8.80/3.83	YES
10.61/4.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.61/4.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.61/4.40	
10.61/4.40	
10.61/4.40	H-Termination with start terms of the given HASKELL could be proven:
10.61/4.40	
10.61/4.40	(0) HASKELL
10.61/4.40	(1) LR [EQUIVALENT, 0 ms]
10.61/4.40	(2) HASKELL
10.61/4.40	(3) BR [EQUIVALENT, 0 ms]
10.61/4.40	(4) HASKELL
10.61/4.40	(5) COR [EQUIVALENT, 0 ms]
10.61/4.40	(6) HASKELL
10.61/4.40	(7) Narrow [EQUIVALENT, 13 ms]
10.61/4.40	(8) YES
10.61/4.40	
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(0)
10.61/4.40	Obligation:
10.61/4.40	mainModule Main 
10.61/4.40	module Maybe where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Main where {
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Monad where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Prelude;
10.61/4.40	liftM :: Monad a => (b  ->  c)  ->  a b  ->  a c;
10.61/4.40	liftM f m1 = m1 >>= (\x1 ->return (f x1));
10.61/4.40	
10.61/4.40	}
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(1) LR (EQUIVALENT)
10.61/4.40	Lambda Reductions:
10.61/4.40	The following Lambda expression
10.61/4.40	"\x1->return (f x1)"
10.61/4.40	is transformed to
10.61/4.40	"liftM0 f x1 = return (f x1);
10.61/4.40	"
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(2)
10.61/4.40	Obligation:
10.61/4.40	mainModule Main 
10.61/4.40	module Maybe where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Main where {
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Monad where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Prelude;
10.61/4.40	liftM :: Monad a => (c  ->  b)  ->  a c  ->  a b;
10.61/4.40	liftM f m1 = m1 >>= liftM0 f;
10.61/4.40	
10.61/4.40	liftM0 f x1 = return (f x1);
10.61/4.40	
10.61/4.40	}
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(3) BR (EQUIVALENT)
10.61/4.40	Replaced joker patterns by fresh variables and removed binding patterns.
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(4)
10.61/4.40	Obligation:
10.61/4.40	mainModule Main 
10.61/4.40	module Maybe where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Main where {
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Monad where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Prelude;
10.61/4.40	liftM :: Monad a => (c  ->  b)  ->  a c  ->  a b;
10.61/4.40	liftM f m1 = m1 >>= liftM0 f;
10.61/4.40	
10.61/4.40	liftM0 f x1 = return (f x1);
10.61/4.40	
10.61/4.40	}
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(5) COR (EQUIVALENT)
10.61/4.40	Cond Reductions:
10.61/4.40	The following Function with conditions
10.61/4.40	"undefined |Falseundefined;
10.61/4.40	"
10.61/4.40	is transformed to
10.61/4.40	"undefined  = undefined1;
10.61/4.40	"
10.61/4.40	"undefined0 True = undefined;
10.61/4.40	"
10.61/4.40	"undefined1  = undefined0 False;
10.61/4.40	"
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(6)
10.61/4.40	Obligation:
10.61/4.40	mainModule Main 
10.61/4.40	module Maybe where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Main where {
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Monad;
10.61/4.40	import qualified Prelude;
10.61/4.40	}
10.61/4.40	module Monad where {
10.61/4.40	import qualified Main;
10.61/4.40	import qualified Maybe;
10.61/4.40	import qualified Prelude;
10.61/4.40	liftM :: Monad a => (b  ->  c)  ->  a b  ->  a c;
10.61/4.40	liftM f m1 = m1 >>= liftM0 f;
10.61/4.40	
10.61/4.40	liftM0 f x1 = return (f x1);
10.61/4.40	
10.61/4.40	}
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(7) Narrow (EQUIVALENT)
10.61/4.40	Haskell To QDPs
10.61/4.40	
10.61/4.40	digraph dp_graph {
10.61/4.40	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.61/4.40	3[label="Monad.liftM vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.61/4.40	4[label="Monad.liftM vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.61/4.40	5[label="vy4 >>= Monad.liftM0 vy3",fontsize=16,color="burlywood",shape="box"];14[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
10.61/4.40	14 -> 6[label="",style="solid", color="burlywood", weight=3];
10.61/4.40	15[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
10.61/4.40	15 -> 7[label="",style="solid", color="burlywood", weight=3];
10.61/4.40	6[label="Nothing >>= Monad.liftM0 vy3",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.61/4.40	7[label="Just vy40 >>= Monad.liftM0 vy3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.61/4.40	8[label="Nothing",fontsize=16,color="green",shape="box"];9[label="Monad.liftM0 vy3 vy40",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10.61/4.40	10[label="return (vy3 vy40)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.61/4.40	11[label="Just (vy3 vy40)",fontsize=16,color="green",shape="box"];11 -> 12[label="",style="dashed", color="green", weight=3];
10.61/4.40	12[label="vy3 vy40",fontsize=16,color="green",shape="box"];12 -> 13[label="",style="dashed", color="green", weight=3];
10.61/4.40	13[label="vy40",fontsize=16,color="green",shape="box"];}
10.61/4.40	
10.61/4.40	----------------------------------------
10.61/4.40	
10.61/4.40	(8)
10.61/4.40	YES
10.94/4.45	EOF