8.64/3.72	YES
10.04/4.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.04/4.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.04/4.15	
10.04/4.15	
10.04/4.15	H-Termination with start terms of the given HASKELL could be proven:
10.04/4.15	
10.04/4.15	(0) HASKELL
10.04/4.15	(1) BR [EQUIVALENT, 0 ms]
10.04/4.15	(2) HASKELL
10.04/4.15	(3) COR [EQUIVALENT, 0 ms]
10.04/4.15	(4) HASKELL
10.04/4.15	(5) Narrow [SOUND, 0 ms]
10.04/4.15	(6) AND
10.04/4.15	    (7) QDP
10.04/4.15	        (8) QDPSizeChangeProof [EQUIVALENT, 1 ms]
10.04/4.15	        (9) YES
10.04/4.15	    (10) QDP
10.04/4.15	        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.04/4.15	        (12) YES
10.04/4.15	
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(0)
10.04/4.15	Obligation:
10.04/4.15	mainModule Main 
10.04/4.15	module Main where {
10.04/4.15	import qualified Prelude;
10.04/4.15	}
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(1) BR (EQUIVALENT)
10.04/4.15	Replaced joker patterns by fresh variables and removed binding patterns.
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(2)
10.04/4.15	Obligation:
10.04/4.15	mainModule Main 
10.04/4.15	module Main where {
10.04/4.15	import qualified Prelude;
10.04/4.15	}
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(3) COR (EQUIVALENT)
10.04/4.15	Cond Reductions:
10.04/4.15	The following Function with conditions
10.04/4.15	"max x y|x <= yy|otherwisex;
10.04/4.15	"
10.04/4.15	is transformed to
10.04/4.15	"max x y = max2 x y;
10.04/4.15	"
10.04/4.15	"max0 x y True = x;
10.04/4.15	"
10.04/4.15	"max1 x y True = y;
10.04/4.15	max1 x y False = max0 x y otherwise;
10.04/4.15	"
10.04/4.15	"max2 x y = max1 x y (x <= y);
10.04/4.15	"
10.04/4.15	The following Function with conditions
10.04/4.15	"undefined |Falseundefined;
10.04/4.15	"
10.04/4.15	is transformed to
10.04/4.15	"undefined  = undefined1;
10.04/4.15	"
10.04/4.15	"undefined0 True = undefined;
10.04/4.15	"
10.04/4.15	"undefined1  = undefined0 False;
10.04/4.15	"
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(4)
10.04/4.15	Obligation:
10.04/4.15	mainModule Main 
10.04/4.15	module Main where {
10.04/4.15	import qualified Prelude;
10.04/4.15	}
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(5) Narrow (SOUND)
10.04/4.15	Haskell To QDPs
10.04/4.15	
10.04/4.15	digraph dp_graph {
10.04/4.15	node [outthreshold=100, inthreshold=100];1[label="maximum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.04/4.15	3[label="maximum vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.04/4.15	4[label="foldl1 max 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];
10.04/4.15	312 -> 5[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	313[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 313[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	313 -> 6[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	5[label="foldl1 max (vx30 : vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
10.04/4.15	6[label="foldl1 max []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.04/4.15	7[label="foldl max 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];
10.04/4.15	314 -> 9[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	315[label="vx31/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 315[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	315 -> 10[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	8[label="error []",fontsize=16,color="red",shape="box"];9[label="foldl max vx30 (vx310 : vx311)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10.04/4.15	10[label="foldl max vx30 []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
10.04/4.15	11 -> 7[label="",style="dashed", color="red", weight=0];
10.04/4.15	11[label="foldl max (max vx30 vx310) vx311",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	11 -> 14[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	12[label="vx30",fontsize=16,color="green",shape="box"];13[label="max vx30 vx310",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
10.04/4.15	14[label="vx311",fontsize=16,color="green",shape="box"];15[label="max2 vx30 vx310",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
10.04/4.15	16[label="max1 vx30 vx310 (vx30 <= vx310)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
10.04/4.15	17[label="max1 vx30 vx310 (compare vx30 vx310 /= GT)",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
10.04/4.15	18[label="max1 vx30 vx310 (not (compare vx30 vx310 == GT))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
10.04/4.15	19[label="max1 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];
10.04/4.15	316 -> 20[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	20[label="max1 (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];
10.04/4.15	317 -> 21[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	21[label="max1 (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];
10.04/4.15	22[label="max1 (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];
10.04/4.15	318 -> 23[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	319[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 319[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	319 -> 24[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	23[label="max1 (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];
10.04/4.15	320 -> 25[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	321[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 321[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	321 -> 26[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	24[label="max1 (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];
10.04/4.15	322 -> 27[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	323[label="vx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 323[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	323 -> 28[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	25[label="max1 (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];
10.04/4.15	26[label="max1 (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];
10.04/4.15	27[label="max1 (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];
10.04/4.15	28[label="max1 (Char Zero) (Char Zero) (not (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
10.04/4.15	29 -> 250[label="",style="dashed", color="red", weight=0];
10.04/4.15	29[label="max1 (Char (Succ vx3000)) (Char (Succ vx31000)) (not (primCmpNat vx3000 vx31000 == GT))",fontsize=16,color="magenta"];29 -> 251[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	29 -> 252[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	29 -> 253[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	29 -> 254[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	30[label="max1 (Char (Succ vx3000)) (Char Zero) (not (GT == GT))",fontsize=16,color="black",shape="box"];30 -> 35[label="",style="solid", color="black", weight=3];
10.04/4.15	31[label="max1 (Char Zero) (Char (Succ vx31000)) (not (LT == GT))",fontsize=16,color="black",shape="box"];31 -> 36[label="",style="solid", color="black", weight=3];
10.04/4.15	32[label="max1 (Char Zero) (Char Zero) (not (EQ == GT))",fontsize=16,color="black",shape="box"];32 -> 37[label="",style="solid", color="black", weight=3];
10.04/4.15	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="max1 (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];
10.04/4.15	324 -> 291[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	325[label="vx28/Zero",fontsize=10,color="white",style="solid",shape="box"];250 -> 325[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	325 -> 292[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	35[label="max1 (Char (Succ vx3000)) (Char Zero) (not True)",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
10.04/4.15	36[label="max1 (Char Zero) (Char (Succ vx31000)) (not False)",fontsize=16,color="black",shape="box"];36 -> 43[label="",style="solid", color="black", weight=3];
10.04/4.15	37[label="max1 (Char Zero) (Char Zero) (not False)",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
10.04/4.15	291[label="max1 (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];
10.04/4.15	326 -> 293[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	327[label="vx29/Zero",fontsize=10,color="white",style="solid",shape="box"];291 -> 327[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	327 -> 294[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	292[label="max1 (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];
10.04/4.15	328 -> 295[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	329[label="vx29/Zero",fontsize=10,color="white",style="solid",shape="box"];292 -> 329[label="",style="solid", color="burlywood", weight=9];
10.04/4.15	329 -> 296[label="",style="solid", color="burlywood", weight=3];
10.04/4.15	42[label="max1 (Char (Succ vx3000)) (Char Zero) False",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
10.04/4.15	43[label="max1 (Char Zero) (Char (Succ vx31000)) True",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
10.04/4.15	44[label="max1 (Char Zero) (Char Zero) True",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
10.04/4.15	293[label="max1 (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];
10.04/4.15	294[label="max1 (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];
10.04/4.15	295[label="max1 (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];
10.04/4.15	296[label="max1 (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];
10.04/4.15	49[label="max0 (Char (Succ vx3000)) (Char Zero) otherwise",fontsize=16,color="black",shape="box"];49 -> 57[label="",style="solid", color="black", weight=3];
10.04/4.15	50[label="Char (Succ vx31000)",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];
10.04/4.15	297[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not (primCmpNat vx280 vx290 == GT))",fontsize=16,color="magenta"];297 -> 301[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	297 -> 302[label="",style="dashed", color="magenta", weight=3];
10.04/4.15	298[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not (GT == GT))",fontsize=16,color="black",shape="box"];298 -> 303[label="",style="solid", color="black", weight=3];
10.04/4.15	299[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not (LT == GT))",fontsize=16,color="black",shape="box"];299 -> 304[label="",style="solid", color="black", weight=3];
10.04/4.15	300[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not (EQ == GT))",fontsize=16,color="black",shape="box"];300 -> 305[label="",style="solid", color="black", weight=3];
10.04/4.15	57[label="max0 (Char (Succ vx3000)) (Char Zero) True",fontsize=16,color="black",shape="box"];57 -> 65[label="",style="solid", color="black", weight=3];
10.04/4.15	301[label="vx280",fontsize=16,color="green",shape="box"];302[label="vx290",fontsize=16,color="green",shape="box"];303[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not True)",fontsize=16,color="black",shape="box"];303 -> 306[label="",style="solid", color="black", weight=3];
10.04/4.15	304[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not False)",fontsize=16,color="black",shape="triangle"];304 -> 307[label="",style="solid", color="black", weight=3];
10.04/4.15	305 -> 304[label="",style="dashed", color="red", weight=0];
10.04/4.15	305[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) (not False)",fontsize=16,color="magenta"];65[label="Char (Succ vx3000)",fontsize=16,color="green",shape="box"];306[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) False",fontsize=16,color="black",shape="box"];306 -> 308[label="",style="solid", color="black", weight=3];
10.04/4.15	307[label="max1 (Char (Succ vx26)) (Char (Succ vx27)) True",fontsize=16,color="black",shape="box"];307 -> 309[label="",style="solid", color="black", weight=3];
10.04/4.15	308[label="max0 (Char (Succ vx26)) (Char (Succ vx27)) otherwise",fontsize=16,color="black",shape="box"];308 -> 310[label="",style="solid", color="black", weight=3];
10.04/4.15	309[label="Char (Succ vx27)",fontsize=16,color="green",shape="box"];310[label="max0 (Char (Succ vx26)) (Char (Succ vx27)) True",fontsize=16,color="black",shape="box"];310 -> 311[label="",style="solid", color="black", weight=3];
10.04/4.15	311[label="Char (Succ vx26)",fontsize=16,color="green",shape="box"];}
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(6)
10.04/4.15	Complex Obligation (AND)
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(7)
10.04/4.15	Obligation:
10.04/4.15	Q DP problem:
10.04/4.15	The TRS P consists of the following rules:
10.04/4.15	
10.04/4.15	   new_max1(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_max1(vx26, vx27, vx280, vx290)
10.04/4.15	
10.04/4.15	R is empty.
10.04/4.15	Q is empty.
10.04/4.15	We have to consider all minimal (P,Q,R)-chains.
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(8) QDPSizeChangeProof (EQUIVALENT)
10.04/4.15	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. 
10.04/4.15	
10.04/4.15	From the DPs we obtained the following set of size-change graphs:
10.04/4.15	*new_max1(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_max1(vx26, vx27, vx280, vx290)
10.04/4.15	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
10.04/4.15	
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(9)
10.04/4.15	YES
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(10)
10.04/4.15	Obligation:
10.04/4.15	Q DP problem:
10.04/4.15	The TRS P consists of the following rules:
10.04/4.15	
10.04/4.15	   new_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_max10(vx30, vx310), vx311)
10.04/4.15	
10.04/4.15	The TRS R consists of the following rules:
10.04/4.15	
10.04/4.15	   new_max11(vx26, vx27, Succ(vx280), Zero) -> Char(Succ(vx26))
10.04/4.15	   new_max11(vx26, vx27, Zero, Succ(vx290)) -> new_max12(vx26, vx27)
10.04/4.15	   new_max12(vx26, vx27) -> Char(Succ(vx27))
10.04/4.15	   new_max10(Char(Succ(vx3000)), Char(Succ(vx31000))) -> new_max11(vx3000, vx31000, vx3000, vx31000)
10.04/4.15	   new_max11(vx26, vx27, Zero, Zero) -> new_max12(vx26, vx27)
10.04/4.15	   new_max11(vx26, vx27, Succ(vx280), Succ(vx290)) -> new_max11(vx26, vx27, vx280, vx290)
10.04/4.15	   new_max10(Char(Succ(vx3000)), Char(Zero)) -> Char(Succ(vx3000))
10.04/4.15	   new_max10(Char(Zero), Char(Succ(vx31000))) -> Char(Succ(vx31000))
10.04/4.15	   new_max10(Char(Zero), Char(Zero)) -> Char(Zero)
10.04/4.15	
10.04/4.15	The set Q consists of the following terms:
10.04/4.15	
10.04/4.15	   new_max11(x0, x1, Succ(x2), Zero)
10.04/4.15	   new_max11(x0, x1, Succ(x2), Succ(x3))
10.04/4.15	   new_max10(Char(Zero), Char(Succ(x0)))
10.04/4.15	   new_max10(Char(Succ(x0)), Char(Zero))
10.04/4.15	   new_max10(Char(Zero), Char(Zero))
10.04/4.15	   new_max11(x0, x1, Zero, Succ(x2))
10.04/4.15	   new_max10(Char(Succ(x0)), Char(Succ(x1)))
10.04/4.15	   new_max11(x0, x1, Zero, Zero)
10.04/4.15	   new_max12(x0, x1)
10.04/4.15	
10.04/4.15	We have to consider all minimal (P,Q,R)-chains.
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(11) QDPSizeChangeProof (EQUIVALENT)
10.04/4.15	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. 
10.04/4.15	
10.04/4.15	From the DPs we obtained the following set of size-change graphs:
10.04/4.15	*new_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_max10(vx30, vx310), vx311)
10.04/4.15	The graph contains the following edges 2 > 2
10.04/4.15	
10.04/4.15	
10.04/4.15	----------------------------------------
10.04/4.15	
10.04/4.15	(12)
10.04/4.15	YES
10.34/4.21	EOF