7.99/3.59	YES
9.21/4.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.21/4.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.21/4.01	
9.21/4.01	
9.21/4.01	H-Termination with start terms of the given HASKELL could be proven:
9.21/4.01	
9.21/4.01	(0) HASKELL
9.21/4.01	(1) BR [EQUIVALENT, 0 ms]
9.21/4.01	(2) HASKELL
9.21/4.01	(3) COR [EQUIVALENT, 0 ms]
9.21/4.01	(4) HASKELL
9.21/4.01	(5) Narrow [SOUND, 0 ms]
9.21/4.01	(6) QDP
9.21/4.01	(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.21/4.01	(8) YES
9.21/4.01	
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(0)
9.21/4.01	Obligation:
9.21/4.01	mainModule Main 
9.21/4.01	module Main where {
9.21/4.01	import qualified Prelude;
9.21/4.01	}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(1) BR (EQUIVALENT)
9.21/4.01	Replaced joker patterns by fresh variables and removed binding patterns.
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(2)
9.21/4.01	Obligation:
9.21/4.01	mainModule Main 
9.21/4.01	module Main where {
9.21/4.01	import qualified Prelude;
9.21/4.01	}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(3) COR (EQUIVALENT)
9.21/4.01	Cond Reductions:
9.21/4.01	The following Function with conditions
9.21/4.01	"undefined |Falseundefined;
9.21/4.01	"
9.21/4.01	is transformed to
9.21/4.01	"undefined  = undefined1;
9.21/4.01	"
9.21/4.01	"undefined0 True = undefined;
9.21/4.01	"
9.21/4.01	"undefined1  = undefined0 False;
9.21/4.01	"
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(4)
9.21/4.01	Obligation:
9.21/4.01	mainModule Main 
9.21/4.01	module Main where {
9.21/4.01	import qualified Prelude;
9.21/4.01	}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(5) Narrow (SOUND)
9.21/4.01	Haskell To QDPs
9.21/4.01	
9.21/4.01	digraph dp_graph {
9.21/4.01	node [outthreshold=100, inthreshold=100];1[label="(>=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.21/4.01	3[label="(>=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.21/4.01	4[label="(>=) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.21/4.01	5[label="compare vx3 vx4 /= LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.21/4.01	6[label="not (compare vx3 vx4 == LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.21/4.01	7[label="not (primCmpChar vx3 vx4 == LT)",fontsize=16,color="burlywood",shape="box"];28[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];7 -> 28[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	28 -> 8[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	8[label="not (primCmpChar (Char vx30) vx4 == LT)",fontsize=16,color="burlywood",shape="box"];29[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];8 -> 29[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	29 -> 9[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	9[label="not (primCmpChar (Char vx30) (Char vx40) == LT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.21/4.01	10[label="not (primCmpNat vx30 vx40 == LT)",fontsize=16,color="burlywood",shape="triangle"];30[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 30[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	30 -> 11[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	31[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 31[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	31 -> 12[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	11[label="not (primCmpNat (Succ vx300) vx40 == LT)",fontsize=16,color="burlywood",shape="box"];32[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];11 -> 32[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	32 -> 13[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	33[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 33[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	33 -> 14[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	12[label="not (primCmpNat Zero vx40 == LT)",fontsize=16,color="burlywood",shape="box"];34[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];12 -> 34[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	34 -> 15[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	35[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 35[label="",style="solid", color="burlywood", weight=9];
9.21/4.01	35 -> 16[label="",style="solid", color="burlywood", weight=3];
9.21/4.01	13[label="not (primCmpNat (Succ vx300) (Succ vx400) == LT)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.21/4.01	14[label="not (primCmpNat (Succ vx300) Zero == LT)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.21/4.01	15[label="not (primCmpNat Zero (Succ vx400) == LT)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.21/4.01	16[label="not (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.21/4.01	17 -> 10[label="",style="dashed", color="red", weight=0];
9.21/4.01	17[label="not (primCmpNat vx300 vx400 == LT)",fontsize=16,color="magenta"];17 -> 21[label="",style="dashed", color="magenta", weight=3];
9.21/4.01	17 -> 22[label="",style="dashed", color="magenta", weight=3];
9.21/4.01	18[label="not (GT == LT)",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
9.21/4.01	19[label="not (LT == LT)",fontsize=16,color="black",shape="box"];19 -> 24[label="",style="solid", color="black", weight=3];
9.21/4.01	20[label="not (EQ == LT)",fontsize=16,color="black",shape="box"];20 -> 25[label="",style="solid", color="black", weight=3];
9.21/4.01	21[label="vx400",fontsize=16,color="green",shape="box"];22[label="vx300",fontsize=16,color="green",shape="box"];23[label="not False",fontsize=16,color="black",shape="triangle"];23 -> 26[label="",style="solid", color="black", weight=3];
9.21/4.01	24[label="not True",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
9.21/4.01	25 -> 23[label="",style="dashed", color="red", weight=0];
9.21/4.01	25[label="not False",fontsize=16,color="magenta"];26[label="True",fontsize=16,color="green",shape="box"];27[label="False",fontsize=16,color="green",shape="box"];}
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(6)
9.21/4.01	Obligation:
9.21/4.01	Q DP problem:
9.21/4.01	The TRS P consists of the following rules:
9.21/4.01	
9.21/4.01	   new_not(Succ(vx300), Succ(vx400)) -> new_not(vx300, vx400)
9.21/4.01	
9.21/4.01	R is empty.
9.21/4.01	Q is empty.
9.21/4.01	We have to consider all minimal (P,Q,R)-chains.
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(7) QDPSizeChangeProof (EQUIVALENT)
9.21/4.01	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. 
9.21/4.01	
9.21/4.01	From the DPs we obtained the following set of size-change graphs:
9.21/4.01	*new_not(Succ(vx300), Succ(vx400)) -> new_not(vx300, vx400)
9.21/4.01	The graph contains the following edges 1 > 1, 2 > 2
9.21/4.01	
9.21/4.01	
9.21/4.01	----------------------------------------
9.21/4.01	
9.21/4.01	(8)
9.21/4.01	YES
9.47/4.07	EOF