10.01/4.27	MAYBE
12.25/4.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.25/4.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.25/4.89	
12.25/4.89	
12.25/4.89	H-Termination with start terms of the given HASKELL could not be shown:
12.25/4.89	
12.25/4.89	(0) HASKELL
12.25/4.89	(1) LR [EQUIVALENT, 0 ms]
12.25/4.89	(2) HASKELL
12.25/4.89	(3) BR [EQUIVALENT, 0 ms]
12.25/4.89	(4) HASKELL
12.25/4.89	(5) COR [EQUIVALENT, 0 ms]
12.25/4.89	(6) HASKELL
12.25/4.89	(7) Narrow [SOUND, 0 ms]
12.25/4.89	(8) AND
12.25/4.89	    (9) QDP
12.25/4.89	        (10) MRRProof [EQUIVALENT, 23 ms]
12.25/4.89	        (11) QDP
12.25/4.89	        (12) NonTerminationLoopProof [COMPLETE, 0 ms]
12.25/4.89	        (13) NO
12.25/4.89	    (14) QDP
12.25/4.89	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.25/4.89	        (16) YES
12.25/4.89	    (17) QDP
12.25/4.89	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.25/4.89	        (19) YES
12.25/4.89	    (20) QDP
12.25/4.89	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.25/4.89	        (22) YES
12.25/4.89	    (23) QDP
12.25/4.89	        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.25/4.89	        (25) YES
12.25/4.89	(26) Narrow [COMPLETE, 0 ms]
12.25/4.89	(27) AND
12.25/4.89	    (28) QDP
12.25/4.89	        (29) DependencyGraphProof [EQUIVALENT, 0 ms]
12.25/4.89	        (30) TRUE
12.25/4.89	    (31) QDP
12.25/4.89	        (32) DependencyGraphProof [EQUIVALENT, 0 ms]
12.25/4.89	        (33) TRUE
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(0)
12.25/4.89	Obligation:
12.25/4.89	mainModule Main 
12.25/4.89	module Maybe where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Main where {
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Monad where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Prelude;
12.25/4.89	foldM :: Monad a => (c  ->  b  ->  a c)  ->  c  ->  [b]  ->  a c;
12.25/4.89	foldM _ a [] = return a;
12.25/4.89	foldM f a (x : xs) = f a x >>= (\fax ->foldM f fax xs);
12.25/4.89	
12.25/4.89	foldM_ :: Monad c => (b  ->  a  ->  c b)  ->  b  ->  [a]  ->  c ();
12.25/4.89	foldM_ f a xs = foldM f a xs >> return ();
12.25/4.89	
12.25/4.89	}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(1) LR (EQUIVALENT)
12.25/4.89	Lambda Reductions:
12.25/4.89	The following Lambda expression
12.25/4.89	"\_->q"
12.25/4.89	is transformed to
12.25/4.89	"gtGt0 q _ = q;
12.25/4.89	"
12.25/4.89	The following Lambda expression
12.25/4.89	"\fax->foldM f fax xs"
12.25/4.89	is transformed to
12.25/4.89	"foldM0 f xs fax = foldM f fax xs;
12.25/4.89	"
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(2)
12.25/4.89	Obligation:
12.25/4.89	mainModule Main 
12.25/4.89	module Maybe where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Main where {
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Monad where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Prelude;
12.25/4.89	foldM :: Monad b => (c  ->  a  ->  b c)  ->  c  ->  [a]  ->  b c;
12.25/4.89	foldM _ a [] = return a;
12.25/4.89	foldM f a (x : xs) = f a x >>= foldM0 f xs;
12.25/4.89	
12.25/4.89	foldM0 f xs fax = foldM f fax xs;
12.25/4.89	
12.25/4.89	foldM_ :: Monad a => (b  ->  c  ->  a b)  ->  b  ->  [c]  ->  a ();
12.25/4.89	foldM_ f a xs = foldM f a xs >> return ();
12.25/4.89	
12.25/4.89	}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(3) BR (EQUIVALENT)
12.25/4.89	Replaced joker patterns by fresh variables and removed binding patterns.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(4)
12.25/4.89	Obligation:
12.25/4.89	mainModule Main 
12.25/4.89	module Maybe where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Main where {
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Monad where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Prelude;
12.25/4.89	foldM :: Monad b => (a  ->  c  ->  b a)  ->  a  ->  [c]  ->  b a;
12.25/4.89	foldM vz a [] = return a;
12.25/4.89	foldM f a (x : xs) = f a x >>= foldM0 f xs;
12.25/4.89	
12.25/4.89	foldM0 f xs fax = foldM f fax xs;
12.25/4.89	
12.25/4.89	foldM_ :: Monad b => (a  ->  c  ->  b a)  ->  a  ->  [c]  ->  b ();
12.25/4.89	foldM_ f a xs = foldM f a xs >> return ();
12.25/4.89	
12.25/4.89	}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(5) COR (EQUIVALENT)
12.25/4.89	Cond Reductions:
12.25/4.89	The following Function with conditions
12.25/4.89	"undefined |Falseundefined;
12.25/4.89	"
12.25/4.89	is transformed to
12.25/4.89	"undefined  = undefined1;
12.25/4.89	"
12.25/4.89	"undefined0 True = undefined;
12.25/4.89	"
12.25/4.89	"undefined1  = undefined0 False;
12.25/4.89	"
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(6)
12.25/4.89	Obligation:
12.25/4.89	mainModule Main 
12.25/4.89	module Maybe where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Main where {
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Monad;
12.25/4.89	import qualified Prelude;
12.25/4.89	}
12.25/4.89	module Monad where {
12.25/4.89	import qualified Main;
12.25/4.89	import qualified Maybe;
12.25/4.89	import qualified Prelude;
12.25/4.89	foldM :: Monad b => (a  ->  c  ->  b a)  ->  a  ->  [c]  ->  b a;
12.25/4.89	foldM vz a [] = return a;
12.25/4.89	foldM f a (x : xs) = f a x >>= foldM0 f xs;
12.25/4.89	
12.25/4.89	foldM0 f xs fax = foldM f fax xs;
12.25/4.89	
12.25/4.89	foldM_ :: Monad b => (a  ->  c  ->  b a)  ->  a  ->  [c]  ->  b ();
12.25/4.89	foldM_ f a xs = foldM f a xs >> return ();
12.25/4.89	
12.25/4.89	}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(7) Narrow (SOUND)
12.25/4.89	Haskell To QDPs
12.25/4.89	
12.25/4.89	digraph dp_graph {
12.25/4.89	node [outthreshold=100, inthreshold=100];1[label="Monad.foldM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.25/4.89	3[label="Monad.foldM_ wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.25/4.89	4[label="Monad.foldM_ wu3 wu4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.25/4.89	5[label="Monad.foldM_ wu3 wu4 wu5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
12.25/4.89	6[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="blue",shape="box"];639[label=">> :: (Maybe a) -> (Maybe ()) -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 639[label="",style="solid", color="blue", weight=9];
12.25/4.89	639 -> 7[label="",style="solid", color="blue", weight=3];
12.25/4.89	640[label=">> :: ([] a) -> ([] ()) -> [] ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 640[label="",style="solid", color="blue", weight=9];
12.25/4.89	640 -> 8[label="",style="solid", color="blue", weight=3];
12.25/4.89	641[label=">> :: (IO a) -> (IO ()) -> IO ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 641[label="",style="solid", color="blue", weight=9];
12.25/4.89	641 -> 9[label="",style="solid", color="blue", weight=3];
12.25/4.89	7[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
12.25/4.89	8[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
12.25/4.89	9[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
12.25/4.89	10[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];642[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];10 -> 642[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	642 -> 13[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	643[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 643[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	643 -> 14[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	11 -> 524[label="",style="dashed", color="red", weight=0];
12.25/4.89	11[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="magenta"];11 -> 525[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	12[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
12.25/4.89	13[label="Monad.foldM wu3 wu4 (wu50 : wu51) >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3];
12.25/4.89	14[label="Monad.foldM wu3 wu4 [] >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3];
12.25/4.89	525[label="Monad.foldM wu3 wu4 wu5",fontsize=16,color="burlywood",shape="triangle"];644[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];525 -> 644[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	644 -> 579[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	645[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];525 -> 645[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	645 -> 580[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	524[label="wu37 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];646[label="wu37/wu370 : wu371",fontsize=10,color="white",style="solid",shape="box"];524 -> 646[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	646 -> 581[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	647[label="wu37/[]",fontsize=10,color="white",style="solid",shape="box"];524 -> 647[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	647 -> 582[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	17[label="primbindIO (Monad.foldM wu3 wu4 wu5) (gtGt0 (return ()))",fontsize=16,color="burlywood",shape="triangle"];648[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];17 -> 648[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	648 -> 22[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	649[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 649[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	649 -> 23[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	18 -> 24[label="",style="dashed", color="red", weight=0];
12.25/4.89	18[label="wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="magenta"];18 -> 25[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	19[label="return wu4 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3];
12.25/4.89	579[label="Monad.foldM wu3 wu4 (wu50 : wu51)",fontsize=16,color="black",shape="box"];579 -> 583[label="",style="solid", color="black", weight=3];
12.25/4.89	580[label="Monad.foldM wu3 wu4 []",fontsize=16,color="black",shape="box"];580 -> 584[label="",style="solid", color="black", weight=3];
12.25/4.89	581[label="wu370 : wu371 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];581 -> 585[label="",style="solid", color="black", weight=3];
12.25/4.89	582[label="[] >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];582 -> 586[label="",style="solid", color="black", weight=3];
12.25/4.89	22[label="primbindIO (Monad.foldM wu3 wu4 (wu50 : wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];22 -> 30[label="",style="solid", color="black", weight=3];
12.25/4.89	23[label="primbindIO (Monad.foldM wu3 wu4 []) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];23 -> 31[label="",style="solid", color="black", weight=3];
12.25/4.89	25[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];25 -> 32[label="",style="dashed", color="green", weight=3];
12.25/4.89	25 -> 33[label="",style="dashed", color="green", weight=3];
12.25/4.89	24[label="wu6 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];650[label="wu6/Nothing",fontsize=10,color="white",style="solid",shape="box"];24 -> 650[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	650 -> 34[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	651[label="wu6/Just wu60",fontsize=10,color="white",style="solid",shape="box"];24 -> 651[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	651 -> 35[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	26[label="Just wu4 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];26 -> 36[label="",style="solid", color="black", weight=3];
12.25/4.89	583 -> 587[label="",style="dashed", color="red", weight=0];
12.25/4.89	583[label="wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="magenta"];583 -> 588[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	584[label="return wu4",fontsize=16,color="black",shape="triangle"];584 -> 589[label="",style="solid", color="black", weight=3];
12.25/4.89	585 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	585[label="gtGt0 (return ()) wu370 ++ (wu371 >>= gtGt0 (return ()))",fontsize=16,color="magenta"];585 -> 612[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	585 -> 613[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	586[label="[]",fontsize=16,color="green",shape="box"];30[label="primbindIO (wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
12.25/4.89	31[label="primbindIO (return wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];31 -> 45[label="",style="solid", color="black", weight=3];
12.25/4.89	32[label="wu4",fontsize=16,color="green",shape="box"];33[label="wu50",fontsize=16,color="green",shape="box"];34[label="Nothing >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];34 -> 46[label="",style="solid", color="black", weight=3];
12.25/4.89	35[label="Just wu60 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];35 -> 47[label="",style="solid", color="black", weight=3];
12.25/4.89	36[label="gtGt0 (return ()) wu4",fontsize=16,color="black",shape="box"];36 -> 48[label="",style="solid", color="black", weight=3];
12.25/4.89	588[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];588 -> 593[label="",style="dashed", color="green", weight=3];
12.25/4.89	588 -> 594[label="",style="dashed", color="green", weight=3];
12.25/4.89	587[label="wu38 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="burlywood",shape="triangle"];652[label="wu38/wu380 : wu381",fontsize=10,color="white",style="solid",shape="box"];587 -> 652[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	652 -> 595[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	653[label="wu38/[]",fontsize=10,color="white",style="solid",shape="box"];587 -> 653[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	653 -> 596[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	589[label="wu4 : []",fontsize=16,color="green",shape="box"];612 -> 524[label="",style="dashed", color="red", weight=0];
12.25/4.89	612[label="wu371 >>= gtGt0 (return ())",fontsize=16,color="magenta"];612 -> 624[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	613 -> 625[label="",style="dashed", color="red", weight=0];
12.25/4.89	613[label="gtGt0 (return ()) wu370",fontsize=16,color="magenta"];613 -> 626[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	611[label="wu43 ++ wu42",fontsize=16,color="burlywood",shape="triangle"];654[label="wu43/wu430 : wu431",fontsize=10,color="white",style="solid",shape="box"];611 -> 654[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	654 -> 627[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	655[label="wu43/[]",fontsize=10,color="white",style="solid",shape="box"];611 -> 655[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	655 -> 628[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	44 -> 52[label="",style="dashed", color="red", weight=0];
12.25/4.89	44[label="primbindIO (primbindIO (wu3 wu4 wu50) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="magenta"];44 -> 53[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	45[label="primbindIO (primretIO wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.25/4.89	46[label="Nothing >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.25/4.89	47[label="Monad.foldM0 wu3 wu51 wu60 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.25/4.89	48[label="return ()",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.25/4.89	593[label="wu4",fontsize=16,color="green",shape="box"];594[label="wu50",fontsize=16,color="green",shape="box"];595[label="wu380 : wu381 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="black",shape="box"];595 -> 600[label="",style="solid", color="black", weight=3];
12.25/4.89	596[label="[] >>= Monad.foldM0 wu3 wu51",fontsize=16,color="black",shape="box"];596 -> 601[label="",style="solid", color="black", weight=3];
12.25/4.89	624[label="wu371",fontsize=16,color="green",shape="box"];626 -> 584[label="",style="dashed", color="red", weight=0];
12.25/4.89	626[label="return ()",fontsize=16,color="magenta"];626 -> 629[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	625[label="gtGt0 wu44 wu370",fontsize=16,color="black",shape="triangle"];625 -> 630[label="",style="solid", color="black", weight=3];
12.25/4.89	627[label="(wu430 : wu431) ++ wu42",fontsize=16,color="black",shape="box"];627 -> 633[label="",style="solid", color="black", weight=3];
12.25/4.89	628[label="[] ++ wu42",fontsize=16,color="black",shape="box"];628 -> 634[label="",style="solid", color="black", weight=3];
12.25/4.89	53[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];53 -> 62[label="",style="dashed", color="green", weight=3];
12.25/4.89	53 -> 63[label="",style="dashed", color="green", weight=3];
12.25/4.89	52[label="primbindIO (primbindIO wu8 (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="burlywood",shape="triangle"];656[label="wu8/IO wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 656[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	656 -> 64[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	657[label="wu8/AProVE_IO wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 657[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	657 -> 65[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	658[label="wu8/AProVE_Exception wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 658[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	658 -> 66[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	659[label="wu8/AProVE_Error wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 659[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	659 -> 67[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	54[label="primbindIO (AProVE_IO wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];54 -> 68[label="",style="solid", color="black", weight=3];
12.25/4.89	55[label="Nothing",fontsize=16,color="green",shape="box"];56 -> 10[label="",style="dashed", color="red", weight=0];
12.25/4.89	56[label="Monad.foldM wu3 wu60 wu51 >>= gtGt0 (return ())",fontsize=16,color="magenta"];56 -> 69[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	56 -> 70[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	57[label="Just ()",fontsize=16,color="green",shape="box"];600 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	600[label="Monad.foldM0 wu3 wu51 wu380 ++ (wu381 >>= Monad.foldM0 wu3 wu51)",fontsize=16,color="magenta"];600 -> 618[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	600 -> 619[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	601[label="[]",fontsize=16,color="green",shape="box"];629[label="()",fontsize=16,color="green",shape="box"];630[label="wu44",fontsize=16,color="green",shape="box"];633[label="wu430 : wu431 ++ wu42",fontsize=16,color="green",shape="box"];633 -> 637[label="",style="dashed", color="green", weight=3];
12.25/4.89	634[label="wu42",fontsize=16,color="green",shape="box"];62[label="wu4",fontsize=16,color="green",shape="box"];63[label="wu50",fontsize=16,color="green",shape="box"];64[label="primbindIO (primbindIO (IO wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];64 -> 74[label="",style="solid", color="black", weight=3];
12.25/4.89	65[label="primbindIO (primbindIO (AProVE_IO wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];65 -> 75[label="",style="solid", color="black", weight=3];
12.25/4.89	66[label="primbindIO (primbindIO (AProVE_Exception wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];66 -> 76[label="",style="solid", color="black", weight=3];
12.25/4.89	67[label="primbindIO (primbindIO (AProVE_Error wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];67 -> 77[label="",style="solid", color="black", weight=3];
12.25/4.89	68[label="gtGt0 (return ()) wu4",fontsize=16,color="black",shape="box"];68 -> 78[label="",style="solid", color="black", weight=3];
12.25/4.89	69[label="wu51",fontsize=16,color="green",shape="box"];70[label="wu60",fontsize=16,color="green",shape="box"];618 -> 587[label="",style="dashed", color="red", weight=0];
12.25/4.89	618[label="wu381 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="magenta"];618 -> 631[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	619[label="Monad.foldM0 wu3 wu51 wu380",fontsize=16,color="black",shape="box"];619 -> 632[label="",style="solid", color="black", weight=3];
12.25/4.89	637 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	637[label="wu431 ++ wu42",fontsize=16,color="magenta"];637 -> 638[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	74[label="error []",fontsize=16,color="red",shape="box"];75[label="primbindIO (Monad.foldM0 wu3 wu51 wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];75 -> 82[label="",style="solid", color="black", weight=3];
12.25/4.89	76[label="primbindIO (AProVE_Exception wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3];
12.25/4.89	77[label="primbindIO (AProVE_Error wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3];
12.25/4.89	78[label="return ()",fontsize=16,color="black",shape="box"];78 -> 85[label="",style="solid", color="black", weight=3];
12.25/4.89	631[label="wu381",fontsize=16,color="green",shape="box"];632 -> 525[label="",style="dashed", color="red", weight=0];
12.25/4.89	632[label="Monad.foldM wu3 wu380 wu51",fontsize=16,color="magenta"];632 -> 635[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	632 -> 636[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	638[label="wu431",fontsize=16,color="green",shape="box"];82 -> 17[label="",style="dashed", color="red", weight=0];
12.25/4.89	82[label="primbindIO (Monad.foldM wu3 wu80 wu51) (gtGt0 (return ()))",fontsize=16,color="magenta"];82 -> 90[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	82 -> 91[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	83[label="AProVE_Exception wu80",fontsize=16,color="green",shape="box"];84[label="AProVE_Error wu80",fontsize=16,color="green",shape="box"];85[label="primretIO ()",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3];
12.25/4.89	635[label="wu51",fontsize=16,color="green",shape="box"];636[label="wu380",fontsize=16,color="green",shape="box"];90[label="wu51",fontsize=16,color="green",shape="box"];91[label="wu80",fontsize=16,color="green",shape="box"];92[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(8)
12.25/4.89	Complex Obligation (AND)
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(9)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_foldM(wu3, :(wu50, wu51), h, ba) -> new_gtGtEs(wu3, wu51, h, ba)
12.25/4.89	   new_gtGtEs(wu3, wu51, h, ba) -> new_gtGtEs(wu3, wu51, h, ba)
12.25/4.89	   new_gtGtEs(wu3, wu51, h, ba) -> new_foldM(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(10) MRRProof (EQUIVALENT)
12.25/4.89	By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
12.25/4.89	
12.25/4.89	Strictly oriented dependency pairs:
12.25/4.89	
12.25/4.89	   new_foldM(wu3, :(wu50, wu51), h, ba) -> new_gtGtEs(wu3, wu51, h, ba)
12.25/4.89	   new_gtGtEs(wu3, wu51, h, ba) -> new_foldM(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	
12.25/4.89	Used ordering: Polynomial interpretation [POLO]:
12.25/4.89	
12.25/4.89	   POL(:(x_1, x_2)) = 2 + x_1 + 2*x_2
12.25/4.89	   POL(new_foldM(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + x_3 + x_4
12.25/4.89	   POL(new_gtGtEs(x_1, x_2, x_3, x_4)) = 2 + x_1 + 2*x_2 + x_3 + x_4
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(11)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_gtGtEs(wu3, wu51, h, ba) -> new_gtGtEs(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(12) NonTerminationLoopProof (COMPLETE)
12.25/4.89	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
12.25/4.89	Found a loop by semiunifying a rule from P directly.
12.25/4.89	
12.25/4.89	s = new_gtGtEs(wu3, wu51, h, ba) evaluates to  t =new_gtGtEs(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
12.25/4.89	* Matcher: [ ]
12.25/4.89	* Semiunifier: [ ]
12.25/4.89	
12.25/4.89	--------------------------------------------------------------------------------
12.25/4.89	Rewriting sequence
12.25/4.89	
12.25/4.89	The DP semiunifies directly so there is only one rewrite step from new_gtGtEs(wu3, wu51, h, ba) to new_gtGtEs(wu3, wu51, h, ba).
12.25/4.89	
12.25/4.89	
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(13)
12.25/4.89	NO
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(14)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_primbindIO(wu3, wu51, h, ba) -> new_primbindIO0(wu3, wu51, h, ba)
12.25/4.89	   new_primbindIO0(wu3, :(wu50, wu51), h, ba) -> new_primbindIO(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(15) QDPSizeChangeProof (EQUIVALENT)
12.25/4.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.25/4.89	
12.25/4.89	From the DPs we obtained the following set of size-change graphs:
12.25/4.89	*new_primbindIO0(wu3, :(wu50, wu51), h, ba) -> new_primbindIO(wu3, wu51, h, ba)
12.25/4.89	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.25/4.89	
12.25/4.89	
12.25/4.89	*new_primbindIO(wu3, wu51, h, ba) -> new_primbindIO0(wu3, wu51, h, ba)
12.25/4.89	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(16)
12.25/4.89	YES
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(17)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_psPs(:(wu430, wu431), wu42, h) -> new_psPs(wu431, wu42, h)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(18) QDPSizeChangeProof (EQUIVALENT)
12.25/4.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.25/4.89	
12.25/4.89	From the DPs we obtained the following set of size-change graphs:
12.25/4.89	*new_psPs(:(wu430, wu431), wu42, h) -> new_psPs(wu431, wu42, h)
12.25/4.89	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(19)
12.25/4.89	YES
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(20)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_gtGtEs2(wu3, :(wu50, wu51), h, ba) -> new_gtGtEs1(wu3, wu51, h, ba)
12.25/4.89	   new_gtGtEs1(wu3, wu51, h, ba) -> new_gtGtEs2(wu3, wu51, h, ba)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(21) QDPSizeChangeProof (EQUIVALENT)
12.25/4.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.25/4.89	
12.25/4.89	From the DPs we obtained the following set of size-change graphs:
12.25/4.89	*new_gtGtEs1(wu3, wu51, h, ba) -> new_gtGtEs2(wu3, wu51, h, ba)
12.25/4.89	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4
12.25/4.89	
12.25/4.89	
12.25/4.89	*new_gtGtEs2(wu3, :(wu50, wu51), h, ba) -> new_gtGtEs1(wu3, wu51, h, ba)
12.25/4.89	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(22)
12.25/4.89	YES
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(23)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_gtGtEs0(:(wu370, wu371), h) -> new_gtGtEs0(wu371, h)
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all minimal (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(24) QDPSizeChangeProof (EQUIVALENT)
12.25/4.89	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.25/4.89	
12.25/4.89	From the DPs we obtained the following set of size-change graphs:
12.25/4.89	*new_gtGtEs0(:(wu370, wu371), h) -> new_gtGtEs0(wu371, h)
12.25/4.89	The graph contains the following edges 1 > 1, 2 >= 2
12.25/4.89	
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(25)
12.25/4.89	YES
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(26) Narrow (COMPLETE)
12.25/4.89	Haskell To QDPs
12.25/4.89	
12.25/4.89	digraph dp_graph {
12.25/4.89	node [outthreshold=100, inthreshold=100];1[label="Monad.foldM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.25/4.89	3[label="Monad.foldM_ wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.25/4.89	4[label="Monad.foldM_ wu3 wu4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.25/4.89	5[label="Monad.foldM_ wu3 wu4 wu5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
12.25/4.89	6[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="blue",shape="box"];639[label=">> :: (Maybe a) -> (Maybe ()) -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 639[label="",style="solid", color="blue", weight=9];
12.25/4.89	639 -> 7[label="",style="solid", color="blue", weight=3];
12.25/4.89	640[label=">> :: ([] a) -> ([] ()) -> [] ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 640[label="",style="solid", color="blue", weight=9];
12.25/4.89	640 -> 8[label="",style="solid", color="blue", weight=3];
12.25/4.89	641[label=">> :: (IO a) -> (IO ()) -> IO ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 641[label="",style="solid", color="blue", weight=9];
12.25/4.89	641 -> 9[label="",style="solid", color="blue", weight=3];
12.25/4.89	7[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
12.25/4.89	8[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
12.25/4.89	9[label="Monad.foldM wu3 wu4 wu5 >> return ()",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
12.25/4.89	10[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];642[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];10 -> 642[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	642 -> 13[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	643[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 643[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	643 -> 14[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	11 -> 524[label="",style="dashed", color="red", weight=0];
12.25/4.89	11[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="magenta"];11 -> 525[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	12[label="Monad.foldM wu3 wu4 wu5 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3];
12.25/4.89	13[label="Monad.foldM wu3 wu4 (wu50 : wu51) >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3];
12.25/4.89	14[label="Monad.foldM wu3 wu4 [] >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];14 -> 19[label="",style="solid", color="black", weight=3];
12.25/4.89	525[label="Monad.foldM wu3 wu4 wu5",fontsize=16,color="burlywood",shape="triangle"];644[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];525 -> 644[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	644 -> 579[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	645[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];525 -> 645[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	645 -> 580[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	524[label="wu37 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];646[label="wu37/wu370 : wu371",fontsize=10,color="white",style="solid",shape="box"];524 -> 646[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	646 -> 581[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	647[label="wu37/[]",fontsize=10,color="white",style="solid",shape="box"];524 -> 647[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	647 -> 582[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	17[label="primbindIO (Monad.foldM wu3 wu4 wu5) (gtGt0 (return ()))",fontsize=16,color="burlywood",shape="triangle"];648[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];17 -> 648[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	648 -> 22[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	649[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];17 -> 649[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	649 -> 23[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	18 -> 24[label="",style="dashed", color="red", weight=0];
12.25/4.89	18[label="wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="magenta"];18 -> 25[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	19[label="return wu4 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3];
12.25/4.89	579[label="Monad.foldM wu3 wu4 (wu50 : wu51)",fontsize=16,color="black",shape="box"];579 -> 583[label="",style="solid", color="black", weight=3];
12.25/4.89	580[label="Monad.foldM wu3 wu4 []",fontsize=16,color="black",shape="box"];580 -> 584[label="",style="solid", color="black", weight=3];
12.25/4.89	581[label="wu370 : wu371 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];581 -> 585[label="",style="solid", color="black", weight=3];
12.25/4.89	582[label="[] >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];582 -> 586[label="",style="solid", color="black", weight=3];
12.25/4.89	22[label="primbindIO (Monad.foldM wu3 wu4 (wu50 : wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];22 -> 30[label="",style="solid", color="black", weight=3];
12.25/4.89	23[label="primbindIO (Monad.foldM wu3 wu4 []) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];23 -> 31[label="",style="solid", color="black", weight=3];
12.25/4.89	25[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];25 -> 32[label="",style="dashed", color="green", weight=3];
12.25/4.89	25 -> 33[label="",style="dashed", color="green", weight=3];
12.25/4.89	24[label="wu6 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="burlywood",shape="triangle"];650[label="wu6/Nothing",fontsize=10,color="white",style="solid",shape="box"];24 -> 650[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	650 -> 34[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	651[label="wu6/Just wu60",fontsize=10,color="white",style="solid",shape="box"];24 -> 651[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	651 -> 35[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	26[label="Just wu4 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];26 -> 36[label="",style="solid", color="black", weight=3];
12.25/4.89	583 -> 587[label="",style="dashed", color="red", weight=0];
12.25/4.89	583[label="wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="magenta"];583 -> 588[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	584[label="return wu4",fontsize=16,color="black",shape="triangle"];584 -> 589[label="",style="solid", color="black", weight=3];
12.25/4.89	585 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	585[label="gtGt0 (return ()) wu370 ++ (wu371 >>= gtGt0 (return ()))",fontsize=16,color="magenta"];585 -> 612[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	585 -> 613[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	586[label="[]",fontsize=16,color="green",shape="box"];30[label="primbindIO (wu3 wu4 wu50 >>= Monad.foldM0 wu3 wu51) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
12.25/4.89	31[label="primbindIO (return wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];31 -> 45[label="",style="solid", color="black", weight=3];
12.25/4.89	32[label="wu4",fontsize=16,color="green",shape="box"];33[label="wu50",fontsize=16,color="green",shape="box"];34[label="Nothing >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];34 -> 46[label="",style="solid", color="black", weight=3];
12.25/4.89	35[label="Just wu60 >>= Monad.foldM0 wu3 wu51 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];35 -> 47[label="",style="solid", color="black", weight=3];
12.25/4.89	36[label="gtGt0 (return ()) wu4",fontsize=16,color="black",shape="box"];36 -> 48[label="",style="solid", color="black", weight=3];
12.25/4.89	588[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];588 -> 593[label="",style="dashed", color="green", weight=3];
12.25/4.89	588 -> 594[label="",style="dashed", color="green", weight=3];
12.25/4.89	587[label="wu38 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="burlywood",shape="triangle"];652[label="wu38/wu380 : wu381",fontsize=10,color="white",style="solid",shape="box"];587 -> 652[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	652 -> 595[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	653[label="wu38/[]",fontsize=10,color="white",style="solid",shape="box"];587 -> 653[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	653 -> 596[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	589[label="wu4 : []",fontsize=16,color="green",shape="box"];612 -> 524[label="",style="dashed", color="red", weight=0];
12.25/4.89	612[label="wu371 >>= gtGt0 (return ())",fontsize=16,color="magenta"];612 -> 624[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	613 -> 625[label="",style="dashed", color="red", weight=0];
12.25/4.89	613[label="gtGt0 (return ()) wu370",fontsize=16,color="magenta"];613 -> 626[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	611[label="wu43 ++ wu42",fontsize=16,color="burlywood",shape="triangle"];654[label="wu43/wu430 : wu431",fontsize=10,color="white",style="solid",shape="box"];611 -> 654[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	654 -> 627[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	655[label="wu43/[]",fontsize=10,color="white",style="solid",shape="box"];611 -> 655[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	655 -> 628[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	44 -> 52[label="",style="dashed", color="red", weight=0];
12.25/4.89	44[label="primbindIO (primbindIO (wu3 wu4 wu50) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="magenta"];44 -> 53[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	45[label="primbindIO (primretIO wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.25/4.89	46[label="Nothing >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.25/4.89	47[label="Monad.foldM0 wu3 wu51 wu60 >>= gtGt0 (return ())",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.25/4.89	48[label="return ()",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.25/4.89	593[label="wu4",fontsize=16,color="green",shape="box"];594[label="wu50",fontsize=16,color="green",shape="box"];595[label="wu380 : wu381 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="black",shape="box"];595 -> 600[label="",style="solid", color="black", weight=3];
12.25/4.89	596[label="[] >>= Monad.foldM0 wu3 wu51",fontsize=16,color="black",shape="box"];596 -> 601[label="",style="solid", color="black", weight=3];
12.25/4.89	624[label="wu371",fontsize=16,color="green",shape="box"];626 -> 584[label="",style="dashed", color="red", weight=0];
12.25/4.89	626[label="return ()",fontsize=16,color="magenta"];626 -> 629[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	625[label="gtGt0 wu44 wu370",fontsize=16,color="black",shape="triangle"];625 -> 630[label="",style="solid", color="black", weight=3];
12.25/4.89	627[label="(wu430 : wu431) ++ wu42",fontsize=16,color="black",shape="box"];627 -> 633[label="",style="solid", color="black", weight=3];
12.25/4.89	628[label="[] ++ wu42",fontsize=16,color="black",shape="box"];628 -> 634[label="",style="solid", color="black", weight=3];
12.25/4.89	53[label="wu3 wu4 wu50",fontsize=16,color="green",shape="box"];53 -> 62[label="",style="dashed", color="green", weight=3];
12.25/4.89	53 -> 63[label="",style="dashed", color="green", weight=3];
12.25/4.89	52[label="primbindIO (primbindIO wu8 (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="burlywood",shape="triangle"];656[label="wu8/IO wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 656[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	656 -> 64[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	657[label="wu8/AProVE_IO wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 657[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	657 -> 65[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	658[label="wu8/AProVE_Exception wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 658[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	658 -> 66[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	659[label="wu8/AProVE_Error wu80",fontsize=10,color="white",style="solid",shape="box"];52 -> 659[label="",style="solid", color="burlywood", weight=9];
12.25/4.89	659 -> 67[label="",style="solid", color="burlywood", weight=3];
12.25/4.89	54[label="primbindIO (AProVE_IO wu4) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];54 -> 68[label="",style="solid", color="black", weight=3];
12.25/4.89	55[label="Nothing",fontsize=16,color="green",shape="box"];56 -> 10[label="",style="dashed", color="red", weight=0];
12.25/4.89	56[label="Monad.foldM wu3 wu60 wu51 >>= gtGt0 (return ())",fontsize=16,color="magenta"];56 -> 69[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	56 -> 70[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	57[label="Just ()",fontsize=16,color="green",shape="box"];600 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	600[label="Monad.foldM0 wu3 wu51 wu380 ++ (wu381 >>= Monad.foldM0 wu3 wu51)",fontsize=16,color="magenta"];600 -> 618[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	600 -> 619[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	601[label="[]",fontsize=16,color="green",shape="box"];629[label="()",fontsize=16,color="green",shape="box"];630[label="wu44",fontsize=16,color="green",shape="box"];633[label="wu430 : wu431 ++ wu42",fontsize=16,color="green",shape="box"];633 -> 637[label="",style="dashed", color="green", weight=3];
12.25/4.89	634[label="wu42",fontsize=16,color="green",shape="box"];62[label="wu4",fontsize=16,color="green",shape="box"];63[label="wu50",fontsize=16,color="green",shape="box"];64[label="primbindIO (primbindIO (IO wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];64 -> 74[label="",style="solid", color="black", weight=3];
12.25/4.89	65[label="primbindIO (primbindIO (AProVE_IO wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];65 -> 75[label="",style="solid", color="black", weight=3];
12.25/4.89	66[label="primbindIO (primbindIO (AProVE_Exception wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];66 -> 76[label="",style="solid", color="black", weight=3];
12.25/4.89	67[label="primbindIO (primbindIO (AProVE_Error wu80) (Monad.foldM0 wu3 wu51)) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];67 -> 77[label="",style="solid", color="black", weight=3];
12.25/4.89	68[label="gtGt0 (return ()) wu4",fontsize=16,color="black",shape="box"];68 -> 78[label="",style="solid", color="black", weight=3];
12.25/4.89	69[label="wu51",fontsize=16,color="green",shape="box"];70[label="wu60",fontsize=16,color="green",shape="box"];618 -> 587[label="",style="dashed", color="red", weight=0];
12.25/4.89	618[label="wu381 >>= Monad.foldM0 wu3 wu51",fontsize=16,color="magenta"];618 -> 631[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	619[label="Monad.foldM0 wu3 wu51 wu380",fontsize=16,color="black",shape="box"];619 -> 632[label="",style="solid", color="black", weight=3];
12.25/4.89	637 -> 611[label="",style="dashed", color="red", weight=0];
12.25/4.89	637[label="wu431 ++ wu42",fontsize=16,color="magenta"];637 -> 638[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	74[label="error []",fontsize=16,color="red",shape="box"];75[label="primbindIO (Monad.foldM0 wu3 wu51 wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];75 -> 82[label="",style="solid", color="black", weight=3];
12.25/4.89	76[label="primbindIO (AProVE_Exception wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];76 -> 83[label="",style="solid", color="black", weight=3];
12.25/4.89	77[label="primbindIO (AProVE_Error wu80) (gtGt0 (return ()))",fontsize=16,color="black",shape="box"];77 -> 84[label="",style="solid", color="black", weight=3];
12.25/4.89	78[label="return ()",fontsize=16,color="black",shape="box"];78 -> 85[label="",style="solid", color="black", weight=3];
12.25/4.89	631[label="wu381",fontsize=16,color="green",shape="box"];632 -> 525[label="",style="dashed", color="red", weight=0];
12.25/4.89	632[label="Monad.foldM wu3 wu380 wu51",fontsize=16,color="magenta"];632 -> 635[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	632 -> 636[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	638[label="wu431",fontsize=16,color="green",shape="box"];82 -> 17[label="",style="dashed", color="red", weight=0];
12.25/4.89	82[label="primbindIO (Monad.foldM wu3 wu80 wu51) (gtGt0 (return ()))",fontsize=16,color="magenta"];82 -> 90[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	82 -> 91[label="",style="dashed", color="magenta", weight=3];
12.25/4.89	83[label="AProVE_Exception wu80",fontsize=16,color="green",shape="box"];84[label="AProVE_Error wu80",fontsize=16,color="green",shape="box"];85[label="primretIO ()",fontsize=16,color="black",shape="box"];85 -> 92[label="",style="solid", color="black", weight=3];
12.25/4.89	635[label="wu51",fontsize=16,color="green",shape="box"];636[label="wu380",fontsize=16,color="green",shape="box"];90[label="wu51",fontsize=16,color="green",shape="box"];91[label="wu80",fontsize=16,color="green",shape="box"];92[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];}
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(27)
12.25/4.89	Complex Obligation (AND)
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(28)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_gtGtEs1(Just(wu60), wu3, wu51, h, ba, []) -> new_gtGtEs2(wu3, wu60, wu51, h, ba, [])
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(29) DependencyGraphProof (EQUIVALENT)
12.25/4.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(30)
12.25/4.89	TRUE
12.25/4.89	
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(31)
12.25/4.89	Obligation:
12.25/4.89	Q DP problem:
12.25/4.89	The TRS P consists of the following rules:
12.25/4.89	
12.25/4.89	   new_primbindIO(AProVE_IO(wu80), wu3, wu51, h, ba, []) -> new_primbindIO0(wu3, wu80, wu51, h, ba, [])
12.25/4.89	
12.25/4.89	R is empty.
12.25/4.89	Q is empty.
12.25/4.89	We have to consider all (P,Q,R)-chains.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(32) DependencyGraphProof (EQUIVALENT)
12.25/4.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
12.25/4.89	----------------------------------------
12.25/4.89	
12.25/4.89	(33)
12.25/4.89	TRUE
12.50/4.95	EOF