8.99/3.89	YES
11.24/4.49	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
11.24/4.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.24/4.49	
11.24/4.49	
11.24/4.49	H-Termination with start terms of the given HASKELL could be proven:
11.24/4.49	
11.24/4.49	(0) HASKELL
11.24/4.49	(1) LR [EQUIVALENT, 0 ms]
11.24/4.49	(2) HASKELL
11.24/4.49	(3) BR [EQUIVALENT, 0 ms]
11.24/4.49	(4) HASKELL
11.24/4.49	(5) COR [EQUIVALENT, 0 ms]
11.24/4.49	(6) HASKELL
11.24/4.49	(7) Narrow [EQUIVALENT, 12 ms]
11.24/4.49	(8) YES
11.24/4.49	
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(0)
11.24/4.49	Obligation:
11.24/4.49	mainModule Main 
11.24/4.49	module Maybe where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Main where {
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Monad where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Prelude;
11.24/4.49	liftM5 :: Monad d => (g  ->  c  ->  a  ->  b  ->  f  ->  e)  ->  d g  ->  d c  ->  d a  ->  d b  ->  d f  ->  d e;
11.24/4.49	liftM5 f m1 m2 m3 m4 m5 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->m5 >>= (\x5 ->return (f x1 x2 x3 x4 x5))))));
11.24/4.49	
11.24/4.49	}
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(1) LR (EQUIVALENT)
11.24/4.49	Lambda Reductions:
11.24/4.49	The following Lambda expression
11.24/4.49	"\x5->return (f x1 x2 x3 x4 x5)"
11.24/4.49	is transformed to
11.24/4.49	"liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.24/4.49	"
11.24/4.49	The following Lambda expression
11.24/4.49	"\x4->m5 >>= liftM50 f x1 x2 x3 x4"
11.24/4.49	is transformed to
11.24/4.49	"liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.24/4.49	"
11.24/4.49	The following Lambda expression
11.24/4.49	"\x3->m4 >>= liftM51 m5 f x1 x2 x3"
11.24/4.49	is transformed to
11.24/4.49	"liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.24/4.49	"
11.24/4.49	The following Lambda expression
11.24/4.49	"\x2->m3 >>= liftM52 m4 m5 f x1 x2"
11.24/4.49	is transformed to
11.24/4.49	"liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.24/4.49	"
11.24/4.49	The following Lambda expression
11.24/4.49	"\x1->m2 >>= liftM53 m3 m4 m5 f x1"
11.24/4.49	is transformed to
11.24/4.49	"liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.24/4.49	"
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(2)
11.24/4.49	Obligation:
11.24/4.49	mainModule Main 
11.24/4.49	module Maybe where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Main where {
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Monad where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Prelude;
11.24/4.49	liftM5 :: Monad e => (f  ->  c  ->  d  ->  a  ->  b  ->  g)  ->  e f  ->  e c  ->  e d  ->  e a  ->  e b  ->  e g;
11.24/4.49	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.24/4.49	
11.24/4.49	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.24/4.49	
11.24/4.49	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.24/4.49	
11.24/4.49	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.24/4.49	
11.24/4.49	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.24/4.49	
11.24/4.49	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.24/4.49	
11.24/4.49	}
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(3) BR (EQUIVALENT)
11.24/4.49	Replaced joker patterns by fresh variables and removed binding patterns.
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(4)
11.24/4.49	Obligation:
11.24/4.49	mainModule Main 
11.24/4.49	module Maybe where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Main where {
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Monad where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Prelude;
11.24/4.49	liftM5 :: Monad a => (g  ->  c  ->  d  ->  b  ->  f  ->  e)  ->  a g  ->  a c  ->  a d  ->  a b  ->  a f  ->  a e;
11.24/4.49	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.24/4.49	
11.24/4.49	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.24/4.49	
11.24/4.49	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.24/4.49	
11.24/4.49	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.24/4.49	
11.24/4.49	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.24/4.49	
11.24/4.49	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.24/4.49	
11.24/4.49	}
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(5) COR (EQUIVALENT)
11.24/4.49	Cond Reductions:
11.24/4.49	The following Function with conditions
11.24/4.49	"undefined |Falseundefined;
11.24/4.49	"
11.24/4.49	is transformed to
11.24/4.49	"undefined  = undefined1;
11.24/4.49	"
11.24/4.49	"undefined0 True = undefined;
11.24/4.49	"
11.24/4.49	"undefined1  = undefined0 False;
11.24/4.49	"
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(6)
11.24/4.49	Obligation:
11.24/4.49	mainModule Main 
11.24/4.49	module Maybe where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Main where {
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Monad;
11.24/4.49	import qualified Prelude;
11.24/4.49	}
11.24/4.49	module Monad where {
11.24/4.49	import qualified Main;
11.24/4.49	import qualified Maybe;
11.24/4.49	import qualified Prelude;
11.24/4.49	liftM5 :: Monad c => (f  ->  b  ->  d  ->  e  ->  g  ->  a)  ->  c f  ->  c b  ->  c d  ->  c e  ->  c g  ->  c a;
11.24/4.49	liftM5 f m1 m2 m3 m4 m5 = m1 >>= liftM54 m2 m3 m4 m5 f;
11.24/4.49	
11.24/4.49	liftM50 f x1 x2 x3 x4 x5 = return (f x1 x2 x3 x4 x5);
11.24/4.49	
11.24/4.49	liftM51 m5 f x1 x2 x3 x4 = m5 >>= liftM50 f x1 x2 x3 x4;
11.24/4.49	
11.24/4.49	liftM52 m4 m5 f x1 x2 x3 = m4 >>= liftM51 m5 f x1 x2 x3;
11.24/4.49	
11.24/4.49	liftM53 m3 m4 m5 f x1 x2 = m3 >>= liftM52 m4 m5 f x1 x2;
11.24/4.49	
11.24/4.49	liftM54 m2 m3 m4 m5 f x1 = m2 >>= liftM53 m3 m4 m5 f x1;
11.24/4.49	
11.24/4.49	}
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(7) Narrow (EQUIVALENT)
11.24/4.49	Haskell To QDPs
11.24/4.49	
11.24/4.49	digraph dp_graph {
11.24/4.49	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM5",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.24/4.49	3[label="Monad.liftM5 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.24/4.49	4[label="Monad.liftM5 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.24/4.49	5[label="Monad.liftM5 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.24/4.49	6[label="Monad.liftM5 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
11.24/4.49	7[label="Monad.liftM5 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="grey",shape="box"];7 -> 8[label="",style="dashed", color="grey", weight=3];
11.24/4.49	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];
11.24/4.49	9[label="vy4 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="burlywood",shape="box"];42[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];9 -> 42[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	42 -> 10[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	43[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 43[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	43 -> 11[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	10[label="Nothing >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11.24/4.49	11[label="Just vy40 >>= Monad.liftM54 vy5 vy6 vy7 vy8 vy3",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
11.24/4.49	12[label="Nothing",fontsize=16,color="green",shape="box"];13[label="Monad.liftM54 vy5 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
11.24/4.49	14[label="vy5 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="burlywood",shape="box"];44[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];14 -> 44[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	44 -> 15[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	45[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];14 -> 45[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	45 -> 16[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	15[label="Nothing >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
11.24/4.49	16[label="Just vy50 >>= Monad.liftM53 vy6 vy7 vy8 vy3 vy40",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
11.24/4.49	17[label="Nothing",fontsize=16,color="green",shape="box"];18[label="Monad.liftM53 vy6 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
11.24/4.49	19[label="vy6 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];46[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];19 -> 46[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	46 -> 20[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	47[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];19 -> 47[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	47 -> 21[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	20[label="Nothing >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
11.24/4.49	21[label="Just vy60 >>= Monad.liftM52 vy7 vy8 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
11.24/4.49	22[label="Nothing",fontsize=16,color="green",shape="box"];23[label="Monad.liftM52 vy7 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
11.24/4.49	24[label="vy7 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];48[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];24 -> 48[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	48 -> 25[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	49[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];24 -> 49[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	49 -> 26[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	25[label="Nothing >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
11.24/4.49	26[label="Just vy70 >>= Monad.liftM51 vy8 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
11.24/4.49	27[label="Nothing",fontsize=16,color="green",shape="box"];28[label="Monad.liftM51 vy8 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
11.24/4.49	29[label="vy8 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="burlywood",shape="box"];50[label="vy8/Nothing",fontsize=10,color="white",style="solid",shape="box"];29 -> 50[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	50 -> 30[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	51[label="vy8/Just vy80",fontsize=10,color="white",style="solid",shape="box"];29 -> 51[label="",style="solid", color="burlywood", weight=9];
11.24/4.49	51 -> 31[label="",style="solid", color="burlywood", weight=3];
11.24/4.49	30[label="Nothing >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
11.24/4.49	31[label="Just vy80 >>= Monad.liftM50 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
11.24/4.49	32[label="Nothing",fontsize=16,color="green",shape="box"];33[label="Monad.liftM50 vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3];
11.24/4.49	34[label="return (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
11.24/4.49	35[label="Just (vy3 vy40 vy50 vy60 vy70 vy80)",fontsize=16,color="green",shape="box"];35 -> 36[label="",style="dashed", color="green", weight=3];
11.24/4.49	36[label="vy3 vy40 vy50 vy60 vy70 vy80",fontsize=16,color="green",shape="box"];36 -> 37[label="",style="dashed", color="green", weight=3];
11.24/4.49	36 -> 38[label="",style="dashed", color="green", weight=3];
11.24/4.49	36 -> 39[label="",style="dashed", color="green", weight=3];
11.24/4.49	36 -> 40[label="",style="dashed", color="green", weight=3];
11.24/4.49	36 -> 41[label="",style="dashed", color="green", weight=3];
11.24/4.49	37[label="vy40",fontsize=16,color="green",shape="box"];38[label="vy50",fontsize=16,color="green",shape="box"];39[label="vy60",fontsize=16,color="green",shape="box"];40[label="vy70",fontsize=16,color="green",shape="box"];41[label="vy80",fontsize=16,color="green",shape="box"];}
11.24/4.49	
11.24/4.49	----------------------------------------
11.24/4.49	
11.24/4.49	(8)
11.24/4.49	YES
11.24/4.52	EOF