7.51/3.47	YES
9.30/3.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.30/3.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.30/3.96	
9.30/3.96	
9.30/3.96	H-Termination with start terms of the given HASKELL could be proven:
9.30/3.96	
9.30/3.96	(0) HASKELL
9.30/3.96	(1) BR [EQUIVALENT, 0 ms]
9.30/3.96	(2) HASKELL
9.30/3.96	(3) COR [EQUIVALENT, 0 ms]
9.30/3.96	(4) HASKELL
9.30/3.96	(5) NumRed [SOUND, 0 ms]
9.30/3.96	(6) HASKELL
9.30/3.96	(7) Narrow [SOUND, 0 ms]
9.30/3.96	(8) AND
9.30/3.96	    (9) QDP
9.30/3.96	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.30/3.96	        (11) YES
9.30/3.96	    (12) QDP
9.30/3.96	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.30/3.96	        (14) YES
9.30/3.96	
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(0)
9.30/3.96	Obligation:
9.30/3.96	mainModule Main 
9.30/3.96	module Main where {
9.30/3.96	import qualified Prelude;
9.30/3.96	}
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(1) BR (EQUIVALENT)
9.30/3.96	Replaced joker patterns by fresh variables and removed binding patterns.
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(2)
9.30/3.96	Obligation:
9.30/3.96	mainModule Main 
9.30/3.96	module Main where {
9.30/3.96	import qualified Prelude;
9.30/3.96	}
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(3) COR (EQUIVALENT)
9.30/3.96	Cond Reductions:
9.30/3.96	The following Function with conditions
9.30/3.96	"undefined |Falseundefined;
9.30/3.96	"
9.30/3.96	is transformed to
9.30/3.96	"undefined  = undefined1;
9.30/3.96	"
9.30/3.96	"undefined0 True = undefined;
9.30/3.96	"
9.30/3.96	"undefined1  = undefined0 False;
9.30/3.96	"
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(4)
9.30/3.96	Obligation:
9.30/3.96	mainModule Main 
9.30/3.96	module Main where {
9.30/3.96	import qualified Prelude;
9.30/3.96	}
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(5) NumRed (SOUND)
9.30/3.96	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(6)
9.30/3.96	Obligation:
9.30/3.96	mainModule Main 
9.30/3.96	module Main where {
9.30/3.96	import qualified Prelude;
9.30/3.96	}
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(7) Narrow (SOUND)
9.30/3.96	Haskell To QDPs
9.30/3.96	
9.30/3.96	digraph dp_graph {
9.30/3.96	node [outthreshold=100, inthreshold=100];1[label="unlines",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.30/3.96	3[label="unlines vx3",fontsize=16,color="burlywood",shape="triangle"];24[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 24[label="",style="solid", color="burlywood", weight=9];
9.30/3.96	24 -> 4[label="",style="solid", color="burlywood", weight=3];
9.30/3.96	25[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 25[label="",style="solid", color="burlywood", weight=9];
9.30/3.96	25 -> 5[label="",style="solid", color="burlywood", weight=3];
9.30/3.96	4[label="unlines (vx30 : vx31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
9.30/3.96	5[label="unlines []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.30/3.96	6 -> 12[label="",style="dashed", color="red", weight=0];
9.30/3.96	6[label="vx30 ++ Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) : unlines vx31",fontsize=16,color="magenta"];6 -> 13[label="",style="dashed", color="magenta", weight=3];
9.30/3.96	6 -> 14[label="",style="dashed", color="magenta", weight=3];
9.30/3.96	6 -> 15[label="",style="dashed", color="magenta", weight=3];
9.30/3.96	7[label="[]",fontsize=16,color="green",shape="box"];13[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];14 -> 3[label="",style="dashed", color="red", weight=0];
9.30/3.96	14[label="unlines vx31",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
9.30/3.96	15[label="vx30",fontsize=16,color="green",shape="box"];12[label="vx5 ++ Char (Succ vx6) : vx8",fontsize=16,color="burlywood",shape="triangle"];26[label="vx5/vx50 : vx51",fontsize=10,color="white",style="solid",shape="box"];12 -> 26[label="",style="solid", color="burlywood", weight=9];
9.30/3.96	26 -> 18[label="",style="solid", color="burlywood", weight=3];
9.30/3.96	27[label="vx5/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 27[label="",style="solid", color="burlywood", weight=9];
9.30/3.96	27 -> 19[label="",style="solid", color="burlywood", weight=3];
9.30/3.96	17[label="vx31",fontsize=16,color="green",shape="box"];18[label="(vx50 : vx51) ++ Char (Succ vx6) : vx8",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
9.30/3.96	19[label="[] ++ Char (Succ vx6) : vx8",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
9.30/3.96	20[label="vx50 : vx51 ++ Char (Succ vx6) : vx8",fontsize=16,color="green",shape="box"];20 -> 22[label="",style="dashed", color="green", weight=3];
9.30/3.96	21[label="Char (Succ vx6) : vx8",fontsize=16,color="green",shape="box"];22 -> 12[label="",style="dashed", color="red", weight=0];
9.30/3.96	22[label="vx51 ++ Char (Succ vx6) : vx8",fontsize=16,color="magenta"];22 -> 23[label="",style="dashed", color="magenta", weight=3];
9.30/3.96	23[label="vx51",fontsize=16,color="green",shape="box"];}
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(8)
9.30/3.96	Complex Obligation (AND)
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(9)
9.30/3.96	Obligation:
9.30/3.96	Q DP problem:
9.30/3.96	The TRS P consists of the following rules:
9.30/3.96	
9.30/3.96	   new_unlines(:(vx30, vx31)) -> new_unlines(vx31)
9.30/3.96	
9.30/3.96	R is empty.
9.30/3.96	Q is empty.
9.30/3.96	We have to consider all minimal (P,Q,R)-chains.
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(10) QDPSizeChangeProof (EQUIVALENT)
9.30/3.96	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. 
9.30/3.96	
9.30/3.96	From the DPs we obtained the following set of size-change graphs:
9.30/3.96	*new_unlines(:(vx30, vx31)) -> new_unlines(vx31)
9.30/3.96	The graph contains the following edges 1 > 1
9.30/3.96	
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(11)
9.30/3.96	YES
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(12)
9.30/3.96	Obligation:
9.30/3.96	Q DP problem:
9.30/3.96	The TRS P consists of the following rules:
9.30/3.96	
9.30/3.96	   new_psPs(:(vx50, vx51), vx6, vx8) -> new_psPs(vx51, vx6, vx8)
9.30/3.96	
9.30/3.96	R is empty.
9.30/3.96	Q is empty.
9.30/3.96	We have to consider all minimal (P,Q,R)-chains.
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(13) QDPSizeChangeProof (EQUIVALENT)
9.30/3.96	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. 
9.30/3.96	
9.30/3.96	From the DPs we obtained the following set of size-change graphs:
9.30/3.96	*new_psPs(:(vx50, vx51), vx6, vx8) -> new_psPs(vx51, vx6, vx8)
9.30/3.96	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.30/3.96	
9.30/3.96	
9.30/3.96	----------------------------------------
9.30/3.96	
9.30/3.96	(14)
9.30/3.96	YES
9.30/4.01	EOF