7.41/3.49	YES
9.21/4.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.21/4.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.21/4.00	
9.21/4.00	
9.21/4.00	H-Termination with start terms of the given HASKELL could be proven:
9.21/4.00	
9.21/4.00	(0) HASKELL
9.21/4.00	(1) BR [EQUIVALENT, 0 ms]
9.21/4.00	(2) HASKELL
9.21/4.00	(3) COR [EQUIVALENT, 0 ms]
9.21/4.00	(4) HASKELL
9.21/4.00	(5) Narrow [SOUND, 0 ms]
9.21/4.00	(6) QDP
9.21/4.00	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.21/4.00	(8) YES
9.21/4.00	
9.21/4.00	
9.21/4.00	----------------------------------------
9.21/4.00	
9.21/4.00	(0)
9.21/4.00	Obligation:
9.21/4.00	mainModule Main 
9.21/4.00	module Main where {
9.21/4.00	import qualified Prelude;
9.21/4.00	data List a = Cons a (List a)  | Nil ;
9.21/4.00	
9.21/4.00	data Tup3 b c a = Tup3 b c a ;
9.21/4.00	
9.21/4.00	zip3 :: List a  ->  List c  ->  List b  ->  List (Tup3 a c b);
9.21/4.00	zip3 = zipWith3 zip30;
9.21/4.00	
9.21/4.00	zip30 a b c = Tup3 a b c;
9.21/4.00	
9.21/4.00	zipWith3 :: (d  ->  a  ->  c  ->  b)  ->  List d  ->  List a  ->  List c  ->  List b;
9.21/4.00	zipWith3 z (Cons a as) (Cons b bs) (Cons c cs) = Cons (z a b c) (zipWith3 z as bs cs);
9.21/4.00	zipWith3 vv vw vx vy = Nil;
9.21/4.00	
9.21/4.00	}
9.21/4.00	
9.21/4.00	----------------------------------------
9.21/4.00	
9.21/4.00	(1) BR (EQUIVALENT)
9.21/4.00	Replaced joker patterns by fresh variables and removed binding patterns.
9.21/4.00	----------------------------------------
9.21/4.00	
9.21/4.00	(2)
9.21/4.00	Obligation:
9.21/4.00	mainModule Main 
9.21/4.00	module Main where {
9.21/4.00	import qualified Prelude;
9.21/4.00	data List a = Cons a (List a)  | Nil ;
9.21/4.00	
9.21/4.00	data Tup3 b c a = Tup3 b c a ;
9.21/4.00	
9.21/4.00	zip3 :: List b  ->  List a  ->  List c  ->  List (Tup3 b a c);
9.21/4.00	zip3 = zipWith3 zip30;
9.21/4.00	
9.21/4.00	zip30 a b c = Tup3 a b c;
9.21/4.00	
9.21/4.00	zipWith3 :: (d  ->  b  ->  a  ->  c)  ->  List d  ->  List b  ->  List a  ->  List c;
9.21/4.00	zipWith3 z (Cons a as) (Cons b bs) (Cons c cs) = Cons (z a b c) (zipWith3 z as bs cs);
9.21/4.00	zipWith3 vv vw vx vy = Nil;
9.21/4.00	
9.21/4.00	}
9.21/4.00	
9.21/4.00	----------------------------------------
9.21/4.00	
9.21/4.00	(3) COR (EQUIVALENT)
9.21/4.00	Cond Reductions:
9.21/4.00	The following Function with conditions
9.21/4.00	"undefined |Falseundefined;
9.21/4.00	"
9.21/4.00	is transformed to
9.21/4.00	"undefined  = undefined1;
9.21/4.00	"
9.21/4.00	"undefined0 True = undefined;
9.21/4.00	"
9.21/4.00	"undefined1  = undefined0 False;
9.21/4.00	"
9.21/4.00	
9.21/4.00	----------------------------------------
9.21/4.00	
9.21/4.00	(4)
9.21/4.00	Obligation:
9.21/4.00	mainModule Main 
9.21/4.00	module Main where {
9.21/4.00	import qualified Prelude;
9.21/4.00	data List a = Cons a (List a)  | Nil ;
9.21/4.00	
9.21/4.00	data Tup3 c a b = Tup3 c a b ;
9.21/4.00	
9.21/4.00	zip3 :: List c  ->  List b  ->  List a  ->  List (Tup3 c b a);
9.21/4.01	zip3 = zipWith3 zip30;
9.21/4.01	
9.21/4.01	zip30 a b c = Tup3 a b c;
9.21/4.01	
9.21/4.01	zipWith3 :: (d  ->  c  ->  a  ->  b)  ->  List d  ->  List c  ->  List a  ->  List b;
9.21/4.01	zipWith3 z (Cons a as) (Cons b bs) (Cons c cs) = Cons (z a b c) (zipWith3 z as bs cs);
9.21/4.01	zipWith3 vv vw vx vy = Nil;
9.21/4.01	
9.21/4.01	}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(5) Narrow (SOUND)
9.21/4.01	Haskell To QDPs
9.21/4.01	
9.21/4.01	digraph dp_graph {
9.21/4.01	node [outthreshold=100, inthreshold=100];1[label="zip3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.21/4.01	3[label="zip3 wv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.21/4.01	4[label="zip3 wv3 wv4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.21/4.01	5[label="zip3 wv3 wv4 wv5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
9.21/4.01	6[label="zipWith3 zip30 wv3 wv4 wv5",fontsize=16,color="burlywood",shape="triangle"];23[label="wv3/Cons wv30 wv31",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	23 -> 7[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	24[label="wv3/Nil",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	24 -> 8[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	7[label="zipWith3 zip30 (Cons wv30 wv31) wv4 wv5",fontsize=16,color="burlywood",shape="box"];25[label="wv4/Cons wv40 wv41",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	25 -> 9[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	26[label="wv4/Nil",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	26 -> 10[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	8[label="zipWith3 zip30 Nil wv4 wv5",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.21/4.01	9[label="zipWith3 zip30 (Cons wv30 wv31) (Cons wv40 wv41) wv5",fontsize=16,color="burlywood",shape="box"];27[label="wv5/Cons wv50 wv51",fontsize=10,color="white",style="solid",shape="box"];9 -> 27[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	27 -> 12[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	28[label="wv5/Nil",fontsize=10,color="white",style="solid",shape="box"];9 -> 28[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	28 -> 13[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	10[label="zipWith3 zip30 (Cons wv30 wv31) Nil wv5",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.21/4.01	11[label="Nil",fontsize=16,color="green",shape="box"];12[label="zipWith3 zip30 (Cons wv30 wv31) (Cons wv40 wv41) (Cons wv50 wv51)",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
9.21/4.01	13[label="zipWith3 zip30 (Cons wv30 wv31) (Cons wv40 wv41) Nil",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
9.21/4.01	14[label="Nil",fontsize=16,color="green",shape="box"];15[label="Cons (zip30 wv30 wv40 wv50) (zipWith3 zip30 wv31 wv41 wv51)",fontsize=16,color="green",shape="box"];15 -> 17[label="",style="dashed", color="green", weight=3];
9.21/4.01	15 -> 18[label="",style="dashed", color="green", weight=3];
9.21/4.01	16[label="Nil",fontsize=16,color="green",shape="box"];17[label="zip30 wv30 wv40 wv50",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
9.21/4.01	18 -> 6[label="",style="dashed", color="red", weight=0];
9.21/4.01	18[label="zipWith3 zip30 wv31 wv41 wv51",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
9.21/4.01	18 -> 21[label="",style="dashed", color="magenta", weight=3];
9.21/4.01	18 -> 22[label="",style="dashed", color="magenta", weight=3];
9.21/4.01	19[label="Tup3 wv30 wv40 wv50",fontsize=16,color="green",shape="box"];20[label="wv41",fontsize=16,color="green",shape="box"];21[label="wv31",fontsize=16,color="green",shape="box"];22[label="wv51",fontsize=16,color="green",shape="box"];}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(6)
9.21/4.01	Obligation:
9.21/4.01	Q DP problem:
9.21/4.01	The TRS P consists of the following rules:
9.21/4.01	
9.21/4.01	   new_zipWith3(Cons(wv30, wv31), Cons(wv40, wv41), Cons(wv50, wv51), h, ba, bb) -> new_zipWith3(wv31, wv41, wv51, h, ba, bb)
9.21/4.01	
9.21/4.01	R is empty.
9.21/4.01	Q is empty.
9.21/4.01	We have to consider all minimal (P,Q,R)-chains.
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(7) QDPSizeChangeProof (EQUIVALENT)
9.21/4.01	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. 
9.21/4.01	
9.21/4.01	From the DPs we obtained the following set of size-change graphs:
9.21/4.01	*new_zipWith3(Cons(wv30, wv31), Cons(wv40, wv41), Cons(wv50, wv51), h, ba, bb) -> new_zipWith3(wv31, wv41, wv51, h, ba, bb)
9.21/4.01	The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
9.21/4.01	
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(8)
9.21/4.01	YES
9.58/4.11	EOF