7.91/3.54	YES
8.99/3.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.99/3.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.99/3.97	
8.99/3.97	
8.99/3.97	H-Termination with start terms of the given HASKELL could be proven:
8.99/3.97	
8.99/3.97	(0) HASKELL
8.99/3.97	(1) BR [EQUIVALENT, 0 ms]
8.99/3.97	(2) HASKELL
8.99/3.97	(3) COR [EQUIVALENT, 0 ms]
8.99/3.97	(4) HASKELL
8.99/3.97	(5) Narrow [SOUND, 0 ms]
8.99/3.97	(6) QDP
8.99/3.97	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
8.99/3.97	(8) YES
8.99/3.97	
8.99/3.97	
8.99/3.97	----------------------------------------
8.99/3.97	
8.99/3.97	(0)
8.99/3.97	Obligation:
8.99/3.97	mainModule Main 
8.99/3.97	module Main where {
8.99/3.97	import qualified Prelude;
8.99/3.97	}
8.99/3.97	
8.99/3.97	----------------------------------------
8.99/3.97	
8.99/3.97	(1) BR (EQUIVALENT)
8.99/3.97	Replaced joker patterns by fresh variables and removed binding patterns.
8.99/3.97	----------------------------------------
8.99/3.97	
8.99/3.97	(2)
8.99/3.97	Obligation:
8.99/3.97	mainModule Main 
8.99/3.97	module Main where {
8.99/3.97	import qualified Prelude;
8.99/3.97	}
8.99/3.97	
8.99/3.97	----------------------------------------
8.99/3.97	
8.99/3.97	(3) COR (EQUIVALENT)
8.99/3.97	Cond Reductions:
8.99/3.97	The following Function with conditions
8.99/3.97	"undefined |Falseundefined;
8.99/3.97	"
8.99/3.97	is transformed to
8.99/3.97	"undefined  = undefined1;
8.99/3.97	"
8.99/3.97	"undefined0 True = undefined;
8.99/3.97	"
8.99/3.97	"undefined1  = undefined0 False;
9.34/3.97	"
9.34/3.97	
9.34/3.97	----------------------------------------
9.34/3.97	
9.34/3.97	(4)
9.34/3.97	Obligation:
9.34/3.97	mainModule Main 
9.34/3.97	module Main where {
9.34/3.97	import qualified Prelude;
9.34/3.97	}
9.34/3.97	
9.34/3.97	----------------------------------------
9.34/3.97	
9.34/3.97	(5) Narrow (SOUND)
9.34/3.97	Haskell To QDPs
9.34/3.97	
9.34/3.97	digraph dp_graph {
9.34/3.97	node [outthreshold=100, inthreshold=100];1[label="foldl1",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.34/3.97	3[label="foldl1 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.34/3.97	4[label="foldl1 vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];17[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
9.34/3.97	17 -> 5[label="",style="solid", color="burlywood", weight=3];
9.34/3.97	18[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 18[label="",style="solid", color="burlywood", weight=9];
9.34/3.97	18 -> 6[label="",style="solid", color="burlywood", weight=3];
9.34/3.97	5[label="foldl1 vx3 (vx40 : vx41)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.34/3.97	6[label="foldl1 vx3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.34/3.97	7[label="foldl vx3 vx40 vx41",fontsize=16,color="burlywood",shape="triangle"];19[label="vx41/vx410 : vx411",fontsize=10,color="white",style="solid",shape="box"];7 -> 19[label="",style="solid", color="burlywood", weight=9];
9.34/3.97	19 -> 9[label="",style="solid", color="burlywood", weight=3];
9.34/3.97	20[label="vx41/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 20[label="",style="solid", color="burlywood", weight=9];
9.34/3.97	20 -> 10[label="",style="solid", color="burlywood", weight=3];
9.34/3.97	8[label="error []",fontsize=16,color="red",shape="box"];9[label="foldl vx3 vx40 (vx410 : vx411)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.34/3.97	10[label="foldl vx3 vx40 []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
9.34/3.97	11 -> 7[label="",style="dashed", color="red", weight=0];
9.34/3.97	11[label="foldl vx3 (vx3 vx40 vx410) vx411",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3];
9.34/3.97	11 -> 14[label="",style="dashed", color="magenta", weight=3];
9.34/3.97	12[label="vx40",fontsize=16,color="green",shape="box"];13[label="vx3 vx40 vx410",fontsize=16,color="green",shape="box"];13 -> 15[label="",style="dashed", color="green", weight=3];
9.34/3.97	13 -> 16[label="",style="dashed", color="green", weight=3];
9.34/3.97	14[label="vx411",fontsize=16,color="green",shape="box"];15[label="vx40",fontsize=16,color="green",shape="box"];16[label="vx410",fontsize=16,color="green",shape="box"];}
9.34/3.97	
9.34/3.97	----------------------------------------
9.34/3.97	
9.34/3.97	(6)
9.34/3.97	Obligation:
9.34/3.97	Q DP problem:
9.34/3.97	The TRS P consists of the following rules:
9.34/3.97	
9.34/3.97	   new_foldl(vx3, :(vx410, vx411), h) -> new_foldl(vx3, vx411, h)
9.34/3.97	
9.34/3.97	R is empty.
9.34/3.97	Q is empty.
9.34/3.97	We have to consider all minimal (P,Q,R)-chains.
9.34/3.97	----------------------------------------
9.34/3.97	
9.34/3.97	(7) QDPSizeChangeProof (EQUIVALENT)
9.34/3.97	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. 
9.34/3.97	
9.34/3.97	From the DPs we obtained the following set of size-change graphs:
9.34/3.97	*new_foldl(vx3, :(vx410, vx411), h) -> new_foldl(vx3, vx411, h)
9.34/3.97	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
9.34/3.97	
9.34/3.97	
9.34/3.97	----------------------------------------
9.34/3.97	
9.34/3.97	(8)
9.34/3.97	YES
9.39/4.04	EOF