8.01/3.49	YES
9.86/4.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.86/4.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.86/4.00	
9.86/4.00	
9.86/4.00	H-Termination with start terms of the given HASKELL could be proven:
9.86/4.00	
9.86/4.00	(0) HASKELL
9.86/4.00	(1) LR [EQUIVALENT, 0 ms]
9.86/4.00	(2) HASKELL
9.86/4.00	(3) BR [EQUIVALENT, 0 ms]
9.86/4.00	(4) HASKELL
9.86/4.00	(5) COR [EQUIVALENT, 0 ms]
9.86/4.00	(6) HASKELL
9.86/4.00	(7) Narrow [SOUND, 0 ms]
9.86/4.00	(8) QDP
9.86/4.00	(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.86/4.00	(10) YES
9.86/4.00	
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(0)
9.86/4.00	Obligation:
9.86/4.00	mainModule Main 
9.86/4.00	module Main where {
9.86/4.00	import qualified Prelude;
9.86/4.00	}
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(1) LR (EQUIVALENT)
9.86/4.00	Lambda Reductions:
9.86/4.00	The following Lambda expression
9.86/4.00	"\ab->(a,b)"
9.86/4.00	is transformed to
9.86/4.00	"zip0 a b = (a,b);
9.86/4.00	"
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(2)
9.86/4.00	Obligation:
9.86/4.00	mainModule Main 
9.86/4.00	module Main where {
9.86/4.00	import qualified Prelude;
9.86/4.00	}
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(3) BR (EQUIVALENT)
9.86/4.00	Replaced joker patterns by fresh variables and removed binding patterns.
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(4)
9.86/4.00	Obligation:
9.86/4.00	mainModule Main 
9.86/4.00	module Main where {
9.86/4.00	import qualified Prelude;
9.86/4.00	}
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(5) COR (EQUIVALENT)
9.86/4.00	Cond Reductions:
9.86/4.00	The following Function with conditions
9.86/4.00	"undefined |Falseundefined;
9.86/4.00	"
9.86/4.00	is transformed to
9.86/4.00	"undefined  = undefined1;
9.86/4.00	"
9.86/4.00	"undefined0 True = undefined;
9.86/4.00	"
9.86/4.00	"undefined1  = undefined0 False;
9.86/4.00	"
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(6)
9.86/4.00	Obligation:
9.86/4.00	mainModule Main 
9.86/4.00	module Main where {
9.86/4.00	import qualified Prelude;
9.86/4.00	}
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(7) Narrow (SOUND)
9.86/4.00	Haskell To QDPs
9.86/4.00	
9.86/4.00	digraph dp_graph {
9.86/4.00	node [outthreshold=100, inthreshold=100];1[label="zip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.86/4.00	3[label="zip wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.86/4.00	4[label="zip wu3 wu4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.86/4.00	5[label="zipWith zip0 wu3 wu4",fontsize=16,color="burlywood",shape="triangle"];18[label="wu3/wu30 : wu31",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.86/4.00	18 -> 6[label="",style="solid", color="burlywood", weight=3];
9.86/4.00	19[label="wu3/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
9.86/4.00	19 -> 7[label="",style="solid", color="burlywood", weight=3];
9.86/4.00	6[label="zipWith zip0 (wu30 : wu31) wu4",fontsize=16,color="burlywood",shape="box"];20[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
9.86/4.00	20 -> 8[label="",style="solid", color="burlywood", weight=3];
9.86/4.00	21[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
9.86/4.00	21 -> 9[label="",style="solid", color="burlywood", weight=3];
9.86/4.00	7[label="zipWith zip0 [] wu4",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9.86/4.00	8[label="zipWith zip0 (wu30 : wu31) (wu40 : wu41)",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.86/4.00	9[label="zipWith zip0 (wu30 : wu31) []",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
9.86/4.00	10[label="[]",fontsize=16,color="green",shape="box"];11[label="zip0 wu30 wu40 : zipWith zip0 wu31 wu41",fontsize=16,color="green",shape="box"];11 -> 13[label="",style="dashed", color="green", weight=3];
9.86/4.00	11 -> 14[label="",style="dashed", color="green", weight=3];
9.86/4.00	12[label="[]",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];
9.86/4.00	14 -> 5[label="",style="dashed", color="red", weight=0];
9.86/4.00	14[label="zipWith zip0 wu31 wu41",fontsize=16,color="magenta"];14 -> 16[label="",style="dashed", color="magenta", weight=3];
9.86/4.00	14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.86/4.00	15[label="(wu30,wu40)",fontsize=16,color="green",shape="box"];16[label="wu41",fontsize=16,color="green",shape="box"];17[label="wu31",fontsize=16,color="green",shape="box"];}
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(8)
9.86/4.00	Obligation:
9.86/4.00	Q DP problem:
9.86/4.00	The TRS P consists of the following rules:
9.86/4.00	
9.86/4.00	   new_zipWith(:(wu30, wu31), :(wu40, wu41), h, ba) -> new_zipWith(wu31, wu41, h, ba)
9.86/4.00	
9.86/4.00	R is empty.
9.86/4.00	Q is empty.
9.86/4.00	We have to consider all minimal (P,Q,R)-chains.
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(9) QDPSizeChangeProof (EQUIVALENT)
9.86/4.00	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. 
9.86/4.00	
9.86/4.00	From the DPs we obtained the following set of size-change graphs:
9.86/4.00	*new_zipWith(:(wu30, wu31), :(wu40, wu41), h, ba) -> new_zipWith(wu31, wu41, h, ba)
9.86/4.00	The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4
9.86/4.00	
9.86/4.00	
9.86/4.00	----------------------------------------
9.86/4.00	
9.86/4.00	(10)
9.86/4.00	YES
9.86/4.04	EOF