8.92/3.93	YES
10.89/4.45	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
10.89/4.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.89/4.45	
10.89/4.45	
10.89/4.45	H-Termination with start terms of the given HASKELL could be proven:
10.89/4.45	
10.89/4.45	(0) HASKELL
10.89/4.45	(1) LR [EQUIVALENT, 0 ms]
10.89/4.45	(2) HASKELL
10.89/4.45	(3) BR [EQUIVALENT, 0 ms]
10.89/4.45	(4) HASKELL
10.89/4.45	(5) COR [EQUIVALENT, 0 ms]
10.89/4.45	(6) HASKELL
10.89/4.45	(7) Narrow [SOUND, 0 ms]
10.89/4.45	(8) AND
10.89/4.45	    (9) QDP
10.89/4.45	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.89/4.45	        (11) YES
10.89/4.45	    (12) QDP
10.89/4.45	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.89/4.45	        (14) YES
10.89/4.45	    (15) QDP
10.89/4.45	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.89/4.45	        (17) YES
10.89/4.45	
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(0)
10.89/4.45	Obligation:
10.89/4.45	mainModule Main 
10.89/4.45	module Maybe where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Main where {
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Monad where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Prelude;
10.89/4.45	liftM2 :: Monad d => (b  ->  a  ->  c)  ->  d b  ->  d a  ->  d c;
10.89/4.45	liftM2 f m1 m2 = m1 >>= (\x1 ->m2 >>= (\x2 ->return (f x1 x2)));
10.89/4.45	
10.89/4.45	}
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(1) LR (EQUIVALENT)
10.89/4.45	Lambda Reductions:
10.89/4.45	The following Lambda expression
10.89/4.45	"\x2->return (f x1 x2)"
10.89/4.45	is transformed to
10.89/4.45	"liftM20 f x1 x2 = return (f x1 x2);
10.89/4.45	"
10.89/4.45	The following Lambda expression
10.89/4.45	"\x1->m2 >>= liftM20 f x1"
10.89/4.45	is transformed to
10.89/4.45	"liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.89/4.45	"
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(2)
10.89/4.45	Obligation:
10.89/4.45	mainModule Main 
10.89/4.45	module Maybe where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Main where {
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Monad where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Prelude;
10.89/4.45	liftM2 :: Monad c => (a  ->  b  ->  d)  ->  c a  ->  c b  ->  c d;
10.89/4.45	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.89/4.45	
10.89/4.45	liftM20 f x1 x2 = return (f x1 x2);
10.89/4.45	
10.89/4.45	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.89/4.45	
10.89/4.45	}
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(3) BR (EQUIVALENT)
10.89/4.45	Replaced joker patterns by fresh variables and removed binding patterns.
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(4)
10.89/4.45	Obligation:
10.89/4.45	mainModule Main 
10.89/4.45	module Maybe where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Main where {
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Monad where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Prelude;
10.89/4.45	liftM2 :: Monad c => (d  ->  a  ->  b)  ->  c d  ->  c a  ->  c b;
10.89/4.45	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.89/4.45	
10.89/4.45	liftM20 f x1 x2 = return (f x1 x2);
10.89/4.45	
10.89/4.45	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.89/4.45	
10.89/4.45	}
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(5) COR (EQUIVALENT)
10.89/4.45	Cond Reductions:
10.89/4.45	The following Function with conditions
10.89/4.45	"undefined |Falseundefined;
10.89/4.45	"
10.89/4.45	is transformed to
10.89/4.45	"undefined  = undefined1;
10.89/4.45	"
10.89/4.45	"undefined0 True = undefined;
10.89/4.45	"
10.89/4.45	"undefined1  = undefined0 False;
10.89/4.45	"
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(6)
10.89/4.45	Obligation:
10.89/4.45	mainModule Main 
10.89/4.45	module Maybe where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Main where {
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Monad;
10.89/4.45	import qualified Prelude;
10.89/4.45	}
10.89/4.45	module Monad where {
10.89/4.45	import qualified Main;
10.89/4.45	import qualified Maybe;
10.89/4.45	import qualified Prelude;
10.89/4.45	liftM2 :: Monad c => (a  ->  d  ->  b)  ->  c a  ->  c d  ->  c b;
10.89/4.45	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.89/4.45	
10.89/4.45	liftM20 f x1 x2 = return (f x1 x2);
10.89/4.45	
10.89/4.45	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.89/4.45	
10.89/4.45	}
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(7) Narrow (SOUND)
10.89/4.45	Haskell To QDPs
10.89/4.45	
10.89/4.45	digraph dp_graph {
10.89/4.45	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM2",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.89/4.45	3[label="Monad.liftM2 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.89/4.45	4[label="Monad.liftM2 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
10.89/4.45	5[label="Monad.liftM2 vy3 vy4 vy5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
10.89/4.45	6[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="blue",shape="box"];91[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];6 -> 91[label="",style="solid", color="blue", weight=9];
10.89/4.45	91 -> 7[label="",style="solid", color="blue", weight=3];
10.89/4.45	92[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];6 -> 92[label="",style="solid", color="blue", weight=9];
10.89/4.45	92 -> 8[label="",style="solid", color="blue", weight=3];
10.89/4.45	93[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];6 -> 93[label="",style="solid", color="blue", weight=9];
10.89/4.45	93 -> 9[label="",style="solid", color="blue", weight=3];
10.89/4.45	7[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="burlywood",shape="box"];94[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];7 -> 94[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	94 -> 10[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	95[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];7 -> 95[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	95 -> 11[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	8[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
10.89/4.45	9[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="burlywood",shape="triangle"];96[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 96[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	96 -> 13[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	97[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 97[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	97 -> 14[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	10[label="Nothing >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3];
10.89/4.45	11[label="Just vy40 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3];
10.89/4.45	12[label="primbindIO vy4 (Monad.liftM21 vy5 vy3)",fontsize=16,color="burlywood",shape="box"];98[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];12 -> 98[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	98 -> 17[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	99[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];12 -> 99[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	99 -> 18[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	100[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];12 -> 100[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	100 -> 19[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	101[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];12 -> 101[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	101 -> 20[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	13[label="vy40 : vy41 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3];
10.89/4.45	14[label="[] >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];14 -> 22[label="",style="solid", color="black", weight=3];
10.89/4.45	15[label="Nothing",fontsize=16,color="green",shape="box"];16[label="Monad.liftM21 vy5 vy3 vy40",fontsize=16,color="black",shape="box"];16 -> 23[label="",style="solid", color="black", weight=3];
10.89/4.45	17[label="primbindIO (IO vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];17 -> 24[label="",style="solid", color="black", weight=3];
10.89/4.45	18[label="primbindIO (AProVE_IO vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];18 -> 25[label="",style="solid", color="black", weight=3];
10.89/4.45	19[label="primbindIO (AProVE_Exception vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3];
10.89/4.45	20[label="primbindIO (AProVE_Error vy40) (Monad.liftM21 vy5 vy3)",fontsize=16,color="black",shape="box"];20 -> 27[label="",style="solid", color="black", weight=3];
10.89/4.45	21 -> 28[label="",style="dashed", color="red", weight=0];
10.89/4.45	21[label="Monad.liftM21 vy5 vy3 vy40 ++ (vy41 >>= Monad.liftM21 vy5 vy3)",fontsize=16,color="magenta"];21 -> 29[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	22[label="[]",fontsize=16,color="green",shape="box"];23[label="vy5 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="burlywood",shape="box"];102[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];23 -> 102[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	102 -> 30[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	103[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];23 -> 103[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	103 -> 31[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	24[label="error []",fontsize=16,color="red",shape="box"];25[label="Monad.liftM21 vy5 vy3 vy40",fontsize=16,color="black",shape="box"];25 -> 32[label="",style="solid", color="black", weight=3];
10.89/4.45	26[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];29 -> 9[label="",style="dashed", color="red", weight=0];
10.89/4.45	29[label="vy41 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="magenta"];29 -> 33[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	28[label="Monad.liftM21 vy5 vy3 vy40 ++ vy6",fontsize=16,color="black",shape="triangle"];28 -> 34[label="",style="solid", color="black", weight=3];
10.89/4.45	30[label="Nothing >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];30 -> 35[label="",style="solid", color="black", weight=3];
10.89/4.45	31[label="Just vy50 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];31 -> 36[label="",style="solid", color="black", weight=3];
10.89/4.45	32[label="vy5 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];32 -> 37[label="",style="solid", color="black", weight=3];
10.89/4.45	33[label="vy41",fontsize=16,color="green",shape="box"];34[label="(vy5 >>= Monad.liftM20 vy3 vy40) ++ vy6",fontsize=16,color="burlywood",shape="box"];104[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];34 -> 104[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	104 -> 38[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	105[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];34 -> 105[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	105 -> 39[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	35[label="Nothing",fontsize=16,color="green",shape="box"];36[label="Monad.liftM20 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3];
10.89/4.45	37[label="primbindIO vy5 (Monad.liftM20 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];106[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];37 -> 106[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	106 -> 41[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	107[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];37 -> 107[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	107 -> 42[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	108[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];37 -> 108[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	108 -> 43[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	109[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];37 -> 109[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	109 -> 44[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	38[label="(vy50 : vy51 >>= Monad.liftM20 vy3 vy40) ++ vy6",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3];
10.89/4.45	39[label="([] >>= Monad.liftM20 vy3 vy40) ++ vy6",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
10.89/4.45	40[label="return (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3];
10.89/4.45	41[label="primbindIO (IO vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
10.89/4.45	42[label="primbindIO (AProVE_IO vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
10.89/4.45	43[label="primbindIO (AProVE_Exception vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
10.89/4.45	44[label="primbindIO (AProVE_Error vy50) (Monad.liftM20 vy3 vy40)",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
10.89/4.45	45[label="(Monad.liftM20 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM20 vy3 vy40)) ++ vy6",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3];
10.89/4.45	46[label="[] ++ vy6",fontsize=16,color="black",shape="triangle"];46 -> 53[label="",style="solid", color="black", weight=3];
10.89/4.45	47[label="Just (vy3 vy40 vy50)",fontsize=16,color="green",shape="box"];47 -> 54[label="",style="dashed", color="green", weight=3];
10.89/4.45	48[label="error []",fontsize=16,color="red",shape="box"];49[label="Monad.liftM20 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];49 -> 55[label="",style="solid", color="black", weight=3];
10.89/4.45	50[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];51[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];52[label="(return (vy3 vy40 vy50) ++ (vy51 >>= Monad.liftM20 vy3 vy40)) ++ vy6",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3];
10.89/4.45	53[label="vy6",fontsize=16,color="green",shape="box"];54[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];54 -> 57[label="",style="dashed", color="green", weight=3];
10.89/4.45	54 -> 58[label="",style="dashed", color="green", weight=3];
10.89/4.45	55[label="return (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
10.89/4.45	56[label="((vy3 vy40 vy50 : []) ++ (vy51 >>= Monad.liftM20 vy3 vy40)) ++ vy6",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
10.89/4.45	57[label="vy40",fontsize=16,color="green",shape="box"];58[label="vy50",fontsize=16,color="green",shape="box"];59[label="primretIO (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];59 -> 61[label="",style="solid", color="black", weight=3];
10.89/4.45	60 -> 62[label="",style="dashed", color="red", weight=0];
10.89/4.45	60[label="(vy3 vy40 vy50 : [] ++ (vy51 >>= Monad.liftM20 vy3 vy40)) ++ vy6",fontsize=16,color="magenta"];60 -> 63[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	61[label="AProVE_IO (vy3 vy40 vy50)",fontsize=16,color="green",shape="box"];61 -> 64[label="",style="dashed", color="green", weight=3];
10.89/4.45	63 -> 46[label="",style="dashed", color="red", weight=0];
10.89/4.45	63[label="[] ++ (vy51 >>= Monad.liftM20 vy3 vy40)",fontsize=16,color="magenta"];63 -> 65[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	62[label="(vy3 vy40 vy50 : vy7) ++ vy6",fontsize=16,color="black",shape="triangle"];62 -> 66[label="",style="solid", color="black", weight=3];
10.89/4.45	64[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];64 -> 67[label="",style="dashed", color="green", weight=3];
10.89/4.45	64 -> 68[label="",style="dashed", color="green", weight=3];
10.89/4.45	65[label="vy51 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];110[label="vy51/vy510 : vy511",fontsize=10,color="white",style="solid",shape="box"];65 -> 110[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	110 -> 69[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	111[label="vy51/[]",fontsize=10,color="white",style="solid",shape="box"];65 -> 111[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	111 -> 70[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	66[label="vy3 vy40 vy50 : vy7 ++ vy6",fontsize=16,color="green",shape="box"];66 -> 71[label="",style="dashed", color="green", weight=3];
10.89/4.45	66 -> 72[label="",style="dashed", color="green", weight=3];
10.89/4.45	67[label="vy40",fontsize=16,color="green",shape="box"];68[label="vy50",fontsize=16,color="green",shape="box"];69[label="vy510 : vy511 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
10.89/4.45	70[label="[] >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];70 -> 74[label="",style="solid", color="black", weight=3];
10.89/4.45	71[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];71 -> 75[label="",style="dashed", color="green", weight=3];
10.89/4.45	71 -> 76[label="",style="dashed", color="green", weight=3];
10.89/4.45	72[label="vy7 ++ vy6",fontsize=16,color="burlywood",shape="triangle"];112[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];72 -> 112[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	112 -> 77[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	113[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];72 -> 113[label="",style="solid", color="burlywood", weight=9];
10.89/4.45	113 -> 78[label="",style="solid", color="burlywood", weight=3];
10.89/4.45	73 -> 72[label="",style="dashed", color="red", weight=0];
10.89/4.45	73[label="Monad.liftM20 vy3 vy40 vy510 ++ (vy511 >>= Monad.liftM20 vy3 vy40)",fontsize=16,color="magenta"];73 -> 79[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	73 -> 80[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	74[label="[]",fontsize=16,color="green",shape="box"];75[label="vy40",fontsize=16,color="green",shape="box"];76[label="vy50",fontsize=16,color="green",shape="box"];77[label="(vy70 : vy71) ++ vy6",fontsize=16,color="black",shape="box"];77 -> 81[label="",style="solid", color="black", weight=3];
10.89/4.45	78[label="[] ++ vy6",fontsize=16,color="black",shape="box"];78 -> 82[label="",style="solid", color="black", weight=3];
10.89/4.45	79 -> 65[label="",style="dashed", color="red", weight=0];
10.89/4.45	79[label="vy511 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="magenta"];79 -> 83[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	80[label="Monad.liftM20 vy3 vy40 vy510",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3];
10.89/4.45	81[label="vy70 : vy71 ++ vy6",fontsize=16,color="green",shape="box"];81 -> 85[label="",style="dashed", color="green", weight=3];
10.89/4.45	82[label="vy6",fontsize=16,color="green",shape="box"];83[label="vy511",fontsize=16,color="green",shape="box"];84[label="return (vy3 vy40 vy510)",fontsize=16,color="black",shape="box"];84 -> 86[label="",style="solid", color="black", weight=3];
10.89/4.45	85 -> 72[label="",style="dashed", color="red", weight=0];
10.89/4.45	85[label="vy71 ++ vy6",fontsize=16,color="magenta"];85 -> 87[label="",style="dashed", color="magenta", weight=3];
10.89/4.45	86[label="vy3 vy40 vy510 : []",fontsize=16,color="green",shape="box"];86 -> 88[label="",style="dashed", color="green", weight=3];
10.89/4.45	87[label="vy71",fontsize=16,color="green",shape="box"];88[label="vy3 vy40 vy510",fontsize=16,color="green",shape="box"];88 -> 89[label="",style="dashed", color="green", weight=3];
10.89/4.45	88 -> 90[label="",style="dashed", color="green", weight=3];
10.89/4.45	89[label="vy40",fontsize=16,color="green",shape="box"];90[label="vy510",fontsize=16,color="green",shape="box"];}
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(8)
10.89/4.45	Complex Obligation (AND)
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(9)
10.89/4.45	Obligation:
10.89/4.45	Q DP problem:
10.89/4.45	The TRS P consists of the following rules:
10.89/4.45	
10.89/4.45	   new_gtGtEs0(:(vy40, vy41), vy5, vy3, h, ba, bb) -> new_gtGtEs0(vy41, vy5, vy3, h, ba, bb)
10.89/4.45	
10.89/4.45	R is empty.
10.89/4.45	Q is empty.
10.89/4.45	We have to consider all minimal (P,Q,R)-chains.
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(10) QDPSizeChangeProof (EQUIVALENT)
10.89/4.45	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. 
10.89/4.45	
10.89/4.45	From the DPs we obtained the following set of size-change graphs:
10.89/4.45	*new_gtGtEs0(:(vy40, vy41), vy5, vy3, h, ba, bb) -> new_gtGtEs0(vy41, vy5, vy3, h, ba, bb)
10.89/4.45	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6
10.89/4.45	
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(11)
10.89/4.45	YES
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(12)
10.89/4.45	Obligation:
10.89/4.45	Q DP problem:
10.89/4.45	The TRS P consists of the following rules:
10.89/4.45	
10.89/4.45	   new_gtGtEs(:(vy510, vy511), vy3, vy40, h, ba, bb) -> new_gtGtEs(vy511, vy3, vy40, h, ba, bb)
10.89/4.45	
10.89/4.45	R is empty.
10.89/4.45	Q is empty.
10.89/4.45	We have to consider all minimal (P,Q,R)-chains.
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(13) QDPSizeChangeProof (EQUIVALENT)
10.89/4.45	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. 
10.89/4.45	
10.89/4.45	From the DPs we obtained the following set of size-change graphs:
10.89/4.45	*new_gtGtEs(:(vy510, vy511), vy3, vy40, h, ba, bb) -> new_gtGtEs(vy511, vy3, vy40, h, ba, bb)
10.89/4.45	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6
10.89/4.45	
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(14)
10.89/4.45	YES
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(15)
10.89/4.45	Obligation:
10.89/4.45	Q DP problem:
10.89/4.45	The TRS P consists of the following rules:
10.89/4.45	
10.89/4.45	   new_psPs(:(vy70, vy71), vy6, h) -> new_psPs(vy71, vy6, h)
10.89/4.45	
10.89/4.45	R is empty.
10.89/4.45	Q is empty.
10.89/4.45	We have to consider all minimal (P,Q,R)-chains.
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(16) QDPSizeChangeProof (EQUIVALENT)
10.89/4.45	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. 
10.89/4.45	
10.89/4.45	From the DPs we obtained the following set of size-change graphs:
10.89/4.45	*new_psPs(:(vy70, vy71), vy6, h) -> new_psPs(vy71, vy6, h)
10.89/4.45	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
10.89/4.45	
10.89/4.45	
10.89/4.45	----------------------------------------
10.89/4.45	
10.89/4.45	(17)
10.89/4.45	YES
11.04/5.99	EOF