/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) NumRed [SOUND, 0 ms]
(10) HASKELL
(11) Narrow [SOUND, 0 ms]
(12) AND
    (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\(m,_)->m"
is transformed to
"m0 (m,_) = m;
"

----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(3) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"power wv 0 = 1.0;
power x ww@(y+1) = fromInt x * power x y;
power x y = 1.0 / power x (`negate` y);
"
is transformed to
"power wv xw = power4 wv xw;
power x ww = power2 x ww;
power x y = power0 x y;
"
"power0 x y = 1.0 / power x (`negate` y);
"
"power1 True x ww = fromInt x * power x (ww - 1);
power1 wx wy wz = power0 wy wz;
"
"power2 x ww = power1 (ww >= 1) x ww;
power2 xu xv = power0 xu xv;
"
"power3 True wv xw = 1.0;
power3 xx xy xz = power2 xy xz;
"
"power4 wv xw = power3 (xw == 0) wv xw;
power4 yu yv = power2 yu yv;
"

----------------------------------------

(6)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(7) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"encodeFloat m (`negate` floatDigits x) where {
m  = m0 vu11;
;
m0 (m,vv) = m;
;
vu11  = decodeFloat x;
} 
"
are unpacked to the following functions on top level
"significandM0 yw (m,vv) = m;
"
"significandVu11 yw = decodeFloat yw;
"
"significandM yw = significandM0 yw (significandVu11 yw);
"
The bindings of the following Let/Where expression
"fromInteger x * power 2 y where {
power wv xw = power4 wv xw;
power x ww = power2 x ww;
power x y = power0 x y;
;
power0 x y = 1.0 / power x (`negate` y);
;
power1 True x ww = fromInt x * power x (ww - 1);
power1 wx wy wz = power0 wy wz;
;
power2 x ww = power1 (ww >= 1) x ww;
power2 xu xv = power0 xu xv;
;
power3 True wv xw = 1.0;
power3 xx xy xz = power2 xy xz;
;
power4 wv xw = power3 (xw == 0) wv xw;
power4 yu yv = power2 yu yv;
} 
"
are unpacked to the following functions on top level
"primFloatEncodePower1 True x ww = fromInt x * primFloatEncodePower x (ww - 1);
primFloatEncodePower1 wx wy wz = primFloatEncodePower0 wy wz;
"
"primFloatEncodePower2 x ww = primFloatEncodePower1 (ww >= 1) x ww;
primFloatEncodePower2 xu xv = primFloatEncodePower0 xu xv;
"
"primFloatEncodePower3 True wv xw = 1.0;
primFloatEncodePower3 xx xy xz = primFloatEncodePower2 xy xz;
"
"primFloatEncodePower4 wv xw = primFloatEncodePower3 (xw == 0) wv xw;
primFloatEncodePower4 yu yv = primFloatEncodePower2 yu yv;
"
"primFloatEncodePower0 x y = 1.0 / primFloatEncodePower x (`negate` y);
"
"primFloatEncodePower wv xw = primFloatEncodePower4 wv xw;
primFloatEncodePower x ww = primFloatEncodePower2 x ww;
primFloatEncodePower x y = primFloatEncodePower0 x y;
"

----------------------------------------

(8)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(9) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

(10)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(11) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="significand",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="significand yx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="encodeFloat (significandM yx3) (`negate` floatDigits yx3)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primFloatEncode (significandM yx3) (`negate` floatDigits yx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="fromInteger (significandM yx3) * primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="primMulFloat (fromInteger (significandM yx3)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="primMulFloat (primIntegerToFloat (significandM yx3)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9 -> 14[label="",style="dashed", color="red", weight=0];
9[label="primMulFloat (primIntegerToFloat (significandM0 yx3 (significandVu11 yx3))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="magenta"];9 -> 15[label="",style="dashed", color="magenta", weight=3];
15[label="significandVu11 yx3",fontsize=16,color="black",shape="box"];15 -> 20[label="",style="solid", color="black", weight=3];
14[label="primMulFloat (primIntegerToFloat (significandM0 yx3 yx4)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="burlywood",shape="triangle"];1196[label="yx4/(yx40,yx41)",fontsize=10,color="white",style="solid",shape="box"];14 -> 1196[label="",style="solid", color="burlywood", weight=9];
1196 -> 21[label="",style="solid", color="burlywood", weight=3];
20[label="decodeFloat yx3",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
21[label="primMulFloat (primIntegerToFloat (significandM0 yx3 (yx40,yx41))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
23[label="primFloatDecode yx3",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="primMulFloat (primIntegerToFloat yx40) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="burlywood",shape="box"];1197[label="yx40/Integer yx400",fontsize=10,color="white",style="solid",shape="box"];24 -> 1197[label="",style="solid", color="burlywood", weight=9];
1197 -> 26[label="",style="solid", color="burlywood", weight=3];
25[label="terminator yx3",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="primMulFloat (primIntegerToFloat (Integer yx400)) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="ter1m yx3",fontsize=16,color="green",shape="box"];27 -> 29[label="",style="dashed", color="green", weight=3];
28[label="primMulFloat (primIntToFloat yx400) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
29[label="yx3",fontsize=16,color="green",shape="box"];30[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];30 -> 31[label="",style="solid", color="black", weight=3];
31[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower4 (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];31 -> 32[label="",style="solid", color="black", weight=3];
32[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower3 (`negate` floatDigits yx3 == Pos Zero) (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];32 -> 33[label="",style="solid", color="black", weight=3];
33[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (`negate` floatDigits yx3) (Pos Zero)) (Pos (Succ (Succ Zero))) (`negate` floatDigits yx3))",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3];
34[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (primNegInt (floatDigits yx3)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt (floatDigits yx3)))",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
35[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (primNegInt primFloatDigits) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt primFloatDigits))",fontsize=16,color="black",shape="box"];35 -> 36[label="",style="solid", color="black", weight=3];
36 -> 37[label="",style="dashed", color="red", weight=0];
36[label="primMulFloat (Float yx400 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (primNegInt (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)))))))))))))))))))))))))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt (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"];36 -> 38[label="",style="dashed", color="magenta", weight=3];
36 -> 39[label="",style="dashed", color="magenta", weight=3];
38[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"];39[label="yx400",fontsize=16,color="green",shape="box"];37[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (primNegInt (Pos (Succ yx7))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt (Pos (Succ yx7))))",fontsize=16,color="black",shape="triangle"];37 -> 40[label="",style="solid", color="black", weight=3];
40[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower3 (primEqInt (Neg (Succ yx7)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
41[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3];
42[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3];
43[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (Neg (Succ yx7) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
44[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (compare (Neg (Succ yx7)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
45[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (not (compare (Neg (Succ yx7)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];45 -> 46[label="",style="solid", color="black", weight=3];
46[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (not (primCmpInt (Neg (Succ yx7)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];46 -> 47[label="",style="solid", color="black", weight=3];
47[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (not (LT == LT)) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
48[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 (not True) (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
49[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower1 False (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];49 -> 50[label="",style="solid", color="black", weight=3];
50[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primFloatEncodePower0 (Pos (Succ (Succ Zero))) (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];50 -> 51[label="",style="solid", color="black", weight=3];
51[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) / primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];51 -> 52[label="",style="solid", color="black", weight=3];
52[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primDivFloat (fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))))",fontsize=16,color="black",shape="box"];52 -> 53[label="",style="solid", color="black", weight=3];
53[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primDivFloat (doubleToFloat (Double (Pos (Succ Zero)) (Pos (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))))",fontsize=16,color="black",shape="box"];53 -> 54[label="",style="solid", color="black", weight=3];
54 -> 616[label="",style="dashed", color="red", weight=0];
54[label="primMulFloat (Float yx6 (Pos (Succ Zero))) (primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))))",fontsize=16,color="magenta"];54 -> 617[label="",style="dashed", color="magenta", weight=3];
54 -> 618[label="",style="dashed", color="magenta", weight=3];
617[label="yx6",fontsize=16,color="green",shape="box"];618[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))",fontsize=16,color="black",shape="box"];618 -> 999[label="",style="solid", color="black", weight=3];
616[label="primMulFloat (Float yx26 (Pos (Succ Zero))) (primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) yx27)",fontsize=16,color="burlywood",shape="triangle"];1198[label="yx27/Float yx270 yx271",fontsize=10,color="white",style="solid",shape="box"];616 -> 1198[label="",style="solid", color="burlywood", weight=9];
1198 -> 1000[label="",style="solid", color="burlywood", weight=3];
999[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))",fontsize=16,color="black",shape="box"];999 -> 1001[label="",style="solid", color="black", weight=3];
1000[label="primMulFloat (Float yx26 (Pos (Succ Zero))) (primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float yx270 yx271))",fontsize=16,color="black",shape="box"];1000 -> 1002[label="",style="solid", color="black", weight=3];
1001[label="primFloatEncodePower3 (`negate` Neg (Succ yx7) == Pos Zero) (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))",fontsize=16,color="black",shape="box"];1001 -> 1003[label="",style="solid", color="black", weight=3];
1002[label="primMulFloat (Float yx26 (Pos (Succ Zero))) (Float (Pos (Succ Zero) * yx271) (Pos (Succ Zero) * yx270))",fontsize=16,color="black",shape="box"];1002 -> 1004[label="",style="solid", color="black", weight=3];
1003[label="primFloatEncodePower3 (primEqInt (`negate` Neg (Succ yx7)) (Pos Zero)) (Pos (Succ (Succ Zero))) (`negate` Neg (Succ yx7))",fontsize=16,color="black",shape="box"];1003 -> 1005[label="",style="solid", color="black", weight=3];
1004[label="Float (yx26 * (Pos (Succ Zero) * yx271)) (Pos (Succ Zero) * (Pos (Succ Zero) * yx270))",fontsize=16,color="green",shape="box"];1004 -> 1006[label="",style="dashed", color="green", weight=3];
1004 -> 1007[label="",style="dashed", color="green", weight=3];
1005[label="primFloatEncodePower3 (primEqInt (primNegInt (Neg (Succ yx7))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primNegInt (Neg (Succ yx7)))",fontsize=16,color="black",shape="box"];1005 -> 1008[label="",style="solid", color="black", weight=3];
1006[label="yx26 * (Pos (Succ Zero) * yx271)",fontsize=16,color="black",shape="triangle"];1006 -> 1009[label="",style="solid", color="black", weight=3];
1007 -> 1006[label="",style="dashed", color="red", weight=0];
1007[label="Pos (Succ Zero) * (Pos (Succ Zero) * yx270)",fontsize=16,color="magenta"];1007 -> 1010[label="",style="dashed", color="magenta", weight=3];
1007 -> 1011[label="",style="dashed", color="magenta", weight=3];
1008[label="primFloatEncodePower3 (primEqInt (Pos (Succ yx7)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="triangle"];1008 -> 1012[label="",style="solid", color="black", weight=3];
1009[label="primMulInt yx26 (Pos (Succ Zero) * yx271)",fontsize=16,color="burlywood",shape="box"];1199[label="yx26/Pos yx260",fontsize=10,color="white",style="solid",shape="box"];1009 -> 1199[label="",style="solid", color="burlywood", weight=9];
1199 -> 1013[label="",style="solid", color="burlywood", weight=3];
1200[label="yx26/Neg yx260",fontsize=10,color="white",style="solid",shape="box"];1009 -> 1200[label="",style="solid", color="burlywood", weight=9];
1200 -> 1014[label="",style="solid", color="burlywood", weight=3];
1010[label="yx270",fontsize=16,color="green",shape="box"];1011[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];1012[label="primFloatEncodePower3 False (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1012 -> 1015[label="",style="solid", color="black", weight=3];
1013[label="primMulInt (Pos yx260) (Pos (Succ Zero) * yx271)",fontsize=16,color="black",shape="box"];1013 -> 1016[label="",style="solid", color="black", weight=3];
1014[label="primMulInt (Neg yx260) (Pos (Succ Zero) * yx271)",fontsize=16,color="black",shape="box"];1014 -> 1017[label="",style="solid", color="black", weight=3];
1015[label="primFloatEncodePower2 (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1015 -> 1018[label="",style="solid", color="black", weight=3];
1016[label="primMulInt (Pos yx260) (primMulInt (Pos (Succ Zero)) yx271)",fontsize=16,color="burlywood",shape="box"];1201[label="yx271/Pos yx2710",fontsize=10,color="white",style="solid",shape="box"];1016 -> 1201[label="",style="solid", color="burlywood", weight=9];
1201 -> 1019[label="",style="solid", color="burlywood", weight=3];
1202[label="yx271/Neg yx2710",fontsize=10,color="white",style="solid",shape="box"];1016 -> 1202[label="",style="solid", color="burlywood", weight=9];
1202 -> 1020[label="",style="solid", color="burlywood", weight=3];
1017[label="primMulInt (Neg yx260) (primMulInt (Pos (Succ Zero)) yx271)",fontsize=16,color="burlywood",shape="box"];1203[label="yx271/Pos yx2710",fontsize=10,color="white",style="solid",shape="box"];1017 -> 1203[label="",style="solid", color="burlywood", weight=9];
1203 -> 1021[label="",style="solid", color="burlywood", weight=3];
1204[label="yx271/Neg yx2710",fontsize=10,color="white",style="solid",shape="box"];1017 -> 1204[label="",style="solid", color="burlywood", weight=9];
1204 -> 1022[label="",style="solid", color="burlywood", weight=3];
1018[label="primFloatEncodePower1 (Pos (Succ yx7) >= Pos (Succ Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1018 -> 1023[label="",style="solid", color="black", weight=3];
1019[label="primMulInt (Pos yx260) (primMulInt (Pos (Succ Zero)) (Pos yx2710))",fontsize=16,color="black",shape="box"];1019 -> 1024[label="",style="solid", color="black", weight=3];
1020[label="primMulInt (Pos yx260) (primMulInt (Pos (Succ Zero)) (Neg yx2710))",fontsize=16,color="black",shape="box"];1020 -> 1025[label="",style="solid", color="black", weight=3];
1021[label="primMulInt (Neg yx260) (primMulInt (Pos (Succ Zero)) (Pos yx2710))",fontsize=16,color="black",shape="box"];1021 -> 1026[label="",style="solid", color="black", weight=3];
1022[label="primMulInt (Neg yx260) (primMulInt (Pos (Succ Zero)) (Neg yx2710))",fontsize=16,color="black",shape="box"];1022 -> 1027[label="",style="solid", color="black", weight=3];
1023[label="primFloatEncodePower1 (compare (Pos (Succ yx7)) (Pos (Succ Zero)) /= LT) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1023 -> 1028[label="",style="solid", color="black", weight=3];
1024[label="primMulInt (Pos yx260) (Pos (primMulNat (Succ Zero) yx2710))",fontsize=16,color="black",shape="box"];1024 -> 1029[label="",style="solid", color="black", weight=3];
1025[label="primMulInt (Pos yx260) (Neg (primMulNat (Succ Zero) yx2710))",fontsize=16,color="black",shape="box"];1025 -> 1030[label="",style="solid", color="black", weight=3];
1026[label="primMulInt (Neg yx260) (Pos (primMulNat (Succ Zero) yx2710))",fontsize=16,color="black",shape="box"];1026 -> 1031[label="",style="solid", color="black", weight=3];
1027[label="primMulInt (Neg yx260) (Neg (primMulNat (Succ Zero) yx2710))",fontsize=16,color="black",shape="box"];1027 -> 1032[label="",style="solid", color="black", weight=3];
1028[label="primFloatEncodePower1 (not (compare (Pos (Succ yx7)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1028 -> 1033[label="",style="solid", color="black", weight=3];
1029[label="Pos (primMulNat yx260 (primMulNat (Succ Zero) yx2710))",fontsize=16,color="green",shape="box"];1029 -> 1034[label="",style="dashed", color="green", weight=3];
1030[label="Neg (primMulNat yx260 (primMulNat (Succ Zero) yx2710))",fontsize=16,color="green",shape="box"];1030 -> 1035[label="",style="dashed", color="green", weight=3];
1031[label="Neg (primMulNat yx260 (primMulNat (Succ Zero) yx2710))",fontsize=16,color="green",shape="box"];1031 -> 1036[label="",style="dashed", color="green", weight=3];
1032[label="Pos (primMulNat yx260 (primMulNat (Succ Zero) yx2710))",fontsize=16,color="green",shape="box"];1032 -> 1037[label="",style="dashed", color="green", weight=3];
1033[label="primFloatEncodePower1 (not (primCmpInt (Pos (Succ yx7)) (Pos (Succ Zero)) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1033 -> 1038[label="",style="solid", color="black", weight=3];
1034[label="primMulNat yx260 (primMulNat (Succ Zero) yx2710)",fontsize=16,color="burlywood",shape="triangle"];1205[label="yx260/Succ yx2600",fontsize=10,color="white",style="solid",shape="box"];1034 -> 1205[label="",style="solid", color="burlywood", weight=9];
1205 -> 1039[label="",style="solid", color="burlywood", weight=3];
1206[label="yx260/Zero",fontsize=10,color="white",style="solid",shape="box"];1034 -> 1206[label="",style="solid", color="burlywood", weight=9];
1206 -> 1040[label="",style="solid", color="burlywood", weight=3];
1035 -> 1034[label="",style="dashed", color="red", weight=0];
1035[label="primMulNat yx260 (primMulNat (Succ Zero) yx2710)",fontsize=16,color="magenta"];1035 -> 1041[label="",style="dashed", color="magenta", weight=3];
1036 -> 1034[label="",style="dashed", color="red", weight=0];
1036[label="primMulNat yx260 (primMulNat (Succ Zero) yx2710)",fontsize=16,color="magenta"];1036 -> 1042[label="",style="dashed", color="magenta", weight=3];
1037 -> 1034[label="",style="dashed", color="red", weight=0];
1037[label="primMulNat yx260 (primMulNat (Succ Zero) yx2710)",fontsize=16,color="magenta"];1037 -> 1043[label="",style="dashed", color="magenta", weight=3];
1037 -> 1044[label="",style="dashed", color="magenta", weight=3];
1038[label="primFloatEncodePower1 (not (primCmpNat (Succ yx7) (Succ Zero) == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="black",shape="box"];1038 -> 1045[label="",style="solid", color="black", weight=3];
1039[label="primMulNat (Succ yx2600) (primMulNat (Succ Zero) yx2710)",fontsize=16,color="burlywood",shape="box"];1207[label="yx2710/Succ yx27100",fontsize=10,color="white",style="solid",shape="box"];1039 -> 1207[label="",style="solid", color="burlywood", weight=9];
1207 -> 1046[label="",style="solid", color="burlywood", weight=3];
1208[label="yx2710/Zero",fontsize=10,color="white",style="solid",shape="box"];1039 -> 1208[label="",style="solid", color="burlywood", weight=9];
1208 -> 1047[label="",style="solid", color="burlywood", weight=3];
1040[label="primMulNat Zero (primMulNat (Succ Zero) yx2710)",fontsize=16,color="burlywood",shape="box"];1209[label="yx2710/Succ yx27100",fontsize=10,color="white",style="solid",shape="box"];1040 -> 1209[label="",style="solid", color="burlywood", weight=9];
1209 -> 1048[label="",style="solid", color="burlywood", weight=3];
1210[label="yx2710/Zero",fontsize=10,color="white",style="solid",shape="box"];1040 -> 1210[label="",style="solid", color="burlywood", weight=9];
1210 -> 1049[label="",style="solid", color="burlywood", weight=3];
1041[label="yx2710",fontsize=16,color="green",shape="box"];1042[label="yx260",fontsize=16,color="green",shape="box"];1043[label="yx260",fontsize=16,color="green",shape="box"];1044[label="yx2710",fontsize=16,color="green",shape="box"];1045[label="primFloatEncodePower1 (not (primCmpNat yx7 Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ yx7))",fontsize=16,color="burlywood",shape="box"];1211[label="yx7/Succ yx70",fontsize=10,color="white",style="solid",shape="box"];1045 -> 1211[label="",style="solid", color="burlywood", weight=9];
1211 -> 1050[label="",style="solid", color="burlywood", weight=3];
1212[label="yx7/Zero",fontsize=10,color="white",style="solid",shape="box"];1045 -> 1212[label="",style="solid", color="burlywood", weight=9];
1212 -> 1051[label="",style="solid", color="burlywood", weight=3];
1046[label="primMulNat (Succ yx2600) (primMulNat (Succ Zero) (Succ yx27100))",fontsize=16,color="black",shape="box"];1046 -> 1052[label="",style="solid", color="black", weight=3];
1047[label="primMulNat (Succ yx2600) (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];1047 -> 1053[label="",style="solid", color="black", weight=3];
1048[label="primMulNat Zero (primMulNat (Succ Zero) (Succ yx27100))",fontsize=16,color="black",shape="box"];1048 -> 1054[label="",style="solid", color="black", weight=3];
1049[label="primMulNat Zero (primMulNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];1049 -> 1055[label="",style="solid", color="black", weight=3];
1050[label="primFloatEncodePower1 (not (primCmpNat (Succ yx70) Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)))",fontsize=16,color="black",shape="box"];1050 -> 1056[label="",style="solid", color="black", weight=3];
1051[label="primFloatEncodePower1 (not (primCmpNat Zero Zero == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1051 -> 1057[label="",style="solid", color="black", weight=3];
1052[label="primMulNat (Succ yx2600) (primPlusNat (primMulNat Zero (Succ yx27100)) (Succ yx27100))",fontsize=16,color="black",shape="box"];1052 -> 1058[label="",style="solid", color="black", weight=3];
1053[label="primMulNat (Succ yx2600) Zero",fontsize=16,color="black",shape="box"];1053 -> 1059[label="",style="solid", color="black", weight=3];
1054[label="primMulNat Zero (primPlusNat (primMulNat Zero (Succ yx27100)) (Succ yx27100))",fontsize=16,color="black",shape="box"];1054 -> 1060[label="",style="solid", color="black", weight=3];
1055[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1055 -> 1061[label="",style="solid", color="black", weight=3];
1056[label="primFloatEncodePower1 (not (GT == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)))",fontsize=16,color="black",shape="box"];1056 -> 1062[label="",style="solid", color="black", weight=3];
1057[label="primFloatEncodePower1 (not (EQ == LT)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1057 -> 1063[label="",style="solid", color="black", weight=3];
1058[label="primMulNat (Succ yx2600) (primPlusNat Zero (Succ yx27100))",fontsize=16,color="black",shape="box"];1058 -> 1064[label="",style="solid", color="black", weight=3];
1059[label="Zero",fontsize=16,color="green",shape="box"];1060[label="primMulNat Zero (primPlusNat Zero (Succ yx27100))",fontsize=16,color="black",shape="box"];1060 -> 1065[label="",style="solid", color="black", weight=3];
1061[label="Zero",fontsize=16,color="green",shape="box"];1062[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)))",fontsize=16,color="black",shape="box"];1062 -> 1066[label="",style="solid", color="black", weight=3];
1063[label="primFloatEncodePower1 (not False) (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1063 -> 1067[label="",style="solid", color="black", weight=3];
1064[label="primMulNat (Succ yx2600) (Succ yx27100)",fontsize=16,color="black",shape="box"];1064 -> 1068[label="",style="solid", color="black", weight=3];
1065[label="primMulNat Zero (Succ yx27100)",fontsize=16,color="black",shape="box"];1065 -> 1069[label="",style="solid", color="black", weight=3];
1066[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)))",fontsize=16,color="black",shape="box"];1066 -> 1070[label="",style="solid", color="black", weight=3];
1067[label="primFloatEncodePower1 True (Pos (Succ (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1067 -> 1071[label="",style="solid", color="black", weight=3];
1068 -> 1080[label="",style="dashed", color="red", weight=0];
1068[label="primPlusNat (primMulNat yx2600 (Succ yx27100)) (Succ yx27100)",fontsize=16,color="magenta"];1068 -> 1081[label="",style="dashed", color="magenta", weight=3];
1069[label="Zero",fontsize=16,color="green",shape="box"];1070[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1070 -> 1074[label="",style="solid", color="black", weight=3];
1071[label="fromInt (Pos (Succ (Succ Zero))) * primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1071 -> 1075[label="",style="solid", color="black", weight=3];
1081[label="primMulNat yx2600 (Succ yx27100)",fontsize=16,color="burlywood",shape="triangle"];1213[label="yx2600/Succ yx26000",fontsize=10,color="white",style="solid",shape="box"];1081 -> 1213[label="",style="solid", color="burlywood", weight=9];
1213 -> 1084[label="",style="solid", color="burlywood", weight=3];
1214[label="yx2600/Zero",fontsize=10,color="white",style="solid",shape="box"];1081 -> 1214[label="",style="solid", color="burlywood", weight=9];
1214 -> 1085[label="",style="solid", color="burlywood", weight=3];
1080[label="primPlusNat yx28 (Succ yx27100)",fontsize=16,color="burlywood",shape="triangle"];1215[label="yx28/Succ yx280",fontsize=10,color="white",style="solid",shape="box"];1080 -> 1215[label="",style="solid", color="burlywood", weight=9];
1215 -> 1086[label="",style="solid", color="burlywood", weight=3];
1216[label="yx28/Zero",fontsize=10,color="white",style="solid",shape="box"];1080 -> 1216[label="",style="solid", color="burlywood", weight=9];
1216 -> 1087[label="",style="solid", color="burlywood", weight=3];
1074[label="primMulFloat (fromInt (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1074 -> 1078[label="",style="solid", color="black", weight=3];
1075[label="primMulFloat (fromInt (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1075 -> 1079[label="",style="solid", color="black", weight=3];
1084[label="primMulNat (Succ yx26000) (Succ yx27100)",fontsize=16,color="black",shape="box"];1084 -> 1090[label="",style="solid", color="black", weight=3];
1085[label="primMulNat Zero (Succ yx27100)",fontsize=16,color="black",shape="box"];1085 -> 1091[label="",style="solid", color="black", weight=3];
1086[label="primPlusNat (Succ yx280) (Succ yx27100)",fontsize=16,color="black",shape="box"];1086 -> 1092[label="",style="solid", color="black", weight=3];
1087[label="primPlusNat Zero (Succ yx27100)",fontsize=16,color="black",shape="box"];1087 -> 1093[label="",style="solid", color="black", weight=3];
1078[label="primMulFloat (primIntToFloat (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1078 -> 1088[label="",style="solid", color="black", weight=3];
1079[label="primMulFloat (primIntToFloat (Pos (Succ (Succ Zero)))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1079 -> 1089[label="",style="solid", color="black", weight=3];
1090 -> 1080[label="",style="dashed", color="red", weight=0];
1090[label="primPlusNat (primMulNat yx26000 (Succ yx27100)) (Succ yx27100)",fontsize=16,color="magenta"];1090 -> 1096[label="",style="dashed", color="magenta", weight=3];
1091[label="Zero",fontsize=16,color="green",shape="box"];1092[label="Succ (Succ (primPlusNat yx280 yx27100))",fontsize=16,color="green",shape="box"];1092 -> 1097[label="",style="dashed", color="green", weight=3];
1093[label="Succ yx27100",fontsize=16,color="green",shape="box"];1088 -> 1124[label="",style="dashed", color="red", weight=0];
1088[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero)))",fontsize=16,color="magenta"];1088 -> 1125[label="",style="dashed", color="magenta", weight=3];
1089 -> 1124[label="",style="dashed", color="red", weight=0];
1089[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero)))",fontsize=16,color="magenta"];1089 -> 1126[label="",style="dashed", color="magenta", weight=3];
1096 -> 1081[label="",style="dashed", color="red", weight=0];
1096[label="primMulNat yx26000 (Succ yx27100)",fontsize=16,color="magenta"];1096 -> 1100[label="",style="dashed", color="magenta", weight=3];
1097[label="primPlusNat yx280 yx27100",fontsize=16,color="burlywood",shape="triangle"];1217[label="yx280/Succ yx2800",fontsize=10,color="white",style="solid",shape="box"];1097 -> 1217[label="",style="solid", color="burlywood", weight=9];
1217 -> 1101[label="",style="solid", color="burlywood", weight=3];
1218[label="yx280/Zero",fontsize=10,color="white",style="solid",shape="box"];1097 -> 1218[label="",style="solid", color="burlywood", weight=9];
1218 -> 1102[label="",style="solid", color="burlywood", weight=3];
1125[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1125 -> 1141[label="",style="solid", color="black", weight=3];
1124[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) yx29",fontsize=16,color="burlywood",shape="triangle"];1219[label="yx29/Float yx290 yx291",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1219[label="",style="solid", color="burlywood", weight=9];
1219 -> 1142[label="",style="solid", color="burlywood", weight=3];
1126[label="primFloatEncodePower (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1126 -> 1143[label="",style="solid", color="black", weight=3];
1100[label="yx26000",fontsize=16,color="green",shape="box"];1101[label="primPlusNat (Succ yx2800) yx27100",fontsize=16,color="burlywood",shape="box"];1220[label="yx27100/Succ yx271000",fontsize=10,color="white",style="solid",shape="box"];1101 -> 1220[label="",style="solid", color="burlywood", weight=9];
1220 -> 1105[label="",style="solid", color="burlywood", weight=3];
1221[label="yx27100/Zero",fontsize=10,color="white",style="solid",shape="box"];1101 -> 1221[label="",style="solid", color="burlywood", weight=9];
1221 -> 1106[label="",style="solid", color="burlywood", weight=3];
1102[label="primPlusNat Zero yx27100",fontsize=16,color="burlywood",shape="box"];1222[label="yx27100/Succ yx271000",fontsize=10,color="white",style="solid",shape="box"];1102 -> 1222[label="",style="solid", color="burlywood", weight=9];
1222 -> 1107[label="",style="solid", color="burlywood", weight=3];
1223[label="yx27100/Zero",fontsize=10,color="white",style="solid",shape="box"];1102 -> 1223[label="",style="solid", color="burlywood", weight=9];
1223 -> 1108[label="",style="solid", color="burlywood", weight=3];
1141[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1141 -> 1144[label="",style="solid", color="black", weight=3];
1142[label="primMulFloat (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (Float yx290 yx291)",fontsize=16,color="black",shape="box"];1142 -> 1145[label="",style="solid", color="black", weight=3];
1143[label="primFloatEncodePower4 (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1143 -> 1146[label="",style="solid", color="black", weight=3];
1105[label="primPlusNat (Succ yx2800) (Succ yx271000)",fontsize=16,color="black",shape="box"];1105 -> 1111[label="",style="solid", color="black", weight=3];
1106[label="primPlusNat (Succ yx2800) Zero",fontsize=16,color="black",shape="box"];1106 -> 1112[label="",style="solid", color="black", weight=3];
1107[label="primPlusNat Zero (Succ yx271000)",fontsize=16,color="black",shape="box"];1107 -> 1113[label="",style="solid", color="black", weight=3];
1108[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1108 -> 1114[label="",style="solid", color="black", weight=3];
1144[label="primFloatEncodePower3 (Pos (Succ (Succ yx70)) - Pos (Succ Zero) == Pos Zero) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1144 -> 1147[label="",style="solid", color="black", weight=3];
1145[label="Float (Pos (Succ (Succ Zero)) * yx290) (Pos (Succ Zero) * yx291)",fontsize=16,color="green",shape="box"];1145 -> 1148[label="",style="dashed", color="green", weight=3];
1145 -> 1149[label="",style="dashed", color="green", weight=3];
1146[label="primFloatEncodePower3 (Pos (Succ Zero) - Pos (Succ Zero) == Pos Zero) (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1146 -> 1150[label="",style="solid", color="black", weight=3];
1111[label="Succ (Succ (primPlusNat yx2800 yx271000))",fontsize=16,color="green",shape="box"];1111 -> 1117[label="",style="dashed", color="green", weight=3];
1112[label="Succ yx2800",fontsize=16,color="green",shape="box"];1113[label="Succ yx271000",fontsize=16,color="green",shape="box"];1114[label="Zero",fontsize=16,color="green",shape="box"];1147[label="primFloatEncodePower3 (primEqInt (Pos (Succ (Succ yx70)) - Pos (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ (Succ yx70)) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1147 -> 1151[label="",style="solid", color="black", weight=3];
1148[label="Pos (Succ (Succ Zero)) * yx290",fontsize=16,color="black",shape="box"];1148 -> 1152[label="",style="solid", color="black", weight=3];
1149[label="Pos (Succ Zero) * yx291",fontsize=16,color="black",shape="box"];1149 -> 1153[label="",style="solid", color="black", weight=3];
1150[label="primFloatEncodePower3 (primEqInt (Pos (Succ Zero) - Pos (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ Zero) - Pos (Succ Zero))",fontsize=16,color="black",shape="box"];1150 -> 1154[label="",style="solid", color="black", weight=3];
1117 -> 1097[label="",style="dashed", color="red", weight=0];
1117[label="primPlusNat yx2800 yx271000",fontsize=16,color="magenta"];1117 -> 1120[label="",style="dashed", color="magenta", weight=3];
1117 -> 1121[label="",style="dashed", color="magenta", weight=3];
1151[label="primFloatEncodePower3 (primEqInt (primMinusInt (Pos (Succ (Succ yx70))) (Pos (Succ Zero))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusInt (Pos (Succ (Succ yx70))) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1151 -> 1155[label="",style="solid", color="black", weight=3];
1152[label="primMulInt (Pos (Succ (Succ Zero))) yx290",fontsize=16,color="burlywood",shape="box"];1224[label="yx290/Pos yx2900",fontsize=10,color="white",style="solid",shape="box"];1152 -> 1224[label="",style="solid", color="burlywood", weight=9];
1224 -> 1156[label="",style="solid", color="burlywood", weight=3];
1225[label="yx290/Neg yx2900",fontsize=10,color="white",style="solid",shape="box"];1152 -> 1225[label="",style="solid", color="burlywood", weight=9];
1225 -> 1157[label="",style="solid", color="burlywood", weight=3];
1153[label="primMulInt (Pos (Succ Zero)) yx291",fontsize=16,color="burlywood",shape="box"];1226[label="yx291/Pos yx2910",fontsize=10,color="white",style="solid",shape="box"];1153 -> 1226[label="",style="solid", color="burlywood", weight=9];
1226 -> 1158[label="",style="solid", color="burlywood", weight=3];
1227[label="yx291/Neg yx2910",fontsize=10,color="white",style="solid",shape="box"];1153 -> 1227[label="",style="solid", color="burlywood", weight=9];
1227 -> 1159[label="",style="solid", color="burlywood", weight=3];
1154[label="primFloatEncodePower3 (primEqInt (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1154 -> 1160[label="",style="solid", color="black", weight=3];
1120[label="yx2800",fontsize=16,color="green",shape="box"];1121[label="yx271000",fontsize=16,color="green",shape="box"];1155[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ (Succ yx70)) (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ (Succ yx70)) (Succ Zero))",fontsize=16,color="black",shape="box"];1155 -> 1161[label="",style="solid", color="black", weight=3];
1156[label="primMulInt (Pos (Succ (Succ Zero))) (Pos yx2900)",fontsize=16,color="black",shape="box"];1156 -> 1162[label="",style="solid", color="black", weight=3];
1157[label="primMulInt (Pos (Succ (Succ Zero))) (Neg yx2900)",fontsize=16,color="black",shape="box"];1157 -> 1163[label="",style="solid", color="black", weight=3];
1158[label="primMulInt (Pos (Succ Zero)) (Pos yx2910)",fontsize=16,color="black",shape="box"];1158 -> 1164[label="",style="solid", color="black", weight=3];
1159[label="primMulInt (Pos (Succ Zero)) (Neg yx2910)",fontsize=16,color="black",shape="box"];1159 -> 1165[label="",style="solid", color="black", weight=3];
1160[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ Zero) (Succ Zero)) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ Zero) (Succ Zero))",fontsize=16,color="black",shape="box"];1160 -> 1166[label="",style="solid", color="black", weight=3];
1161[label="primFloatEncodePower3 (primEqInt (primMinusNat (Succ yx70) Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat (Succ yx70) Zero)",fontsize=16,color="black",shape="box"];1161 -> 1167[label="",style="solid", color="black", weight=3];
1162[label="Pos (primMulNat (Succ (Succ Zero)) yx2900)",fontsize=16,color="green",shape="box"];1162 -> 1168[label="",style="dashed", color="green", weight=3];
1163[label="Neg (primMulNat (Succ (Succ Zero)) yx2900)",fontsize=16,color="green",shape="box"];1163 -> 1169[label="",style="dashed", color="green", weight=3];
1164[label="Pos (primMulNat (Succ Zero) yx2910)",fontsize=16,color="green",shape="box"];1164 -> 1170[label="",style="dashed", color="green", weight=3];
1165[label="Neg (primMulNat (Succ Zero) yx2910)",fontsize=16,color="green",shape="box"];1165 -> 1171[label="",style="dashed", color="green", weight=3];
1166[label="primFloatEncodePower3 (primEqInt (primMinusNat Zero Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (primMinusNat Zero Zero)",fontsize=16,color="black",shape="box"];1166 -> 1172[label="",style="solid", color="black", weight=3];
1167 -> 1008[label="",style="dashed", color="red", weight=0];
1167[label="primFloatEncodePower3 (primEqInt (Pos (Succ yx70)) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos (Succ yx70))",fontsize=16,color="magenta"];1167 -> 1173[label="",style="dashed", color="magenta", weight=3];
1168[label="primMulNat (Succ (Succ Zero)) yx2900",fontsize=16,color="burlywood",shape="triangle"];1228[label="yx2900/Succ yx29000",fontsize=10,color="white",style="solid",shape="box"];1168 -> 1228[label="",style="solid", color="burlywood", weight=9];
1228 -> 1174[label="",style="solid", color="burlywood", weight=3];
1229[label="yx2900/Zero",fontsize=10,color="white",style="solid",shape="box"];1168 -> 1229[label="",style="solid", color="burlywood", weight=9];
1229 -> 1175[label="",style="solid", color="burlywood", weight=3];
1169 -> 1168[label="",style="dashed", color="red", weight=0];
1169[label="primMulNat (Succ (Succ Zero)) yx2900",fontsize=16,color="magenta"];1169 -> 1176[label="",style="dashed", color="magenta", weight=3];
1170[label="primMulNat (Succ Zero) yx2910",fontsize=16,color="burlywood",shape="triangle"];1230[label="yx2910/Succ yx29100",fontsize=10,color="white",style="solid",shape="box"];1170 -> 1230[label="",style="solid", color="burlywood", weight=9];
1230 -> 1177[label="",style="solid", color="burlywood", weight=3];
1231[label="yx2910/Zero",fontsize=10,color="white",style="solid",shape="box"];1170 -> 1231[label="",style="solid", color="burlywood", weight=9];
1231 -> 1178[label="",style="solid", color="burlywood", weight=3];
1171 -> 1170[label="",style="dashed", color="red", weight=0];
1171[label="primMulNat (Succ Zero) yx2910",fontsize=16,color="magenta"];1171 -> 1179[label="",style="dashed", color="magenta", weight=3];
1172[label="primFloatEncodePower3 (primEqInt (Pos Zero) (Pos Zero)) (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="box"];1172 -> 1180[label="",style="solid", color="black", weight=3];
1173[label="yx70",fontsize=16,color="green",shape="box"];1174[label="primMulNat (Succ (Succ Zero)) (Succ yx29000)",fontsize=16,color="black",shape="box"];1174 -> 1181[label="",style="solid", color="black", weight=3];
1175[label="primMulNat (Succ (Succ Zero)) Zero",fontsize=16,color="black",shape="box"];1175 -> 1182[label="",style="solid", color="black", weight=3];
1176[label="yx2900",fontsize=16,color="green",shape="box"];1177[label="primMulNat (Succ Zero) (Succ yx29100)",fontsize=16,color="black",shape="box"];1177 -> 1183[label="",style="solid", color="black", weight=3];
1178[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];1178 -> 1184[label="",style="solid", color="black", weight=3];
1179[label="yx2910",fontsize=16,color="green",shape="box"];1180[label="primFloatEncodePower3 True (Pos (Succ (Succ Zero))) (Pos Zero)",fontsize=16,color="black",shape="box"];1180 -> 1185[label="",style="solid", color="black", weight=3];
1181 -> 1097[label="",style="dashed", color="red", weight=0];
1181[label="primPlusNat (primMulNat (Succ Zero) (Succ yx29000)) (Succ yx29000)",fontsize=16,color="magenta"];1181 -> 1186[label="",style="dashed", color="magenta", weight=3];
1181 -> 1187[label="",style="dashed", color="magenta", weight=3];
1182[label="Zero",fontsize=16,color="green",shape="box"];1183 -> 1097[label="",style="dashed", color="red", weight=0];
1183[label="primPlusNat (primMulNat Zero (Succ yx29100)) (Succ yx29100)",fontsize=16,color="magenta"];1183 -> 1188[label="",style="dashed", color="magenta", weight=3];
1183 -> 1189[label="",style="dashed", color="magenta", weight=3];
1184[label="Zero",fontsize=16,color="green",shape="box"];1185[label="fromDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1185 -> 1190[label="",style="solid", color="black", weight=3];
1186 -> 1081[label="",style="dashed", color="red", weight=0];
1186[label="primMulNat (Succ Zero) (Succ yx29000)",fontsize=16,color="magenta"];1186 -> 1191[label="",style="dashed", color="magenta", weight=3];
1186 -> 1192[label="",style="dashed", color="magenta", weight=3];
1187[label="Succ yx29000",fontsize=16,color="green",shape="box"];1188 -> 1081[label="",style="dashed", color="red", weight=0];
1188[label="primMulNat Zero (Succ yx29100)",fontsize=16,color="magenta"];1188 -> 1193[label="",style="dashed", color="magenta", weight=3];
1188 -> 1194[label="",style="dashed", color="magenta", weight=3];
1189[label="Succ yx29100",fontsize=16,color="green",shape="box"];1190[label="doubleToFloat (Double (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];1190 -> 1195[label="",style="solid", color="black", weight=3];
1191[label="Succ Zero",fontsize=16,color="green",shape="box"];1192[label="yx29000",fontsize=16,color="green",shape="box"];1193[label="Zero",fontsize=16,color="green",shape="box"];1194[label="yx29100",fontsize=16,color="green",shape="box"];1195[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];}

----------------------------------------

(12)
Complex Obligation (AND)

----------------------------------------

(13)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMulNat(Succ(yx26000), yx27100) -> new_primMulNat(yx26000, yx27100)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(14) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_primMulNat(Succ(yx26000), yx27100) -> new_primMulNat(yx26000, yx27100)
The graph contains the following edges 1 > 1, 2 >= 2


----------------------------------------

(15)
YES

----------------------------------------

(16)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primFloatEncodePower3(Succ(yx70)) -> new_primFloatEncodePower3(yx70)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(17) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_primFloatEncodePower3(Succ(yx70)) -> new_primFloatEncodePower3(yx70)
The graph contains the following edges 1 > 1


----------------------------------------

(18)
YES

----------------------------------------

(19)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat(Succ(yx2800), Succ(yx271000)) -> new_primPlusNat(yx2800, yx271000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(20) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*new_primPlusNat(Succ(yx2800), Succ(yx271000)) -> new_primPlusNat(yx2800, yx271000)
The graph contains the following edges 1 > 1, 2 > 2


----------------------------------------

(21)
YES