/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES


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

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

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

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

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

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

(3) 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
"signumReal x|x == 00|x > 01|otherwise-1;
"
is transformed to
"signumReal x = signumReal3 x;
"
"signumReal1 x True = 1;
signumReal1 x False = signumReal0 x otherwise;
"
"signumReal0 x True = -1;
"
"signumReal2 x True = 0;
signumReal2 x False = signumReal1 x (x > 0);
"
"signumReal3 x = signumReal2 x (x == 0);
"

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

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

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

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

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="signum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="signum vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="signumReal vz3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="signumReal3 vz3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="signumReal2 vz3 (vz3 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="signumReal2 vz3 (primEqInt vz3 (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];359[label="vz3/Pos vz30",fontsize=10,color="white",style="solid",shape="box"];7 -> 359[label="",style="solid", color="burlywood", weight=9];
359 -> 8[label="",style="solid", color="burlywood", weight=3];
360[label="vz3/Neg vz30",fontsize=10,color="white",style="solid",shape="box"];7 -> 360[label="",style="solid", color="burlywood", weight=9];
360 -> 9[label="",style="solid", color="burlywood", weight=3];
8[label="signumReal2 (Pos vz30) (primEqInt (Pos vz30) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];361[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];8 -> 361[label="",style="solid", color="burlywood", weight=9];
361 -> 10[label="",style="solid", color="burlywood", weight=3];
362[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 362[label="",style="solid", color="burlywood", weight=9];
362 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="signumReal2 (Neg vz30) (primEqInt (Neg vz30) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];363[label="vz30/Succ vz300",fontsize=10,color="white",style="solid",shape="box"];9 -> 363[label="",style="solid", color="burlywood", weight=9];
363 -> 12[label="",style="solid", color="burlywood", weight=3];
364[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 364[label="",style="solid", color="burlywood", weight=9];
364 -> 13[label="",style="solid", color="burlywood", weight=3];
10[label="signumReal2 (Pos (Succ vz300)) (primEqInt (Pos (Succ vz300)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="signumReal2 (Pos Zero) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="signumReal2 (Neg (Succ vz300)) (primEqInt (Neg (Succ vz300)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="signumReal2 (Neg Zero) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="signumReal2 (Pos (Succ vz300)) (primEqInt (Pos (Succ vz300)) (Pos Zero))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="signumReal2 (Pos Zero) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="signumReal2 (Neg (Succ vz300)) (primEqInt (Neg (Succ vz300)) (Pos Zero))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="signumReal2 (Neg Zero) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="signumReal2 (Pos (Succ vz300)) False",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="signumReal2 (Pos Zero) True",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="signumReal2 (Neg (Succ vz300)) False",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="signumReal2 (Neg Zero) True",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="signumReal1 (Pos (Succ vz300)) (Pos (Succ vz300) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="fromInt (Pos Zero)",fontsize=16,color="black",shape="triangle"];23 -> 27[label="",style="solid", color="black", weight=3];
24 -> 28[label="",style="dashed", color="red", weight=0];
24[label="signumReal1 (Neg (Succ vz300)) (Neg (Succ vz300) > fromInt (Pos Zero))",fontsize=16,color="magenta"];24 -> 29[label="",style="dashed", color="magenta", weight=3];
25 -> 23[label="",style="dashed", color="red", weight=0];
25[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];26 -> 30[label="",style="dashed", color="red", weight=0];
26[label="signumReal1 (Pos (Succ vz300)) (compare (Pos (Succ vz300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="magenta"];26 -> 31[label="",style="dashed", color="magenta", weight=3];
27[label="Pos Zero",fontsize=16,color="green",shape="box"];29 -> 23[label="",style="dashed", color="red", weight=0];
29[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];28[label="signumReal1 (Neg (Succ vz300)) (Neg (Succ vz300) > vz4)",fontsize=16,color="black",shape="triangle"];28 -> 32[label="",style="solid", color="black", weight=3];
31 -> 23[label="",style="dashed", color="red", weight=0];
31[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];30[label="signumReal1 (Pos (Succ vz300)) (compare (Pos (Succ vz300)) vz5 == GT)",fontsize=16,color="black",shape="triangle"];30 -> 33[label="",style="solid", color="black", weight=3];
32[label="signumReal1 (Neg (Succ vz300)) (compare (Neg (Succ vz300)) vz4 == GT)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
33[label="signumReal1 (Pos (Succ vz300)) (primCmpInt (Pos (Succ vz300)) vz5 == GT)",fontsize=16,color="burlywood",shape="box"];365[label="vz5/Pos vz50",fontsize=10,color="white",style="solid",shape="box"];33 -> 365[label="",style="solid", color="burlywood", weight=9];
365 -> 35[label="",style="solid", color="burlywood", weight=3];
366[label="vz5/Neg vz50",fontsize=10,color="white",style="solid",shape="box"];33 -> 366[label="",style="solid", color="burlywood", weight=9];
366 -> 36[label="",style="solid", color="burlywood", weight=3];
34[label="signumReal1 (Neg (Succ vz300)) (primCmpInt (Neg (Succ vz300)) vz4 == GT)",fontsize=16,color="burlywood",shape="box"];367[label="vz4/Pos vz40",fontsize=10,color="white",style="solid",shape="box"];34 -> 367[label="",style="solid", color="burlywood", weight=9];
367 -> 37[label="",style="solid", color="burlywood", weight=3];
368[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];34 -> 368[label="",style="solid", color="burlywood", weight=9];
368 -> 38[label="",style="solid", color="burlywood", weight=3];
35[label="signumReal1 (Pos (Succ vz300)) (primCmpInt (Pos (Succ vz300)) (Pos vz50) == GT)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
36[label="signumReal1 (Pos (Succ vz300)) (primCmpInt (Pos (Succ vz300)) (Neg vz50) == GT)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3];
37[label="signumReal1 (Neg (Succ vz300)) (primCmpInt (Neg (Succ vz300)) (Pos vz40) == GT)",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
38[label="signumReal1 (Neg (Succ vz300)) (primCmpInt (Neg (Succ vz300)) (Neg vz40) == GT)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3];
39 -> 202[label="",style="dashed", color="red", weight=0];
39[label="signumReal1 (Pos (Succ vz300)) (primCmpNat (Succ vz300) vz50 == GT)",fontsize=16,color="magenta"];39 -> 203[label="",style="dashed", color="magenta", weight=3];
39 -> 204[label="",style="dashed", color="magenta", weight=3];
39 -> 205[label="",style="dashed", color="magenta", weight=3];
40[label="signumReal1 (Pos (Succ vz300)) (GT == GT)",fontsize=16,color="black",shape="triangle"];40 -> 45[label="",style="solid", color="black", weight=3];
41[label="signumReal1 (Neg (Succ vz300)) (LT == GT)",fontsize=16,color="black",shape="triangle"];41 -> 46[label="",style="solid", color="black", weight=3];
42 -> 265[label="",style="dashed", color="red", weight=0];
42[label="signumReal1 (Neg (Succ vz300)) (primCmpNat vz40 (Succ vz300) == GT)",fontsize=16,color="magenta"];42 -> 266[label="",style="dashed", color="magenta", weight=3];
42 -> 267[label="",style="dashed", color="magenta", weight=3];
42 -> 268[label="",style="dashed", color="magenta", weight=3];
203[label="vz300",fontsize=16,color="green",shape="box"];204[label="vz50",fontsize=16,color="green",shape="box"];205[label="Succ vz300",fontsize=16,color="green",shape="box"];202[label="signumReal1 (Pos (Succ vz7)) (primCmpNat vz8 vz9 == GT)",fontsize=16,color="burlywood",shape="triangle"];369[label="vz8/Succ vz80",fontsize=10,color="white",style="solid",shape="box"];202 -> 369[label="",style="solid", color="burlywood", weight=9];
369 -> 224[label="",style="solid", color="burlywood", weight=3];
370[label="vz8/Zero",fontsize=10,color="white",style="solid",shape="box"];202 -> 370[label="",style="solid", color="burlywood", weight=9];
370 -> 225[label="",style="solid", color="burlywood", weight=3];
45[label="signumReal1 (Pos (Succ vz300)) True",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3];
46[label="signumReal1 (Neg (Succ vz300)) False",fontsize=16,color="black",shape="triangle"];46 -> 52[label="",style="solid", color="black", weight=3];
266[label="vz300",fontsize=16,color="green",shape="box"];267[label="vz40",fontsize=16,color="green",shape="box"];268[label="Succ vz300",fontsize=16,color="green",shape="box"];265[label="signumReal1 (Neg (Succ vz13)) (primCmpNat vz14 vz15 == GT)",fontsize=16,color="burlywood",shape="triangle"];371[label="vz14/Succ vz140",fontsize=10,color="white",style="solid",shape="box"];265 -> 371[label="",style="solid", color="burlywood", weight=9];
371 -> 290[label="",style="solid", color="burlywood", weight=3];
372[label="vz14/Zero",fontsize=10,color="white",style="solid",shape="box"];265 -> 372[label="",style="solid", color="burlywood", weight=9];
372 -> 291[label="",style="solid", color="burlywood", weight=3];
224[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) vz9 == GT)",fontsize=16,color="burlywood",shape="box"];373[label="vz9/Succ vz90",fontsize=10,color="white",style="solid",shape="box"];224 -> 373[label="",style="solid", color="burlywood", weight=9];
373 -> 234[label="",style="solid", color="burlywood", weight=3];
374[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];224 -> 374[label="",style="solid", color="burlywood", weight=9];
374 -> 235[label="",style="solid", color="burlywood", weight=3];
225[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero vz9 == GT)",fontsize=16,color="burlywood",shape="box"];375[label="vz9/Succ vz90",fontsize=10,color="white",style="solid",shape="box"];225 -> 375[label="",style="solid", color="burlywood", weight=9];
375 -> 236[label="",style="solid", color="burlywood", weight=3];
376[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];225 -> 376[label="",style="solid", color="burlywood", weight=9];
376 -> 237[label="",style="solid", color="burlywood", weight=3];
51[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3];
52[label="signumReal0 (Neg (Succ vz300)) otherwise",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3];
290[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) vz15 == GT)",fontsize=16,color="burlywood",shape="box"];377[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];290 -> 377[label="",style="solid", color="burlywood", weight=9];
377 -> 294[label="",style="solid", color="burlywood", weight=3];
378[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];290 -> 378[label="",style="solid", color="burlywood", weight=9];
378 -> 295[label="",style="solid", color="burlywood", weight=3];
291[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero vz15 == GT)",fontsize=16,color="burlywood",shape="box"];379[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];291 -> 379[label="",style="solid", color="burlywood", weight=9];
379 -> 296[label="",style="solid", color="burlywood", weight=3];
380[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];291 -> 380[label="",style="solid", color="burlywood", weight=9];
380 -> 297[label="",style="solid", color="burlywood", weight=3];
234[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) (Succ vz90) == GT)",fontsize=16,color="black",shape="box"];234 -> 245[label="",style="solid", color="black", weight=3];
235[label="signumReal1 (Pos (Succ vz7)) (primCmpNat (Succ vz80) Zero == GT)",fontsize=16,color="black",shape="box"];235 -> 246[label="",style="solid", color="black", weight=3];
236[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero (Succ vz90) == GT)",fontsize=16,color="black",shape="box"];236 -> 247[label="",style="solid", color="black", weight=3];
237[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];237 -> 248[label="",style="solid", color="black", weight=3];
57[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];58[label="signumReal0 (Neg (Succ vz300)) True",fontsize=16,color="black",shape="box"];58 -> 65[label="",style="solid", color="black", weight=3];
294[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) (Succ vz150) == GT)",fontsize=16,color="black",shape="box"];294 -> 304[label="",style="solid", color="black", weight=3];
295[label="signumReal1 (Neg (Succ vz13)) (primCmpNat (Succ vz140) Zero == GT)",fontsize=16,color="black",shape="box"];295 -> 305[label="",style="solid", color="black", weight=3];
296[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero (Succ vz150) == GT)",fontsize=16,color="black",shape="box"];296 -> 306[label="",style="solid", color="black", weight=3];
297[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];297 -> 307[label="",style="solid", color="black", weight=3];
245 -> 202[label="",style="dashed", color="red", weight=0];
245[label="signumReal1 (Pos (Succ vz7)) (primCmpNat vz80 vz90 == GT)",fontsize=16,color="magenta"];245 -> 255[label="",style="dashed", color="magenta", weight=3];
245 -> 256[label="",style="dashed", color="magenta", weight=3];
246[label="signumReal1 (Pos (Succ vz7)) (GT == GT)",fontsize=16,color="black",shape="box"];246 -> 257[label="",style="solid", color="black", weight=3];
247[label="signumReal1 (Pos (Succ vz7)) (LT == GT)",fontsize=16,color="black",shape="box"];247 -> 258[label="",style="solid", color="black", weight=3];
248[label="signumReal1 (Pos (Succ vz7)) (EQ == GT)",fontsize=16,color="black",shape="box"];248 -> 259[label="",style="solid", color="black", weight=3];
65[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];65 -> 74[label="",style="solid", color="black", weight=3];
304 -> 265[label="",style="dashed", color="red", weight=0];
304[label="signumReal1 (Neg (Succ vz13)) (primCmpNat vz140 vz150 == GT)",fontsize=16,color="magenta"];304 -> 313[label="",style="dashed", color="magenta", weight=3];
304 -> 314[label="",style="dashed", color="magenta", weight=3];
305[label="signumReal1 (Neg (Succ vz13)) (GT == GT)",fontsize=16,color="black",shape="box"];305 -> 315[label="",style="solid", color="black", weight=3];
306[label="signumReal1 (Neg (Succ vz13)) (LT == GT)",fontsize=16,color="black",shape="box"];306 -> 316[label="",style="solid", color="black", weight=3];
307[label="signumReal1 (Neg (Succ vz13)) (EQ == GT)",fontsize=16,color="black",shape="box"];307 -> 317[label="",style="solid", color="black", weight=3];
255[label="vz90",fontsize=16,color="green",shape="box"];256[label="vz80",fontsize=16,color="green",shape="box"];257[label="signumReal1 (Pos (Succ vz7)) True",fontsize=16,color="black",shape="box"];257 -> 292[label="",style="solid", color="black", weight=3];
258[label="signumReal1 (Pos (Succ vz7)) False",fontsize=16,color="black",shape="triangle"];258 -> 293[label="",style="solid", color="black", weight=3];
259 -> 258[label="",style="dashed", color="red", weight=0];
259[label="signumReal1 (Pos (Succ vz7)) False",fontsize=16,color="magenta"];74[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];313[label="vz140",fontsize=16,color="green",shape="box"];314[label="vz150",fontsize=16,color="green",shape="box"];315[label="signumReal1 (Neg (Succ vz13)) True",fontsize=16,color="black",shape="box"];315 -> 326[label="",style="solid", color="black", weight=3];
316[label="signumReal1 (Neg (Succ vz13)) False",fontsize=16,color="black",shape="triangle"];316 -> 327[label="",style="solid", color="black", weight=3];
317 -> 316[label="",style="dashed", color="red", weight=0];
317[label="signumReal1 (Neg (Succ vz13)) False",fontsize=16,color="magenta"];292[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];381[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];292 -> 381[label="",style="solid", color="blue", weight=9];
381 -> 298[label="",style="solid", color="blue", weight=3];
382[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];292 -> 382[label="",style="solid", color="blue", weight=9];
382 -> 299[label="",style="solid", color="blue", weight=3];
383[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];292 -> 383[label="",style="solid", color="blue", weight=9];
383 -> 300[label="",style="solid", color="blue", weight=3];
384[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];292 -> 384[label="",style="solid", color="blue", weight=9];
384 -> 301[label="",style="solid", color="blue", weight=3];
385[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];292 -> 385[label="",style="solid", color="blue", weight=9];
385 -> 302[label="",style="solid", color="blue", weight=3];
293[label="signumReal0 (Pos (Succ vz7)) otherwise",fontsize=16,color="black",shape="box"];293 -> 303[label="",style="solid", color="black", weight=3];
326[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];386[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];326 -> 386[label="",style="solid", color="blue", weight=9];
386 -> 334[label="",style="solid", color="blue", weight=3];
387[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];326 -> 387[label="",style="solid", color="blue", weight=9];
387 -> 335[label="",style="solid", color="blue", weight=3];
388[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];326 -> 388[label="",style="solid", color="blue", weight=9];
388 -> 336[label="",style="solid", color="blue", weight=3];
389[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];326 -> 389[label="",style="solid", color="blue", weight=9];
389 -> 337[label="",style="solid", color="blue", weight=3];
390[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];326 -> 390[label="",style="solid", color="blue", weight=9];
390 -> 338[label="",style="solid", color="blue", weight=3];
327[label="signumReal0 (Neg (Succ vz13)) otherwise",fontsize=16,color="black",shape="box"];327 -> 339[label="",style="solid", color="black", weight=3];
298[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];298 -> 308[label="",style="solid", color="black", weight=3];
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391 -> 321[label="",style="solid", color="blue", weight=3];
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392 -> 322[label="",style="solid", color="blue", weight=3];
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358[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];}

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h)

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

(10) 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_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4


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

(11)
YES

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

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h)

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

(13) 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_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4


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

(14)
YES