7.57/3.59	YES
9.05/4.03	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.05/4.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.05/4.03	
9.05/4.03	
9.05/4.03	H-Termination with start terms of the given HASKELL could be proven:
9.05/4.03	
9.05/4.03	(0) HASKELL
9.05/4.03	(1) BR [EQUIVALENT, 0 ms]
9.05/4.03	(2) HASKELL
9.05/4.03	(3) COR [EQUIVALENT, 0 ms]
9.05/4.03	(4) HASKELL
9.05/4.03	(5) Narrow [SOUND, 0 ms]
9.05/4.03	(6) QDP
9.05/4.03	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.05/4.03	(8) YES
9.05/4.03	
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(0)
9.05/4.03	Obligation:
9.05/4.03	mainModule Main 
9.05/4.03	module Main where {
9.05/4.03	import qualified Prelude;
9.05/4.03	}
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(1) BR (EQUIVALENT)
9.05/4.03	Replaced joker patterns by fresh variables and removed binding patterns.
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(2)
9.05/4.03	Obligation:
9.05/4.03	mainModule Main 
9.05/4.03	module Main where {
9.05/4.03	import qualified Prelude;
9.05/4.03	}
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(3) COR (EQUIVALENT)
9.05/4.03	Cond Reductions:
9.05/4.03	The following Function with conditions
9.05/4.03	"undefined |Falseundefined;
9.05/4.03	"
9.05/4.03	is transformed to
9.05/4.03	"undefined  = undefined1;
9.05/4.03	"
9.05/4.03	"undefined0 True = undefined;
9.05/4.03	"
9.05/4.03	"undefined1  = undefined0 False;
9.05/4.03	"
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(4)
9.05/4.03	Obligation:
9.05/4.03	mainModule Main 
9.05/4.03	module Main where {
9.05/4.03	import qualified Prelude;
9.05/4.03	}
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(5) Narrow (SOUND)
9.05/4.03	Haskell To QDPs
9.05/4.03	
9.05/4.03	digraph dp_graph {
9.05/4.03	node [outthreshold=100, inthreshold=100];1[label="zipWith",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.05/4.03	3[label="zipWith wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.05/4.03	4[label="zipWith wu3 wu4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.05/4.03	5[label="zipWith wu3 wu4 wu5",fontsize=16,color="burlywood",shape="triangle"];19[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
9.05/4.03	19 -> 6[label="",style="solid", color="burlywood", weight=3];
9.05/4.03	20[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 20[label="",style="solid", color="burlywood", weight=9];
9.05/4.03	20 -> 7[label="",style="solid", color="burlywood", weight=3];
9.05/4.03	6[label="zipWith wu3 (wu40 : wu41) wu5",fontsize=16,color="burlywood",shape="box"];21[label="wu5/wu50 : wu51",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
9.05/4.03	21 -> 8[label="",style="solid", color="burlywood", weight=3];
9.05/4.03	22[label="wu5/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
9.05/4.03	22 -> 9[label="",style="solid", color="burlywood", weight=3];
9.05/4.03	7[label="zipWith wu3 [] wu5",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9.05/4.03	8[label="zipWith wu3 (wu40 : wu41) (wu50 : wu51)",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.05/4.03	9[label="zipWith wu3 (wu40 : wu41) []",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
9.05/4.03	10[label="[]",fontsize=16,color="green",shape="box"];11[label="wu3 wu40 wu50 : zipWith wu3 wu41 wu51",fontsize=16,color="green",shape="box"];11 -> 13[label="",style="dashed", color="green", weight=3];
9.05/4.03	11 -> 14[label="",style="dashed", color="green", weight=3];
9.05/4.03	12[label="[]",fontsize=16,color="green",shape="box"];13[label="wu3 wu40 wu50",fontsize=16,color="green",shape="box"];13 -> 15[label="",style="dashed", color="green", weight=3];
9.05/4.03	13 -> 16[label="",style="dashed", color="green", weight=3];
9.05/4.03	14 -> 5[label="",style="dashed", color="red", weight=0];
9.05/4.03	14[label="zipWith wu3 wu41 wu51",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.05/4.03	14 -> 18[label="",style="dashed", color="magenta", weight=3];
9.05/4.03	15[label="wu40",fontsize=16,color="green",shape="box"];16[label="wu50",fontsize=16,color="green",shape="box"];17[label="wu41",fontsize=16,color="green",shape="box"];18[label="wu51",fontsize=16,color="green",shape="box"];}
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(6)
9.05/4.03	Obligation:
9.05/4.03	Q DP problem:
9.05/4.03	The TRS P consists of the following rules:
9.05/4.03	
9.05/4.03	   new_zipWith(wu3, :(wu40, wu41), :(wu50, wu51), h, ba, bb) -> new_zipWith(wu3, wu41, wu51, h, ba, bb)
9.05/4.03	
9.05/4.03	R is empty.
9.05/4.03	Q is empty.
9.05/4.03	We have to consider all minimal (P,Q,R)-chains.
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(7) QDPSizeChangeProof (EQUIVALENT)
9.05/4.03	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. 
9.05/4.03	
9.05/4.03	From the DPs we obtained the following set of size-change graphs:
9.05/4.03	*new_zipWith(wu3, :(wu40, wu41), :(wu50, wu51), h, ba, bb) -> new_zipWith(wu3, wu41, wu51, h, ba, bb)
9.05/4.03	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 6
9.05/4.03	
9.05/4.03	
9.05/4.03	----------------------------------------
9.05/4.03	
9.05/4.03	(8)
9.05/4.03	YES
9.26/4.06	EOF