9.40/4.04	YES
11.46/4.62	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
11.46/4.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.46/4.62	
11.46/4.62	
11.46/4.62	H-Termination with start terms of the given HASKELL could be proven:
11.46/4.62	
11.46/4.62	(0) HASKELL
11.46/4.62	(1) LR [EQUIVALENT, 0 ms]
11.46/4.62	(2) HASKELL
11.46/4.62	(3) BR [EQUIVALENT, 0 ms]
11.46/4.62	(4) HASKELL
11.46/4.62	(5) COR [EQUIVALENT, 0 ms]
11.46/4.62	(6) HASKELL
11.46/4.62	(7) Narrow [SOUND, 0 ms]
11.46/4.62	(8) AND
11.46/4.62	    (9) QDP
11.46/4.62	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (11) YES
11.46/4.62	    (12) QDP
11.46/4.62	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (14) YES
11.46/4.62	    (15) QDP
11.46/4.62	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (17) YES
11.46/4.62	    (18) QDP
11.46/4.62	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (20) YES
11.46/4.62	    (21) QDP
11.46/4.62	        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (23) YES
11.46/4.62	    (24) QDP
11.46/4.62	        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.46/4.62	        (26) YES
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(0)
11.46/4.62	Obligation:
11.46/4.62	mainModule Main 
11.46/4.62	module Maybe where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Main where {
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Monad where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Prelude;
11.46/4.62	liftM5 :: Monad g => (a  ->  b  ->  e  ->  d  ->  c  ->  f)  ->  g a  ->  g b  ->  g e  ->  g d  ->  g c  ->  g f;
11.46/4.62	liftM5 f m1 m2 m3 m4 m5 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->m5 >>= (\x5 ->return (f x1 x2 x3 x4 x5))))));
11.46/4.62	
11.46/4.62	}
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(1) LR (EQUIVALENT)
11.46/4.62	Lambda Reductions:
11.46/4.62	The following Lambda expression
11.46/4.62	"\x5->return (f x1 x2 x3 x4 x5)"
11.46/4.62	is transformed to
11.46/4.62	"liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.46/4.62	"
11.46/4.62	The following Lambda expression
11.46/4.62	"\x4->m5 >>= liftM50 f x1 x2 x3 x4"
11.46/4.62	is transformed to
11.46/4.62	"liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.46/4.62	"
11.46/4.62	The following Lambda expression
11.46/4.62	"\x3->m4 >>= liftM51 m5 f x1 x2 x3"
11.46/4.62	is transformed to
11.46/4.62	"liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.46/4.62	"
11.46/4.62	The following Lambda expression
11.46/4.62	"\x2->m3 >>= liftM52 m4 m5 f x1 x2"
11.46/4.62	is transformed to
11.46/4.62	"liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.46/4.62	"
11.46/4.62	The following Lambda expression
11.46/4.62	"\x1->m2 >>= liftM53 m3 m4 m5 f x1"
11.46/4.62	is transformed to
11.46/4.62	"liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.46/4.62	"
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(2)
11.46/4.62	Obligation:
11.46/4.62	mainModule Main 
11.46/4.62	module Maybe where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Main where {
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Monad where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Prelude;
11.46/4.62	liftM5 :: Monad f => (e  ->  b  ->  a  ->  g  ->  c  ->  d)  ->  f e  ->  f b  ->  f a  ->  f g  ->  f c  ->  f d;
11.46/4.62	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.46/4.62	
11.46/4.62	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.46/4.62	
11.46/4.62	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.46/4.62	
11.46/4.62	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.46/4.62	
11.46/4.62	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.46/4.62	
11.46/4.62	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.46/4.62	
11.46/4.62	}
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(3) BR (EQUIVALENT)
11.46/4.62	Replaced joker patterns by fresh variables and removed binding patterns.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(4)
11.46/4.62	Obligation:
11.46/4.62	mainModule Main 
11.46/4.62	module Maybe where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Main where {
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Monad where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Prelude;
11.46/4.62	liftM5 :: Monad d => (g  ->  a  ->  b  ->  e  ->  f  ->  c)  ->  d g  ->  d a  ->  d b  ->  d e  ->  d f  ->  d c;
11.46/4.62	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.46/4.62	
11.46/4.62	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.46/4.62	
11.46/4.62	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.46/4.62	
11.46/4.62	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.46/4.62	
11.46/4.62	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.46/4.62	
11.46/4.62	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.46/4.62	
11.46/4.62	}
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(5) COR (EQUIVALENT)
11.46/4.62	Cond Reductions:
11.46/4.62	The following Function with conditions
11.46/4.62	"undefined |Falseundefined;
11.46/4.62	"
11.46/4.62	is transformed to
11.46/4.62	"undefined  = undefined1;
11.46/4.62	"
11.46/4.62	"undefined0 True = undefined;
11.46/4.62	"
11.46/4.62	"undefined1  = undefined0 False;
11.46/4.62	"
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(6)
11.46/4.62	Obligation:
11.46/4.62	mainModule Main 
11.46/4.62	module Maybe where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Main where {
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Monad;
11.46/4.62	import qualified Prelude;
11.46/4.62	}
11.46/4.62	module Monad where {
11.46/4.62	import qualified Main;
11.46/4.62	import qualified Maybe;
11.46/4.62	import qualified Prelude;
11.46/4.62	liftM5 :: Monad c => (d  ->  a  ->  g  ->  e  ->  f  ->  b)  ->  c d  ->  c a  ->  c g  ->  c e  ->  c f  ->  c b;
11.46/4.62	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.46/4.62	
11.46/4.62	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.46/4.62	
11.46/4.62	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.46/4.62	
11.46/4.62	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.46/4.62	
11.46/4.62	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.46/4.62	
11.46/4.62	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.46/4.62	
11.46/4.62	}
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(7) Narrow (SOUND)
11.46/4.62	Haskell To QDPs
11.46/4.62	
11.46/4.62	digraph dp_graph {
11.46/4.62	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM5",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.46/4.62	3[label="Monad.liftM5 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.46/4.62	4[label="Monad.liftM5 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.46/4.62	5[label="Monad.liftM5 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.46/4.62	6[label="Monad.liftM5 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
11.46/4.62	7[label="Monad.liftM5 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="grey",shape="box"];7 -> 8[label="",style="dashed", color="grey", weight=3];
11.46/4.62	8[label="Monad.liftM5 vy3 vy4 vy5 vy6 vy7 vy8",fontsize=16,color="black",shape="triangle"];8 -> 9[label="",style="solid", color="black", weight=3];
11.46/4.62	9[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="burlywood",shape="triangle"];87[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];9 -> 87[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	87 -> 10[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	88[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 88[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	88 -> 11[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	10[label="vy40 : vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11.46/4.62	11[label="[] >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
11.46/4.62	12 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	12[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40 ++ (vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3)",fontsize=16,color="magenta"];12 -> 30[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	12 -> 31[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	13[label="[]",fontsize=16,color="green",shape="box"];30[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];30 -> 40[label="",style="solid", color="black", weight=3];
11.46/4.62	31 -> 9[label="",style="dashed", color="red", weight=0];
11.46/4.62	31[label="vy41 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="magenta"];31 -> 41[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	29[label="vy10 ++ vy9",fontsize=16,color="burlywood",shape="triangle"];89[label="vy10/vy100 : vy101",fontsize=10,color="white",style="solid",shape="box"];29 -> 89[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	89 -> 42[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	90[label="vy10/[]",fontsize=10,color="white",style="solid",shape="box"];29 -> 90[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	90 -> 43[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	40[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="triangle"];91[label="vy5/vy50 : vy51",fontsize=10,color="white",style="solid",shape="box"];40 -> 91[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	91 -> 44[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	92[label="vy5/[]",fontsize=10,color="white",style="solid",shape="box"];40 -> 92[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	92 -> 45[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	41[label="vy41",fontsize=16,color="green",shape="box"];42[label="(vy100 : vy101) ++ vy9",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
11.46/4.62	43[label="[] ++ vy9",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
11.46/4.62	44[label="vy50 : vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3];
11.46/4.62	45[label="[] >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
11.46/4.62	46[label="vy100 : vy101 ++ vy9",fontsize=16,color="green",shape="box"];46 -> 50[label="",style="dashed", color="green", weight=3];
11.46/4.62	47[label="vy9",fontsize=16,color="green",shape="box"];48 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	48[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50 ++ (vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40)",fontsize=16,color="magenta"];48 -> 51[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	48 -> 52[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	49[label="[]",fontsize=16,color="green",shape="box"];50 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	50[label="vy101 ++ vy9",fontsize=16,color="magenta"];50 -> 53[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	51[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
11.46/4.62	52 -> 40[label="",style="dashed", color="red", weight=0];
11.46/4.62	52[label="vy51 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="magenta"];52 -> 55[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	53[label="vy101",fontsize=16,color="green",shape="box"];54[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="triangle"];93[label="vy6/vy60 : vy61",fontsize=10,color="white",style="solid",shape="box"];54 -> 93[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	93 -> 56[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	94[label="vy6/[]",fontsize=10,color="white",style="solid",shape="box"];54 -> 94[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	94 -> 57[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	55[label="vy51",fontsize=16,color="green",shape="box"];56[label="vy60 : vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];56 -> 58[label="",style="solid", color="black", weight=3];
11.46/4.62	57[label="[] >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];57 -> 59[label="",style="solid", color="black", weight=3];
11.46/4.62	58 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	58[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60 ++ (vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50)",fontsize=16,color="magenta"];58 -> 60[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	58 -> 61[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	59[label="[]",fontsize=16,color="green",shape="box"];60[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
11.46/4.62	61 -> 54[label="",style="dashed", color="red", weight=0];
11.46/4.62	61[label="vy61 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="magenta"];61 -> 63[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	62[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="triangle"];95[label="vy7/vy70 : vy71",fontsize=10,color="white",style="solid",shape="box"];62 -> 95[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	95 -> 64[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	96[label="vy7/[]",fontsize=10,color="white",style="solid",shape="box"];62 -> 96[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	96 -> 65[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	63[label="vy61",fontsize=16,color="green",shape="box"];64[label="vy70 : vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3];
11.46/4.62	65[label="[] >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3];
11.46/4.62	66 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	66[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70 ++ (vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60)",fontsize=16,color="magenta"];66 -> 68[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	66 -> 69[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	67[label="[]",fontsize=16,color="green",shape="box"];68[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];68 -> 70[label="",style="solid", color="black", weight=3];
11.46/4.62	69 -> 62[label="",style="dashed", color="red", weight=0];
11.46/4.62	69[label="vy71 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="magenta"];69 -> 71[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	70[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="triangle"];97[label="vy8/vy80 : vy81",fontsize=10,color="white",style="solid",shape="box"];70 -> 97[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	97 -> 72[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	98[label="vy8/[]",fontsize=10,color="white",style="solid",shape="box"];70 -> 98[label="",style="solid", color="burlywood", weight=9];
11.46/4.62	98 -> 73[label="",style="solid", color="burlywood", weight=3];
11.46/4.62	71[label="vy71",fontsize=16,color="green",shape="box"];72[label="vy80 : vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];72 -> 74[label="",style="solid", color="black", weight=3];
11.46/4.62	73[label="[] >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];73 -> 75[label="",style="solid", color="black", weight=3];
11.46/4.62	74 -> 29[label="",style="dashed", color="red", weight=0];
11.46/4.62	74[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80 ++ (vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="magenta"];74 -> 76[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	74 -> 77[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	75[label="[]",fontsize=16,color="green",shape="box"];76[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];76 -> 78[label="",style="solid", color="black", weight=3];
11.46/4.62	77 -> 70[label="",style="dashed", color="red", weight=0];
11.46/4.62	77[label="vy81 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="magenta"];77 -> 79[label="",style="dashed", color="magenta", weight=3];
11.46/4.62	78[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];78 -> 80[label="",style="solid", color="black", weight=3];
11.46/4.62	79[label="vy81",fontsize=16,color="green",shape="box"];80[label="vy3 vy40 vy50 vy60 vy70 vy80 : []",fontsize=16,color="green",shape="box"];80 -> 81[label="",style="dashed", color="green", weight=3];
11.46/4.62	81[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];81 -> 82[label="",style="dashed", color="green", weight=3];
11.46/4.62	81 -> 83[label="",style="dashed", color="green", weight=3];
11.46/4.62	81 -> 84[label="",style="dashed", color="green", weight=3];
11.46/4.62	81 -> 85[label="",style="dashed", color="green", weight=3];
11.46/4.62	81 -> 86[label="",style="dashed", color="green", weight=3];
11.46/4.62	82[label="vy40",fontsize=16,color="green",shape="box"];83[label="vy50",fontsize=16,color="green",shape="box"];84[label="vy60",fontsize=16,color="green",shape="box"];85[label="vy70",fontsize=16,color="green",shape="box"];86[label="vy80",fontsize=16,color="green",shape="box"];}
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(8)
11.46/4.62	Complex Obligation (AND)
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(9)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) -> new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(10) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_gtGtEs(:(vy80, vy81), vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be) -> new_gtGtEs(vy81, vy3, vy40, vy50, vy60, vy70, h, ba, bb, bc, bd, be)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(11)
11.46/4.62	YES
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(12)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) -> new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(13) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_gtGtEs3(:(vy40, vy41), vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be) -> new_gtGtEs3(vy41, vy5, vy6, vy7, vy8, vy3, h, ba, bb, bc, bd, be)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(14)
11.46/4.62	YES
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(15)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) -> new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(16) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_gtGtEs2(:(vy50, vy51), vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be) -> new_gtGtEs2(vy51, vy6, vy7, vy8, vy3, vy40, h, ba, bb, bc, bd, be)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(17)
11.46/4.62	YES
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(18)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) -> new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(19) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_gtGtEs0(:(vy70, vy71), vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be) -> new_gtGtEs0(vy71, vy8, vy3, vy40, vy50, vy60, h, ba, bb, bc, bd, be)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(20)
11.46/4.62	YES
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(21)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) -> new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(22) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_gtGtEs1(:(vy60, vy61), vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be) -> new_gtGtEs1(vy61, vy7, vy8, vy3, vy40, vy50, h, ba, bb, bc, bd, be)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(23)
11.46/4.62	YES
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(24)
11.46/4.62	Obligation:
11.46/4.62	Q DP problem:
11.46/4.62	The TRS P consists of the following rules:
11.46/4.62	
11.46/4.62	   new_psPs(:(vy100, vy101), vy9, h) -> new_psPs(vy101, vy9, h)
11.46/4.62	
11.46/4.62	R is empty.
11.46/4.62	Q is empty.
11.46/4.62	We have to consider all minimal (P,Q,R)-chains.
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(25) QDPSizeChangeProof (EQUIVALENT)
11.46/4.62	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. 
11.46/4.62	
11.46/4.62	From the DPs we obtained the following set of size-change graphs:
11.46/4.62	*new_psPs(:(vy100, vy101), vy9, h) -> new_psPs(vy101, vy9, h)
11.46/4.62	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
11.46/4.62	
11.46/4.62	
11.46/4.62	----------------------------------------
11.46/4.62	
11.46/4.62	(26)
11.46/4.62	YES
11.61/4.66	EOF