight=3];
11.37/4.57	143 -> 132[label="",style="dashed", color="red", weight=0];
11.37/4.57	143[label="vy71 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];143 -> 145[label="",style="dashed", color="magenta", weight=3];
11.37/4.57	144[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];144 -> 146[label="",style="solid", color="black", weight=3];
11.37/4.57	117[label="vy40",fontsize=16,color="green",shape="box"];118[label="vy50",fontsize=16,color="green",shape="box"];119[label="vy60",fontsize=16,color="green",shape="box"];120[label="vy70",fontsize=16,color="green",shape="box"];121[label="error []",fontsize=16,color="red",shape="box"];122[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];122 -> 127[label="",style="solid", color="black", weight=3];
11.37/4.57	123[label="AProVE_Exception vy70",fontsize=16,color="green",shape="box"];124[label="AProVE_Error vy70",fontsize=16,color="green",shape="box"];145[label="vy71",fontsize=16,color="green",shape="box"];146[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];146 -> 147[label="",style="solid", color="black", weight=3];
11.37/4.57	127[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];127 -> 130[label="",style="solid", color="black", weight=3];
11.37/4.57	147[label="vy3 vy40 vy50 vy60 vy70 : []",fontsize=16,color="green",shape="box"];147 -> 148[label="",style="dashed", color="green", weight=3];
11.37/4.57	130[label="primretIO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];130 -> 133[label="",style="solid", color="black", weight=3];
11.37/4.57	148[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];148 -> 149[label="",style="dashed", color="green", weight=3];
11.37/4.57	148 -> 150[label="",style="dashed", color="green", weight=3];
11.37/4.57	148 -> 151[label="",style="dashed", color="green", weight=3];
11.37/4.57	148 -> 152[label="",style="dashed", color="green", weight=3];
11.37/4.57	133[label="AProVE_IO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];133 -> 136[label="",style="dashed", color="green", weight=3];
11.37/4.57	149[label="vy40",fontsize=16,color="green",shape="box"];150[label="vy50",fontsize=16,color="green",shape="box"];151[label="vy60",fontsize=16,color="green",shape="box"];152[label="vy70",fontsize=16,color="green",shape="box"];136[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];136 -> 139[label="",style="dashed", color="green", weight=3];
11.37/4.57	136 -> 140[label="",style="dashed", color="green", weight=3];
11.37/4.57	136 -> 141[label="",style="dashed", color="green", weight=3];
11.37/4.57	136 -> 142[label="",style="dashed", color="green", weight=3];
11.37/4.57	139[label="vy40",fontsize=16,color="green",shape="box"];140[label="vy50",fontsize=16,color="green",shape="box"];141[label="vy60",fontsize=16,color="green",shape="box"];142[label="vy70",fontsize=16,color="green",shape="box"];}
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(8)
11.37/4.57	Complex Obligation (AND)
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(9)
11.37/4.57	Obligation:
11.37/4.57	Q DP problem:
11.37/4.57	The TRS P consists of the following rules:
11.37/4.57	
11.37/4.57	   new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) -> new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd)
11.37/4.57	
11.37/4.57	R is empty.
11.37/4.57	Q is empty.
11.37/4.57	We have to consider all minimal (P,Q,R)-chains.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(10) QDPSizeChangeProof (EQUIVALENT)
11.37/4.57	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. 
11.37/4.57	
11.37/4.57	From the DPs we obtained the following set of size-change graphs:
11.37/4.57	*new_gtGtEs0(:(vy60, vy61), vy7, vy3, vy40, vy50, h, ba, bb, bc, bd) -> new_gtGtEs0(vy61, vy7, vy3, vy40, vy50, h, ba, bb, bc, bd)
11.37/4.57	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
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(11)
11.37/4.57	YES
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(12)
11.37/4.57	Obligation:
11.37/4.57	Q DP problem:
11.37/4.57	The TRS P consists of the following rules:
11.37/4.57	
11.37/4.57	   new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) -> new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd)
11.37/4.57	
11.37/4.57	R is empty.
11.37/4.57	Q is empty.
11.37/4.57	We have to consider all minimal (P,Q,R)-chains.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(13) QDPSizeChangeProof (EQUIVALENT)
11.37/4.57	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. 
11.37/4.57	
11.37/4.57	From the DPs we obtained the following set of size-change graphs:
11.37/4.57	*new_gtGtEs1(:(vy50, vy51), vy6, vy7, vy3, vy40, h, ba, bb, bc, bd) -> new_gtGtEs1(vy51, vy6, vy7, vy3, vy40, h, ba, bb, bc, bd)
11.37/4.57	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
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(14)
11.37/4.57	YES
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(15)
11.37/4.57	Obligation:
11.37/4.57	Q DP problem:
11.37/4.57	The TRS P consists of the following rules:
11.37/4.57	
11.37/4.57	   new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) -> new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd)
11.37/4.57	
11.37/4.57	R is empty.
11.37/4.57	Q is empty.
11.37/4.57	We have to consider all minimal (P,Q,R)-chains.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(16) QDPSizeChangeProof (EQUIVALENT)
11.37/4.57	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. 
11.37/4.57	
11.37/4.57	From the DPs we obtained the following set of size-change graphs:
11.37/4.57	*new_gtGtEs(:(vy70, vy71), vy3, vy40, vy50, vy60, h, ba, bb, bc, bd) -> new_gtGtEs(vy71, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd)
11.37/4.57	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
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(17)
11.37/4.57	YES
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(18)
11.37/4.57	Obligation:
11.37/4.57	Q DP problem:
11.37/4.57	The TRS P consists of the following rules:
11.37/4.57	
11.37/4.57	   new_psPs(:(vy90, vy91), vy8, h) -> new_psPs(vy91, vy8, h)
11.37/4.57	
11.37/4.57	R is empty.
11.37/4.57	Q is empty.
11.37/4.57	We have to consider all minimal (P,Q,R)-chains.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(19) QDPSizeChangeProof (EQUIVALENT)
11.37/4.57	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. 
11.37/4.57	
11.37/4.57	From the DPs we obtained the following set of size-change graphs:
11.37/4.57	*new_psPs(:(vy90, vy91), vy8, h) -> new_psPs(vy91, vy8, h)
11.37/4.57	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(20)
11.37/4.57	YES
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(21)
11.37/4.57	Obligation:
11.37/4.57	Q DP problem:
11.37/4.57	The TRS P consists of the following rules:
11.37/4.57	
11.37/4.57	   new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) -> new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd)
11.37/4.57	
11.37/4.57	R is empty.
11.37/4.57	Q is empty.
11.37/4.57	We have to consider all minimal (P,Q,R)-chains.
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(22) QDPSizeChangeProof (EQUIVALENT)
11.37/4.57	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. 
11.37/4.57	
11.37/4.57	From the DPs we obtained the following set of size-change graphs:
11.37/4.57	*new_gtGtEs2(:(vy40, vy41), vy5, vy6, vy7, vy3, h, ba, bb, bc, bd) -> new_gtGtEs2(vy41, vy5, vy6, vy7, vy3, h, ba, bb, bc, bd)
11.37/4.57	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
11.37/4.57	
11.37/4.57	
11.37/4.57	----------------------------------------
11.37/4.57	
11.37/4.57	(23)
11.37/4.57	YES
11.51/4.63	EOF