7.58/3.58	YES
9.11/3.99	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.11/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.11/3.99	
9.11/3.99	
9.11/3.99	H-Termination with start terms of the given HASKELL could be proven:
9.11/3.99	
9.11/3.99	(0) HASKELL
9.11/3.99	(1) BR [EQUIVALENT, 0 ms]
9.11/3.99	(2) HASKELL
9.11/3.99	(3) COR [EQUIVALENT, 0 ms]
9.11/3.99	(4) HASKELL
9.11/3.99	(5) Narrow [SOUND, 0 ms]
9.11/3.99	(6) QDP
9.11/3.99	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.11/3.99	(8) YES
9.11/3.99	
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(0)
9.11/3.99	Obligation:
9.11/3.99	mainModule Main 
9.11/3.99	module Main where {
9.11/3.99	import qualified Prelude;
9.11/3.99	}
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(1) BR (EQUIVALENT)
9.11/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(2)
9.11/3.99	Obligation:
9.11/3.99	mainModule Main 
9.11/3.99	module Main where {
9.11/3.99	import qualified Prelude;
9.11/3.99	}
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(3) COR (EQUIVALENT)
9.11/3.99	Cond Reductions:
9.11/3.99	The following Function with conditions
9.11/3.99	"undefined |Falseundefined;
9.11/3.99	"
9.11/3.99	is transformed to
9.11/3.99	"undefined  = undefined1;
9.11/3.99	"
9.11/3.99	"undefined0 True = undefined;
9.11/3.99	"
9.11/3.99	"undefined1  = undefined0 False;
9.11/3.99	"
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(4)
9.11/3.99	Obligation:
9.11/3.99	mainModule Main 
9.11/3.99	module Main where {
9.11/3.99	import qualified Prelude;
9.11/3.99	}
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(5) Narrow (SOUND)
9.11/3.99	Haskell To QDPs
9.11/3.99	
9.11/3.99	digraph dp_graph {
9.11/3.99	node [outthreshold=100, inthreshold=100];1[label="(==)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.11/3.99	3[label="(==) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.11/3.99	4[label="(==) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.11/3.99	5[label="primEqChar vx3 vx4",fontsize=16,color="burlywood",shape="box"];21[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 21[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	21 -> 6[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	6[label="primEqChar (Char vx30) vx4",fontsize=16,color="burlywood",shape="box"];22[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	22 -> 7[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	7[label="primEqChar (Char vx30) (Char vx40)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.11/3.99	8[label="primEqNat vx30 vx40",fontsize=16,color="burlywood",shape="triangle"];23[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 23[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	23 -> 9[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	24[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 24[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	24 -> 10[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	9[label="primEqNat (Succ vx300) vx40",fontsize=16,color="burlywood",shape="box"];25[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];9 -> 25[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	25 -> 11[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	26[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 26[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	26 -> 12[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	10[label="primEqNat Zero vx40",fontsize=16,color="burlywood",shape="box"];27[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];10 -> 27[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	27 -> 13[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	28[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 28[label="",style="solid", color="burlywood", weight=9];
9.11/3.99	28 -> 14[label="",style="solid", color="burlywood", weight=3];
9.11/3.99	11[label="primEqNat (Succ vx300) (Succ vx400)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.11/3.99	12[label="primEqNat (Succ vx300) Zero",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.11/3.99	13[label="primEqNat Zero (Succ vx400)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.11/3.99	14[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.11/3.99	15 -> 8[label="",style="dashed", color="red", weight=0];
9.11/3.99	15[label="primEqNat vx300 vx400",fontsize=16,color="magenta"];15 -> 19[label="",style="dashed", color="magenta", weight=3];
9.11/3.99	15 -> 20[label="",style="dashed", color="magenta", weight=3];
9.11/3.99	16[label="False",fontsize=16,color="green",shape="box"];17[label="False",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="vx300",fontsize=16,color="green",shape="box"];20[label="vx400",fontsize=16,color="green",shape="box"];}
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(6)
9.11/3.99	Obligation:
9.11/3.99	Q DP problem:
9.11/3.99	The TRS P consists of the following rules:
9.11/3.99	
9.11/3.99	   new_primEqNat(Succ(vx300), Succ(vx400)) -> new_primEqNat(vx300, vx400)
9.11/3.99	
9.11/3.99	R is empty.
9.11/3.99	Q is empty.
9.11/3.99	We have to consider all minimal (P,Q,R)-chains.
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(7) QDPSizeChangeProof (EQUIVALENT)
9.11/3.99	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. 
9.11/3.99	
9.11/3.99	From the DPs we obtained the following set of size-change graphs:
9.11/3.99	*new_primEqNat(Succ(vx300), Succ(vx400)) -> new_primEqNat(vx300, vx400)
9.11/3.99	The graph contains the following edges 1 > 1, 2 > 2
9.11/3.99	
9.11/3.99	
9.11/3.99	----------------------------------------
9.11/3.99	
9.11/3.99	(8)
9.11/3.99	YES
9.11/4.04	EOF