7.64/3.54	YES
9.08/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.08/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.08/3.98	
9.08/3.98	
9.08/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.08/3.98	
9.08/3.98	(0) HASKELL
9.08/3.98	(1) BR [EQUIVALENT, 0 ms]
9.08/3.98	(2) HASKELL
9.08/3.98	(3) COR [EQUIVALENT, 0 ms]
9.08/3.98	(4) HASKELL
9.08/3.98	(5) Narrow [SOUND, 0 ms]
9.08/3.98	(6) QDP
9.08/3.98	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.08/3.98	(8) YES
9.08/3.98	
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(0)
9.08/3.98	Obligation:
9.08/3.98	mainModule Main 
9.08/3.98	module Main where {
9.08/3.98	import qualified Prelude;
9.08/3.98	}
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(1) BR (EQUIVALENT)
9.08/3.98	Replaced joker patterns by fresh variables and removed binding patterns.
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(2)
9.08/3.98	Obligation:
9.08/3.98	mainModule Main 
9.08/3.98	module Main where {
9.08/3.98	import qualified Prelude;
9.08/3.98	}
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(3) COR (EQUIVALENT)
9.08/3.98	Cond Reductions:
9.08/3.98	The following Function with conditions
9.08/3.98	"undefined |Falseundefined;
9.08/3.98	"
9.08/3.98	is transformed to
9.08/3.98	"undefined  = undefined1;
9.08/3.98	"
9.08/3.98	"undefined0 True = undefined;
9.08/3.98	"
9.08/3.98	"undefined1  = undefined0 False;
9.08/3.98	"
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(4)
9.08/3.98	Obligation:
9.08/3.98	mainModule Main 
9.08/3.98	module Main where {
9.08/3.98	import qualified Prelude;
9.08/3.98	}
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(5) Narrow (SOUND)
9.08/3.98	Haskell To QDPs
9.08/3.98	
9.08/3.98	digraph dp_graph {
9.08/3.98	node [outthreshold=100, inthreshold=100];1[label="zipWith3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.08/3.98	3[label="zipWith3 wv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.08/3.98	4[label="zipWith3 wv3 wv4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.08/3.98	5[label="zipWith3 wv3 wv4 wv5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
9.08/3.98	6[label="zipWith3 wv3 wv4 wv5 wv6",fontsize=16,color="burlywood",shape="triangle"];25[label="wv4/wv40 : wv41",fontsize=10,color="white",style="solid",shape="box"];6 -> 25[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	25 -> 7[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	26[label="wv4/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 26[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	26 -> 8[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	7[label="zipWith3 wv3 (wv40 : wv41) wv5 wv6",fontsize=16,color="burlywood",shape="box"];27[label="wv5/wv50 : wv51",fontsize=10,color="white",style="solid",shape="box"];7 -> 27[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	27 -> 9[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	28[label="wv5/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 28[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	28 -> 10[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	8[label="zipWith3 wv3 [] wv5 wv6",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.08/3.98	9[label="zipWith3 wv3 (wv40 : wv41) (wv50 : wv51) wv6",fontsize=16,color="burlywood",shape="box"];29[label="wv6/wv60 : wv61",fontsize=10,color="white",style="solid",shape="box"];9 -> 29[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	29 -> 12[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	30[label="wv6/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 30[label="",style="solid", color="burlywood", weight=9];
9.08/3.98	30 -> 13[label="",style="solid", color="burlywood", weight=3];
9.08/3.98	10[label="zipWith3 wv3 (wv40 : wv41) [] wv6",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.08/3.98	11[label="[]",fontsize=16,color="green",shape="box"];12[label="zipWith3 wv3 (wv40 : wv41) (wv50 : wv51) (wv60 : wv61)",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
9.08/3.98	13[label="zipWith3 wv3 (wv40 : wv41) (wv50 : wv51) []",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
9.08/3.98	14[label="[]",fontsize=16,color="green",shape="box"];15[label="wv3 wv40 wv50 wv60 : zipWith3 wv3 wv41 wv51 wv61",fontsize=16,color="green",shape="box"];15 -> 17[label="",style="dashed", color="green", weight=3];
9.08/3.98	15 -> 18[label="",style="dashed", color="green", weight=3];
9.08/3.98	16[label="[]",fontsize=16,color="green",shape="box"];17[label="wv3 wv40 wv50 wv60",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3];
9.08/3.98	17 -> 20[label="",style="dashed", color="green", weight=3];
9.08/3.98	17 -> 21[label="",style="dashed", color="green", weight=3];
9.08/3.98	18 -> 6[label="",style="dashed", color="red", weight=0];
9.08/3.98	18[label="zipWith3 wv3 wv41 wv51 wv61",fontsize=16,color="magenta"];18 -> 22[label="",style="dashed", color="magenta", weight=3];
9.08/3.98	18 -> 23[label="",style="dashed", color="magenta", weight=3];
9.08/3.98	18 -> 24[label="",style="dashed", color="magenta", weight=3];
9.08/3.98	19[label="wv40",fontsize=16,color="green",shape="box"];20[label="wv50",fontsize=16,color="green",shape="box"];21[label="wv60",fontsize=16,color="green",shape="box"];22[label="wv61",fontsize=16,color="green",shape="box"];23[label="wv41",fontsize=16,color="green",shape="box"];24[label="wv51",fontsize=16,color="green",shape="box"];}
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(6)
9.08/3.98	Obligation:
9.08/3.98	Q DP problem:
9.08/3.98	The TRS P consists of the following rules:
9.08/3.98	
9.08/3.98	   new_zipWith3(wv3, :(wv40, wv41), :(wv50, wv51), :(wv60, wv61), h, ba, bb, bc) -> new_zipWith3(wv3, wv41, wv51, wv61, h, ba, bb, bc)
9.08/3.98	
9.08/3.98	R is empty.
9.08/3.98	Q is empty.
9.08/3.98	We have to consider all minimal (P,Q,R)-chains.
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(7) QDPSizeChangeProof (EQUIVALENT)
9.08/3.98	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. 
9.08/3.98	
9.08/3.98	From the DPs we obtained the following set of size-change graphs:
9.08/3.98	*new_zipWith3(wv3, :(wv40, wv41), :(wv50, wv51), :(wv60, wv61), h, ba, bb, bc) -> new_zipWith3(wv3, wv41, wv51, wv61, h, ba, bb, bc)
9.08/3.98	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 > 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8
9.08/3.98	
9.08/3.98	
9.08/3.98	----------------------------------------
9.08/3.98	
9.08/3.98	(8)
9.08/3.98	YES
9.28/4.03	EOF