7.42/3.47	YES
9.03/3.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.03/3.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.03/3.94	
9.03/3.94	
9.03/3.94	H-Termination with start terms of the given HASKELL could be proven:
9.03/3.94	
9.03/3.94	(0) HASKELL
9.03/3.94	(1) BR [EQUIVALENT, 0 ms]
9.03/3.94	(2) HASKELL
9.03/3.94	(3) COR [EQUIVALENT, 0 ms]
9.03/3.94	(4) HASKELL
9.03/3.94	(5) Narrow [SOUND, 0 ms]
9.03/3.94	(6) QDP
9.03/3.94	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.03/3.94	(8) YES
9.03/3.94	
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(0)
9.03/3.94	Obligation:
9.03/3.94	mainModule Main 
9.03/3.94	module Main where {
9.03/3.94	import qualified Prelude;
9.03/3.94	data List a = Cons a (List a)  | Nil ;
9.03/3.94	
9.03/3.94	data Tup2 a b = Tup2 a b ;
9.03/3.94	
9.03/3.94	zip :: List a  ->  List b  ->  List (Tup2 a b);
9.03/3.94	zip = zipWith zip0;
9.03/3.94	
9.03/3.94	zip0 a b = Tup2 a b;
9.03/3.94	
9.03/3.94	zipWith :: (c  ->  a  ->  b)  ->  List c  ->  List a  ->  List b;
9.03/3.94	zipWith z (Cons a as) (Cons b bs) = Cons (z a b) (zipWith z as bs);
9.03/3.94	zipWith vv vw vx = Nil;
9.03/3.94	
9.03/3.94	}
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(1) BR (EQUIVALENT)
9.03/3.94	Replaced joker patterns by fresh variables and removed binding patterns.
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(2)
9.03/3.94	Obligation:
9.03/3.94	mainModule Main 
9.03/3.94	module Main where {
9.03/3.94	import qualified Prelude;
9.03/3.94	data List a = Cons a (List a)  | Nil ;
9.03/3.94	
9.03/3.94	data Tup2 b a = Tup2 b a ;
9.03/3.94	
9.03/3.94	zip :: List b  ->  List a  ->  List (Tup2 b a);
9.03/3.94	zip = zipWith zip0;
9.03/3.94	
9.03/3.94	zip0 a b = Tup2 a b;
9.03/3.94	
9.03/3.94	zipWith :: (c  ->  a  ->  b)  ->  List c  ->  List a  ->  List b;
9.03/3.94	zipWith z (Cons a as) (Cons b bs) = Cons (z a b) (zipWith z as bs);
9.03/3.94	zipWith vv vw vx = Nil;
9.03/3.94	
9.03/3.94	}
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(3) COR (EQUIVALENT)
9.03/3.94	Cond Reductions:
9.03/3.94	The following Function with conditions
9.03/3.94	"undefined |Falseundefined;
9.03/3.94	"
9.03/3.94	is transformed to
9.03/3.94	"undefined  = undefined1;
9.03/3.94	"
9.03/3.94	"undefined0 True = undefined;
9.03/3.94	"
9.03/3.94	"undefined1  = undefined0 False;
9.03/3.94	"
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(4)
9.03/3.94	Obligation:
9.03/3.94	mainModule Main 
9.03/3.94	module Main where {
9.03/3.94	import qualified Prelude;
9.03/3.94	data List a = Cons a (List a)  | Nil ;
9.03/3.94	
9.03/3.94	data Tup2 b a = Tup2 b a ;
9.03/3.94	
9.03/3.94	zip :: List a  ->  List b  ->  List (Tup2 a b);
9.03/3.94	zip = zipWith zip0;
9.03/3.94	
9.03/3.94	zip0 a b = Tup2 a b;
9.03/3.94	
9.03/3.94	zipWith :: (b  ->  c  ->  a)  ->  List b  ->  List c  ->  List a;
9.03/3.94	zipWith z (Cons a as) (Cons b bs) = Cons (z a b) (zipWith z as bs);
9.03/3.94	zipWith vv vw vx = Nil;
9.03/3.94	
9.03/3.94	}
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(5) Narrow (SOUND)
9.03/3.94	Haskell To QDPs
9.03/3.94	
9.03/3.94	digraph dp_graph {
9.03/3.94	node [outthreshold=100, inthreshold=100];1[label="zip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.03/3.94	3[label="zip wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.03/3.94	4[label="zip wu3 wu4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.03/3.94	5[label="zipWith zip0 wu3 wu4",fontsize=16,color="burlywood",shape="triangle"];18[label="wu3/Cons wu30 wu31",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.03/3.94	18 -> 6[label="",style="solid", color="burlywood", weight=3];
9.03/3.94	19[label="wu3/Nil",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
9.03/3.94	19 -> 7[label="",style="solid", color="burlywood", weight=3];
9.03/3.94	6[label="zipWith zip0 (Cons wu30 wu31) wu4",fontsize=16,color="burlywood",shape="box"];20[label="wu4/Cons wu40 wu41",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
9.03/3.94	20 -> 8[label="",style="solid", color="burlywood", weight=3];
9.03/3.94	21[label="wu4/Nil",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
9.03/3.94	21 -> 9[label="",style="solid", color="burlywood", weight=3];
9.03/3.94	7[label="zipWith zip0 Nil wu4",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9.03/3.94	8[label="zipWith zip0 (Cons wu30 wu31) (Cons wu40 wu41)",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.03/3.94	9[label="zipWith zip0 (Cons wu30 wu31) Nil",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
9.03/3.94	10[label="Nil",fontsize=16,color="green",shape="box"];11[label="Cons (zip0 wu30 wu40) (zipWith zip0 wu31 wu41)",fontsize=16,color="green",shape="box"];11 -> 13[label="",style="dashed", color="green", weight=3];
9.03/3.94	11 -> 14[label="",style="dashed", color="green", weight=3];
9.03/3.94	12[label="Nil",fontsize=16,color="green",shape="box"];13[label="zip0 wu30 wu40",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.03/3.94	14 -> 5[label="",style="dashed", color="red", weight=0];
9.03/3.94	14[label="zipWith zip0 wu31 wu41",fontsize=16,color="magenta"];14 -> 16[label="",style="dashed", color="magenta", weight=3];
9.03/3.94	14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.03/3.94	15[label="Tup2 wu30 wu40",fontsize=16,color="green",shape="box"];16[label="wu31",fontsize=16,color="green",shape="box"];17[label="wu41",fontsize=16,color="green",shape="box"];}
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(6)
9.03/3.94	Obligation:
9.03/3.94	Q DP problem:
9.03/3.94	The TRS P consists of the following rules:
9.03/3.94	
9.03/3.94	   new_zipWith(Cons(wu30, wu31), Cons(wu40, wu41), h, ba) -> new_zipWith(wu31, wu41, h, ba)
9.03/3.94	
9.03/3.94	R is empty.
9.03/3.94	Q is empty.
9.03/3.94	We have to consider all minimal (P,Q,R)-chains.
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(7) QDPSizeChangeProof (EQUIVALENT)
9.03/3.94	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. 
9.03/3.94	
9.03/3.94	From the DPs we obtained the following set of size-change graphs:
9.03/3.94	*new_zipWith(Cons(wu30, wu31), Cons(wu40, wu41), h, ba) -> new_zipWith(wu31, wu41, h, ba)
9.03/3.94	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4
9.03/3.94	
9.03/3.94	
9.03/3.94	----------------------------------------
9.03/3.94	
9.03/3.94	(8)
9.03/3.94	YES
9.03/3.97	EOF