8.16/3.54	YES
10.13/4.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.13/4.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.13/4.08	
10.13/4.08	
10.13/4.08	H-Termination with start terms of the given HASKELL could be proven:
10.13/4.08	
10.13/4.08	(0) HASKELL
10.13/4.08	(1) BR [EQUIVALENT, 0 ms]
10.13/4.08	(2) HASKELL
10.13/4.08	(3) COR [EQUIVALENT, 0 ms]
10.13/4.08	(4) HASKELL
10.13/4.08	(5) NumRed [SOUND, 0 ms]
10.13/4.08	(6) HASKELL
10.13/4.08	(7) Narrow [EQUIVALENT, 13 ms]
10.13/4.08	(8) YES
10.13/4.08	
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(0)
10.13/4.08	Obligation:
10.13/4.08	mainModule Main 
10.13/4.08	module Main where {
10.13/4.08	import qualified Prelude;
10.13/4.08	}
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(1) BR (EQUIVALENT)
10.13/4.08	Replaced joker patterns by fresh variables and removed binding patterns.
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(2)
10.13/4.08	Obligation:
10.13/4.08	mainModule Main 
10.13/4.08	module Main where {
10.13/4.08	import qualified Prelude;
10.13/4.08	}
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(3) COR (EQUIVALENT)
10.13/4.08	Cond Reductions:
10.13/4.08	The following Function with conditions
10.13/4.08	"toEnum 0 = False;
10.13/4.08	toEnum 1 = True;
10.13/4.08	"
10.13/4.08	is transformed to
10.13/4.08	"toEnum wu = toEnum3 wu;
10.13/4.08	toEnum vz = toEnum1 vz;
10.13/4.08	"
10.13/4.08	"toEnum0 True vz = True;
10.13/4.08	"
10.13/4.08	"toEnum1 vz = toEnum0 (vz == 1) vz;
10.13/4.08	"
10.13/4.08	"toEnum2 True wu = False;
10.13/4.08	toEnum2 wv ww = toEnum1 ww;
10.13/4.08	"
10.13/4.08	"toEnum3 wu = toEnum2 (wu == 0) wu;
10.13/4.08	toEnum3 wx = toEnum1 wx;
10.13/4.08	"
10.13/4.08	The following Function with conditions
10.13/4.08	"undefined |Falseundefined;
10.13/4.08	"
10.13/4.08	is transformed to
10.13/4.08	"undefined  = undefined1;
10.13/4.08	"
10.13/4.08	"undefined0 True = undefined;
10.13/4.08	"
10.13/4.08	"undefined1  = undefined0 False;
10.13/4.08	"
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(4)
10.13/4.08	Obligation:
10.13/4.08	mainModule Main 
10.13/4.08	module Main where {
10.13/4.08	import qualified Prelude;
10.13/4.08	}
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(5) NumRed (SOUND)
10.13/4.08	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(6)
10.13/4.08	Obligation:
10.13/4.08	mainModule Main 
10.13/4.08	module Main where {
10.13/4.08	import qualified Prelude;
10.13/4.08	}
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(7) Narrow (EQUIVALENT)
10.13/4.08	Haskell To QDPs
10.13/4.08	
10.13/4.08	digraph dp_graph {
10.13/4.08	node [outthreshold=100, inthreshold=100];1[label="toEnum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.13/4.08	3[label="toEnum wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.13/4.08	4[label="toEnum3 wy3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.13/4.08	5[label="toEnum2 (wy3 == Pos Zero) wy3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.13/4.08	6[label="toEnum2 (primEqInt wy3 (Pos Zero)) wy3",fontsize=16,color="burlywood",shape="box"];34[label="wy3/Pos wy30",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	34 -> 7[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	35[label="wy3/Neg wy30",fontsize=10,color="white",style="solid",shape="box"];6 -> 35[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	35 -> 8[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	7[label="toEnum2 (primEqInt (Pos wy30) (Pos Zero)) (Pos wy30)",fontsize=16,color="burlywood",shape="box"];36[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	36 -> 9[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	37[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	37 -> 10[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	8[label="toEnum2 (primEqInt (Neg wy30) (Pos Zero)) (Neg wy30)",fontsize=16,color="burlywood",shape="box"];38[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	38 -> 11[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	39[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	39 -> 12[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	9[label="toEnum2 (primEqInt (Pos (Succ wy300)) (Pos Zero)) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10.13/4.08	10[label="toEnum2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
10.13/4.08	11[label="toEnum2 (primEqInt (Neg (Succ wy300)) (Pos Zero)) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
10.13/4.08	12[label="toEnum2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
10.13/4.08	13[label="toEnum2 False (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
10.13/4.08	14[label="toEnum2 True (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
10.13/4.08	15[label="toEnum2 False (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
10.13/4.08	16[label="toEnum2 True (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
10.13/4.08	17[label="toEnum1 (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
10.13/4.08	18[label="False",fontsize=16,color="green",shape="box"];19[label="toEnum1 (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
10.13/4.08	20[label="False",fontsize=16,color="green",shape="box"];21[label="toEnum0 (Pos (Succ wy300) == Pos (Succ Zero)) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
10.13/4.08	22[label="toEnum0 (Neg (Succ wy300) == Pos (Succ Zero)) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
10.13/4.08	23[label="toEnum0 (primEqInt (Pos (Succ wy300)) (Pos (Succ Zero))) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
10.13/4.08	24[label="toEnum0 (primEqInt (Neg (Succ wy300)) (Pos (Succ Zero))) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
10.13/4.08	25[label="toEnum0 (primEqNat wy300 Zero) (Pos (Succ wy300))",fontsize=16,color="burlywood",shape="box"];40[label="wy300/Succ wy3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 40[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	40 -> 27[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	41[label="wy300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 41[label="",style="solid", color="burlywood", weight=9];
10.13/4.08	41 -> 28[label="",style="solid", color="burlywood", weight=3];
10.13/4.08	26[label="toEnum0 False (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3];
10.13/4.08	27[label="toEnum0 (primEqNat (Succ wy3000) Zero) (Pos (Succ (Succ wy3000)))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
10.13/4.08	28[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
10.13/4.08	29[label="error []",fontsize=16,color="red",shape="box"];30[label="toEnum0 False (Pos (Succ (Succ wy3000)))",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
10.13/4.08	31[label="toEnum0 True (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
10.13/4.08	32[label="error []",fontsize=16,color="red",shape="box"];33[label="True",fontsize=16,color="green",shape="box"];}
10.13/4.08	
10.13/4.08	----------------------------------------
10.13/4.08	
10.13/4.08	(8)
10.13/4.08	YES
10.33/4.12	EOF