H-Termination proof of /home/matraf/haskell/eval_FullyBlown

MAYBE 2.898 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could not be shown:

↳ HASKELL

  ↳ BR

mainModule Main

((enumFromThen :: Int -> Int -> [Int]) :: Int -> Int -> [Int])

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((enumFromThen :: Int -> Int -> [Int]) :: Int -> Int -> [Int])

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

          ↳ Narrow

mainModule Main

(enumFromThen :: Int -> Int -> [Int])

module Main where

import qualified Prelude

Haskell To QDPs

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202[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 202[label="",style="solid", color="burlywood", weight=9];
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204[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];29 -> 204[label="",style="solid", color="burlywood", weight=9];
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43[label="primPlusInt (primMinusNat Zero Zero) vx5",fontsize=16,color="black",shape="box"];43 -> 51[label="",style="solid", color="black", weight=3];
44[label="Pos (primPlusNat (primPlusNat vx40 vx30) vx50)",fontsize=16,color="green",shape="box"];44 -> 52[label="",style="dashed", color="green", weight=3];
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213[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 213[label="",style="solid", color="burlywood", weight=9];
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215[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 215[label="",style="solid", color="burlywood", weight=9];
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220[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];50 -> 220[label="",style="solid", color="burlywood", weight=9];
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222[label="vx5/Neg vx50",fontsize=10,color="white",style="solid",shape="box"];51 -> 222[label="",style="solid", color="burlywood", weight=9];
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223 -> 66[label="",style="solid", color="burlywood", weight=3];
224[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 224[label="",style="solid", color="burlywood", weight=9];
224 -> 67[label="",style="solid", color="burlywood", weight=3];
53[label="primMinusNat (primPlusNat (Succ vx400) vx30) vx50",fontsize=16,color="burlywood",shape="box"];225[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];53 -> 225[label="",style="solid", color="burlywood", weight=9];
225 -> 68[label="",style="solid", color="burlywood", weight=3];
226[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];53 -> 226[label="",style="solid", color="burlywood", weight=9];
226 -> 69[label="",style="solid", color="burlywood", weight=3];
54[label="primMinusNat (primPlusNat Zero vx30) vx50",fontsize=16,color="burlywood",shape="box"];227[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];54 -> 227[label="",style="solid", color="burlywood", weight=9];
227 -> 70[label="",style="solid", color="burlywood", weight=3];
228[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 228[label="",style="solid", color="burlywood", weight=9];
228 -> 71[label="",style="solid", color="burlywood", weight=3];
55[label="primMinusNat (Succ vx500) (primPlusNat vx40 vx30)",fontsize=16,color="burlywood",shape="box"];229[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];55 -> 229[label="",style="solid", color="burlywood", weight=9];
229 -> 72[label="",style="solid", color="burlywood", weight=3];
230[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 230[label="",style="solid", color="burlywood", weight=9];
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231 -> 74[label="",style="solid", color="burlywood", weight=3];
232[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];56 -> 232[label="",style="solid", color="burlywood", weight=9];
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57 -> 78[label="",style="dashed", color="magenta", weight=3];
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61[label="primPlusInt (Pos (Succ vx400)) (Neg vx50)",fontsize=16,color="black",shape="box"];61 -> 80[label="",style="solid", color="black", weight=3];
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63[label="primPlusInt (Neg (Succ vx300)) (Neg vx50)",fontsize=16,color="black",shape="box"];63 -> 82[label="",style="solid", color="black", weight=3];
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65[label="primPlusInt (Pos Zero) (Neg vx50)",fontsize=16,color="black",shape="box"];65 -> 84[label="",style="solid", color="black", weight=3];
66[label="primPlusNat (primPlusNat (Succ vx400) vx30) vx50",fontsize=16,color="burlywood",shape="box"];234[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];66 -> 234[label="",style="solid", color="burlywood", weight=9];
234 -> 85[label="",style="solid", color="burlywood", weight=3];
235[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];66 -> 235[label="",style="solid", color="burlywood", weight=9];
235 -> 86[label="",style="solid", color="burlywood", weight=3];
67[label="primPlusNat (primPlusNat Zero vx30) vx50",fontsize=16,color="burlywood",shape="box"];236[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];67 -> 236[label="",style="solid", color="burlywood", weight=9];
236 -> 87[label="",style="solid", color="burlywood", weight=3];
237[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 237[label="",style="solid", color="burlywood", weight=9];
237 -> 88[label="",style="solid", color="burlywood", weight=3];
68[label="primMinusNat (primPlusNat (Succ vx400) (Succ vx300)) vx50",fontsize=16,color="black",shape="box"];68 -> 89[label="",style="solid", color="black", weight=3];
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71[label="primMinusNat (primPlusNat Zero Zero) vx50",fontsize=16,color="black",shape="box"];71 -> 92[label="",style="solid", color="black", weight=3];
72[label="primMinusNat (Succ vx500) (primPlusNat (Succ vx400) vx30)",fontsize=16,color="burlywood",shape="box"];238[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];72 -> 238[label="",style="solid", color="burlywood", weight=9];
238 -> 93[label="",style="solid", color="burlywood", weight=3];
239[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 239[label="",style="solid", color="burlywood", weight=9];
239 -> 94[label="",style="solid", color="burlywood", weight=3];
73[label="primMinusNat (Succ vx500) (primPlusNat Zero vx30)",fontsize=16,color="burlywood",shape="box"];240[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];73 -> 240[label="",style="solid", color="burlywood", weight=9];
240 -> 95[label="",style="solid", color="burlywood", weight=3];
241[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];73 -> 241[label="",style="solid", color="burlywood", weight=9];
241 -> 96[label="",style="solid", color="burlywood", weight=3];
74[label="primMinusNat Zero (primPlusNat (Succ vx400) vx30)",fontsize=16,color="burlywood",shape="box"];242[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];74 -> 242[label="",style="solid", color="burlywood", weight=9];
242 -> 97[label="",style="solid", color="burlywood", weight=3];
243[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];74 -> 243[label="",style="solid", color="burlywood", weight=9];
243 -> 98[label="",style="solid", color="burlywood", weight=3];
75[label="primMinusNat Zero (primPlusNat Zero vx30)",fontsize=16,color="burlywood",shape="box"];244[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];75 -> 244[label="",style="solid", color="burlywood", weight=9];
244 -> 99[label="",style="solid", color="burlywood", weight=3];
245[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];75 -> 245[label="",style="solid", color="burlywood", weight=9];
245 -> 100[label="",style="solid", color="burlywood", weight=3];
76[label="vx30",fontsize=16,color="green",shape="box"];77[label="vx50",fontsize=16,color="green",shape="box"];78[label="vx40",fontsize=16,color="green",shape="box"];79[label="Pos (primPlusNat (Succ vx400) vx50)",fontsize=16,color="green",shape="box"];79 -> 101[label="",style="dashed", color="green", weight=3];
80[label="primMinusNat (Succ vx400) vx50",fontsize=16,color="burlywood",shape="triangle"];246[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];80 -> 246[label="",style="solid", color="burlywood", weight=9];
246 -> 102[label="",style="solid", color="burlywood", weight=3];
247[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];80 -> 247[label="",style="solid", color="burlywood", weight=9];
247 -> 103[label="",style="solid", color="burlywood", weight=3];
81[label="primMinusNat vx50 (Succ vx300)",fontsize=16,color="burlywood",shape="triangle"];248[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];81 -> 248[label="",style="solid", color="burlywood", weight=9];
248 -> 104[label="",style="solid", color="burlywood", weight=3];
249[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];81 -> 249[label="",style="solid", color="burlywood", weight=9];
249 -> 105[label="",style="solid", color="burlywood", weight=3];
82[label="Neg (primPlusNat (Succ vx300) vx50)",fontsize=16,color="green",shape="box"];82 -> 106[label="",style="dashed", color="green", weight=3];
83[label="Pos (primPlusNat Zero vx50)",fontsize=16,color="green",shape="box"];83 -> 107[label="",style="dashed", color="green", weight=3];
84[label="primMinusNat Zero vx50",fontsize=16,color="burlywood",shape="triangle"];250[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];84 -> 250[label="",style="solid", color="burlywood", weight=9];
250 -> 108[label="",style="solid", color="burlywood", weight=3];
251[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];84 -> 251[label="",style="solid", color="burlywood", weight=9];
251 -> 109[label="",style="solid", color="burlywood", weight=3];
85[label="primPlusNat (primPlusNat (Succ vx400) (Succ vx300)) vx50",fontsize=16,color="black",shape="box"];85 -> 110[label="",style="solid", color="black", weight=3];
86[label="primPlusNat (primPlusNat (Succ vx400) Zero) vx50",fontsize=16,color="black",shape="box"];86 -> 111[label="",style="solid", color="black", weight=3];
87[label="primPlusNat (primPlusNat Zero (Succ vx300)) vx50",fontsize=16,color="black",shape="box"];87 -> 112[label="",style="solid", color="black", weight=3];
88[label="primPlusNat (primPlusNat Zero Zero) vx50",fontsize=16,color="black",shape="box"];88 -> 113[label="",style="solid", color="black", weight=3];
89 -> 80[label="",style="dashed", color="red", weight=0];
89[label="primMinusNat (Succ (Succ (primPlusNat vx400 vx300))) vx50",fontsize=16,color="magenta"];89 -> 114[label="",style="dashed", color="magenta", weight=3];
90 -> 80[label="",style="dashed", color="red", weight=0];
90[label="primMinusNat (Succ vx400) vx50",fontsize=16,color="magenta"];91 -> 80[label="",style="dashed", color="red", weight=0];
91[label="primMinusNat (Succ vx300) vx50",fontsize=16,color="magenta"];91 -> 115[label="",style="dashed", color="magenta", weight=3];
92 -> 84[label="",style="dashed", color="red", weight=0];
92[label="primMinusNat Zero vx50",fontsize=16,color="magenta"];93[label="primMinusNat (Succ vx500) (primPlusNat (Succ vx400) (Succ vx300))",fontsize=16,color="black",shape="box"];93 -> 116[label="",style="solid", color="black", weight=3];
94[label="primMinusNat (Succ vx500) (primPlusNat (Succ vx400) Zero)",fontsize=16,color="black",shape="box"];94 -> 117[label="",style="solid", color="black", weight=3];
95[label="primMinusNat (Succ vx500) (primPlusNat Zero (Succ vx300))",fontsize=16,color="black",shape="box"];95 -> 118[label="",style="solid", color="black", weight=3];
96[label="primMinusNat (Succ vx500) (primPlusNat Zero Zero)",fontsize=16,color="black",shape="box"];96 -> 119[label="",style="solid", color="black", weight=3];
97[label="primMinusNat Zero (primPlusNat (Succ vx400) (Succ vx300))",fontsize=16,color="black",shape="box"];97 -> 120[label="",style="solid", color="black", weight=3];
98[label="primMinusNat Zero (primPlusNat (Succ vx400) Zero)",fontsize=16,color="black",shape="box"];98 -> 121[label="",style="solid", color="black", weight=3];
99[label="primMinusNat Zero (primPlusNat Zero (Succ vx300))",fontsize=16,color="black",shape="box"];99 -> 122[label="",style="solid", color="black", weight=3];
100[label="primMinusNat Zero (primPlusNat Zero Zero)",fontsize=16,color="black",shape="box"];100 -> 123[label="",style="solid", color="black", weight=3];
101[label="primPlusNat (Succ vx400) vx50",fontsize=16,color="burlywood",shape="triangle"];256[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];101 -> 256[label="",style="solid", color="burlywood", weight=9];
256 -> 124[label="",style="solid", color="burlywood", weight=3];
257[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];101 -> 257[label="",style="solid", color="burlywood", weight=9];
257 -> 125[label="",style="solid", color="burlywood", weight=3];
102[label="primMinusNat (Succ vx400) (Succ vx500)",fontsize=16,color="black",shape="box"];102 -> 126[label="",style="solid", color="black", weight=3];
103[label="primMinusNat (Succ vx400) Zero",fontsize=16,color="black",shape="box"];103 -> 127[label="",style="solid", color="black", weight=3];
104[label="primMinusNat (Succ vx500) (Succ vx300)",fontsize=16,color="black",shape="box"];104 -> 128[label="",style="solid", color="black", weight=3];
105[label="primMinusNat Zero (Succ vx300)",fontsize=16,color="black",shape="box"];105 -> 129[label="",style="solid", color="black", weight=3];
106 -> 101[label="",style="dashed", color="red", weight=0];
106[label="primPlusNat (Succ vx300) vx50",fontsize=16,color="magenta"];106 -> 130[label="",style="dashed", color="magenta", weight=3];
106 -> 131[label="",style="dashed", color="magenta", weight=3];
107[label="primPlusNat Zero vx50",fontsize=16,color="burlywood",shape="triangle"];259[label="vx50/Succ vx500",fontsize=10,color="white",style="solid",shape="box"];107 -> 259[label="",style="solid", color="burlywood", weight=9];
259 -> 132[label="",style="solid", color="burlywood", weight=3];
260[label="vx50/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 260[label="",style="solid", color="burlywood", weight=9];
260 -> 133[label="",style="solid", color="burlywood", weight=3];
108[label="primMinusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];108 -> 134[label="",style="solid", color="black", weight=3];
109[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];109 -> 135[label="",style="solid", color="black", weight=3];
110 -> 101[label="",style="dashed", color="red", weight=0];
110[label="primPlusNat (Succ (Succ (primPlusNat vx400 vx300))) vx50",fontsize=16,color="magenta"];110 -> 136[label="",style="dashed", color="magenta", weight=3];
111 -> 101[label="",style="dashed", color="red", weight=0];
111[label="primPlusNat (Succ vx400) vx50",fontsize=16,color="magenta"];112 -> 101[label="",style="dashed", color="red", weight=0];
112[label="primPlusNat (Succ vx300) vx50",fontsize=16,color="magenta"];112 -> 137[label="",style="dashed", color="magenta", weight=3];
113 -> 107[label="",style="dashed", color="red", weight=0];
113[label="primPlusNat Zero vx50",fontsize=16,color="magenta"];114[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];114 -> 138[label="",style="dashed", color="green", weight=3];
115[label="vx300",fontsize=16,color="green",shape="box"];116 -> 81[label="",style="dashed", color="red", weight=0];
116[label="primMinusNat (Succ vx500) (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];116 -> 139[label="",style="dashed", color="magenta", weight=3];
116 -> 140[label="",style="dashed", color="magenta", weight=3];
117 -> 81[label="",style="dashed", color="red", weight=0];
117[label="primMinusNat (Succ vx500) (Succ vx400)",fontsize=16,color="magenta"];117 -> 141[label="",style="dashed", color="magenta", weight=3];
117 -> 142[label="",style="dashed", color="magenta", weight=3];
118 -> 81[label="",style="dashed", color="red", weight=0];
118[label="primMinusNat (Succ vx500) (Succ vx300)",fontsize=16,color="magenta"];118 -> 143[label="",style="dashed", color="magenta", weight=3];
119 -> 80[label="",style="dashed", color="red", weight=0];
119[label="primMinusNat (Succ vx500) Zero",fontsize=16,color="magenta"];119 -> 144[label="",style="dashed", color="magenta", weight=3];
119 -> 145[label="",style="dashed", color="magenta", weight=3];
120 -> 81[label="",style="dashed", color="red", weight=0];
120[label="primMinusNat Zero (Succ (Succ (primPlusNat vx400 vx300)))",fontsize=16,color="magenta"];120 -> 146[label="",style="dashed", color="magenta", weight=3];
120 -> 147[label="",style="dashed", color="magenta", weight=3];
121 -> 81[label="",style="dashed", color="red", weight=0];
121[label="primMinusNat Zero (Succ vx400)",fontsize=16,color="magenta"];121 -> 148[label="",style="dashed", color="magenta", weight=3];
121 -> 149[label="",style="dashed", color="magenta", weight=3];
122 -> 81[label="",style="dashed", color="red", weight=0];
122[label="primMinusNat Zero (Succ vx300)",fontsize=16,color="magenta"];122 -> 150[label="",style="dashed", color="magenta", weight=3];
123 -> 84[label="",style="dashed", color="red", weight=0];
123[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];123 -> 151[label="",style="dashed", color="magenta", weight=3];
124[label="primPlusNat (Succ vx400) (Succ vx500)",fontsize=16,color="black",shape="box"];124 -> 152[label="",style="solid", color="black", weight=3];
125[label="primPlusNat (Succ vx400) Zero",fontsize=16,color="black",shape="box"];125 -> 153[label="",style="solid", color="black", weight=3];
126[label="primMinusNat vx400 vx500",fontsize=16,color="burlywood",shape="triangle"];273[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];126 -> 273[label="",style="solid", color="burlywood", weight=9];
273 -> 154[label="",style="solid", color="burlywood", weight=3];
274[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];126 -> 274[label="",style="solid", color="burlywood", weight=9];
274 -> 155[label="",style="solid", color="burlywood", weight=3];
127[label="Pos (Succ vx400)",fontsize=16,color="green",shape="box"];128 -> 126[label="",style="dashed", color="red", weight=0];
128[label="primMinusNat vx500 vx300",fontsize=16,color="magenta"];128 -> 156[label="",style="dashed", color="magenta", weight=3];
128 -> 157[label="",style="dashed", color="magenta", weight=3];
129[label="Neg (Succ vx300)",fontsize=16,color="green",shape="box"];130[label="vx300",fontsize=16,color="green",shape="box"];131[label="vx50",fontsize=16,color="green",shape="box"];132[label="primPlusNat Zero (Succ vx500)",fontsize=16,color="black",shape="box"];132 -> 158[label="",style="solid", color="black", weight=3];
133[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];133 -> 159[label="",style="solid", color="black", weight=3];
134[label="Neg (Succ vx500)",fontsize=16,color="green",shape="box"];135[label="Pos Zero",fontsize=16,color="green",shape="box"];136[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];136 -> 160[label="",style="dashed", color="green", weight=3];
137[label="vx300",fontsize=16,color="green",shape="box"];138[label="primPlusNat vx400 vx300",fontsize=16,color="burlywood",shape="triangle"];276[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];138 -> 276[label="",style="solid", color="burlywood", weight=9];
276 -> 161[label="",style="solid", color="burlywood", weight=3];
277[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 277[label="",style="solid", color="burlywood", weight=9];
277 -> 162[label="",style="solid", color="burlywood", weight=3];
139[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];139 -> 163[label="",style="dashed", color="green", weight=3];
140[label="Succ vx500",fontsize=16,color="green",shape="box"];141[label="vx400",fontsize=16,color="green",shape="box"];142[label="Succ vx500",fontsize=16,color="green",shape="box"];143[label="Succ vx500",fontsize=16,color="green",shape="box"];144[label="vx500",fontsize=16,color="green",shape="box"];145[label="Zero",fontsize=16,color="green",shape="box"];146[label="Succ (primPlusNat vx400 vx300)",fontsize=16,color="green",shape="box"];146 -> 164[label="",style="dashed", color="green", weight=3];
147[label="Zero",fontsize=16,color="green",shape="box"];148[label="vx400",fontsize=16,color="green",shape="box"];149[label="Zero",fontsize=16,color="green",shape="box"];150[label="Zero",fontsize=16,color="green",shape="box"];151[label="Zero",fontsize=16,color="green",shape="box"];152[label="Succ (Succ (primPlusNat vx400 vx500))",fontsize=16,color="green",shape="box"];152 -> 165[label="",style="dashed", color="green", weight=3];
153[label="Succ vx400",fontsize=16,color="green",shape="box"];154[label="primMinusNat (Succ vx4000) vx500",fontsize=16,color="burlywood",shape="box"];278[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];154 -> 278[label="",style="solid", color="burlywood", weight=9];
278 -> 166[label="",style="solid", color="burlywood", weight=3];
279[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];154 -> 279[label="",style="solid", color="burlywood", weight=9];
279 -> 167[label="",style="solid", color="burlywood", weight=3];
155[label="primMinusNat Zero vx500",fontsize=16,color="burlywood",shape="box"];280[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];155 -> 280[label="",style="solid", color="burlywood", weight=9];
280 -> 168[label="",style="solid", color="burlywood", weight=3];
281[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];155 -> 281[label="",style="solid", color="burlywood", weight=9];
281 -> 169[label="",style="solid", color="burlywood", weight=3];
156[label="vx500",fontsize=16,color="green",shape="box"];157[label="vx300",fontsize=16,color="green",shape="box"];158[label="Succ vx500",fontsize=16,color="green",shape="box"];159[label="Zero",fontsize=16,color="green",shape="box"];160 -> 138[label="",style="dashed", color="red", weight=0];
160[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];161[label="primPlusNat (Succ vx4000) vx300",fontsize=16,color="burlywood",shape="box"];283[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];161 -> 283[label="",style="solid", color="burlywood", weight=9];
283 -> 170[label="",style="solid", color="burlywood", weight=3];
284[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];161 -> 284[label="",style="solid", color="burlywood", weight=9];
284 -> 171[label="",style="solid", color="burlywood", weight=3];
162[label="primPlusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];285[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];162 -> 285[label="",style="solid", color="burlywood", weight=9];
285 -> 172[label="",style="solid", color="burlywood", weight=3];
286[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];162 -> 286[label="",style="solid", color="burlywood", weight=9];
286 -> 173[label="",style="solid", color="burlywood", weight=3];
163 -> 138[label="",style="dashed", color="red", weight=0];
163[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];163 -> 174[label="",style="dashed", color="magenta", weight=3];
163 -> 175[label="",style="dashed", color="magenta", weight=3];
164 -> 138[label="",style="dashed", color="red", weight=0];
164[label="primPlusNat vx400 vx300",fontsize=16,color="magenta"];164 -> 176[label="",style="dashed", color="magenta", weight=3];
164 -> 177[label="",style="dashed", color="magenta", weight=3];
165 -> 138[label="",style="dashed", color="red", weight=0];
165[label="primPlusNat vx400 vx500",fontsize=16,color="magenta"];165 -> 178[label="",style="dashed", color="magenta", weight=3];
166[label="primMinusNat (Succ vx4000) (Succ vx5000)",fontsize=16,color="black",shape="box"];166 -> 179[label="",style="solid", color="black", weight=3];
167[label="primMinusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];167 -> 180[label="",style="solid", color="black", weight=3];
168[label="primMinusNat Zero (Succ vx5000)",fontsize=16,color="black",shape="box"];168 -> 181[label="",style="solid", color="black", weight=3];
169[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];169 -> 182[label="",style="solid", color="black", weight=3];
170[label="primPlusNat (Succ vx4000) (Succ vx3000)",fontsize=16,color="black",shape="box"];170 -> 183[label="",style="solid", color="black", weight=3];
171[label="primPlusNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];171 -> 184[label="",style="solid", color="black", weight=3];
172[label="primPlusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];172 -> 185[label="",style="solid", color="black", weight=3];
173[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];173 -> 186[label="",style="solid", color="black", weight=3];
174[label="vx400",fontsize=16,color="green",shape="box"];175[label="vx300",fontsize=16,color="green",shape="box"];176[label="vx400",fontsize=16,color="green",shape="box"];177[label="vx300",fontsize=16,color="green",shape="box"];178[label="vx500",fontsize=16,color="green",shape="box"];179 -> 126[label="",style="dashed", color="red", weight=0];
179[label="primMinusNat vx4000 vx5000",fontsize=16,color="magenta"];179 -> 187[label="",style="dashed", color="magenta", weight=3];
179 -> 188[label="",style="dashed", color="magenta", weight=3];
180[label="Pos (Succ vx4000)",fontsize=16,color="green",shape="box"];181[label="Neg (Succ vx5000)",fontsize=16,color="green",shape="box"];182[label="Pos Zero",fontsize=16,color="green",shape="box"];183[label="Succ (Succ (primPlusNat vx4000 vx3000))",fontsize=16,color="green",shape="box"];183 -> 189[label="",style="dashed", color="green", weight=3];
184[label="Succ vx4000",fontsize=16,color="green",shape="box"];185[label="Succ vx3000",fontsize=16,color="green",shape="box"];186[label="Zero",fontsize=16,color="green",shape="box"];187[label="vx4000",fontsize=16,color="green",shape="box"];188[label="vx5000",fontsize=16,color="green",shape="box"];189 -> 138[label="",style="dashed", color="red", weight=0];
189[label="primPlusNat vx4000 vx3000",fontsize=16,color="magenta"];189 -> 190[label="",style="dashed", color="magenta", weight=3];
189 -> 191[label="",style="dashed", color="magenta", weight=3];
190[label="vx4000",fontsize=16,color="green",shape="box"];191[label="vx3000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

          ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_primMinusNat(Succ(vx4000), Succ(vx5000)) → new_primMinusNat(vx4000, vx5000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] 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_primMinusNat(Succ(vx4000), Succ(vx5000)) → new_primMinusNat(vx4000, vx5000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

          ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_primPlusNat(Succ(vx4000), Succ(vx3000)) → new_primPlusNat(vx4000, vx3000)

From the DPs we obtained the following set of size-change graphs:

new_primPlusNat(Succ(vx4000), Succ(vx3000)) → new_primPlusNat(vx4000, vx3000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

          ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_primPlusInt(Succ(vx400), Succ(vx300), vx5) → new_primPlusInt(vx400, vx300, vx5)

From the DPs we obtained the following set of size-change graphs:

new_primPlusInt(Succ(vx400), Succ(vx300), vx5) → new_primPlusInt(vx400, vx300, vx5)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ MNOCProof

          ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_iterate(vx4, vx3, vx5) → new_iterate(vx4, vx3, new_ps(vx4, vx3, vx5))

The TRS R consists of the following rules:

new_primMinusNat3(Succ(vx500)) → Neg(Succ(vx500))
new_primMinusNat0(vx400, Succ(vx500)) → new_primMinusNat1(vx400, vx500)
new_primMinusNat3(Zero) → Pos(Zero)
new_ps(Neg(vx40), Neg(vx30), vx5) → new_primPlusInt0(vx30, vx40, vx5)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusNat2(vx400, Zero) → Succ(vx400)
new_primPlusNat3(Succ(vx4000), Zero) → Succ(vx4000)
new_primPlusNat3(Zero, Succ(vx3000)) → Succ(vx3000)
new_primPlusNat0(Zero) → Zero
new_primPlusInt0(Zero, Succ(vx300), Pos(vx50)) → new_primMinusNat2(vx50, vx300)
new_primMinusNat0(vx400, Zero) → Pos(Succ(vx400))
new_primPlusNat3(Zero, Zero) → Zero
new_primMinusNat1(Succ(vx4000), Zero) → Pos(Succ(vx4000))
new_primMinusNat2(Zero, vx300) → Neg(Succ(vx300))
new_ps(Neg(Zero), Pos(Zero), Pos(Zero)) → new_primMinusNat3(Zero)
new_primPlusInt0(Succ(vx400), Succ(vx300), vx5) → new_primPlusInt0(vx400, vx300, vx5)
new_ps(Pos(Zero), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(vx300, vx50)
new_ps(Pos(Succ(vx400)), Neg(Zero), Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Zero)) → new_primMinusNat2(Zero, vx400)
new_primPlusNat2(vx400, Succ(vx500)) → Succ(Succ(new_primPlusNat3(vx400, vx500)))
new_ps(Pos(Zero), Neg(Zero), Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusInt0(Zero, Zero, Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Pos(Succ(vx400)), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_ps(Neg(Zero), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat0(vx500, Zero)
new_primMinusNat2(Succ(vx500), vx300) → new_primMinusNat1(vx500, vx300)
new_ps(Pos(vx40), Pos(vx30), vx5) → new_primPlusInt0(vx40, vx30, vx5)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx400)
new_primPlusInt0(Zero, Succ(vx300), Neg(vx50)) → Neg(new_primPlusNat2(vx300, vx50))
new_primPlusNat1(Succ(vx400), Succ(vx300), vx50) → new_primPlusNat2(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_primPlusNat1(Succ(vx400), Zero, vx50) → new_primPlusNat2(vx400, vx50)
new_primPlusNat1(Zero, Succ(vx300), vx50) → new_primPlusNat2(vx300, vx50)
new_primMinusNat1(Zero, Succ(vx5000)) → Neg(Succ(vx5000))
new_ps(Pos(vx40), Neg(vx30), Pos(vx50)) → Pos(new_primPlusNat1(vx40, vx30, vx50))
new_primPlusNat3(Succ(vx4000), Succ(vx3000)) → Succ(Succ(new_primPlusNat3(vx4000, vx3000)))
new_primPlusNat1(Zero, Zero, vx50) → new_primPlusNat0(vx50)
new_ps(Neg(vx40), Pos(vx30), Neg(vx50)) → Neg(new_primPlusNat1(vx40, vx30, vx50))
new_primMinusNat1(Succ(vx4000), Succ(vx5000)) → new_primMinusNat1(vx4000, vx5000)
new_primPlusNat0(Succ(vx500)) → Succ(vx500)
new_primPlusInt0(Succ(vx400), Zero, Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_primPlusInt0(Succ(vx400), Zero, Pos(vx50)) → Pos(new_primPlusNat2(vx400, vx50))
new_primMinusNat1(Zero, Zero) → Pos(Zero)
new_primPlusInt0(Zero, Zero, Pos(vx50)) → Pos(new_primPlusNat0(vx50))

The set Q consists of the following terms:

new_ps(Pos(x0), Neg(x1), Pos(x2))
new_primPlusInt0(Zero, Zero, Pos(x0))
new_primPlusNat0(Succ(x0))
new_primMinusNat2(Succ(x0), x1)
new_primMinusNat0(x0, Succ(x1))
new_primPlusNat2(x0, Succ(x1))
new_ps(Neg(Zero), Pos(Zero), Pos(Zero))
new_primPlusNat3(Succ(x0), Succ(x1))
new_primPlusInt0(Zero, Succ(x0), Pos(x1))
new_primPlusNat3(Succ(x0), Zero)
new_ps(Pos(Zero), Neg(Succ(x0)), Neg(x1))
new_primMinusNat1(Succ(x0), Succ(x1))
new_ps(Pos(Succ(x0)), Neg(Zero), Neg(x1))
new_ps(Pos(Succ(x0)), Neg(Succ(x1)), Neg(x2))
new_primMinusNat1(Succ(x0), Zero)
new_primPlusInt0(Succ(x0), Zero, Pos(x1))
new_ps(Neg(Zero), Pos(Succ(x0)), Pos(Zero))
new_primPlusNat3(Zero, Zero)
new_primPlusNat1(Zero, Zero, x0)
new_primMinusNat1(Zero, Succ(x0))
new_primMinusNat3(Succ(x0))
new_ps(Neg(Succ(x0)), Pos(Succ(x1)), Pos(Zero))
new_primPlusNat2(x0, Zero)
new_ps(Pos(x0), Pos(x1), x2)
new_ps(Neg(Succ(x0)), Pos(Zero), Pos(Succ(x1)))
new_ps(Neg(Zero), Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0), x1)
new_primPlusNat3(Zero, Succ(x0))
new_ps(Neg(x0), Pos(x1), Neg(x2))
new_primPlusInt0(Zero, Succ(x0), Neg(x1))
new_ps(Neg(Succ(x0)), Pos(Succ(x1)), Pos(Succ(x2)))
new_ps(Neg(x0), Neg(x1), x2)
new_primPlusInt0(Zero, Zero, Neg(x0))
new_primMinusNat0(x0, Zero)
new_primPlusNat1(Succ(x0), Zero, x1)
new_ps(Neg(Zero), Pos(Zero), Pos(Succ(x0)))
new_ps(Neg(Succ(x0)), Pos(Zero), Pos(Zero))
new_primPlusInt0(Succ(x0), Zero, Neg(x1))
new_primMinusNat3(Zero)
new_primPlusNat1(Succ(x0), Succ(x1), x2)
new_primPlusNat0(Zero)
new_primMinusNat2(Zero, x0)
new_primPlusInt0(Succ(x0), Succ(x1), x2)
new_primMinusNat1(Zero, Zero)
new_ps(Pos(Zero), Neg(Zero), Neg(x0))

We have to consider all minimal (P,Q,R)-chains.
We use the modular non-overlap check [17] to decrease Q to the empty set.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ MNOCProof

                  ↳ QDP

                    ↳ NonTerminationProof

          ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_iterate(vx4, vx3, vx5) → new_iterate(vx4, vx3, new_ps(vx4, vx3, vx5))

The TRS R consists of the following rules:

new_primMinusNat3(Succ(vx500)) → Neg(Succ(vx500))
new_primMinusNat0(vx400, Succ(vx500)) → new_primMinusNat1(vx400, vx500)
new_primMinusNat3(Zero) → Pos(Zero)
new_ps(Neg(vx40), Neg(vx30), vx5) → new_primPlusInt0(vx30, vx40, vx5)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusNat2(vx400, Zero) → Succ(vx400)
new_primPlusNat3(Succ(vx4000), Zero) → Succ(vx4000)
new_primPlusNat3(Zero, Succ(vx3000)) → Succ(vx3000)
new_primPlusNat0(Zero) → Zero
new_primPlusInt0(Zero, Succ(vx300), Pos(vx50)) → new_primMinusNat2(vx50, vx300)
new_primMinusNat0(vx400, Zero) → Pos(Succ(vx400))
new_primPlusNat3(Zero, Zero) → Zero
new_primMinusNat1(Succ(vx4000), Zero) → Pos(Succ(vx4000))
new_primMinusNat2(Zero, vx300) → Neg(Succ(vx300))
new_ps(Neg(Zero), Pos(Zero), Pos(Zero)) → new_primMinusNat3(Zero)
new_primPlusInt0(Succ(vx400), Succ(vx300), vx5) → new_primPlusInt0(vx400, vx300, vx5)
new_ps(Pos(Zero), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(vx300, vx50)
new_ps(Pos(Succ(vx400)), Neg(Zero), Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Zero)) → new_primMinusNat2(Zero, vx400)
new_primPlusNat2(vx400, Succ(vx500)) → Succ(Succ(new_primPlusNat3(vx400, vx500)))
new_ps(Pos(Zero), Neg(Zero), Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusInt0(Zero, Zero, Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Pos(Succ(vx400)), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_ps(Neg(Zero), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat0(vx500, Zero)
new_primMinusNat2(Succ(vx500), vx300) → new_primMinusNat1(vx500, vx300)
new_ps(Pos(vx40), Pos(vx30), vx5) → new_primPlusInt0(vx40, vx30, vx5)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx400)
new_primPlusInt0(Zero, Succ(vx300), Neg(vx50)) → Neg(new_primPlusNat2(vx300, vx50))
new_primPlusNat1(Succ(vx400), Succ(vx300), vx50) → new_primPlusNat2(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_primPlusNat1(Succ(vx400), Zero, vx50) → new_primPlusNat2(vx400, vx50)
new_primPlusNat1(Zero, Succ(vx300), vx50) → new_primPlusNat2(vx300, vx50)
new_primMinusNat1(Zero, Succ(vx5000)) → Neg(Succ(vx5000))
new_ps(Pos(vx40), Neg(vx30), Pos(vx50)) → Pos(new_primPlusNat1(vx40, vx30, vx50))
new_primPlusNat3(Succ(vx4000), Succ(vx3000)) → Succ(Succ(new_primPlusNat3(vx4000, vx3000)))
new_primPlusNat1(Zero, Zero, vx50) → new_primPlusNat0(vx50)
new_ps(Neg(vx40), Pos(vx30), Neg(vx50)) → Neg(new_primPlusNat1(vx40, vx30, vx50))
new_primMinusNat1(Succ(vx4000), Succ(vx5000)) → new_primMinusNat1(vx4000, vx5000)
new_primPlusNat0(Succ(vx500)) → Succ(vx500)
new_primPlusInt0(Succ(vx400), Zero, Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_primPlusInt0(Succ(vx400), Zero, Pos(vx50)) → Pos(new_primPlusNat2(vx400, vx50))
new_primMinusNat1(Zero, Zero) → Pos(Zero)
new_primPlusInt0(Zero, Zero, Pos(vx50)) → Pos(new_primPlusNat0(vx50))

Q is empty.
We have to consider all (P,Q,R)-chains.
We used the non-termination processor [17] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

The TRS P consists of the following rules:

new_iterate(vx4, vx3, vx5) → new_iterate(vx4, vx3, new_ps(vx4, vx3, vx5))

The TRS R consists of the following rules:

new_primMinusNat3(Succ(vx500)) → Neg(Succ(vx500))
new_primMinusNat0(vx400, Succ(vx500)) → new_primMinusNat1(vx400, vx500)
new_primMinusNat3(Zero) → Pos(Zero)
new_ps(Neg(vx40), Neg(vx30), vx5) → new_primPlusInt0(vx30, vx40, vx5)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusNat2(vx400, Zero) → Succ(vx400)
new_primPlusNat3(Succ(vx4000), Zero) → Succ(vx4000)
new_primPlusNat3(Zero, Succ(vx3000)) → Succ(vx3000)
new_primPlusNat0(Zero) → Zero
new_primPlusInt0(Zero, Succ(vx300), Pos(vx50)) → new_primMinusNat2(vx50, vx300)
new_primMinusNat0(vx400, Zero) → Pos(Succ(vx400))
new_primPlusNat3(Zero, Zero) → Zero
new_primMinusNat1(Succ(vx4000), Zero) → Pos(Succ(vx4000))
new_primMinusNat2(Zero, vx300) → Neg(Succ(vx300))
new_ps(Neg(Zero), Pos(Zero), Pos(Zero)) → new_primMinusNat3(Zero)
new_primPlusInt0(Succ(vx400), Succ(vx300), vx5) → new_primPlusInt0(vx400, vx300, vx5)
new_ps(Pos(Zero), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(vx300, vx50)
new_ps(Pos(Succ(vx400)), Neg(Zero), Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Zero)) → new_primMinusNat2(Zero, vx400)
new_primPlusNat2(vx400, Succ(vx500)) → Succ(Succ(new_primPlusNat3(vx400, vx500)))
new_ps(Pos(Zero), Neg(Zero), Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Neg(Succ(vx400)), Pos(Succ(vx300)), Pos(Zero)) → new_primMinusNat2(Zero, Succ(new_primPlusNat3(vx400, vx300)))
new_primPlusInt0(Zero, Zero, Neg(vx50)) → new_primMinusNat3(vx50)
new_ps(Pos(Succ(vx400)), Neg(Succ(vx300)), Neg(vx50)) → new_primMinusNat0(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_ps(Neg(Zero), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat0(vx500, Zero)
new_primMinusNat2(Succ(vx500), vx300) → new_primMinusNat1(vx500, vx300)
new_ps(Pos(vx40), Pos(vx30), vx5) → new_primPlusInt0(vx40, vx30, vx5)
new_ps(Neg(Zero), Pos(Succ(vx300)), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx300)
new_ps(Neg(Succ(vx400)), Pos(Zero), Pos(Succ(vx500))) → new_primMinusNat2(Succ(vx500), vx400)
new_primPlusInt0(Zero, Succ(vx300), Neg(vx50)) → Neg(new_primPlusNat2(vx300, vx50))
new_primPlusNat1(Succ(vx400), Succ(vx300), vx50) → new_primPlusNat2(Succ(new_primPlusNat3(vx400, vx300)), vx50)
new_primPlusNat1(Succ(vx400), Zero, vx50) → new_primPlusNat2(vx400, vx50)
new_primPlusNat1(Zero, Succ(vx300), vx50) → new_primPlusNat2(vx300, vx50)
new_primMinusNat1(Zero, Succ(vx5000)) → Neg(Succ(vx5000))
new_ps(Pos(vx40), Neg(vx30), Pos(vx50)) → Pos(new_primPlusNat1(vx40, vx30, vx50))
new_primPlusNat3(Succ(vx4000), Succ(vx3000)) → Succ(Succ(new_primPlusNat3(vx4000, vx3000)))
new_primPlusNat1(Zero, Zero, vx50) → new_primPlusNat0(vx50)
new_ps(Neg(vx40), Pos(vx30), Neg(vx50)) → Neg(new_primPlusNat1(vx40, vx30, vx50))
new_primMinusNat1(Succ(vx4000), Succ(vx5000)) → new_primMinusNat1(vx4000, vx5000)
new_primPlusNat0(Succ(vx500)) → Succ(vx500)
new_primPlusInt0(Succ(vx400), Zero, Neg(vx50)) → new_primMinusNat0(vx400, vx50)
new_primPlusInt0(Succ(vx400), Zero, Pos(vx50)) → Pos(new_primPlusNat2(vx400, vx50))
new_primMinusNat1(Zero, Zero) → Pos(Zero)
new_primPlusInt0(Zero, Zero, Pos(vx50)) → Pos(new_primPlusNat0(vx50))

s = new_iterate(vx4, vx3, vx5) evaluates to t =new_iterate(vx4, vx3, new_ps(vx4, vx3, vx5))

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [vx5 / new_ps(vx4, vx3, vx5)]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from new_iterate(vx4, vx3, vx5) to new_iterate(vx4, vx3, new_ps(vx4, vx3, vx5)).

Haskell To QDPs