11.30/4.48	YES
12.83/4.95	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
12.83/4.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.83/4.95	
12.83/4.95	
12.83/4.95	H-Termination with start terms of the given HASKELL could be proven:
12.83/4.95	
12.83/4.95	(0) HASKELL
12.83/4.95	(1) BR [EQUIVALENT, 0 ms]
12.83/4.95	(2) HASKELL
12.83/4.95	(3) COR [EQUIVALENT, 0 ms]
12.83/4.95	(4) HASKELL
12.83/4.95	(5) Narrow [SOUND, 0 ms]
12.83/4.95	(6) QDP
12.83/4.95	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.83/4.95	(8) YES
12.83/4.95	
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(0)
12.83/4.95	Obligation:
12.83/4.95	mainModule Main 
12.83/4.95	module Maybe where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	module List where {
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	intersperse :: a  ->  [a]  ->  [a];
12.83/4.95	intersperse _ [] = [];
12.83/4.95	intersperse _ (x : []) = x : [];
12.83/4.95	intersperse sep (x : xs) = x : sep : intersperse sep xs;
12.83/4.95	
12.83/4.95	}
12.83/4.95	module Main where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(1) BR (EQUIVALENT)
12.83/4.95	Replaced joker patterns by fresh variables and removed binding patterns.
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(2)
12.83/4.95	Obligation:
12.83/4.95	mainModule Main 
12.83/4.95	module Maybe where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	module List where {
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	intersperse :: a  ->  [a]  ->  [a];
12.83/4.95	intersperse vy [] = [];
12.83/4.95	intersperse vz (x : []) = x : [];
12.83/4.95	intersperse sep (x : xs) = x : sep : intersperse sep xs;
12.83/4.95	
12.83/4.95	}
12.83/4.95	module Main where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(3) COR (EQUIVALENT)
12.83/4.95	Cond Reductions:
12.83/4.95	The following Function with conditions
12.83/4.95	"undefined |Falseundefined;
12.83/4.95	"
12.83/4.95	is transformed to
12.83/4.95	"undefined  = undefined1;
12.83/4.95	"
12.83/4.95	"undefined0 True = undefined;
12.83/4.95	"
12.83/4.95	"undefined1  = undefined0 False;
12.83/4.95	"
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(4)
12.83/4.95	Obligation:
12.83/4.95	mainModule Main 
12.83/4.95	module Maybe where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	module List where {
12.83/4.95	import qualified Main;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	intersperse :: a  ->  [a]  ->  [a];
12.83/4.95	intersperse vy [] = [];
12.83/4.95	intersperse vz (x : []) = x : [];
12.83/4.95	intersperse sep (x : xs) = x : sep : intersperse sep xs;
12.83/4.95	
12.83/4.95	}
12.83/4.95	module Main where {
12.83/4.95	import qualified List;
12.83/4.95	import qualified Maybe;
12.83/4.95	import qualified Prelude;
12.83/4.95	}
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(5) Narrow (SOUND)
12.83/4.95	Haskell To QDPs
12.83/4.95	
12.83/4.95	digraph dp_graph {
12.83/4.95	node [outthreshold=100, inthreshold=100];1[label="List.intersperse",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.83/4.95	3[label="List.intersperse wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.83/4.95	4[label="List.intersperse wu3 wu4",fontsize=16,color="burlywood",shape="triangle"];14[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 14[label="",style="solid", color="burlywood", weight=9];
12.83/4.95	14 -> 5[label="",style="solid", color="burlywood", weight=3];
12.83/4.95	15[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9];
12.83/4.95	15 -> 6[label="",style="solid", color="burlywood", weight=3];
12.83/4.95	5[label="List.intersperse wu3 (wu40 : wu41)",fontsize=16,color="burlywood",shape="box"];16[label="wu41/wu410 : wu411",fontsize=10,color="white",style="solid",shape="box"];5 -> 16[label="",style="solid", color="burlywood", weight=9];
12.83/4.95	16 -> 7[label="",style="solid", color="burlywood", weight=3];
12.83/4.95	17[label="wu41/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
12.83/4.95	17 -> 8[label="",style="solid", color="burlywood", weight=3];
12.83/4.95	6[label="List.intersperse wu3 []",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3];
12.83/4.95	7[label="List.intersperse wu3 (wu40 : wu410 : wu411)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
12.83/4.95	8[label="List.intersperse wu3 (wu40 : [])",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
12.83/4.95	9[label="[]",fontsize=16,color="green",shape="box"];10[label="wu40 : wu3 : List.intersperse wu3 (wu410 : wu411)",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="green", weight=3];
12.83/4.95	11[label="wu40 : []",fontsize=16,color="green",shape="box"];12 -> 4[label="",style="dashed", color="red", weight=0];
12.83/4.95	12[label="List.intersperse wu3 (wu410 : wu411)",fontsize=16,color="magenta"];12 -> 13[label="",style="dashed", color="magenta", weight=3];
12.83/4.95	13[label="wu410 : wu411",fontsize=16,color="green",shape="box"];}
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(6)
12.83/4.95	Obligation:
12.83/4.95	Q DP problem:
12.83/4.95	The TRS P consists of the following rules:
12.83/4.95	
12.83/4.95	   new_intersperse(wu3, :(wu40, :(wu410, wu411)), ba) -> new_intersperse(wu3, :(wu410, wu411), ba)
12.83/4.95	
12.83/4.95	R is empty.
12.83/4.95	Q is empty.
12.83/4.95	We have to consider all minimal (P,Q,R)-chains.
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(7) QDPSizeChangeProof (EQUIVALENT)
12.83/4.95	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. 
12.83/4.95	
12.83/4.95	From the DPs we obtained the following set of size-change graphs:
12.83/4.95	*new_intersperse(wu3, :(wu40, :(wu410, wu411)), ba) -> new_intersperse(wu3, :(wu410, wu411), ba)
12.83/4.95	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.83/4.95	
12.83/4.95	
12.83/4.95	----------------------------------------
12.83/4.95	
12.83/4.95	(8)
12.83/4.95	YES
12.94/5.01	EOF