8.53/3.67	YES
9.96/4.12	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.96/4.12	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.96/4.12	
9.96/4.12	
9.96/4.12	H-Termination with start terms of the given HASKELL could be proven:
9.96/4.12	
9.96/4.12	(0) HASKELL
9.96/4.12	(1) BR [EQUIVALENT, 0 ms]
9.96/4.12	(2) HASKELL
9.96/4.12	(3) COR [EQUIVALENT, 0 ms]
9.96/4.12	(4) HASKELL
9.96/4.12	(5) Narrow [SOUND, 0 ms]
9.96/4.12	(6) AND
9.96/4.12	    (7) QDP
9.96/4.12	        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.96/4.12	        (9) YES
9.96/4.12	    (10) QDP
9.96/4.12	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.96/4.12	        (12) YES
9.96/4.12	
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(0)
9.96/4.12	Obligation:
9.96/4.12	mainModule Main 
9.96/4.12	module Main where {
9.96/4.12	import qualified Prelude;
9.96/4.12	}
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(1) BR (EQUIVALENT)
9.96/4.12	Replaced joker patterns by fresh variables and removed binding patterns.
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(2)
9.96/4.12	Obligation:
9.96/4.12	mainModule Main 
9.96/4.12	module Main where {
9.96/4.12	import qualified Prelude;
9.96/4.12	}
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(3) COR (EQUIVALENT)
9.96/4.12	Cond Reductions:
9.96/4.12	The following Function with conditions
9.96/4.12	"min x y|x <= yx|otherwisey;
9.96/4.12	"
9.96/4.12	is transformed to
9.96/4.12	"min x y = min2 x y;
9.96/4.12	"
9.96/4.12	"min0 x y True = y;
9.96/4.12	"
9.96/4.12	"min1 x y True = x;
9.96/4.12	min1 x y False = min0 x y otherwise;
9.96/4.12	"
9.96/4.12	"min2 x y = min1 x y (x <= y);
9.96/4.12	"
9.96/4.12	The following Function with conditions
9.96/4.12	"undefined |Falseundefined;
9.96/4.12	"
9.96/4.12	is transformed to
9.96/4.12	"undefined  = undefined1;
9.96/4.12	"
9.96/4.12	"undefined0 True = undefined;
9.96/4.12	"
9.96/4.12	"undefined1  = undefined0 False;
9.96/4.12	"
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(4)
9.96/4.12	Obligation:
9.96/4.12	mainModule Main 
9.96/4.12	module Main where {
9.96/4.12	import qualified Prelude;
9.96/4.12	}
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(5) Narrow (SOUND)
9.96/4.12	Haskell To QDPs
9.96/4.12	
9.96/4.12	digraph dp_graph {
9.96/4.12	node [outthreshold=100, inthreshold=100];1[label="minimum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.96/4.12	3[label="minimum vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.96/4.12	4[label="foldl1 min vx3",fontsize=16,color="burlywood",shape="box"];312[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 312[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	312 -> 5[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	313[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 313[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	313 -> 6[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	5[label="foldl1 min (vx30 : vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.96/4.12	6[label="foldl1 min []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.96/4.12	7[label="foldl min vx30 vx31",fontsize=16,color="burlywood",shape="triangle"];314[label="vx31/vx310 : vx311",fontsize=10,color="white",style="solid",shape="box"];7 -> 314[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	314 -> 9[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	315[label="vx31/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 315[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	315 -> 10[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	8[label="error []",fontsize=16,color="red",shape="box"];9[label="foldl min vx30 (vx310 : vx311)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.96/4.12	10[label="foldl min vx30 []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
9.96/4.12	11 -> 7[label="",style="dashed", color="red", weight=0];
9.96/4.12	11[label="foldl min (min vx30 vx310) vx311",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	11 -> 14[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	12[label="vx30",fontsize=16,color="green",shape="box"];13[label="min vx30 vx310",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.96/4.12	14[label="vx311",fontsize=16,color="green",shape="box"];15[label="min2 vx30 vx310",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
9.96/4.12	16[label="min1 vx30 vx310 (vx30 <= vx310)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
9.96/4.12	17[label="min1 vx30 vx310 (compare vx30 vx310 /= GT)",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
9.96/4.12	18[label="min1 vx30 vx310 (not (compare vx30 vx310 == GT))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
9.96/4.12	19[label="min1 vx30 vx310 (not (primCmpChar vx30 vx310 == GT))",fontsize=16,color="burlywood",shape="box"];316[label="vx30/Char vx300",fontsize=10,color="white",style="solid",shape="box"];19 -> 316[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	316 -> 20[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	20[label="min1 (Char vx300) vx310 (not (primCmpChar (Char vx300) vx310 == GT))",fontsize=16,color="burlywood",shape="box"];317[label="vx310/Char vx3100",fontsize=10,color="white",style="solid",shape="box"];20 -> 317[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	317 -> 21[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	21[label="min1 (Char vx300) (Char vx3100) (not (primCmpChar (Char vx300) (Char vx3100) == GT))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
9.96/4.12	22[label="min1 (Char vx300) (Char vx3100) (not (primCmpNat vx300 vx3100 == GT))",fontsize=16,color="burlywood",shape="box"];318[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 318[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	318 -> 23[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	319[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 319[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	319 -> 24[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	23[label="min1 (Char (Succ vx3000)) (Char vx3100) (not (primCmpNat (Succ vx3000) vx3100 == GT))",fontsize=16,color="burlywood",shape="box"];320[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];23 -> 320[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	320 -> 25[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	321[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 321[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	321 -> 26[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	24[label="min1 (Char Zero) (Char vx3100) (not (primCmpNat Zero vx3100 == GT))",fontsize=16,color="burlywood",shape="box"];322[label="vx3100/Succ vx31000",fontsize=10,color="white",style="solid",shape="box"];24 -> 322[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	322 -> 27[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	323[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 323[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	323 -> 28[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	25[label="min1 (Char (Succ vx3000)) (Char (Succ vx31000)) (not (primCmpNat (Succ vx3000) (Succ vx31000) == GT))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
9.96/4.12	26[label="min1 (Char (Succ vx3000)) (Char Zero) (not (primCmpNat (Succ vx3000) Zero == GT))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
9.96/4.12	27[label="min1 (Char Zero) (Char (Succ vx31000)) (not (primCmpNat Zero (Succ vx31000) == GT))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
9.96/4.12	28[label="min1 (Char Zero) (Char Zero) (not (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
9.96/4.12	29 -> 250[label="",style="dashed", color="red", weight=0];
9.96/4.12	29[label="min1 (Char (Succ vx3000)) (Char (Succ vx31000)) (not (primCmpNat vx3000 vx31000 == GT))",fontsize=16,color="magenta"];29 -> 251[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	29 -> 252[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	29 -> 253[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	29 -> 254[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	30[label="min1 (Char (Succ vx3000)) (Char Zero) (not (GT == GT))",fontsize=16,color="black",shape="box"];30 -> 35[label="",style="solid", color="black", weight=3];
9.96/4.12	31[label="min1 (Char Zero) (Char (Succ vx31000)) (not (LT == GT))",fontsize=16,color="black",shape="box"];31 -> 36[label="",style="solid", color="black", weight=3];
9.96/4.12	32[label="min1 (Char Zero) (Char Zero) (not (EQ == GT))",fontsize=16,color="black",shape="box"];32 -> 37[label="",style="solid", color="black", weight=3];
9.96/4.12	251[label="vx3000",fontsize=16,color="green",shape="box"];252[label="vx31000",fontsize=16,color="green",shape="box"];253[label="vx3000",fontsize=16,color="green",shape="box"];254[label="vx31000",fontsize=16,color="green",shape="box"];250[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat vx28 vx29 == GT))",fontsize=16,color="burlywood",shape="triangle"];324[label="vx28/Succ vx280",fontsize=10,color="white",style="solid",shape="box"];250 -> 324[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	324 -> 291[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	325[label="vx28/Zero",fontsize=10,color="white",style="solid",shape="box"];250 -> 325[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	325 -> 292[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	35[label="min1 (Char (Succ vx3000)) (Char Zero) (not True)",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
9.96/4.12	36[label="min1 (Char Zero) (Char (Succ vx31000)) (not False)",fontsize=16,color="black",shape="box"];36 -> 43[label="",style="solid", color="black", weight=3];
9.96/4.12	37[label="min1 (Char Zero) (Char Zero) (not False)",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
9.96/4.12	291[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat (Succ vx280) vx29 == GT))",fontsize=16,color="burlywood",shape="box"];326[label="vx29/Succ vx290",fontsize=10,color="white",style="solid",shape="box"];291 -> 326[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	326 -> 293[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	327[label="vx29/Zero",fontsize=10,color="white",style="solid",shape="box"];291 -> 327[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	327 -> 294[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	292[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat Zero vx29 == GT))",fontsize=16,color="burlywood",shape="box"];328[label="vx29/Succ vx290",fontsize=10,color="white",style="solid",shape="box"];292 -> 328[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	328 -> 295[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	329[label="vx29/Zero",fontsize=10,color="white",style="solid",shape="box"];292 -> 329[label="",style="solid", color="burlywood", weight=9];
9.96/4.12	329 -> 296[label="",style="solid", color="burlywood", weight=3];
9.96/4.12	42[label="min1 (Char (Succ vx3000)) (Char Zero) False",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
9.96/4.12	43[label="min1 (Char Zero) (Char (Succ vx31000)) True",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
9.96/4.12	44[label="min1 (Char Zero) (Char Zero) True",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
9.96/4.12	293[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat (Succ vx280) (Succ vx290) == GT))",fontsize=16,color="black",shape="box"];293 -> 297[label="",style="solid", color="black", weight=3];
9.96/4.12	294[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat (Succ vx280) Zero == GT))",fontsize=16,color="black",shape="box"];294 -> 298[label="",style="solid", color="black", weight=3];
9.96/4.12	295[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat Zero (Succ vx290) == GT))",fontsize=16,color="black",shape="box"];295 -> 299[label="",style="solid", color="black", weight=3];
9.96/4.12	296[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];296 -> 300[label="",style="solid", color="black", weight=3];
9.96/4.12	49[label="min0 (Char (Succ vx3000)) (Char Zero) otherwise",fontsize=16,color="black",shape="box"];49 -> 57[label="",style="solid", color="black", weight=3];
9.96/4.12	50[label="Char Zero",fontsize=16,color="green",shape="box"];51[label="Char Zero",fontsize=16,color="green",shape="box"];297 -> 250[label="",style="dashed", color="red", weight=0];
9.96/4.12	297[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat vx280 vx290 == GT))",fontsize=16,color="magenta"];297 -> 301[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	297 -> 302[label="",style="dashed", color="magenta", weight=3];
9.96/4.12	298[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (GT == GT))",fontsize=16,color="black",shape="box"];298 -> 303[label="",style="solid", color="black", weight=3];
9.96/4.12	299[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (LT == GT))",fontsize=16,color="black",shape="box"];299 -> 304[label="",style="solid", color="black", weight=3];
9.96/4.12	300[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not (EQ == GT))",fontsize=16,color="black",shape="box"];300 -> 305[label="",style="solid", color="black", weight=3];
9.96/4.12	57[label="min0 (Char (Succ vx3000)) (Char Zero) True",fontsize=16,color="black",shape="box"];57 -> 65[label="",style="solid", color="black", weight=3];
9.96/4.12	301[label="vx280",fontsize=16,color="green",shape="box"];302[label="vx290",fontsize=16,color="green",shape="box"];303[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not True)",fontsize=16,color="black",shape="box"];303 -> 306[label="",style="solid", color="black", weight=3];
9.96/4.12	304[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not False)",fontsize=16,color="black",shape="triangle"];304 -> 307[label="",style="solid", color="black", weight=3];
9.96/4.12	305 -> 304[label="",style="dashed", color="red", weight=0];
9.96/4.12	305[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) (not False)",fontsize=16,color="magenta"];65[label="Char Zero",fontsize=16,color="green",shape="box"];306[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) False",fontsize=16,color="black",shape="box"];306 -> 308[label="",style="solid", color="black", weight=3];
9.96/4.12	307[label="min1 (Char (Succ vx26)) (Char (Succ vx27)) True",fontsize=16,color="black",shape="box"];307 -> 309[label="",style="solid", color="black", weight=3];
9.96/4.12	308[label="min0 (Char (Succ vx26)) (Char (Succ vx27)) otherwise",fontsize=16,color="black",shape="box"];308 -> 310[label="",style="solid", color="black", weight=3];
9.96/4.12	309[label="Char (Succ vx26)",fontsize=16,color="green",shape="box"];310[label="min0 (Char (Succ vx26)) (Char (Succ vx27)) True",fontsize=16,color="black",shape="box"];310 -> 311[label="",style="solid", color="black", weight=3];
9.96/4.12	311[label="Char (Succ vx27)",fontsize=16,color="green",shape="box"];}
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(6)
9.96/4.12	Complex Obligation (AND)
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(7)
9.96/4.12	Obligation:
9.96/4.12	Q DP problem:
9.96/4.12	The TRS P consists of the following rules:
9.96/4.12	
9.96/4.12	   new_min1(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_min1(vx26, vx27, vx280, vx290)
9.96/4.12	
9.96/4.12	R is empty.
9.96/4.12	Q is empty.
9.96/4.12	We have to consider all minimal (P,Q,R)-chains.
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(8) QDPSizeChangeProof (EQUIVALENT)
9.96/4.12	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. 
9.96/4.12	
9.96/4.12	From the DPs we obtained the following set of size-change graphs:
9.96/4.12	*new_min1(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_min1(vx26, vx27, vx280, vx290)
9.96/4.12	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
9.96/4.12	
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(9)
9.96/4.12	YES
9.96/4.12	
9.96/4.12	----------------------------------------
9.96/4.12	
9.96/4.12	(10)
9.96/4.12	Obligation:
9.96/4.12	Q DP problem:
9.96/4.12	The TRS P consists of the following rules:
9.96/4.12	
9.96/4.12	   new_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_min10(vx30, vx310), vx311)
9.96/4.12	
9.96/4.12	The TRS R consists of the following rules:
9.96/4.12	
9.96/4.12	   new_min12(vx26, vx27) -> Char(Succ(vx26))
9.96/4.12	   new_min10(Char(Succ(vx3000)), Char(Succ(vx31000))) -> new_min11(vx3000, vx31000, vx3000, vx31000)
9.96/4.12	   new_min11(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_min11(vx26, vx27, vx280, vx290)
9.96/4.12	   new_min11(vx26, vx27, Succ(vx280), Zero) -> Char(Succ(vx27))
9.96/4.12	   new_min11(vx26, vx27, Zero, Zero) -> new_min12(vx26, vx27)
9.96/4.12	   new_min11(vx26, vx27, Zero, Succ(vx290)) -> new_min12(vx26, vx27)
9.96/4.12	   new_min10(Char(Succ(vx3000)), Char(Zero)) -> Char(Zero)
9.96/4.12	   new_min10(Char(Zero), Char(Succ(vx31000))) -> Char(Zero)
9.96/4.12	   new_min10(Char(Zero), Char(Zero)) -> Char(Zero)
9.96/4.12	
9.96/4.12	The set Q consists of the following terms:
9.96/4.12	
9.96/4.12	   new_min11(x0, x1, Succ(x2), Succ(x3))
9.96/4.12	   new_min11(x0, x1, Succ(x2), Zero)
9.96/4.12	   new_min10(Char(Zero), Char(Succ(x0)))
9.96/4.12	   new_min11(x0, x1, Zero, Zero)
9.96/4.12	   new_min10(Char(Succ(x0)), Char(Zero))
9.96/4.12	   new_min11(x0, x1, Zero, Succ(x2))
9.96/4.12	   new_min10(Char(Zero), Char(Zero))
9.96/4.12	   new_min12(x0, x1)
9.96/4.12	   new_min10(Char(Succ(x0)), Char(Succ(x1)))
9.96/4.12	
9.96/4.12	We have to consider all minimal (P,Q,R)-chains.
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9.96/4.12	
9.96/4.12	(11) QDPSizeChangeProof (EQUIVALENT)
9.96/4.12	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. 
9.96/4.12	
9.96/4.12	From the DPs we obtained the following set of size-change graphs:
9.96/4.12	*new_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_min10(vx30, vx310), vx311)
9.96/4.12	The graph contains the following edges 2 > 2
9.96/4.12	
9.96/4.12	
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9.96/4.12	
9.96/4.12	(12)
9.96/4.12	YES
10.21/4.17	EOF