8.53/3.63 YES 10.22/4.12 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 10.22/4.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.22/4.12 10.22/4.12 10.22/4.12 H-Termination with start terms of the given HASKELL could be proven: 10.22/4.12 10.22/4.12 (0) HASKELL 10.22/4.12 (1) BR [EQUIVALENT, 0 ms] 10.22/4.12 (2) HASKELL 10.22/4.12 (3) COR [EQUIVALENT, 0 ms] 10.22/4.12 (4) HASKELL 10.22/4.12 (5) LetRed [EQUIVALENT, 0 ms] 10.22/4.12 (6) HASKELL 10.22/4.12 (7) Narrow [SOUND, 0 ms] 10.22/4.12 (8) AND 10.22/4.12 (9) QDP 10.22/4.12 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.22/4.12 (11) YES 10.22/4.12 (12) QDP 10.22/4.12 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.22/4.12 (14) YES 10.22/4.12 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (0) 10.22/4.12 Obligation: 10.22/4.12 mainModule Main 10.22/4.12 module Main where { 10.22/4.12 import qualified Prelude; 10.22/4.12 } 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (1) BR (EQUIVALENT) 10.22/4.12 Replaced joker patterns by fresh variables and removed binding patterns. 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (2) 10.22/4.12 Obligation: 10.22/4.12 mainModule Main 10.22/4.12 module Main where { 10.22/4.12 import qualified Prelude; 10.22/4.12 } 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (3) COR (EQUIVALENT) 10.22/4.12 Cond Reductions: 10.22/4.12 The following Function with conditions 10.22/4.12 "undefined |Falseundefined; 10.22/4.12 " 10.22/4.12 is transformed to 10.22/4.12 "undefined = undefined1; 10.22/4.12 " 10.22/4.12 "undefined0 True = undefined; 10.22/4.12 " 10.22/4.12 "undefined1 = undefined0 False; 10.22/4.12 " 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (4) 10.22/4.12 Obligation: 10.22/4.12 mainModule Main 10.22/4.12 module Main where { 10.22/4.12 import qualified Prelude; 10.22/4.12 } 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (5) LetRed (EQUIVALENT) 10.22/4.12 Let/Where Reductions: 10.22/4.12 The bindings of the following Let/Where expression 10.22/4.12 "fromEnum c <= i && i <= fromEnum c' where { 10.22/4.12 i = fromEnum ci; 10.22/4.12 } 10.22/4.12 " 10.22/4.12 are unpacked to the following functions on top level 10.22/4.12 "inRangeI vx = fromEnum vx; 10.22/4.12 " 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (6) 10.22/4.12 Obligation: 10.22/4.12 mainModule Main 10.22/4.12 module Main where { 10.22/4.12 import qualified Prelude; 10.22/4.12 } 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (7) Narrow (SOUND) 10.22/4.12 Haskell To QDPs 10.22/4.12 10.22/4.12 digraph dp_graph { 10.22/4.12 node [outthreshold=100, inthreshold=100];1[label="inRange",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.22/4.12 3[label="inRange vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 10.22/4.12 4[label="inRange vy3 vy4",fontsize=16,color="burlywood",shape="triangle"];157[label="vy3/(vy30,vy31)",fontsize=10,color="white",style="solid",shape="box"];4 -> 157[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 157 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 5[label="inRange (vy30,vy31) vy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 10.22/4.12 6[label="fromEnum vy30 <= inRangeI vy4 && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 10.22/4.12 7[label="compare (fromEnum vy30) (inRangeI vy4) /= GT && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 10.22/4.12 8[label="not (compare (fromEnum vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 10.22/4.12 9[label="not (primCmpInt (fromEnum vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10.22/4.12 10[label="not (primCmpInt (primCharToInt vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];158[label="vy30/Char vy300",fontsize=10,color="white",style="solid",shape="box"];10 -> 158[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 158 -> 11[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 11[label="not (primCmpInt (primCharToInt (Char vy300)) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 10.22/4.12 12[label="not (primCmpInt (Pos vy300) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];159[label="vy300/Succ vy3000",fontsize=10,color="white",style="solid",shape="box"];12 -> 159[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 159 -> 13[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 160[label="vy300/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 160[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 160 -> 14[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 13[label="not (primCmpInt (Pos (Succ vy3000)) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 10.22/4.12 14[label="not (primCmpInt (Pos Zero) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 10.22/4.12 15[label="not (primCmpInt (Pos (Succ vy3000)) (fromEnum vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 10.22/4.12 16[label="not (primCmpInt (Pos Zero) (fromEnum vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 10.22/4.12 17[label="not (primCmpInt (Pos (Succ vy3000)) (primCharToInt vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];161[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];17 -> 161[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 161 -> 19[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 18[label="not (primCmpInt (Pos Zero) (primCharToInt vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];162[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];18 -> 162[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 162 -> 20[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 19[label="not (primCmpInt (Pos (Succ vy3000)) (primCharToInt (Char vy40)) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 10.22/4.12 20[label="not (primCmpInt (Pos Zero) (primCharToInt (Char vy40)) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 10.22/4.12 21[label="not (primCmpInt (Pos (Succ vy3000)) (Pos vy40) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 10.22/4.12 22[label="not (primCmpInt (Pos Zero) (Pos vy40) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];163[label="vy40/Succ vy400",fontsize=10,color="white",style="solid",shape="box"];22 -> 163[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 163 -> 24[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 164[label="vy40/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 164[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 164 -> 25[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 23 -> 79[label="",style="dashed", color="red", weight=0]; 10.22/4.12 23[label="not (primCmpNat (Succ vy3000) vy40 == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="magenta"];23 -> 80[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 23 -> 81[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 23 -> 82[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 24[label="not (primCmpInt (Pos Zero) (Pos (Succ vy400)) == GT) && inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 10.22/4.12 25[label="not (primCmpInt (Pos Zero) (Pos Zero) == GT) && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 10.22/4.12 80[label="inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="triangle"];80 -> 93[label="",style="solid", color="black", weight=3]; 10.22/4.12 81[label="Succ vy3000",fontsize=16,color="green",shape="box"];82[label="vy40",fontsize=16,color="green",shape="box"];79[label="not (primCmpNat vy300000 vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="triangle"];165[label="vy300000/Succ vy3000000",fontsize=10,color="white",style="solid",shape="box"];79 -> 165[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 165 -> 94[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 166[label="vy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 166[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 166 -> 95[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 28 -> 79[label="",style="dashed", color="red", weight=0]; 10.22/4.12 28[label="not (primCmpNat Zero (Succ vy400) == GT) && inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="magenta"];28 -> 83[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 28 -> 84[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 28 -> 85[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 29[label="not (EQ == GT) && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 10.22/4.12 93[label="compare (inRangeI (Char vy40)) (fromEnum vy31) /= GT",fontsize=16,color="black",shape="box"];93 -> 98[label="",style="solid", color="black", weight=3]; 10.22/4.12 94[label="not (primCmpNat (Succ vy3000000) vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="box"];167[label="vy40000/Succ vy400000",fontsize=10,color="white",style="solid",shape="box"];94 -> 167[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 167 -> 99[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 168[label="vy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 168[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 168 -> 100[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 95[label="not (primCmpNat Zero vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="box"];169[label="vy40000/Succ vy400000",fontsize=10,color="white",style="solid",shape="box"];95 -> 169[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 169 -> 101[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 170[label="vy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];95 -> 170[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 170 -> 102[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 83 -> 80[label="",style="dashed", color="red", weight=0]; 10.22/4.12 83[label="inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="magenta"];83 -> 96[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 84[label="Zero",fontsize=16,color="green",shape="box"];85[label="Succ vy400",fontsize=16,color="green",shape="box"];33[label="not False && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];33 -> 38[label="",style="solid", color="black", weight=3]; 10.22/4.12 98[label="not (compare (inRangeI (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];98 -> 104[label="",style="solid", color="black", weight=3]; 10.22/4.12 99[label="not (primCmpNat (Succ vy3000000) (Succ vy400000) == GT) && vy6",fontsize=16,color="black",shape="box"];99 -> 105[label="",style="solid", color="black", weight=3]; 10.22/4.12 100[label="not (primCmpNat (Succ vy3000000) Zero == GT) && vy6",fontsize=16,color="black",shape="box"];100 -> 106[label="",style="solid", color="black", weight=3]; 10.22/4.12 101[label="not (primCmpNat Zero (Succ vy400000) == GT) && vy6",fontsize=16,color="black",shape="box"];101 -> 107[label="",style="solid", color="black", weight=3]; 10.22/4.12 102[label="not (primCmpNat Zero Zero == GT) && vy6",fontsize=16,color="black",shape="box"];102 -> 108[label="",style="solid", color="black", weight=3]; 10.22/4.12 96[label="Succ vy400",fontsize=16,color="green",shape="box"];38[label="True && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3]; 10.22/4.12 104[label="not (primCmpInt (inRangeI (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];104 -> 110[label="",style="solid", color="black", weight=3]; 10.22/4.12 105 -> 79[label="",style="dashed", color="red", weight=0]; 10.22/4.12 105[label="not (primCmpNat vy3000000 vy400000 == GT) && vy6",fontsize=16,color="magenta"];105 -> 111[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 105 -> 112[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 106[label="not (GT == GT) && vy6",fontsize=16,color="black",shape="box"];106 -> 113[label="",style="solid", color="black", weight=3]; 10.22/4.12 107[label="not (LT == GT) && vy6",fontsize=16,color="black",shape="box"];107 -> 114[label="",style="solid", color="black", weight=3]; 10.22/4.12 108[label="not (EQ == GT) && vy6",fontsize=16,color="black",shape="box"];108 -> 115[label="",style="solid", color="black", weight=3]; 10.22/4.12 45[label="inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="triangle"];45 -> 52[label="",style="solid", color="black", weight=3]; 10.22/4.12 110[label="not (primCmpInt (fromEnum (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];110 -> 117[label="",style="solid", color="black", weight=3]; 10.22/4.12 111[label="vy3000000",fontsize=16,color="green",shape="box"];112[label="vy400000",fontsize=16,color="green",shape="box"];113[label="not True && vy6",fontsize=16,color="black",shape="box"];113 -> 118[label="",style="solid", color="black", weight=3]; 10.22/4.12 114[label="not False && vy6",fontsize=16,color="black",shape="triangle"];114 -> 119[label="",style="solid", color="black", weight=3]; 10.22/4.12 115 -> 114[label="",style="dashed", color="red", weight=0]; 10.22/4.12 115[label="not False && vy6",fontsize=16,color="magenta"];52[label="compare (inRangeI (Char Zero)) (fromEnum vy31) /= GT",fontsize=16,color="black",shape="box"];52 -> 59[label="",style="solid", color="black", weight=3]; 10.22/4.12 117[label="not (primCmpInt (primCharToInt (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];117 -> 121[label="",style="solid", color="black", weight=3]; 10.22/4.12 118[label="False && vy6",fontsize=16,color="black",shape="box"];118 -> 122[label="",style="solid", color="black", weight=3]; 10.22/4.12 119[label="True && vy6",fontsize=16,color="black",shape="box"];119 -> 123[label="",style="solid", color="black", weight=3]; 10.22/4.12 59[label="not (compare (inRangeI (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];59 -> 70[label="",style="solid", color="black", weight=3]; 10.22/4.12 121[label="not (primCmpInt (Pos vy40) (fromEnum vy31) == GT)",fontsize=16,color="burlywood",shape="box"];171[label="vy40/Succ vy400",fontsize=10,color="white",style="solid",shape="box"];121 -> 171[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 171 -> 126[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 172[label="vy40/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 172[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 172 -> 127[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 122[label="False",fontsize=16,color="green",shape="box"];123[label="vy6",fontsize=16,color="green",shape="box"];70[label="not (primCmpInt (inRangeI (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];70 -> 78[label="",style="solid", color="black", weight=3]; 10.22/4.12 126[label="not (primCmpInt (Pos (Succ vy400)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3]; 10.22/4.12 127[label="not (primCmpInt (Pos Zero) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3]; 10.22/4.12 78[label="not (primCmpInt (fromEnum (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];78 -> 97[label="",style="solid", color="black", weight=3]; 10.22/4.12 130[label="not (primCmpInt (Pos (Succ vy400)) (primCharToInt vy31) == GT)",fontsize=16,color="burlywood",shape="box"];173[label="vy31/Char vy310",fontsize=10,color="white",style="solid",shape="box"];130 -> 173[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 173 -> 134[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 131 -> 109[label="",style="dashed", color="red", weight=0]; 10.22/4.12 131[label="not (primCmpInt (Pos Zero) (primCharToInt vy31) == GT)",fontsize=16,color="magenta"];97[label="not (primCmpInt (primCharToInt (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];97 -> 103[label="",style="solid", color="black", weight=3]; 10.22/4.12 134[label="not (primCmpInt (Pos (Succ vy400)) (primCharToInt (Char vy310)) == GT)",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3]; 10.22/4.12 109[label="not (primCmpInt (Pos Zero) (primCharToInt vy31) == GT)",fontsize=16,color="burlywood",shape="triangle"];174[label="vy31/Char vy310",fontsize=10,color="white",style="solid",shape="box"];109 -> 174[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 174 -> 116[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 103[label="not (primCmpInt (Pos Zero) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];103 -> 109[label="",style="solid", color="black", weight=3]; 10.22/4.12 137[label="not (primCmpInt (Pos (Succ vy400)) (Pos vy310) == GT)",fontsize=16,color="black",shape="box"];137 -> 138[label="",style="solid", color="black", weight=3]; 10.22/4.12 116[label="not (primCmpInt (Pos Zero) (primCharToInt (Char vy310)) == GT)",fontsize=16,color="black",shape="box"];116 -> 120[label="",style="solid", color="black", weight=3]; 10.22/4.12 138[label="not (primCmpNat (Succ vy400) vy310 == GT)",fontsize=16,color="burlywood",shape="box"];175[label="vy310/Succ vy3100",fontsize=10,color="white",style="solid",shape="box"];138 -> 175[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 175 -> 139[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 176[label="vy310/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 176[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 176 -> 140[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 120[label="not (primCmpInt (Pos Zero) (Pos vy310) == GT)",fontsize=16,color="burlywood",shape="box"];177[label="vy310/Succ vy3100",fontsize=10,color="white",style="solid",shape="box"];120 -> 177[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 177 -> 124[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 178[label="vy310/Zero",fontsize=10,color="white",style="solid",shape="box"];120 -> 178[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 178 -> 125[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 139[label="not (primCmpNat (Succ vy400) (Succ vy3100) == GT)",fontsize=16,color="black",shape="box"];139 -> 141[label="",style="solid", color="black", weight=3]; 10.22/4.12 140[label="not (primCmpNat (Succ vy400) Zero == GT)",fontsize=16,color="black",shape="box"];140 -> 142[label="",style="solid", color="black", weight=3]; 10.22/4.12 124[label="not (primCmpInt (Pos Zero) (Pos (Succ vy3100)) == GT)",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3]; 10.22/4.12 125[label="not (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3]; 10.22/4.12 141[label="not (primCmpNat vy400 vy3100 == GT)",fontsize=16,color="burlywood",shape="triangle"];179[label="vy400/Succ vy4000",fontsize=10,color="white",style="solid",shape="box"];141 -> 179[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 179 -> 143[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 180[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 180[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 180 -> 144[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 142[label="not (GT == GT)",fontsize=16,color="black",shape="triangle"];142 -> 145[label="",style="solid", color="black", weight=3]; 10.22/4.12 128[label="not (primCmpNat Zero (Succ vy3100) == GT)",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3]; 10.22/4.12 129[label="not (EQ == GT)",fontsize=16,color="black",shape="triangle"];129 -> 133[label="",style="solid", color="black", weight=3]; 10.22/4.12 143[label="not (primCmpNat (Succ vy4000) vy3100 == GT)",fontsize=16,color="burlywood",shape="box"];181[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];143 -> 181[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 181 -> 146[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 182[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];143 -> 182[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 182 -> 147[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 144[label="not (primCmpNat Zero vy3100 == GT)",fontsize=16,color="burlywood",shape="box"];183[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];144 -> 183[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 183 -> 148[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 184[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];144 -> 184[label="",style="solid", color="burlywood", weight=9]; 10.22/4.12 184 -> 149[label="",style="solid", color="burlywood", weight=3]; 10.22/4.12 145[label="not True",fontsize=16,color="black",shape="box"];145 -> 150[label="",style="solid", color="black", weight=3]; 10.22/4.12 132[label="not (LT == GT)",fontsize=16,color="black",shape="triangle"];132 -> 135[label="",style="solid", color="black", weight=3]; 10.22/4.12 133[label="not False",fontsize=16,color="black",shape="triangle"];133 -> 136[label="",style="solid", color="black", weight=3]; 10.22/4.12 146[label="not (primCmpNat (Succ vy4000) (Succ vy31000) == GT)",fontsize=16,color="black",shape="box"];146 -> 151[label="",style="solid", color="black", weight=3]; 10.22/4.12 147[label="not (primCmpNat (Succ vy4000) Zero == GT)",fontsize=16,color="black",shape="box"];147 -> 152[label="",style="solid", color="black", weight=3]; 10.22/4.12 148[label="not (primCmpNat Zero (Succ vy31000) == GT)",fontsize=16,color="black",shape="box"];148 -> 153[label="",style="solid", color="black", weight=3]; 10.22/4.12 149[label="not (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];149 -> 154[label="",style="solid", color="black", weight=3]; 10.22/4.12 150[label="False",fontsize=16,color="green",shape="box"];135 -> 133[label="",style="dashed", color="red", weight=0]; 10.22/4.12 135[label="not False",fontsize=16,color="magenta"];136[label="True",fontsize=16,color="green",shape="box"];151 -> 141[label="",style="dashed", color="red", weight=0]; 10.22/4.12 151[label="not (primCmpNat vy4000 vy31000 == GT)",fontsize=16,color="magenta"];151 -> 155[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 151 -> 156[label="",style="dashed", color="magenta", weight=3]; 10.22/4.12 152 -> 142[label="",style="dashed", color="red", weight=0]; 10.22/4.12 152[label="not (GT == GT)",fontsize=16,color="magenta"];153 -> 132[label="",style="dashed", color="red", weight=0]; 10.22/4.12 153[label="not (LT == GT)",fontsize=16,color="magenta"];154 -> 129[label="",style="dashed", color="red", weight=0]; 10.22/4.12 154[label="not (EQ == GT)",fontsize=16,color="magenta"];155[label="vy4000",fontsize=16,color="green",shape="box"];156[label="vy31000",fontsize=16,color="green",shape="box"];} 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (8) 10.22/4.12 Complex Obligation (AND) 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (9) 10.22/4.12 Obligation: 10.22/4.12 Q DP problem: 10.22/4.12 The TRS P consists of the following rules: 10.22/4.12 10.22/4.12 new_not(Succ(vy4000), Succ(vy31000)) -> new_not(vy4000, vy31000) 10.22/4.12 10.22/4.12 R is empty. 10.22/4.12 Q is empty. 10.22/4.12 We have to consider all minimal (P,Q,R)-chains. 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (10) QDPSizeChangeProof (EQUIVALENT) 10.22/4.12 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 10.22/4.12 10.22/4.12 From the DPs we obtained the following set of size-change graphs: 10.22/4.12 *new_not(Succ(vy4000), Succ(vy31000)) -> new_not(vy4000, vy31000) 10.22/4.12 The graph contains the following edges 1 > 1, 2 > 2 10.22/4.12 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (11) 10.22/4.12 YES 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (12) 10.22/4.12 Obligation: 10.22/4.12 Q DP problem: 10.22/4.12 The TRS P consists of the following rules: 10.22/4.12 10.22/4.12 new_asAs(Succ(vy3000000), Succ(vy400000), vy6) -> new_asAs(vy3000000, vy400000, vy6) 10.22/4.12 10.22/4.12 R is empty. 10.22/4.12 Q is empty. 10.22/4.12 We have to consider all minimal (P,Q,R)-chains. 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (13) QDPSizeChangeProof (EQUIVALENT) 10.22/4.12 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 10.22/4.12 10.22/4.12 From the DPs we obtained the following set of size-change graphs: 10.22/4.12 *new_asAs(Succ(vy3000000), Succ(vy400000), vy6) -> new_asAs(vy3000000, vy400000, vy6) 10.22/4.12 The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 10.22/4.12 10.22/4.12 10.22/4.12 ---------------------------------------- 10.22/4.12 10.22/4.12 (14) 10.22/4.12 YES 10.50/4.18 EOF