8.82/3.82	YES
11.04/4.38	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.04/4.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.04/4.38	
11.04/4.38	
11.04/4.38	H-Termination with start terms of the given HASKELL could be proven:
11.04/4.38	
11.04/4.38	(0) HASKELL
11.04/4.38	(1) LR [EQUIVALENT, 0 ms]
11.04/4.38	(2) HASKELL
11.04/4.38	(3) BR [EQUIVALENT, 0 ms]
11.04/4.38	(4) HASKELL
11.04/4.38	(5) COR [EQUIVALENT, 0 ms]
11.04/4.38	(6) HASKELL
11.04/4.38	(7) Narrow [EQUIVALENT, 16 ms]
11.04/4.38	(8) YES
11.04/4.38	
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(0)
11.04/4.38	Obligation:
11.04/4.38	mainModule Main 
11.04/4.38	module Maybe where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Main where {
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Monad where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Prelude;
11.04/4.38	liftM4 :: Monad f => (c  ->  d  ->  a  ->  e  ->  b)  ->  f c  ->  f d  ->  f a  ->  f e  ->  f b;
11.04/4.38	liftM4 f m1 m2 m3 m4 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4)))));
11.04/4.38	
11.04/4.38	}
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(1) LR (EQUIVALENT)
11.04/4.38	Lambda Reductions:
11.04/4.38	The following Lambda expression
11.04/4.38	"\x4->return (f x1 x2 x3 x4)"
11.04/4.38	is transformed to
11.04/4.38	"liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.38	"
11.04/4.38	The following Lambda expression
11.04/4.38	"\x3->m4 >>= liftM40 f x1 x2 x3"
11.04/4.38	is transformed to
11.04/4.38	"liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.38	"
11.04/4.38	The following Lambda expression
11.04/4.38	"\x2->m3 >>= liftM41 m4 f x1 x2"
11.04/4.38	is transformed to
11.04/4.38	"liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.38	"
11.04/4.38	The following Lambda expression
11.04/4.38	"\x1->m2 >>= liftM42 m3 m4 f x1"
11.04/4.38	is transformed to
11.04/4.38	"liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.38	"
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(2)
11.04/4.38	Obligation:
11.04/4.38	mainModule Main 
11.04/4.38	module Maybe where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Main where {
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Monad where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Prelude;
11.04/4.38	liftM4 :: Monad f => (a  ->  b  ->  d  ->  e  ->  c)  ->  f a  ->  f b  ->  f d  ->  f e  ->  f c;
11.04/4.38	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.38	
11.04/4.38	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.38	
11.04/4.38	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.38	
11.04/4.38	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.38	
11.04/4.38	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.38	
11.04/4.38	}
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(3) BR (EQUIVALENT)
11.04/4.38	Replaced joker patterns by fresh variables and removed binding patterns.
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(4)
11.04/4.38	Obligation:
11.04/4.38	mainModule Main 
11.04/4.38	module Maybe where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Main where {
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Monad where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Prelude;
11.04/4.38	liftM4 :: Monad d => (f  ->  a  ->  b  ->  c  ->  e)  ->  d f  ->  d a  ->  d b  ->  d c  ->  d e;
11.04/4.38	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.38	
11.04/4.38	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.38	
11.04/4.38	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.38	
11.04/4.38	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.38	
11.04/4.38	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.38	
11.04/4.38	}
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(5) COR (EQUIVALENT)
11.04/4.38	Cond Reductions:
11.04/4.38	The following Function with conditions
11.04/4.38	"undefined |Falseundefined;
11.04/4.38	"
11.04/4.38	is transformed to
11.04/4.38	"undefined  = undefined1;
11.04/4.38	"
11.04/4.38	"undefined0 True = undefined;
11.04/4.38	"
11.04/4.38	"undefined1  = undefined0 False;
11.04/4.38	"
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(6)
11.04/4.38	Obligation:
11.04/4.38	mainModule Main 
11.04/4.38	module Maybe where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Main where {
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Monad;
11.04/4.38	import qualified Prelude;
11.04/4.38	}
11.04/4.38	module Monad where {
11.04/4.38	import qualified Main;
11.04/4.38	import qualified Maybe;
11.04/4.38	import qualified Prelude;
11.04/4.38	liftM4 :: Monad d => (b  ->  f  ->  e  ->  c  ->  a)  ->  d b  ->  d f  ->  d e  ->  d c  ->  d a;
11.04/4.38	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.38	
11.04/4.38	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.38	
11.04/4.38	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.38	
11.04/4.38	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.38	
11.04/4.38	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.38	
11.04/4.38	}
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(7) Narrow (EQUIVALENT)
11.04/4.38	Haskell To QDPs
11.04/4.38	
11.04/4.38	digraph dp_graph {
11.04/4.38	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM4",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.04/4.38	3[label="Monad.liftM4 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.04/4.38	4[label="Monad.liftM4 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.04/4.38	5[label="Monad.liftM4 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.04/4.38	6[label="Monad.liftM4 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
11.04/4.38	7[label="Monad.liftM4 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
11.04/4.38	8[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="burlywood",shape="box"];35[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];8 -> 35[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	35 -> 9[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	36[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 36[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	36 -> 10[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	9[label="Nothing >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
11.04/4.38	10[label="Just vy40 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11.04/4.38	11[label="Nothing",fontsize=16,color="green",shape="box"];12[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
11.04/4.38	13[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="burlywood",shape="box"];37[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];13 -> 37[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	37 -> 14[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	38[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	38 -> 15[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	14[label="Nothing >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
11.04/4.38	15[label="Just vy50 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
11.04/4.38	16[label="Nothing",fontsize=16,color="green",shape="box"];17[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
11.04/4.38	18[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="burlywood",shape="box"];39[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];18 -> 39[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	39 -> 19[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	40[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];18 -> 40[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	40 -> 20[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	19[label="Nothing >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
11.04/4.38	20[label="Just vy60 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
11.04/4.38	21[label="Nothing",fontsize=16,color="green",shape="box"];22[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
11.04/4.38	23[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="burlywood",shape="box"];41[label="vy7/Nothing",fontsize=10,color="white",style="solid",shape="box"];23 -> 41[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	41 -> 24[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	42[label="vy7/Just vy70",fontsize=10,color="white",style="solid",shape="box"];23 -> 42[label="",style="solid", color="burlywood", weight=9];
11.04/4.38	42 -> 25[label="",style="solid", color="burlywood", weight=3];
11.04/4.38	24[label="Nothing >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
11.04/4.38	25[label="Just vy70 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
11.04/4.38	26[label="Nothing",fontsize=16,color="green",shape="box"];27[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
11.04/4.38	28[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
11.04/4.38	29[label="Just (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];29 -> 30[label="",style="dashed", color="green", weight=3];
11.04/4.38	30[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];30 -> 31[label="",style="dashed", color="green", weight=3];
11.04/4.38	30 -> 32[label="",style="dashed", color="green", weight=3];
11.04/4.38	30 -> 33[label="",style="dashed", color="green", weight=3];
11.04/4.38	30 -> 34[label="",style="dashed", color="green", weight=3];
11.04/4.38	31[label="vy40",fontsize=16,color="green",shape="box"];32[label="vy50",fontsize=16,color="green",shape="box"];33[label="vy60",fontsize=16,color="green",shape="box"];34[label="vy70",fontsize=16,color="green",shape="box"];}
11.04/4.38	
11.04/4.38	----------------------------------------
11.04/4.38	
11.04/4.38	(8)
11.04/4.38	YES
11.09/4.42	EOF