8.17/3.64 YES 9.92/4.13 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.92/4.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.92/4.13 9.92/4.13 9.92/4.13 H-Termination with start terms of the given HASKELL could be proven: 9.92/4.13 9.92/4.13 (0) HASKELL 9.92/4.13 (1) BR [EQUIVALENT, 0 ms] 9.92/4.13 (2) HASKELL 9.92/4.13 (3) COR [EQUIVALENT, 0 ms] 9.92/4.13 (4) HASKELL 9.92/4.13 (5) NumRed [SOUND, 2 ms] 9.92/4.13 (6) HASKELL 9.92/4.13 (7) Narrow [SOUND, 0 ms] 9.92/4.13 (8) AND 9.92/4.13 (9) QDP 9.92/4.13 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.92/4.13 (11) YES 9.92/4.13 (12) QDP 9.92/4.13 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.92/4.13 (14) YES 9.92/4.13 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (0) 9.92/4.13 Obligation: 9.92/4.13 mainModule Main 9.92/4.13 module Main where { 9.92/4.13 import qualified Prelude; 9.92/4.13 } 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (1) BR (EQUIVALENT) 9.92/4.13 Replaced joker patterns by fresh variables and removed binding patterns. 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (2) 9.92/4.13 Obligation: 9.92/4.13 mainModule Main 9.92/4.13 module Main where { 9.92/4.13 import qualified Prelude; 9.92/4.13 } 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (3) COR (EQUIVALENT) 9.92/4.13 Cond Reductions: 9.92/4.13 The following Function with conditions 9.92/4.13 "undefined |Falseundefined; 9.92/4.13 " 9.92/4.13 is transformed to 9.92/4.13 "undefined = undefined1; 9.92/4.13 " 9.92/4.13 "undefined0 True = undefined; 9.92/4.13 " 9.92/4.13 "undefined1 = undefined0 False; 9.92/4.13 " 9.92/4.13 The following Function with conditions 9.92/4.13 "signumReal x|x == 00|x > 01|otherwise-1; 9.92/4.13 " 9.92/4.13 is transformed to 9.92/4.13 "signumReal x = signumReal3 x; 9.92/4.13 " 9.92/4.13 "signumReal2 x True = 0; 9.92/4.13 signumReal2 x False = signumReal1 x (x > 0); 9.92/4.13 " 9.92/4.13 "signumReal0 x True = -1; 9.92/4.13 " 9.92/4.13 "signumReal1 x True = 1; 9.92/4.13 signumReal1 x False = signumReal0 x otherwise; 9.92/4.13 " 9.92/4.13 "signumReal3 x = signumReal2 x (x == 0); 9.92/4.13 " 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (4) 9.92/4.13 Obligation: 9.92/4.13 mainModule Main 9.92/4.13 module Main where { 9.92/4.13 import qualified Prelude; 9.92/4.13 } 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (5) NumRed (SOUND) 9.92/4.13 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (6) 9.92/4.13 Obligation: 9.92/4.13 mainModule Main 9.92/4.13 module Main where { 9.92/4.13 import qualified Prelude; 9.92/4.13 } 9.92/4.13 9.92/4.13 ---------------------------------------- 9.92/4.13 9.92/4.13 (7) Narrow (SOUND) 9.92/4.13 Haskell To QDPs 9.92/4.13 9.92/4.13 digraph dp_graph { 9.92/4.13 node [outthreshold=100, inthreshold=100];1[label="signum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.92/4.13 3[label="signum vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.92/4.13 4[label="signumReal vz3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.92/4.13 5[label="signumReal3 vz3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.92/4.13 6[label="signumReal2 vz3 (vz3 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.92/4.13 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]; 9.92/4.13 359 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 360[label="vz3/Neg vz30",fontsize=10,color="white",style="solid",shape="box"];7 -> 360[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 360 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 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]; 9.92/4.13 361 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 362[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 362[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 362 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 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]; 9.92/4.13 363 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 364[label="vz30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 364[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 364 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 18[label="signumReal2 (Pos (Succ vz300)) False",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 9.92/4.13 19[label="signumReal2 (Pos Zero) True",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 9.92/4.13 20[label="signumReal2 (Neg (Succ vz300)) False",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 9.92/4.13 21[label="signumReal2 (Neg Zero) True",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 9.92/4.13 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]; 9.92/4.13 23[label="fromInt (Pos Zero)",fontsize=16,color="black",shape="triangle"];23 -> 27[label="",style="solid", color="black", weight=3]; 9.92/4.13 24 -> 28[label="",style="dashed", color="red", weight=0]; 9.92/4.13 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]; 9.92/4.13 25 -> 23[label="",style="dashed", color="red", weight=0]; 9.92/4.13 25[label="fromInt (Pos Zero)",fontsize=16,color="magenta"];26 -> 30[label="",style="dashed", color="red", weight=0]; 9.92/4.13 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]; 9.92/4.13 27[label="Pos Zero",fontsize=16,color="green",shape="box"];29 -> 23[label="",style="dashed", color="red", weight=0]; 9.92/4.13 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]; 9.92/4.13 31 -> 23[label="",style="dashed", color="red", weight=0]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 365 -> 35[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 366[label="vz5/Neg vz50",fontsize=10,color="white",style="solid",shape="box"];33 -> 366[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 366 -> 36[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 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]; 9.92/4.13 367 -> 37[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 368[label="vz4/Neg vz40",fontsize=10,color="white",style="solid",shape="box"];34 -> 368[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 368 -> 38[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 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]; 9.92/4.13 39 -> 202[label="",style="dashed", color="red", weight=0]; 9.92/4.13 39[label="signumReal1 (Pos (Succ vz300)) (primCmpNat (Succ vz300) vz50 == GT)",fontsize=16,color="magenta"];39 -> 203[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 39 -> 204[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 39 -> 205[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 40[label="signumReal1 (Pos (Succ vz300)) (GT == GT)",fontsize=16,color="black",shape="triangle"];40 -> 45[label="",style="solid", color="black", weight=3]; 9.92/4.13 41[label="signumReal1 (Neg (Succ vz300)) (LT == GT)",fontsize=16,color="black",shape="triangle"];41 -> 46[label="",style="solid", color="black", weight=3]; 9.92/4.13 42 -> 265[label="",style="dashed", color="red", weight=0]; 9.92/4.13 42[label="signumReal1 (Neg (Succ vz300)) (primCmpNat vz40 (Succ vz300) == GT)",fontsize=16,color="magenta"];42 -> 266[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 42 -> 267[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 42 -> 268[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 203[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]; 9.92/4.13 369 -> 224[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 370[label="vz8/Zero",fontsize=10,color="white",style="solid",shape="box"];202 -> 370[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 370 -> 225[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 45[label="signumReal1 (Pos (Succ vz300)) True",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3]; 9.92/4.13 46[label="signumReal1 (Neg (Succ vz300)) False",fontsize=16,color="black",shape="triangle"];46 -> 52[label="",style="solid", color="black", weight=3]; 9.92/4.13 266[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]; 9.92/4.13 371 -> 290[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 372[label="vz14/Zero",fontsize=10,color="white",style="solid",shape="box"];265 -> 372[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 372 -> 291[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 224[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]; 9.92/4.13 373 -> 234[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 374[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];224 -> 374[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 374 -> 235[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 225[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]; 9.92/4.13 375 -> 236[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 376[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];225 -> 376[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 376 -> 237[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 51[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];51 -> 57[label="",style="solid", color="black", weight=3]; 9.92/4.13 52[label="signumReal0 (Neg (Succ vz300)) otherwise",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3]; 9.92/4.13 290[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]; 9.92/4.13 377 -> 294[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 378[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];290 -> 378[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 378 -> 295[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 291[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]; 9.92/4.13 379 -> 296[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 380[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];291 -> 380[label="",style="solid", color="burlywood", weight=9]; 9.92/4.13 380 -> 297[label="",style="solid", color="burlywood", weight=3]; 9.92/4.13 234[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]; 9.92/4.13 235[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]; 9.92/4.13 236[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]; 9.92/4.13 237[label="signumReal1 (Pos (Succ vz7)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];237 -> 248[label="",style="solid", color="black", weight=3]; 9.92/4.13 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]; 9.92/4.13 294[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]; 9.92/4.13 295[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]; 9.92/4.13 296[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]; 9.92/4.13 297[label="signumReal1 (Neg (Succ vz13)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];297 -> 307[label="",style="solid", color="black", weight=3]; 9.92/4.13 245 -> 202[label="",style="dashed", color="red", weight=0]; 9.92/4.13 245[label="signumReal1 (Pos (Succ vz7)) (primCmpNat vz80 vz90 == GT)",fontsize=16,color="magenta"];245 -> 255[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 245 -> 256[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 246[label="signumReal1 (Pos (Succ vz7)) (GT == GT)",fontsize=16,color="black",shape="box"];246 -> 257[label="",style="solid", color="black", weight=3]; 9.92/4.13 247[label="signumReal1 (Pos (Succ vz7)) (LT == GT)",fontsize=16,color="black",shape="box"];247 -> 258[label="",style="solid", color="black", weight=3]; 9.92/4.13 248[label="signumReal1 (Pos (Succ vz7)) (EQ == GT)",fontsize=16,color="black",shape="box"];248 -> 259[label="",style="solid", color="black", weight=3]; 9.92/4.13 65[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];65 -> 74[label="",style="solid", color="black", weight=3]; 9.92/4.13 304 -> 265[label="",style="dashed", color="red", weight=0]; 9.92/4.13 304[label="signumReal1 (Neg (Succ vz13)) (primCmpNat vz140 vz150 == GT)",fontsize=16,color="magenta"];304 -> 313[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 304 -> 314[label="",style="dashed", color="magenta", weight=3]; 9.92/4.13 305[label="signumReal1 (Neg (Succ vz13)) (GT == GT)",fontsize=16,color="black",shape="box"];305 -> 315[label="",style="solid", color="black", weight=3]; 9.92/4.13 306[label="signumReal1 (Neg (Succ vz13)) (LT == GT)",fontsize=16,color="black",shape="box"];306 -> 316[label="",style="solid", color="black", weight=3]; 9.92/4.13 307[label="signumReal1 (Neg (Succ vz13)) (EQ == GT)",fontsize=16,color="black",shape="box"];307 -> 317[label="",style="solid", color="black", weight=3]; 9.92/4.13 255[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]; 9.92/4.13 258[label="signumReal1 (Pos (Succ vz7)) False",fontsize=16,color="black",shape="triangle"];258 -> 293[label="",style="solid", color="black", weight=3]; 9.92/4.13 259 -> 258[label="",style="dashed", color="red", weight=0]; 9.92/4.13 259[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]; 9.92/4.13 316[label="signumReal1 (Neg (Succ vz13)) False",fontsize=16,color="black",shape="triangle"];316 -> 327[label="",style="solid", color="black", weight=3]; 9.92/4.13 317 -> 316[label="",style="dashed", color="red", weight=0]; 9.92/4.13 317[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]; 9.92/4.13 381 -> 298[label="",style="solid", color="blue", weight=3]; 9.92/4.13 382[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];292 -> 382[label="",style="solid", color="blue", weight=9]; 9.92/4.13 382 -> 299[label="",style="solid", color="blue", weight=3]; 9.92/4.13 383[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];292 -> 383[label="",style="solid", color="blue", weight=9]; 9.92/4.13 383 -> 300[label="",style="solid", color="blue", weight=3]; 9.92/4.13 384[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];292 -> 384[label="",style="solid", color="blue", weight=9]; 9.92/4.13 384 -> 301[label="",style="solid", color="blue", weight=3]; 9.92/4.13 385[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];292 -> 385[label="",style="solid", color="blue", weight=9]; 9.92/4.13 385 -> 302[label="",style="solid", color="blue", weight=3]; 9.92/4.13 293[label="signumReal0 (Pos (Succ vz7)) otherwise",fontsize=16,color="black",shape="box"];293 -> 303[label="",style="solid", color="black", weight=3]; 9.92/4.13 326[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]; 9.92/4.13 386 -> 334[label="",style="solid", color="blue", weight=3]; 9.92/4.13 387[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];326 -> 387[label="",style="solid", color="blue", weight=9]; 9.92/4.13 387 -> 335[label="",style="solid", color="blue", weight=3]; 9.92/4.13 388[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];326 -> 388[label="",style="solid", color="blue", weight=9]; 9.92/4.13 388 -> 336[label="",style="solid", color="blue", weight=3]; 9.92/4.13 389[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];326 -> 389[label="",style="solid", color="blue", weight=9]; 9.92/4.13 389 -> 337[label="",style="solid", color="blue", weight=3]; 9.92/4.13 390[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];326 -> 390[label="",style="solid", color="blue", weight=9]; 9.92/4.13 390 -> 338[label="",style="solid", color="blue", weight=3]; 9.92/4.13 327[label="signumReal0 (Neg (Succ vz13)) otherwise",fontsize=16,color="black",shape="box"];327 -> 339[label="",style="solid", color="black", weight=3]; 9.92/4.13 298[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];298 -> 308[label="",style="solid", color="black", weight=3]; 9.92/4.13 299[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];299 -> 309[label="",style="solid", color="black", weight=3]; 9.92/4.13 300[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];300 -> 310[label="",style="solid", color="black", weight=3]; 9.92/4.13 301[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];301 -> 311[label="",style="solid", color="black", weight=3]; 9.92/4.13 302 -> 51[label="",style="dashed", color="red", weight=0]; 9.92/4.13 302[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];303[label="signumReal0 (Pos (Succ vz7)) True",fontsize=16,color="black",shape="box"];303 -> 312[label="",style="solid", color="black", weight=3]; 9.92/4.13 334 -> 298[label="",style="dashed", color="red", weight=0]; 9.92/4.13 334[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];335 -> 299[label="",style="dashed", color="red", weight=0]; 9.92/4.13 335[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];336 -> 300[label="",style="dashed", color="red", weight=0]; 9.92/4.13 336[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];337 -> 301[label="",style="dashed", color="red", weight=0]; 9.92/4.13 337[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];338 -> 51[label="",style="dashed", color="red", weight=0]; 9.92/4.13 338[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];339[label="signumReal0 (Neg (Succ vz13)) True",fontsize=16,color="black",shape="box"];339 -> 347[label="",style="solid", color="black", weight=3]; 9.92/4.13 308[label="Integer (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];309[label="primIntToDouble (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];309 -> 318[label="",style="solid", color="black", weight=3]; 9.92/4.13 310[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];310 -> 319[label="",style="solid", color="black", weight=3]; 9.92/4.13 311[label="intToRatio (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];311 -> 320[label="",style="solid", color="black", weight=3]; 9.92/4.13 312[label="fromInt (Neg (Succ Zero))",fontsize=16,color="blue",shape="box"];391[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];312 -> 391[label="",style="solid", color="blue", weight=9]; 9.92/4.13 391 -> 321[label="",style="solid", color="blue", weight=3]; 9.92/4.13 392[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];312 -> 392[label="",style="solid", color="blue", weight=9]; 9.92/4.13 392 -> 322[label="",style="solid", color="blue", weight=3]; 9.92/4.13 393[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];312 -> 393[label="",style="solid", color="blue", weight=9]; 9.92/4.13 393 -> 323[label="",style="solid", color="blue", weight=3]; 9.92/4.13 394[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];312 -> 394[label="",style="solid", color="blue", weight=9]; 9.92/4.13 394 -> 324[label="",style="solid", color="blue", weight=3]; 9.92/4.13 395[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];312 -> 395[label="",style="solid", color="blue", weight=9]; 9.92/4.13 395 -> 325[label="",style="solid", color="blue", weight=3]; 9.92/4.13 347[label="fromInt (Neg (Succ Zero))",fontsize=16,color="blue",shape="box"];396[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];347 -> 396[label="",style="solid", color="blue", weight=9]; 9.92/4.13 396 -> 350[label="",style="solid", color="blue", weight=3]; 9.92/4.13 397[label="fromInt :: -> Int Double",fontsize=10,color="white",style="solid",shape="box"];347 -> 397[label="",style="solid", color="blue", weight=9]; 9.92/4.14 397 -> 351[label="",style="solid", color="blue", weight=3]; 9.92/4.14 398[label="fromInt :: -> Int Float",fontsize=10,color="white",style="solid",shape="box"];347 -> 398[label="",style="solid", color="blue", weight=9]; 9.92/4.14 398 -> 352[label="",style="solid", color="blue", weight=3]; 9.92/4.14 399[label="fromInt :: -> Int (Ratio a)",fontsize=10,color="white",style="solid",shape="box"];347 -> 399[label="",style="solid", color="blue", weight=9]; 9.92/4.14 399 -> 353[label="",style="solid", color="blue", weight=3]; 9.92/4.14 400[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];347 -> 400[label="",style="solid", color="blue", weight=9]; 9.92/4.14 400 -> 354[label="",style="solid", color="blue", weight=3]; 9.92/4.14 318[label="Double (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];319[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];320[label="fromInt (Pos (Succ Zero)) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];320 -> 328[label="",style="dashed", color="green", weight=3]; 9.92/4.14 320 -> 329[label="",style="dashed", color="green", weight=3]; 9.92/4.14 321[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];321 -> 330[label="",style="solid", color="black", weight=3]; 9.92/4.14 322[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];322 -> 331[label="",style="solid", color="black", weight=3]; 9.92/4.14 323[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];323 -> 332[label="",style="solid", color="black", weight=3]; 9.92/4.14 324[label="fromInt (Neg (Succ Zero))",fontsize=16,color="black",shape="triangle"];324 -> 333[label="",style="solid", color="black", weight=3]; 9.92/4.14 325 -> 65[label="",style="dashed", color="red", weight=0]; 9.92/4.14 325[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];350 -> 321[label="",style="dashed", color="red", weight=0]; 9.92/4.14 350[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];351 -> 322[label="",style="dashed", color="red", weight=0]; 9.92/4.14 351[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];352 -> 323[label="",style="dashed", color="red", weight=0]; 9.92/4.14 352[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];353 -> 324[label="",style="dashed", color="red", weight=0]; 9.92/4.14 353[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];354 -> 65[label="",style="dashed", color="red", weight=0]; 9.92/4.14 354[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];328[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];401[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];328 -> 401[label="",style="solid", color="blue", weight=9]; 9.92/4.14 401 -> 340[label="",style="solid", color="blue", weight=3]; 9.92/4.14 402[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];328 -> 402[label="",style="solid", color="blue", weight=9]; 9.92/4.14 402 -> 341[label="",style="solid", color="blue", weight=3]; 9.92/4.14 329[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];403[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];329 -> 403[label="",style="solid", color="blue", weight=9]; 9.92/4.14 403 -> 342[label="",style="solid", color="blue", weight=3]; 9.92/4.14 404[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];329 -> 404[label="",style="solid", color="blue", weight=9]; 9.92/4.14 404 -> 343[label="",style="solid", color="blue", weight=3]; 9.92/4.14 330[label="Integer (Neg (Succ Zero))",fontsize=16,color="green",shape="box"];331[label="primIntToDouble (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];331 -> 344[label="",style="solid", color="black", weight=3]; 9.92/4.14 332[label="primIntToFloat (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];332 -> 345[label="",style="solid", color="black", weight=3]; 9.92/4.14 333[label="intToRatio (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];333 -> 346[label="",style="solid", color="black", weight=3]; 9.92/4.14 340 -> 298[label="",style="dashed", color="red", weight=0]; 9.92/4.14 340[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];341 -> 51[label="",style="dashed", color="red", weight=0]; 9.92/4.14 341[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];342 -> 298[label="",style="dashed", color="red", weight=0]; 9.92/4.14 342[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];343 -> 51[label="",style="dashed", color="red", weight=0]; 9.92/4.14 343[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];344[label="Double (Neg (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];345[label="Float (Neg (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];346[label="fromInt (Neg (Succ Zero)) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];346 -> 348[label="",style="dashed", color="green", weight=3]; 9.92/4.14 346 -> 349[label="",style="dashed", color="green", weight=3]; 9.92/4.14 348[label="fromInt (Neg (Succ Zero))",fontsize=16,color="blue",shape="box"];405[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];348 -> 405[label="",style="solid", color="blue", weight=9]; 9.92/4.14 405 -> 355[label="",style="solid", color="blue", weight=3]; 9.92/4.14 406[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];348 -> 406[label="",style="solid", color="blue", weight=9]; 9.92/4.14 406 -> 356[label="",style="solid", color="blue", weight=3]; 9.92/4.14 349[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];407[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];349 -> 407[label="",style="solid", color="blue", weight=9]; 9.92/4.14 407 -> 357[label="",style="solid", color="blue", weight=3]; 9.92/4.14 408[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];349 -> 408[label="",style="solid", color="blue", weight=9]; 9.92/4.14 408 -> 358[label="",style="solid", color="blue", weight=3]; 9.92/4.14 355 -> 321[label="",style="dashed", color="red", weight=0]; 9.92/4.14 355[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];356 -> 65[label="",style="dashed", color="red", weight=0]; 9.92/4.14 356[label="fromInt (Neg (Succ Zero))",fontsize=16,color="magenta"];357 -> 298[label="",style="dashed", color="red", weight=0]; 9.92/4.14 357[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];358 -> 51[label="",style="dashed", color="red", weight=0]; 9.92/4.14 358[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];} 9.92/4.14 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (8) 9.92/4.14 Complex Obligation (AND) 9.92/4.14 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (9) 9.92/4.14 Obligation: 9.92/4.14 Q DP problem: 9.92/4.14 The TRS P consists of the following rules: 9.92/4.14 9.92/4.14 new_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h) 9.92/4.14 9.92/4.14 R is empty. 9.92/4.14 Q is empty. 9.92/4.14 We have to consider all minimal (P,Q,R)-chains. 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (10) QDPSizeChangeProof (EQUIVALENT) 9.92/4.14 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. 9.92/4.14 9.92/4.14 From the DPs we obtained the following set of size-change graphs: 9.92/4.14 *new_signumReal1(vz13, Succ(vz140), Succ(vz150), h) -> new_signumReal1(vz13, vz140, vz150, h) 9.92/4.14 The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4 9.92/4.14 9.92/4.14 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (11) 9.92/4.14 YES 9.92/4.14 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (12) 9.92/4.14 Obligation: 9.92/4.14 Q DP problem: 9.92/4.14 The TRS P consists of the following rules: 9.92/4.14 9.92/4.14 new_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h) 9.92/4.14 9.92/4.14 R is empty. 9.92/4.14 Q is empty. 9.92/4.14 We have to consider all minimal (P,Q,R)-chains. 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (13) QDPSizeChangeProof (EQUIVALENT) 9.92/4.14 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. 9.92/4.14 9.92/4.14 From the DPs we obtained the following set of size-change graphs: 9.92/4.14 *new_signumReal10(vz7, Succ(vz80), Succ(vz90), h) -> new_signumReal10(vz7, vz80, vz90, h) 9.92/4.14 The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4 9.92/4.14 9.92/4.14 9.92/4.14 ---------------------------------------- 9.92/4.14 9.92/4.14 (14) 9.92/4.14 YES 9.92/4.17 EOF