9.03/4.14	YES
11.17/4.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.17/4.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.17/4.69	
11.17/4.69	
11.17/4.69	H-Termination with start terms of the given HASKELL could be proven:
11.17/4.69	
11.17/4.69	(0) HASKELL
11.17/4.69	(1) LR [EQUIVALENT, 0 ms]
11.17/4.69	(2) HASKELL
11.17/4.69	(3) BR [EQUIVALENT, 0 ms]
11.17/4.69	(4) HASKELL
11.17/4.69	(5) COR [EQUIVALENT, 0 ms]
11.17/4.69	(6) HASKELL
11.17/4.69	(7) Narrow [EQUIVALENT, 28 ms]
11.17/4.69	(8) YES
11.17/4.69	
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(0)
11.17/4.69	Obligation:
11.17/4.69	mainModule Main 
11.17/4.69	module Maybe where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Main where {
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Monad where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Prelude;
11.17/4.69	liftM :: Monad c => (a  ->  b)  ->  c a  ->  c b;
11.17/4.69	liftM f m1 = m1 >>= (\x1 ->return (f x1));
11.17/4.69	
11.17/4.69	}
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(1) LR (EQUIVALENT)
11.17/4.69	Lambda Reductions:
11.17/4.69	The following Lambda expression
11.17/4.69	"\x1->return (f x1)"
11.17/4.69	is transformed to
11.17/4.69	"liftM0 f x1 = return (f x1);
11.17/4.69	"
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(2)
11.17/4.69	Obligation:
11.17/4.69	mainModule Main 
11.17/4.69	module Maybe where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Main where {
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Monad where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Prelude;
11.17/4.69	liftM :: Monad c => (a  ->  b)  ->  c a  ->  c b;
11.17/4.69	liftM f m1 = m1 >>= liftM0 f;
11.17/4.69	
11.17/4.69	liftM0 f x1 = return (f x1);
11.17/4.69	
11.17/4.69	}
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(3) BR (EQUIVALENT)
11.17/4.69	Replaced joker patterns by fresh variables and removed binding patterns.
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(4)
11.17/4.69	Obligation:
11.17/4.69	mainModule Main 
11.17/4.69	module Maybe where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Main where {
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Monad where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Prelude;
11.17/4.69	liftM :: Monad a => (b  ->  c)  ->  a b  ->  a c;
11.17/4.69	liftM f m1 = m1 >>= liftM0 f;
11.17/4.69	
11.17/4.69	liftM0 f x1 = return (f x1);
11.17/4.69	
11.17/4.69	}
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(5) COR (EQUIVALENT)
11.17/4.69	Cond Reductions:
11.17/4.69	The following Function with conditions
11.17/4.69	"undefined |Falseundefined;
11.17/4.69	"
11.17/4.69	is transformed to
11.17/4.69	"undefined  = undefined1;
11.17/4.69	"
11.17/4.69	"undefined0 True = undefined;
11.17/4.69	"
11.17/4.69	"undefined1  = undefined0 False;
11.17/4.69	"
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(6)
11.17/4.69	Obligation:
11.17/4.69	mainModule Main 
11.17/4.69	module Maybe where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Main where {
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Monad;
11.17/4.69	import qualified Prelude;
11.17/4.69	}
11.17/4.69	module Monad where {
11.17/4.69	import qualified Main;
11.17/4.69	import qualified Maybe;
11.17/4.69	import qualified Prelude;
11.17/4.69	liftM :: Monad a => (c  ->  b)  ->  a c  ->  a b;
11.17/4.69	liftM f m1 = m1 >>= liftM0 f;
11.17/4.69	
11.17/4.69	liftM0 f x1 = return (f x1);
11.17/4.69	
11.17/4.69	}
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(7) Narrow (EQUIVALENT)
11.17/4.69	Haskell To QDPs
11.17/4.69	
11.17/4.69	digraph dp_graph {
11.17/4.69	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.17/4.69	3[label="Monad.liftM vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.17/4.69	4[label="Monad.liftM vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.17/4.69	5[label="vy4 >>= Monad.liftM0 vy3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
11.17/4.69	6[label="primbindIO vy4 (Monad.liftM0 vy3)",fontsize=16,color="burlywood",shape="box"];20[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
11.17/4.69	20 -> 7[label="",style="solid", color="burlywood", weight=3];
11.17/4.69	21[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
11.17/4.69	21 -> 8[label="",style="solid", color="burlywood", weight=3];
11.17/4.69	22[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
11.17/4.69	22 -> 9[label="",style="solid", color="burlywood", weight=3];
11.17/4.69	23[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9];
11.17/4.69	23 -> 10[label="",style="solid", color="burlywood", weight=3];
11.17/4.69	7[label="primbindIO (IO vy40) (Monad.liftM0 vy3)",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
11.17/4.69	8[label="primbindIO (AProVE_IO vy40) (Monad.liftM0 vy3)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
11.17/4.69	9[label="primbindIO (AProVE_Exception vy40) (Monad.liftM0 vy3)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
11.17/4.69	10[label="primbindIO (AProVE_Error vy40) (Monad.liftM0 vy3)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11.17/4.69	11[label="error []",fontsize=16,color="red",shape="box"];12[label="Monad.liftM0 vy3 vy40",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
11.17/4.69	13[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];14[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];15[label="return (vy3 vy40)",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
11.17/4.69	16[label="primretIO (vy3 vy40)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
11.17/4.69	17[label="AProVE_IO (vy3 vy40)",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3];
11.17/4.69	18[label="vy3 vy40",fontsize=16,color="green",shape="box"];18 -> 19[label="",style="dashed", color="green", weight=3];
11.17/4.69	19[label="vy40",fontsize=16,color="green",shape="box"];}
11.17/4.69	
11.17/4.69	----------------------------------------
11.17/4.69	
11.17/4.69	(8)
11.17/4.69	YES
11.22/4.73	EOF