9.36/4.02	YES
11.87/4.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.87/4.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.87/4.69	
11.87/4.69	
11.87/4.69	H-Termination with start terms of the given HASKELL could be proven:
11.87/4.69	
11.87/4.69	(0) HASKELL
11.87/4.69	(1) LR [EQUIVALENT, 0 ms]
11.87/4.69	(2) HASKELL
11.87/4.69	(3) BR [EQUIVALENT, 0 ms]
11.87/4.69	(4) HASKELL
11.87/4.69	(5) COR [EQUIVALENT, 0 ms]
11.87/4.69	(6) HASKELL
11.87/4.69	(7) LetRed [EQUIVALENT, 6 ms]
11.87/4.69	(8) HASKELL
11.87/4.69	(9) NumRed [SOUND, 0 ms]
11.87/4.69	(10) HASKELL
11.87/4.69	(11) Narrow [SOUND, 0 ms]
11.87/4.69	(12) QDP
11.87/4.69	(13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
11.87/4.69	(14) YES
11.87/4.69	
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(0)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(1) LR (EQUIVALENT)
11.87/4.69	Lambda Reductions:
11.87/4.69	The following Lambda expression
11.87/4.69	"\xs->return (x : xs)"
11.87/4.69	is transformed to
11.87/4.69	"sequence0 x xs = return (x : xs);
11.87/4.69	"
11.87/4.69	The following Lambda expression
11.87/4.69	"\x->sequence cs >>= sequence0 x"
11.87/4.69	is transformed to
11.87/4.69	"sequence1 cs x = sequence cs >>= sequence0 x;
11.87/4.69	"
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(2)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(3) BR (EQUIVALENT)
11.87/4.69	Replaced joker patterns by fresh variables and removed binding patterns.
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(4)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(5) COR (EQUIVALENT)
11.87/4.69	Cond Reductions:
11.87/4.69	The following Function with conditions
11.87/4.69	"undefined |Falseundefined;
11.87/4.69	"
11.87/4.69	is transformed to
11.87/4.69	"undefined  = undefined1;
11.87/4.69	"
11.87/4.69	"undefined0 True = undefined;
11.87/4.69	"
11.87/4.69	"undefined1  = undefined0 False;
11.87/4.69	"
11.87/4.69	The following Function with conditions
11.87/4.69	"take n vy|n <= 0[];
11.87/4.69	take vz [] = [];
11.87/4.69	take n (x : xs) = x : take (n - 1) xs;
11.87/4.69	"
11.87/4.69	is transformed to
11.87/4.69	"take n vy = take3 n vy;
11.87/4.69	take vz [] = take1 vz [];
11.87/4.69	take n (x : xs) = take0 n (x : xs);
11.87/4.69	"
11.87/4.69	"take0 n (x : xs) = x : take (n - 1) xs;
11.87/4.69	"
11.87/4.69	"take1 vz [] = [];
11.87/4.69	take1 ww wx = take0 ww wx;
11.87/4.69	"
11.87/4.69	"take2 n vy True = [];
11.87/4.69	take2 n vy False = take1 n vy;
11.87/4.69	"
11.87/4.69	"take3 n vy = take2 n vy (n <= 0);
11.87/4.69	take3 wy wz = take1 wy wz;
11.87/4.69	"
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(6)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(7) LetRed (EQUIVALENT)
11.87/4.69	Let/Where Reductions:
11.87/4.69	The bindings of the following Let/Where expression
11.87/4.69	"xs where {
11.87/4.69	xs  = x : xs;
11.87/4.69	} 
11.87/4.69	"
11.87/4.69	are unpacked to the following functions on top level
11.87/4.69	"repeatXs xu = xu : repeatXs xu;
11.87/4.69	"
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(8)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(9) NumRed (SOUND)
11.87/4.69	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(10)
11.87/4.69	Obligation:
11.87/4.69	mainModule Main 
11.87/4.69	module Maybe where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Main where {
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Monad;
11.87/4.69	import qualified Prelude;
11.87/4.69	}
11.87/4.69	module Monad where {
11.87/4.69	import qualified Main;
11.87/4.69	import qualified Maybe;
11.87/4.69	import qualified Prelude;
11.87/4.69	replicateM :: Monad b => Int  ->  b a  ->  b [a];
11.87/4.69	replicateM n x = sequence (replicate n x);
11.87/4.69	
11.87/4.69	}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(11) Narrow (SOUND)
11.87/4.69	Haskell To QDPs
11.87/4.69	
11.87/4.69	digraph dp_graph {
11.87/4.69	node [outthreshold=100, inthreshold=100];1[label="Monad.replicateM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.87/4.69	3[label="Monad.replicateM xv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.87/4.69	4[label="Monad.replicateM xv3 xv4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.87/4.69	5[label="sequence (replicate xv3 xv4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
11.87/4.69	6[label="sequence (take xv3 (repeat xv4))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
11.87/4.69	7[label="sequence (take3 xv3 (repeat xv4))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
11.87/4.69	8[label="sequence (take2 xv3 (repeat xv4) (xv3 <= Pos Zero))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
11.87/4.69	9[label="sequence (take2 xv3 (repeat xv4) (compare xv3 (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
11.87/4.69	10[label="sequence (take2 xv3 (repeat xv4) (not (compare xv3 (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11.87/4.69	11[label="sequence (take2 xv3 (repeat xv4) (not (primCmpInt xv3 (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];118[label="xv3/Pos xv30",fontsize=10,color="white",style="solid",shape="box"];11 -> 118[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	118 -> 12[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	119[label="xv3/Neg xv30",fontsize=10,color="white",style="solid",shape="box"];11 -> 119[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	119 -> 13[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	12[label="sequence (take2 (Pos xv30) (repeat xv4) (not (primCmpInt (Pos xv30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];120[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];12 -> 120[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	120 -> 14[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	121[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 121[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	121 -> 15[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	13[label="sequence (take2 (Neg xv30) (repeat xv4) (not (primCmpInt (Neg xv30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];122[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];13 -> 122[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	122 -> 16[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	123[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 123[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	123 -> 17[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	14[label="sequence (take2 (Pos (Succ xv300)) (repeat xv4) (not (primCmpInt (Pos (Succ xv300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
11.87/4.69	15[label="sequence (take2 (Pos Zero) (repeat xv4) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
11.87/4.69	16[label="sequence (take2 (Neg (Succ xv300)) (repeat xv4) (not (primCmpInt (Neg (Succ xv300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
11.87/4.69	17[label="sequence (take2 (Neg Zero) (repeat xv4) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
11.87/4.69	18[label="sequence (take2 (Pos (Succ xv300)) (repeat xv4) (not (primCmpNat (Succ xv300) Zero == GT)))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
11.87/4.69	19[label="sequence (take2 (Pos Zero) (repeat xv4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
11.87/4.69	20[label="sequence (take2 (Neg (Succ xv300)) (repeat xv4) (not (LT == GT)))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
11.87/4.69	21[label="sequence (take2 (Neg Zero) (repeat xv4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
11.87/4.69	22[label="sequence (take2 (Pos (Succ xv300)) (repeat xv4) (not (GT == GT)))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
11.87/4.69	23[label="sequence (take2 (Pos Zero) (repeat xv4) (not False))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
11.87/4.69	24[label="sequence (take2 (Neg (Succ xv300)) (repeat xv4) (not False))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
11.87/4.69	25[label="sequence (take2 (Neg Zero) (repeat xv4) (not False))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
11.87/4.69	26[label="sequence (take2 (Pos (Succ xv300)) (repeat xv4) (not True))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
11.87/4.69	27[label="sequence (take2 (Pos Zero) (repeat xv4) True)",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
11.87/4.69	28[label="sequence (take2 (Neg (Succ xv300)) (repeat xv4) True)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
11.87/4.69	29[label="sequence (take2 (Neg Zero) (repeat xv4) True)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
11.87/4.69	30[label="sequence (take2 (Pos (Succ xv300)) (repeat xv4) False)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
11.87/4.69	31[label="sequence []",fontsize=16,color="black",shape="triangle"];31 -> 35[label="",style="solid", color="black", weight=3];
11.87/4.69	32 -> 31[label="",style="dashed", color="red", weight=0];
11.87/4.69	32[label="sequence []",fontsize=16,color="magenta"];33 -> 31[label="",style="dashed", color="red", weight=0];
11.87/4.69	33[label="sequence []",fontsize=16,color="magenta"];34[label="sequence (take1 (Pos (Succ xv300)) (repeat xv4))",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
11.87/4.69	35[label="return []",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
11.87/4.69	36[label="sequence (take1 (Pos (Succ xv300)) (repeatXs xv4))",fontsize=16,color="black",shape="triangle"];36 -> 38[label="",style="solid", color="black", weight=3];
11.87/4.69	37[label="Just []",fontsize=16,color="green",shape="box"];38[label="sequence (take1 (Pos (Succ xv300)) (xv4 : repeatXs xv4))",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
11.87/4.69	39[label="sequence (take0 (Pos (Succ xv300)) (xv4 : repeatXs xv4))",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3];
11.87/4.69	40[label="sequence (xv4 : take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs xv4))",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
11.87/4.69	41[label="xv4 >>= sequence1 (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs xv4))",fontsize=16,color="burlywood",shape="box"];124[label="xv4/Nothing",fontsize=10,color="white",style="solid",shape="box"];41 -> 124[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	124 -> 42[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	125[label="xv4/Just xv40",fontsize=10,color="white",style="solid",shape="box"];41 -> 125[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	125 -> 43[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	42[label="Nothing >>= sequence1 (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs Nothing))",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
11.87/4.69	43[label="Just xv40 >>= sequence1 (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)))",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
11.87/4.69	44[label="Nothing",fontsize=16,color="green",shape="box"];45[label="sequence1 (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40))) xv40",fontsize=16,color="black",shape="box"];45 -> 46[label="",style="solid", color="black", weight=3];
11.87/4.69	46 -> 68[label="",style="dashed", color="red", weight=0];
11.87/4.69	46[label="sequence (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40))) >>= sequence0 xv40",fontsize=16,color="magenta"];46 -> 69[label="",style="dashed", color="magenta", weight=3];
11.87/4.69	69[label="sequence (take (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)))",fontsize=16,color="black",shape="box"];69 -> 89[label="",style="solid", color="black", weight=3];
11.87/4.69	68[label="xv5 >>= sequence0 xv40",fontsize=16,color="burlywood",shape="triangle"];126[label="xv5/Nothing",fontsize=10,color="white",style="solid",shape="box"];68 -> 126[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	126 -> 90[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	127[label="xv5/Just xv50",fontsize=10,color="white",style="solid",shape="box"];68 -> 127[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	127 -> 91[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	89[label="sequence (take3 (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)))",fontsize=16,color="black",shape="box"];89 -> 92[label="",style="solid", color="black", weight=3];
11.87/4.69	90[label="Nothing >>= sequence0 xv40",fontsize=16,color="black",shape="box"];90 -> 93[label="",style="solid", color="black", weight=3];
11.87/4.69	91[label="Just xv50 >>= sequence0 xv40",fontsize=16,color="black",shape="box"];91 -> 94[label="",style="solid", color="black", weight=3];
11.87/4.69	92[label="sequence (take2 (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)) (Pos (Succ xv300) - Pos (Succ Zero) <= Pos Zero))",fontsize=16,color="black",shape="box"];92 -> 95[label="",style="solid", color="black", weight=3];
11.87/4.69	93[label="Nothing",fontsize=16,color="green",shape="box"];94[label="sequence0 xv40 xv50",fontsize=16,color="black",shape="box"];94 -> 96[label="",style="solid", color="black", weight=3];
11.87/4.69	95[label="sequence (take2 (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)) (compare (Pos (Succ xv300) - Pos (Succ Zero)) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];95 -> 97[label="",style="solid", color="black", weight=3];
11.87/4.69	96[label="return (xv40 : xv50)",fontsize=16,color="black",shape="box"];96 -> 98[label="",style="solid", color="black", weight=3];
11.87/4.69	97[label="sequence (take2 (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)) (not (compare (Pos (Succ xv300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];97 -> 99[label="",style="solid", color="black", weight=3];
11.87/4.69	98[label="Just (xv40 : xv50)",fontsize=16,color="green",shape="box"];99[label="sequence (take2 (Pos (Succ xv300) - Pos (Succ Zero)) (repeatXs (Just xv40)) (not (primCmpInt (Pos (Succ xv300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];99 -> 100[label="",style="solid", color="black", weight=3];
11.87/4.69	100[label="sequence (take2 (primMinusInt (Pos (Succ xv300)) (Pos (Succ Zero))) (repeatXs (Just xv40)) (not (primCmpInt (primMinusInt (Pos (Succ xv300)) (Pos (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];100 -> 101[label="",style="solid", color="black", weight=3];
11.87/4.69	101[label="sequence (take2 (primMinusNat (Succ xv300) (Succ Zero)) (repeatXs (Just xv40)) (not (primCmpInt (primMinusNat (Succ xv300) (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];101 -> 102[label="",style="solid", color="black", weight=3];
11.87/4.69	102[label="sequence (take2 (primMinusNat xv300 Zero) (repeatXs (Just xv40)) (not (primCmpInt (primMinusNat xv300 Zero) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];128[label="xv300/Succ xv3000",fontsize=10,color="white",style="solid",shape="box"];102 -> 128[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	128 -> 103[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	129[label="xv300/Zero",fontsize=10,color="white",style="solid",shape="box"];102 -> 129[label="",style="solid", color="burlywood", weight=9];
11.87/4.69	129 -> 104[label="",style="solid", color="burlywood", weight=3];
11.87/4.69	103[label="sequence (take2 (primMinusNat (Succ xv3000) Zero) (repeatXs (Just xv40)) (not (primCmpInt (primMinusNat (Succ xv3000) Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];103 -> 105[label="",style="solid", color="black", weight=3];
11.87/4.69	104[label="sequence (take2 (primMinusNat Zero Zero) (repeatXs (Just xv40)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];104 -> 106[label="",style="solid", color="black", weight=3];
11.87/4.69	105[label="sequence (take2 (Pos (Succ xv3000)) (repeatXs (Just xv40)) (not (primCmpInt (Pos (Succ xv3000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];105 -> 107[label="",style="solid", color="black", weight=3];
11.87/4.69	106[label="sequence (take2 (Pos Zero) (repeatXs (Just xv40)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];106 -> 108[label="",style="solid", color="black", weight=3];
11.87/4.69	107[label="sequence (take2 (Pos (Succ xv3000)) (repeatXs (Just xv40)) (not (primCmpNat (Succ xv3000) Zero == GT)))",fontsize=16,color="black",shape="box"];107 -> 109[label="",style="solid", color="black", weight=3];
11.87/4.69	108[label="sequence (take2 (Pos Zero) (repeatXs (Just xv40)) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];108 -> 110[label="",style="solid", color="black", weight=3];
11.87/4.69	109[label="sequence (take2 (Pos (Succ xv3000)) (repeatXs (Just xv40)) (not (GT == GT)))",fontsize=16,color="black",shape="box"];109 -> 111[label="",style="solid", color="black", weight=3];
11.87/4.69	110[label="sequence (take2 (Pos Zero) (repeatXs (Just xv40)) (not False))",fontsize=16,color="black",shape="box"];110 -> 112[label="",style="solid", color="black", weight=3];
11.87/4.69	111[label="sequence (take2 (Pos (Succ xv3000)) (repeatXs (Just xv40)) (not True))",fontsize=16,color="black",shape="box"];111 -> 113[label="",style="solid", color="black", weight=3];
11.87/4.69	112[label="sequence (take2 (Pos Zero) (repeatXs (Just xv40)) True)",fontsize=16,color="black",shape="box"];112 -> 114[label="",style="solid", color="black", weight=3];
11.87/4.69	113[label="sequence (take2 (Pos (Succ xv3000)) (repeatXs (Just xv40)) False)",fontsize=16,color="black",shape="box"];113 -> 115[label="",style="solid", color="black", weight=3];
11.87/4.69	114 -> 31[label="",style="dashed", color="red", weight=0];
11.87/4.69	114[label="sequence []",fontsize=16,color="magenta"];115 -> 36[label="",style="dashed", color="red", weight=0];
11.87/4.69	115[label="sequence (take1 (Pos (Succ xv3000)) (repeatXs (Just xv40)))",fontsize=16,color="magenta"];115 -> 116[label="",style="dashed", color="magenta", weight=3];
11.87/4.69	115 -> 117[label="",style="dashed", color="magenta", weight=3];
11.87/4.69	116[label="xv3000",fontsize=16,color="green",shape="box"];117[label="Just xv40",fontsize=16,color="green",shape="box"];}
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(12)
11.87/4.69	Obligation:
11.87/4.69	Q DP problem:
11.87/4.69	The TRS P consists of the following rules:
11.87/4.69	
11.87/4.69	   new_sequence(Succ(xv3000), Just(xv40), h) -> new_sequence(xv3000, Just(xv40), h)
11.87/4.69	
11.87/4.69	R is empty.
11.87/4.69	Q is empty.
11.87/4.69	We have to consider all minimal (P,Q,R)-chains.
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(13) QDPSizeChangeProof (EQUIVALENT)
11.87/4.69	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. 
11.87/4.69	
11.87/4.69	From the DPs we obtained the following set of size-change graphs:
11.87/4.69	*new_sequence(Succ(xv3000), Just(xv40), h) -> new_sequence(xv3000, Just(xv40), h)
11.87/4.69	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
11.87/4.69	
11.87/4.69	
11.87/4.69	----------------------------------------
11.87/4.69	
11.87/4.69	(14)
11.87/4.69	YES
11.94/4.74	EOF