7.95/3.59	YES
10.47/4.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.47/4.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.47/4.26	
10.47/4.26	
10.47/4.26	H-Termination with start terms of the given HASKELL could be proven:
10.47/4.26	
10.47/4.26	(0) HASKELL
10.47/4.26	(1) LR [EQUIVALENT, 0 ms]
10.47/4.26	(2) HASKELL
10.47/4.26	(3) IFR [EQUIVALENT, 0 ms]
10.47/4.26	(4) HASKELL
10.47/4.26	(5) BR [EQUIVALENT, 0 ms]
10.47/4.26	(6) HASKELL
10.47/4.26	(7) COR [EQUIVALENT, 0 ms]
10.47/4.26	(8) HASKELL
10.47/4.26	(9) LetRed [EQUIVALENT, 0 ms]
10.47/4.26	(10) HASKELL
10.47/4.26	(11) NumRed [SOUND, 5 ms]
10.47/4.26	(12) HASKELL
10.47/4.26	(13) Narrow [SOUND, 0 ms]
10.47/4.26	(14) AND
10.47/4.26	    (15) QDP
10.47/4.26	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.47/4.26	        (17) YES
10.47/4.26	    (18) QDP
10.47/4.26	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.47/4.26	        (20) YES
10.47/4.26	
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(0)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(1) LR (EQUIVALENT)
10.47/4.26	Lambda Reductions:
10.47/4.26	The following Lambda expression
10.47/4.26	"\(m,_)->m"
10.47/4.26	is transformed to
10.47/4.26	"m0 (m,_) = m;
10.47/4.26	"
10.47/4.26	The following Lambda expression
10.47/4.26	"\(_,n)->n"
10.47/4.26	is transformed to
10.47/4.26	"n0 (_,n) = n;
10.47/4.26	"
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(2)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(3) IFR (EQUIVALENT)
10.47/4.26	If Reductions:
10.47/4.26	The following If expression
10.47/4.26	"if m == 0 then 0 else n + floatDigits x"
10.47/4.26	is transformed to
10.47/4.26	"exponent0 x True = 0;
10.47/4.26	exponent0 x False = n + floatDigits x;
10.47/4.26	"
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(4)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(5) BR (EQUIVALENT)
10.47/4.26	Replaced joker patterns by fresh variables and removed binding patterns.
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(6)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(7) COR (EQUIVALENT)
10.47/4.26	Cond Reductions:
10.47/4.26	The following Function with conditions
10.47/4.26	"undefined |Falseundefined;
10.47/4.26	"
10.47/4.26	is transformed to
10.47/4.26	"undefined  = undefined1;
10.47/4.26	"
10.47/4.26	"undefined0 True = undefined;
10.47/4.26	"
10.47/4.26	"undefined1  = undefined0 False;
10.47/4.26	"
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(8)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(9) LetRed (EQUIVALENT)
10.47/4.26	Let/Where Reductions:
10.47/4.26	The bindings of the following Let/Where expression
10.47/4.26	"exponent0 x (m == 0) where {
10.47/4.26	exponent0 x True = 0;
10.47/4.26	exponent0 x False = n + floatDigits x;
10.47/4.26	;
10.47/4.26	m  = m0 vu10;
10.47/4.26	;
10.47/4.26	m0 (m,vw) = m;
10.47/4.26	;
10.47/4.26	n  = n0 vu10;
10.47/4.26	;
10.47/4.26	n0 (vv,n) = n;
10.47/4.26	;
10.47/4.26	vu10  = decodeFloat x;
10.47/4.26	} 
10.47/4.26	"
10.47/4.26	are unpacked to the following functions on top level
10.47/4.26	"exponentN0 ww (vv,n) = n;
10.47/4.26	"
10.47/4.26	"exponentVu10 ww = decodeFloat ww;
10.47/4.26	"
10.47/4.26	"exponentM ww = exponentM0 ww (exponentVu10 ww);
10.47/4.26	"
10.47/4.26	"exponentM0 ww (m,vw) = m;
10.47/4.26	"
10.47/4.26	"exponentN ww = exponentN0 ww (exponentVu10 ww);
10.47/4.26	"
10.47/4.26	"exponentExponent0 ww x True = 0;
10.47/4.26	exponentExponent0 ww x False = exponentN ww + floatDigits x;
10.47/4.26	"
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(10)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(11) NumRed (SOUND)
10.47/4.26	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(12)
10.47/4.26	Obligation:
10.47/4.26	mainModule Main 
10.47/4.26	module Main where {
10.47/4.26	import qualified Prelude;
10.47/4.26	}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(13) Narrow (SOUND)
10.47/4.26	Haskell To QDPs
10.47/4.26	
10.47/4.26	digraph dp_graph {
10.47/4.26	node [outthreshold=100, inthreshold=100];1[label="exponent",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.47/4.26	3[label="exponent wx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.47/4.26	4[label="exponentExponent0 wx3 wx3 (exponentM wx3 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.47/4.26	5 -> 10[label="",style="dashed", color="red", weight=0];
10.47/4.26	5[label="exponentExponent0 wx3 wx3 (exponentM0 wx3 (exponentVu10 wx3) == fromInt (Pos Zero))",fontsize=16,color="magenta"];5 -> 11[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	11[label="exponentVu10 wx3",fontsize=16,color="black",shape="triangle"];11 -> 16[label="",style="solid", color="black", weight=3];
10.47/4.26	10[label="exponentExponent0 wx3 wx3 (exponentM0 wx3 wx4 == fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];94[label="wx4/(wx40,wx41)",fontsize=10,color="white",style="solid",shape="box"];10 -> 94[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	94 -> 17[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	16[label="decodeFloat wx3",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
10.47/4.26	17[label="exponentExponent0 wx3 wx3 (exponentM0 wx3 (wx40,wx41) == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3];
10.47/4.26	19[label="primFloatDecode wx3",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
10.47/4.26	20[label="exponentExponent0 wx3 wx3 (wx40 == fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];95[label="wx40/Integer wx400",fontsize=10,color="white",style="solid",shape="box"];20 -> 95[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	95 -> 22[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	21[label="terminator wx3",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
10.47/4.26	22[label="exponentExponent0 wx3 wx3 (Integer wx400 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
10.47/4.26	23[label="ter1m wx3",fontsize=16,color="green",shape="box"];23 -> 25[label="",style="dashed", color="green", weight=3];
10.47/4.26	24[label="exponentExponent0 wx3 wx3 (Integer wx400 == Integer (Pos Zero))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
10.47/4.26	25[label="wx3",fontsize=16,color="green",shape="box"];26[label="exponentExponent0 wx3 wx3 (primEqInt wx400 (Pos Zero))",fontsize=16,color="burlywood",shape="box"];96[label="wx400/Pos wx4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 96[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	96 -> 27[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	97[label="wx400/Neg wx4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 97[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	97 -> 28[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	27[label="exponentExponent0 wx3 wx3 (primEqInt (Pos wx4000) (Pos Zero))",fontsize=16,color="burlywood",shape="box"];98[label="wx4000/Succ wx40000",fontsize=10,color="white",style="solid",shape="box"];27 -> 98[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	98 -> 29[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	99[label="wx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 99[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	99 -> 30[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	28[label="exponentExponent0 wx3 wx3 (primEqInt (Neg wx4000) (Pos Zero))",fontsize=16,color="burlywood",shape="box"];100[label="wx4000/Succ wx40000",fontsize=10,color="white",style="solid",shape="box"];28 -> 100[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	100 -> 31[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	101[label="wx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 101[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	101 -> 32[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	29[label="exponentExponent0 wx3 wx3 (primEqInt (Pos (Succ wx40000)) (Pos Zero))",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
10.47/4.26	30[label="exponentExponent0 wx3 wx3 (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
10.47/4.26	31[label="exponentExponent0 wx3 wx3 (primEqInt (Neg (Succ wx40000)) (Pos Zero))",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
10.47/4.26	32[label="exponentExponent0 wx3 wx3 (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
10.47/4.26	33[label="exponentExponent0 wx3 wx3 False",fontsize=16,color="black",shape="triangle"];33 -> 37[label="",style="solid", color="black", weight=3];
10.47/4.26	34[label="exponentExponent0 wx3 wx3 True",fontsize=16,color="black",shape="triangle"];34 -> 38[label="",style="solid", color="black", weight=3];
10.47/4.26	35 -> 33[label="",style="dashed", color="red", weight=0];
10.47/4.26	35[label="exponentExponent0 wx3 wx3 False",fontsize=16,color="magenta"];36 -> 34[label="",style="dashed", color="red", weight=0];
10.47/4.26	36[label="exponentExponent0 wx3 wx3 True",fontsize=16,color="magenta"];37[label="exponentN wx3 + floatDigits wx3",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
10.47/4.26	38[label="Pos Zero",fontsize=16,color="green",shape="box"];39[label="primPlusInt (exponentN wx3) (floatDigits wx3)",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3];
10.47/4.26	40 -> 41[label="",style="dashed", color="red", weight=0];
10.47/4.26	40[label="primPlusInt (exponentN0 wx3 (exponentVu10 wx3)) (floatDigits wx3)",fontsize=16,color="magenta"];40 -> 42[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	42 -> 11[label="",style="dashed", color="red", weight=0];
10.47/4.26	42[label="exponentVu10 wx3",fontsize=16,color="magenta"];41[label="primPlusInt (exponentN0 wx3 wx5) (floatDigits wx3)",fontsize=16,color="burlywood",shape="triangle"];102[label="wx5/(wx50,wx51)",fontsize=10,color="white",style="solid",shape="box"];41 -> 102[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	102 -> 43[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	43[label="primPlusInt (exponentN0 wx3 (wx50,wx51)) (floatDigits wx3)",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
10.47/4.26	44[label="primPlusInt wx51 (floatDigits wx3)",fontsize=16,color="burlywood",shape="box"];103[label="wx51/Pos wx510",fontsize=10,color="white",style="solid",shape="box"];44 -> 103[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	103 -> 45[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	104[label="wx51/Neg wx510",fontsize=10,color="white",style="solid",shape="box"];44 -> 104[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	104 -> 46[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	45[label="primPlusInt (Pos wx510) (floatDigits wx3)",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
10.47/4.26	46[label="primPlusInt (Neg wx510) (floatDigits wx3)",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3];
10.47/4.26	47[label="primPlusInt (Pos wx510) primFloatDigits",fontsize=16,color="black",shape="box"];47 -> 49[label="",style="solid", color="black", weight=3];
10.47/4.26	48[label="primPlusInt (Neg wx510) primFloatDigits",fontsize=16,color="black",shape="box"];48 -> 50[label="",style="solid", color="black", weight=3];
10.47/4.26	49 -> 51[label="",style="dashed", color="red", weight=0];
10.47/4.26	49[label="primPlusInt (Pos wx510) (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 Zero)))))))))))))))))))))))))",fontsize=16,color="magenta"];49 -> 52[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	49 -> 53[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	50 -> 54[label="",style="dashed", color="red", weight=0];
10.47/4.26	50[label="primPlusInt (Neg wx510) (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 Zero)))))))))))))))))))))))))",fontsize=16,color="magenta"];50 -> 55[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	50 -> 56[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	52[label="wx510",fontsize=16,color="green",shape="box"];53[label="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"];51[label="primPlusInt (Pos wx7) (Pos (Succ wx8))",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3];
10.47/4.26	55[label="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"];56[label="wx510",fontsize=16,color="green",shape="box"];54[label="primPlusInt (Neg wx10) (Pos (Succ wx11))",fontsize=16,color="black",shape="triangle"];54 -> 58[label="",style="solid", color="black", weight=3];
10.47/4.26	57[label="Pos (primPlusNat wx7 (Succ wx8))",fontsize=16,color="green",shape="box"];57 -> 59[label="",style="dashed", color="green", weight=3];
10.47/4.26	58[label="primMinusNat (Succ wx11) wx10",fontsize=16,color="burlywood",shape="box"];105[label="wx10/Succ wx100",fontsize=10,color="white",style="solid",shape="box"];58 -> 105[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	105 -> 60[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	106[label="wx10/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 106[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	106 -> 61[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	59[label="primPlusNat wx7 (Succ wx8)",fontsize=16,color="burlywood",shape="box"];107[label="wx7/Succ wx70",fontsize=10,color="white",style="solid",shape="box"];59 -> 107[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	107 -> 62[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	108[label="wx7/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 108[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	108 -> 63[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	60[label="primMinusNat (Succ wx11) (Succ wx100)",fontsize=16,color="black",shape="box"];60 -> 64[label="",style="solid", color="black", weight=3];
10.47/4.26	61[label="primMinusNat (Succ wx11) Zero",fontsize=16,color="black",shape="box"];61 -> 65[label="",style="solid", color="black", weight=3];
10.47/4.26	62[label="primPlusNat (Succ wx70) (Succ wx8)",fontsize=16,color="black",shape="box"];62 -> 66[label="",style="solid", color="black", weight=3];
10.47/4.26	63[label="primPlusNat Zero (Succ wx8)",fontsize=16,color="black",shape="box"];63 -> 67[label="",style="solid", color="black", weight=3];
10.47/4.26	64[label="primMinusNat wx11 wx100",fontsize=16,color="burlywood",shape="triangle"];109[label="wx11/Succ wx110",fontsize=10,color="white",style="solid",shape="box"];64 -> 109[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	109 -> 68[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	110[label="wx11/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 110[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	110 -> 69[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	65[label="Pos (Succ wx11)",fontsize=16,color="green",shape="box"];66[label="Succ (Succ (primPlusNat wx70 wx8))",fontsize=16,color="green",shape="box"];66 -> 70[label="",style="dashed", color="green", weight=3];
10.47/4.26	67[label="Succ wx8",fontsize=16,color="green",shape="box"];68[label="primMinusNat (Succ wx110) wx100",fontsize=16,color="burlywood",shape="box"];111[label="wx100/Succ wx1000",fontsize=10,color="white",style="solid",shape="box"];68 -> 111[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	111 -> 71[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	112[label="wx100/Zero",fontsize=10,color="white",style="solid",shape="box"];68 -> 112[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	112 -> 72[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	69[label="primMinusNat Zero wx100",fontsize=16,color="burlywood",shape="box"];113[label="wx100/Succ wx1000",fontsize=10,color="white",style="solid",shape="box"];69 -> 113[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	113 -> 73[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	114[label="wx100/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 114[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	114 -> 74[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	70[label="primPlusNat wx70 wx8",fontsize=16,color="burlywood",shape="triangle"];115[label="wx70/Succ wx700",fontsize=10,color="white",style="solid",shape="box"];70 -> 115[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	115 -> 75[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	116[label="wx70/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 116[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	116 -> 76[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	71[label="primMinusNat (Succ wx110) (Succ wx1000)",fontsize=16,color="black",shape="box"];71 -> 77[label="",style="solid", color="black", weight=3];
10.47/4.26	72[label="primMinusNat (Succ wx110) Zero",fontsize=16,color="black",shape="box"];72 -> 78[label="",style="solid", color="black", weight=3];
10.47/4.26	73[label="primMinusNat Zero (Succ wx1000)",fontsize=16,color="black",shape="box"];73 -> 79[label="",style="solid", color="black", weight=3];
10.47/4.26	74[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3];
10.47/4.26	75[label="primPlusNat (Succ wx700) wx8",fontsize=16,color="burlywood",shape="box"];117[label="wx8/Succ wx80",fontsize=10,color="white",style="solid",shape="box"];75 -> 117[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	117 -> 81[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	118[label="wx8/Zero",fontsize=10,color="white",style="solid",shape="box"];75 -> 118[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	118 -> 82[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	76[label="primPlusNat Zero wx8",fontsize=16,color="burlywood",shape="box"];119[label="wx8/Succ wx80",fontsize=10,color="white",style="solid",shape="box"];76 -> 119[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	119 -> 83[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	120[label="wx8/Zero",fontsize=10,color="white",style="solid",shape="box"];76 -> 120[label="",style="solid", color="burlywood", weight=9];
10.47/4.26	120 -> 84[label="",style="solid", color="burlywood", weight=3];
10.47/4.26	77 -> 64[label="",style="dashed", color="red", weight=0];
10.47/4.26	77[label="primMinusNat wx110 wx1000",fontsize=16,color="magenta"];77 -> 85[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	77 -> 86[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	78[label="Pos (Succ wx110)",fontsize=16,color="green",shape="box"];79[label="Neg (Succ wx1000)",fontsize=16,color="green",shape="box"];80[label="Pos Zero",fontsize=16,color="green",shape="box"];81[label="primPlusNat (Succ wx700) (Succ wx80)",fontsize=16,color="black",shape="box"];81 -> 87[label="",style="solid", color="black", weight=3];
10.47/4.26	82[label="primPlusNat (Succ wx700) Zero",fontsize=16,color="black",shape="box"];82 -> 88[label="",style="solid", color="black", weight=3];
10.47/4.26	83[label="primPlusNat Zero (Succ wx80)",fontsize=16,color="black",shape="box"];83 -> 89[label="",style="solid", color="black", weight=3];
10.47/4.26	84[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];84 -> 90[label="",style="solid", color="black", weight=3];
10.47/4.26	85[label="wx110",fontsize=16,color="green",shape="box"];86[label="wx1000",fontsize=16,color="green",shape="box"];87[label="Succ (Succ (primPlusNat wx700 wx80))",fontsize=16,color="green",shape="box"];87 -> 91[label="",style="dashed", color="green", weight=3];
10.47/4.26	88[label="Succ wx700",fontsize=16,color="green",shape="box"];89[label="Succ wx80",fontsize=16,color="green",shape="box"];90[label="Zero",fontsize=16,color="green",shape="box"];91 -> 70[label="",style="dashed", color="red", weight=0];
10.47/4.26	91[label="primPlusNat wx700 wx80",fontsize=16,color="magenta"];91 -> 92[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	91 -> 93[label="",style="dashed", color="magenta", weight=3];
10.47/4.26	92[label="wx700",fontsize=16,color="green",shape="box"];93[label="wx80",fontsize=16,color="green",shape="box"];}
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(14)
10.47/4.26	Complex Obligation (AND)
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(15)
10.47/4.26	Obligation:
10.47/4.26	Q DP problem:
10.47/4.26	The TRS P consists of the following rules:
10.47/4.26	
10.47/4.26	   new_primMinusNat(Succ(wx110), Succ(wx1000)) -> new_primMinusNat(wx110, wx1000)
10.47/4.26	
10.47/4.26	R is empty.
10.47/4.26	Q is empty.
10.47/4.26	We have to consider all minimal (P,Q,R)-chains.
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(16) QDPSizeChangeProof (EQUIVALENT)
10.47/4.26	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. 
10.47/4.26	
10.47/4.26	From the DPs we obtained the following set of size-change graphs:
10.47/4.26	*new_primMinusNat(Succ(wx110), Succ(wx1000)) -> new_primMinusNat(wx110, wx1000)
10.47/4.26	The graph contains the following edges 1 > 1, 2 > 2
10.47/4.26	
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(17)
10.47/4.26	YES
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(18)
10.47/4.26	Obligation:
10.47/4.26	Q DP problem:
10.47/4.26	The TRS P consists of the following rules:
10.47/4.26	
10.47/4.26	   new_primPlusNat(Succ(wx700), Succ(wx80)) -> new_primPlusNat(wx700, wx80)
10.47/4.26	
10.47/4.26	R is empty.
10.47/4.26	Q is empty.
10.47/4.26	We have to consider all minimal (P,Q,R)-chains.
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(19) QDPSizeChangeProof (EQUIVALENT)
10.47/4.26	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. 
10.47/4.26	
10.47/4.26	From the DPs we obtained the following set of size-change graphs:
10.47/4.26	*new_primPlusNat(Succ(wx700), Succ(wx80)) -> new_primPlusNat(wx700, wx80)
10.47/4.26	The graph contains the following edges 1 > 1, 2 > 2
10.47/4.26	
10.47/4.26	
10.47/4.26	----------------------------------------
10.47/4.26	
10.47/4.26	(20)
10.47/4.26	YES
10.63/8.01	EOF