8.96/3.90	YES
10.68/4.44	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.68/4.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.68/4.44	
10.68/4.44	
10.68/4.44	H-Termination with start terms of the given HASKELL could be proven:
10.68/4.44	
10.68/4.44	(0) HASKELL
10.68/4.44	(1) LR [EQUIVALENT, 0 ms]
10.68/4.44	(2) HASKELL
10.68/4.44	(3) BR [EQUIVALENT, 0 ms]
10.68/4.44	(4) HASKELL
10.68/4.44	(5) COR [EQUIVALENT, 0 ms]
10.68/4.44	(6) HASKELL
10.68/4.44	(7) Narrow [EQUIVALENT, 16 ms]
10.68/4.44	(8) YES
10.68/4.44	
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(0)
10.68/4.44	Obligation:
10.68/4.44	mainModule Main 
10.68/4.44	module Maybe where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Main where {
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Monad where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Prelude;
10.68/4.44	liftM2 :: Monad d => (b  ->  a  ->  c)  ->  d b  ->  d a  ->  d c;
10.68/4.44	liftM2 f m1 m2 = m1 >>= (\x1 ->m2 >>= (\x2 ->return (f x1 x2)));
10.68/4.44	
10.68/4.44	}
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(1) LR (EQUIVALENT)
10.68/4.44	Lambda Reductions:
10.68/4.44	The following Lambda expression
10.68/4.44	"\x2->return (f x1 x2)"
10.68/4.44	is transformed to
10.68/4.44	"liftM20 f x1 x2 = return (f x1 x2);
10.68/4.44	"
10.68/4.44	The following Lambda expression
10.68/4.44	"\x1->m2 >>= liftM20 f x1"
10.68/4.44	is transformed to
10.68/4.44	"liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.68/4.44	"
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(2)
10.68/4.44	Obligation:
10.68/4.44	mainModule Main 
10.68/4.44	module Maybe where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Main where {
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Monad where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Prelude;
10.68/4.44	liftM2 :: Monad a => (c  ->  d  ->  b)  ->  a c  ->  a d  ->  a b;
10.68/4.44	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.68/4.44	
10.68/4.44	liftM20 f x1 x2 = return (f x1 x2);
10.68/4.44	
10.68/4.44	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.68/4.44	
10.68/4.44	}
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(3) BR (EQUIVALENT)
10.68/4.44	Replaced joker patterns by fresh variables and removed binding patterns.
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(4)
10.68/4.44	Obligation:
10.68/4.44	mainModule Main 
10.68/4.44	module Maybe where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Main where {
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Monad where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Prelude;
10.68/4.44	liftM2 :: Monad a => (c  ->  b  ->  d)  ->  a c  ->  a b  ->  a d;
10.68/4.44	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.68/4.44	
10.68/4.44	liftM20 f x1 x2 = return (f x1 x2);
10.68/4.44	
10.68/4.44	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.68/4.44	
10.68/4.44	}
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(5) COR (EQUIVALENT)
10.68/4.44	Cond Reductions:
10.68/4.44	The following Function with conditions
10.68/4.44	"undefined |Falseundefined;
10.68/4.44	"
10.68/4.44	is transformed to
10.68/4.44	"undefined  = undefined1;
10.68/4.44	"
10.68/4.44	"undefined0 True = undefined;
10.68/4.44	"
10.68/4.44	"undefined1  = undefined0 False;
10.68/4.44	"
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(6)
10.68/4.44	Obligation:
10.68/4.44	mainModule Main 
10.68/4.44	module Maybe where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Main where {
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Monad;
10.68/4.44	import qualified Prelude;
10.68/4.44	}
10.68/4.44	module Monad where {
10.68/4.44	import qualified Main;
10.68/4.44	import qualified Maybe;
10.68/4.44	import qualified Prelude;
10.68/4.44	liftM2 :: Monad d => (c  ->  b  ->  a)  ->  d c  ->  d b  ->  d a;
10.68/4.44	liftM2 f m1 m2 = m1 >>= liftM21 m2 f;
10.68/4.44	
10.68/4.44	liftM20 f x1 x2 = return (f x1 x2);
10.68/4.44	
10.68/4.44	liftM21 m2 f x1 = m2 >>= liftM20 f x1;
10.68/4.44	
10.68/4.44	}
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(7) Narrow (EQUIVALENT)
10.68/4.44	Haskell To QDPs
10.68/4.44	
10.68/4.44	digraph dp_graph {
10.68/4.44	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM2",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.68/4.44	3[label="Monad.liftM2 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.68/4.44	4[label="Monad.liftM2 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
10.68/4.44	5[label="Monad.liftM2 vy3 vy4 vy5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
10.68/4.44	6[label="vy4 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="burlywood",shape="box"];21[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
10.68/4.44	21 -> 7[label="",style="solid", color="burlywood", weight=3];
10.68/4.44	22[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
10.68/4.44	22 -> 8[label="",style="solid", color="burlywood", weight=3];
10.68/4.44	7[label="Nothing >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.68/4.44	8[label="Just vy40 >>= Monad.liftM21 vy5 vy3",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
10.68/4.44	9[label="Nothing",fontsize=16,color="green",shape="box"];10[label="Monad.liftM21 vy5 vy3 vy40",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.68/4.44	11[label="vy5 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="burlywood",shape="box"];23[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];11 -> 23[label="",style="solid", color="burlywood", weight=9];
10.68/4.44	23 -> 12[label="",style="solid", color="burlywood", weight=3];
10.68/4.44	24[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];11 -> 24[label="",style="solid", color="burlywood", weight=9];
10.68/4.44	24 -> 13[label="",style="solid", color="burlywood", weight=3];
10.68/4.44	12[label="Nothing >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
10.68/4.44	13[label="Just vy50 >>= Monad.liftM20 vy3 vy40",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
10.68/4.44	14[label="Nothing",fontsize=16,color="green",shape="box"];15[label="Monad.liftM20 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
10.68/4.44	16[label="return (vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
10.68/4.44	17[label="Just (vy3 vy40 vy50)",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3];
10.68/4.44	18[label="vy3 vy40 vy50",fontsize=16,color="green",shape="box"];18 -> 19[label="",style="dashed", color="green", weight=3];
10.68/4.44	18 -> 20[label="",style="dashed", color="green", weight=3];
10.68/4.44	19[label="vy40",fontsize=16,color="green",shape="box"];20[label="vy50",fontsize=16,color="green",shape="box"];}
10.68/4.44	
10.68/4.44	----------------------------------------
10.68/4.44	
10.68/4.44	(8)
10.68/4.44	YES
10.84/7.07	EOF