7.79/3.51	YES
9.39/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.39/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.39/3.98	
9.39/3.98	
9.39/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.39/3.98	
9.39/3.98	(0) HASKELL
9.39/3.98	(1) BR [EQUIVALENT, 0 ms]
9.39/3.98	(2) HASKELL
9.39/3.98	(3) COR [EQUIVALENT, 0 ms]
9.39/3.98	(4) HASKELL
9.39/3.98	(5) Narrow [SOUND, 0 ms]
9.39/3.98	(6) QDP
9.39/3.98	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.39/3.98	(8) YES
9.39/3.98	
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(0)
9.39/3.98	Obligation:
9.39/3.98	mainModule Main 
9.39/3.98	module Main where {
9.39/3.98	import qualified Prelude;
9.39/3.98	data List a = Cons a (List a)  | Nil ;
9.39/3.98	
9.39/3.98	scanl :: (b  ->  a  ->  b)  ->  b  ->  List a  ->  List b;
9.39/3.98	scanl f q xs = Cons q (scanl0 f q xs);
9.39/3.98	
9.39/3.98	scanl0 f q Nil = Nil;
9.39/3.98	scanl0 f q (Cons x xs) = scanl f (f q x) xs;
9.39/3.98	
9.39/3.98	}
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(1) BR (EQUIVALENT)
9.39/3.98	Replaced joker patterns by fresh variables and removed binding patterns.
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(2)
9.39/3.98	Obligation:
9.39/3.98	mainModule Main 
9.39/3.98	module Main where {
9.39/3.98	import qualified Prelude;
9.39/3.98	data List a = Cons a (List a)  | Nil ;
9.39/3.98	
9.39/3.98	scanl :: (a  ->  b  ->  a)  ->  a  ->  List b  ->  List a;
9.39/3.98	scanl f q xs = Cons q (scanl0 f q xs);
9.39/3.98	
9.39/3.98	scanl0 f q Nil = Nil;
9.39/3.98	scanl0 f q (Cons x xs) = scanl f (f q x) xs;
9.39/3.98	
9.39/3.98	}
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(3) COR (EQUIVALENT)
9.39/3.98	Cond Reductions:
9.39/3.98	The following Function with conditions
9.39/3.98	"undefined |Falseundefined;
9.39/3.98	"
9.39/3.98	is transformed to
9.39/3.98	"undefined  = undefined1;
9.39/3.98	"
9.39/3.98	"undefined0 True = undefined;
9.39/3.98	"
9.39/3.98	"undefined1  = undefined0 False;
9.39/3.98	"
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(4)
9.39/3.98	Obligation:
9.39/3.98	mainModule Main 
9.39/3.98	module Main where {
9.39/3.98	import qualified Prelude;
9.39/3.98	data List a = Cons a (List a)  | Nil ;
9.39/3.98	
9.39/3.98	scanl :: (a  ->  b  ->  a)  ->  a  ->  List b  ->  List a;
9.39/3.98	scanl f q xs = Cons q (scanl0 f q xs);
9.39/3.98	
9.39/3.98	scanl0 f q Nil = Nil;
9.39/3.98	scanl0 f q (Cons x xs) = scanl f (f q x) xs;
9.39/3.98	
9.39/3.98	}
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(5) Narrow (SOUND)
9.39/3.98	Haskell To QDPs
9.39/3.98	
9.39/3.98	digraph dp_graph {
9.39/3.98	node [outthreshold=100, inthreshold=100];1[label="scanl",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.39/3.98	3[label="scanl vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.39/3.98	4[label="scanl vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
9.39/3.98	5[label="scanl vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
9.39/3.98	6[label="Cons vx4 (scanl0 vx3 vx4 vx5)",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
9.39/3.98	7[label="scanl0 vx3 vx4 vx5",fontsize=16,color="burlywood",shape="box"];16[label="vx5/Cons vx50 vx51",fontsize=10,color="white",style="solid",shape="box"];7 -> 16[label="",style="solid", color="burlywood", weight=9];
9.39/3.98	16 -> 8[label="",style="solid", color="burlywood", weight=3];
9.39/3.98	17[label="vx5/Nil",fontsize=10,color="white",style="solid",shape="box"];7 -> 17[label="",style="solid", color="burlywood", weight=9];
9.39/3.98	17 -> 9[label="",style="solid", color="burlywood", weight=3];
9.39/3.98	8[label="scanl0 vx3 vx4 (Cons vx50 vx51)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9.39/3.98	9[label="scanl0 vx3 vx4 Nil",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.39/3.98	10 -> 5[label="",style="dashed", color="red", weight=0];
9.39/3.98	10[label="scanl vx3 (vx3 vx4 vx50) vx51",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
9.39/3.98	10 -> 13[label="",style="dashed", color="magenta", weight=3];
9.39/3.98	11[label="Nil",fontsize=16,color="green",shape="box"];12[label="vx51",fontsize=16,color="green",shape="box"];13[label="vx3 vx4 vx50",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3];
9.39/3.98	13 -> 15[label="",style="dashed", color="green", weight=3];
9.39/3.98	14[label="vx4",fontsize=16,color="green",shape="box"];15[label="vx50",fontsize=16,color="green",shape="box"];}
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(6)
9.39/3.98	Obligation:
9.39/3.98	Q DP problem:
9.39/3.98	The TRS P consists of the following rules:
9.39/3.98	
9.39/3.98	   new_scanl(vx3, Cons(vx50, vx51), h, ba) -> new_scanl(vx3, vx51, h, ba)
9.39/3.98	
9.39/3.98	R is empty.
9.39/3.98	Q is empty.
9.39/3.98	We have to consider all minimal (P,Q,R)-chains.
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(7) QDPSizeChangeProof (EQUIVALENT)
9.39/3.98	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. 
9.39/3.98	
9.39/3.98	From the DPs we obtained the following set of size-change graphs:
9.39/3.98	*new_scanl(vx3, Cons(vx50, vx51), h, ba) -> new_scanl(vx3, vx51, h, ba)
9.39/3.98	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
9.39/3.98	
9.39/3.98	
9.39/3.98	----------------------------------------
9.39/3.98	
9.39/3.98	(8)
9.39/3.98	YES
9.53/4.02	EOF