8.02/3.49	YES
9.60/3.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.60/3.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.60/3.91	
9.60/3.91	
9.60/3.91	H-Termination with start terms of the given HASKELL could be proven:
9.60/3.91	
9.60/3.91	(0) HASKELL
9.60/3.91	(1) BR [EQUIVALENT, 0 ms]
9.60/3.91	(2) HASKELL
9.60/3.91	(3) COR [EQUIVALENT, 0 ms]
9.60/3.91	(4) HASKELL
9.60/3.91	(5) Narrow [SOUND, 0 ms]
9.60/3.91	(6) QDP
9.60/3.91	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.60/3.91	(8) YES
9.60/3.91	
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(0)
9.60/3.91	Obligation:
9.60/3.91	mainModule Main 
9.60/3.91	module Main where {
9.60/3.91	import qualified Prelude;
9.60/3.91	}
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(1) BR (EQUIVALENT)
9.60/3.91	Replaced joker patterns by fresh variables and removed binding patterns.
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(2)
9.60/3.91	Obligation:
9.60/3.91	mainModule Main 
9.60/3.91	module Main where {
9.60/3.91	import qualified Prelude;
9.60/3.91	}
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(3) COR (EQUIVALENT)
9.60/3.91	Cond Reductions:
9.60/3.91	The following Function with conditions
9.60/3.91	"undefined |Falseundefined;
9.60/3.91	"
9.60/3.91	is transformed to
9.60/3.91	"undefined  = undefined1;
9.60/3.91	"
9.60/3.91	"undefined0 True = undefined;
9.60/3.91	"
9.60/3.91	"undefined1  = undefined0 False;
9.60/3.91	"
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(4)
9.60/3.91	Obligation:
9.60/3.91	mainModule Main 
9.60/3.91	module Main where {
9.60/3.91	import qualified Prelude;
9.60/3.91	}
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(5) Narrow (SOUND)
9.60/3.91	Haskell To QDPs
9.60/3.91	
9.60/3.91	digraph dp_graph {
9.60/3.91	node [outthreshold=100, inthreshold=100];1[label="foldl",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.60/3.91	3[label="foldl vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.60/3.91	4[label="foldl vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.60/3.91	5[label="foldl vx3 vx4 vx5",fontsize=16,color="burlywood",shape="triangle"];14[label="vx5/vx50 : vx51",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
9.60/3.91	14 -> 6[label="",style="solid", color="burlywood", weight=3];
9.60/3.91	15[label="vx5/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
9.60/3.91	15 -> 7[label="",style="solid", color="burlywood", weight=3];
9.60/3.91	6[label="foldl vx3 vx4 (vx50 : vx51)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.60/3.91	7[label="foldl vx3 vx4 []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.60/3.91	8 -> 5[label="",style="dashed", color="red", weight=0];
9.60/3.91	8[label="foldl vx3 (vx3 vx4 vx50) vx51",fontsize=16,color="magenta"];8 -> 10[label="",style="dashed", color="magenta", weight=3];
9.60/3.91	8 -> 11[label="",style="dashed", color="magenta", weight=3];
9.60/3.91	9[label="vx4",fontsize=16,color="green",shape="box"];10[label="vx3 vx4 vx50",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="green", weight=3];
9.60/3.91	10 -> 13[label="",style="dashed", color="green", weight=3];
9.60/3.91	11[label="vx51",fontsize=16,color="green",shape="box"];12[label="vx4",fontsize=16,color="green",shape="box"];13[label="vx50",fontsize=16,color="green",shape="box"];}
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(6)
9.60/3.91	Obligation:
9.60/3.91	Q DP problem:
9.60/3.91	The TRS P consists of the following rules:
9.60/3.91	
9.60/3.91	   new_foldl(vx3, :(vx50, vx51), h, ba) -> new_foldl(vx3, vx51, h, ba)
9.60/3.91	
9.60/3.91	R is empty.
9.60/3.91	Q is empty.
9.60/3.91	We have to consider all minimal (P,Q,R)-chains.
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(7) QDPSizeChangeProof (EQUIVALENT)
9.60/3.91	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. 
9.60/3.91	
9.60/3.91	From the DPs we obtained the following set of size-change graphs:
9.60/3.91	*new_foldl(vx3, :(vx50, vx51), h, ba) -> new_foldl(vx3, vx51, h, ba)
9.60/3.91	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
9.60/3.91	
9.60/3.91	
9.60/3.91	----------------------------------------
9.60/3.91	
9.60/3.91	(8)
9.60/3.91	YES
9.60/3.96	EOF