7.81/3.61	YES
9.83/4.16	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.83/4.16	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.83/4.16	
9.83/4.16	
9.83/4.16	H-Termination with start terms of the given HASKELL could be proven:
9.83/4.16	
9.83/4.16	(0) HASKELL
9.83/4.16	(1) BR [EQUIVALENT, 0 ms]
9.83/4.16	(2) HASKELL
9.83/4.16	(3) COR [EQUIVALENT, 0 ms]
9.83/4.16	(4) HASKELL
9.83/4.16	(5) Narrow [EQUIVALENT, 30 ms]
9.83/4.16	(6) YES
9.83/4.16	
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(0)
9.83/4.16	Obligation:
9.83/4.16	mainModule Main 
9.83/4.16	module Main where {
9.83/4.16	import qualified Prelude;
9.83/4.16	data Main.Char = Char MyInt ;
9.83/4.16	
9.83/4.16	data List a = Cons a (List a)  | Nil ;
9.83/4.16	
9.83/4.16	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.83/4.16	
9.83/4.16	data Main.Nat = Succ Main.Nat  | Zero ;
9.83/4.16	
9.83/4.16	data Tup0 = Tup0 ;
9.83/4.16	
9.83/4.16	psPs :: List a  ->  List a  ->  List a;
9.83/4.16	psPs Nil ys = ys;
9.83/4.16	psPs (Cons x xs) ys = Cons x (psPs xs ys);
9.83/4.16	
9.83/4.16	showString :: List Main.Char  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showString = psPs;
9.83/4.16	
9.83/4.16	showsPrecTup0 :: MyInt  ->  Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsPrecTup0 p Tup0 = showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) Nil));
9.83/4.16	
9.83/4.16	showsTup0 :: Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsTup0 = showsPrecTup0 (Main.Pos Main.Zero);
9.83/4.16	
9.83/4.16	}
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(1) BR (EQUIVALENT)
9.83/4.16	Replaced joker patterns by fresh variables and removed binding patterns.
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(2)
9.83/4.16	Obligation:
9.83/4.16	mainModule Main 
9.83/4.16	module Main where {
9.83/4.16	import qualified Prelude;
9.83/4.16	data Main.Char = Char MyInt ;
9.83/4.16	
9.83/4.16	data List a = Cons a (List a)  | Nil ;
9.83/4.16	
9.83/4.16	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.83/4.16	
9.83/4.16	data Main.Nat = Succ Main.Nat  | Zero ;
9.83/4.16	
9.83/4.16	data Tup0 = Tup0 ;
9.83/4.16	
9.83/4.16	psPs :: List a  ->  List a  ->  List a;
9.83/4.16	psPs Nil ys = ys;
9.83/4.16	psPs (Cons x xs) ys = Cons x (psPs xs ys);
9.83/4.16	
9.83/4.16	showString :: List Main.Char  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showString = psPs;
9.83/4.16	
9.83/4.16	showsPrecTup0 :: MyInt  ->  Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsPrecTup0 p Tup0 = showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) Nil));
9.83/4.16	
9.83/4.16	showsTup0 :: Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsTup0 = showsPrecTup0 (Main.Pos Main.Zero);
9.83/4.16	
9.83/4.16	}
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(3) COR (EQUIVALENT)
9.83/4.16	Cond Reductions:
9.83/4.16	The following Function with conditions
9.83/4.16	"undefined |Falseundefined;
9.83/4.16	"
9.83/4.16	is transformed to
9.83/4.16	"undefined  = undefined1;
9.83/4.16	"
9.83/4.16	"undefined0 True = undefined;
9.83/4.16	"
9.83/4.16	"undefined1  = undefined0 False;
9.83/4.16	"
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(4)
9.83/4.16	Obligation:
9.83/4.16	mainModule Main 
9.83/4.16	module Main where {
9.83/4.16	import qualified Prelude;
9.83/4.16	data Main.Char = Char MyInt ;
9.83/4.16	
9.83/4.16	data List a = Cons a (List a)  | Nil ;
9.83/4.16	
9.83/4.16	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.83/4.16	
9.83/4.16	data Main.Nat = Succ Main.Nat  | Zero ;
9.83/4.16	
9.83/4.16	data Tup0 = Tup0 ;
9.83/4.16	
9.83/4.16	psPs :: List a  ->  List a  ->  List a;
9.83/4.16	psPs Nil ys = ys;
9.83/4.16	psPs (Cons x xs) ys = Cons x (psPs xs ys);
9.83/4.16	
9.83/4.16	showString :: List Main.Char  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showString = psPs;
9.83/4.16	
9.83/4.16	showsPrecTup0 :: MyInt  ->  Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsPrecTup0 p Tup0 = showString (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))))))))))))))))))))) (Cons (Main.Char (Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero))))))))))))))))))))))))))))))))))))))))))) Nil));
9.83/4.16	
9.83/4.16	showsTup0 :: Tup0  ->  List Main.Char  ->  List Main.Char;
9.83/4.16	showsTup0 = showsPrecTup0 (Main.Pos Main.Zero);
9.83/4.16	
9.83/4.16	}
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(5) Narrow (EQUIVALENT)
9.83/4.16	Haskell To QDPs
9.83/4.16	
9.83/4.16	digraph dp_graph {
9.83/4.16	node [outthreshold=100, inthreshold=100];1[label="showsTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.83/4.16	3[label="showsTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.83/4.16	4[label="showsTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.83/4.16	5[label="showsPrecTup0 (Pos Zero) vx3 vx4",fontsize=16,color="burlywood",shape="box"];24[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];5 -> 24[label="",style="solid", color="burlywood", weight=9];
9.83/4.16	24 -> 6[label="",style="solid", color="burlywood", weight=3];
9.83/4.16	6[label="showsPrecTup0 (Pos Zero) Tup0 vx4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.83/4.16	7 -> 11[label="",style="dashed", color="red", weight=0];
9.83/4.16	7[label="showString (Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))) (Cons (Char (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))) Nil)) vx4",fontsize=16,color="magenta"];7 -> 12[label="",style="dashed", color="magenta", weight=3];
9.83/4.16	7 -> 13[label="",style="dashed", color="magenta", weight=3];
9.83/4.16	7 -> 14[label="",style="dashed", color="magenta", weight=3];
9.83/4.16	12[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];13[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];14[label="vx4",fontsize=16,color="green",shape="box"];11[label="showString (Cons (Char (Pos (Succ vx9))) (Cons (Char (Pos (Succ vx10))) Nil)) vx11",fontsize=16,color="black",shape="triangle"];11 -> 18[label="",style="solid", color="black", weight=3];
9.83/4.16	18[label="psPs (Cons (Char (Pos (Succ vx9))) (Cons (Char (Pos (Succ vx10))) Nil)) vx11",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
9.83/4.16	19[label="Cons (Char (Pos (Succ vx9))) (psPs (Cons (Char (Pos (Succ vx10))) Nil) vx11)",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="green", weight=3];
9.83/4.16	20[label="psPs (Cons (Char (Pos (Succ vx10))) Nil) vx11",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
9.83/4.16	21[label="Cons (Char (Pos (Succ vx10))) (psPs Nil vx11)",fontsize=16,color="green",shape="box"];21 -> 22[label="",style="dashed", color="green", weight=3];
9.83/4.16	22[label="psPs Nil vx11",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
9.83/4.16	23[label="vx11",fontsize=16,color="green",shape="box"];}
9.83/4.16	
9.83/4.16	----------------------------------------
9.83/4.16	
9.83/4.16	(6)
9.83/4.16	YES
9.94/4.21	EOF