7.97/3.50	YES
9.86/4.04	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.86/4.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.86/4.04	
9.86/4.04	
9.86/4.04	H-Termination with start terms of the given HASKELL could be proven:
9.86/4.04	
9.86/4.04	(0) HASKELL
9.86/4.04	(1) LR [EQUIVALENT, 0 ms]
9.86/4.04	(2) HASKELL
9.86/4.04	(3) BR [EQUIVALENT, 0 ms]
9.86/4.04	(4) HASKELL
9.86/4.04	(5) COR [EQUIVALENT, 0 ms]
9.86/4.04	(6) HASKELL
9.86/4.04	(7) Narrow [SOUND, 0 ms]
9.86/4.04	(8) QDP
9.86/4.04	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.86/4.04	(10) YES
9.86/4.04	
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(0)
9.86/4.04	Obligation:
9.86/4.04	mainModule Main 
9.86/4.04	module Main where {
9.86/4.04	import qualified Prelude;
9.86/4.04	}
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(1) LR (EQUIVALENT)
9.86/4.04	Lambda Reductions:
9.86/4.04	The following Lambda expression
9.86/4.04	"\abc->(a,b,c)"
9.86/4.04	is transformed to
9.86/4.04	"zip30 a b c = (a,b,c);
9.86/4.04	"
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(2)
9.86/4.04	Obligation:
9.86/4.04	mainModule Main 
9.86/4.04	module Main where {
9.86/4.04	import qualified Prelude;
9.86/4.04	}
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(3) BR (EQUIVALENT)
9.86/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(4)
9.86/4.04	Obligation:
9.86/4.04	mainModule Main 
9.86/4.04	module Main where {
9.86/4.04	import qualified Prelude;
9.86/4.04	}
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(5) COR (EQUIVALENT)
9.86/4.04	Cond Reductions:
9.86/4.04	The following Function with conditions
9.86/4.04	"undefined |Falseundefined;
9.86/4.04	"
9.86/4.04	is transformed to
9.86/4.04	"undefined  = undefined1;
9.86/4.04	"
9.86/4.04	"undefined0 True = undefined;
9.86/4.04	"
9.86/4.04	"undefined1  = undefined0 False;
9.86/4.04	"
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(6)
9.86/4.04	Obligation:
9.86/4.04	mainModule Main 
9.86/4.04	module Main where {
9.86/4.04	import qualified Prelude;
9.86/4.04	}
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(7) Narrow (SOUND)
9.86/4.04	Haskell To QDPs
9.86/4.04	
9.86/4.04	digraph dp_graph {
9.86/4.04	node [outthreshold=100, inthreshold=100];1[label="zip3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.86/4.04	3[label="zip3 wv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.86/4.04	4[label="zip3 wv3 wv4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.86/4.04	5[label="zip3 wv3 wv4 wv5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
9.86/4.04	6[label="zipWith3 zip30 wv3 wv4 wv5",fontsize=16,color="burlywood",shape="triangle"];23[label="wv3/wv30 : wv31",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	23 -> 7[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	24[label="wv3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	24 -> 8[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	7[label="zipWith3 zip30 (wv30 : wv31) wv4 wv5",fontsize=16,color="burlywood",shape="box"];25[label="wv4/wv40 : wv41",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	25 -> 9[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	26[label="wv4/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	26 -> 10[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	8[label="zipWith3 zip30 [] wv4 wv5",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.86/4.04	9[label="zipWith3 zip30 (wv30 : wv31) (wv40 : wv41) wv5",fontsize=16,color="burlywood",shape="box"];27[label="wv5/wv50 : wv51",fontsize=10,color="white",style="solid",shape="box"];9 -> 27[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	27 -> 12[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	28[label="wv5/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 28[label="",style="solid", color="burlywood", weight=9];
9.86/4.04	28 -> 13[label="",style="solid", color="burlywood", weight=3];
9.86/4.04	10[label="zipWith3 zip30 (wv30 : wv31) [] wv5",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.86/4.04	11[label="[]",fontsize=16,color="green",shape="box"];12[label="zipWith3 zip30 (wv30 : wv31) (wv40 : wv41) (wv50 : wv51)",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
9.86/4.04	13[label="zipWith3 zip30 (wv30 : wv31) (wv40 : wv41) []",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
9.86/4.04	14[label="[]",fontsize=16,color="green",shape="box"];15[label="zip30 wv30 wv40 wv50 : zipWith3 zip30 wv31 wv41 wv51",fontsize=16,color="green",shape="box"];15 -> 17[label="",style="dashed", color="green", weight=3];
9.86/4.04	15 -> 18[label="",style="dashed", color="green", weight=3];
9.86/4.04	16[label="[]",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];
9.86/4.04	18 -> 6[label="",style="dashed", color="red", weight=0];
9.86/4.04	18[label="zipWith3 zip30 wv31 wv41 wv51",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
9.86/4.04	18 -> 21[label="",style="dashed", color="magenta", weight=3];
9.86/4.04	18 -> 22[label="",style="dashed", color="magenta", weight=3];
9.86/4.04	19[label="(wv30,wv40,wv50)",fontsize=16,color="green",shape="box"];20[label="wv31",fontsize=16,color="green",shape="box"];21[label="wv51",fontsize=16,color="green",shape="box"];22[label="wv41",fontsize=16,color="green",shape="box"];}
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(8)
9.86/4.04	Obligation:
9.86/4.04	Q DP problem:
9.86/4.04	The TRS P consists of the following rules:
9.86/4.04	
9.86/4.04	   new_zipWith3(:(wv30, wv31), :(wv40, wv41), :(wv50, wv51), h, ba, bb) -> new_zipWith3(wv31, wv41, wv51, h, ba, bb)
9.86/4.04	
9.86/4.04	R is empty.
9.86/4.04	Q is empty.
9.86/4.04	We have to consider all minimal (P,Q,R)-chains.
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(9) QDPSizeChangeProof (EQUIVALENT)
9.86/4.04	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. 
9.86/4.04	
9.86/4.04	From the DPs we obtained the following set of size-change graphs:
9.86/4.04	*new_zipWith3(:(wv30, wv31), :(wv40, wv41), :(wv50, wv51), h, ba, bb) -> new_zipWith3(wv31, wv41, wv51, h, ba, bb)
9.86/4.04	The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
9.86/4.04	
9.86/4.04	
9.86/4.04	----------------------------------------
9.86/4.04	
9.86/4.04	(10)
9.86/4.04	YES
9.86/4.08	EOF