8.45/3.66 YES 10.38/4.19 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 10.38/4.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.38/4.19 10.38/4.19 10.38/4.19 H-Termination with start terms of the given HASKELL could be proven: 10.38/4.19 10.38/4.19 (0) HASKELL 10.38/4.19 (1) BR [EQUIVALENT, 0 ms] 10.38/4.19 (2) HASKELL 10.38/4.19 (3) COR [EQUIVALENT, 0 ms] 10.38/4.19 (4) HASKELL 10.38/4.19 (5) NumRed [SOUND, 0 ms] 10.38/4.19 (6) HASKELL 10.38/4.19 (7) Narrow [SOUND, 0 ms] 10.38/4.19 (8) AND 10.38/4.19 (9) QDP 10.38/4.19 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.38/4.19 (11) YES 10.38/4.19 (12) QDP 10.38/4.19 (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.38/4.19 (14) YES 10.38/4.19 (15) QDP 10.38/4.19 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.38/4.19 (17) YES 10.38/4.19 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (0) 10.38/4.19 Obligation: 10.38/4.19 mainModule Main 10.38/4.19 module Main where { 10.38/4.19 import qualified Prelude; 10.38/4.19 } 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (1) BR (EQUIVALENT) 10.38/4.19 Replaced joker patterns by fresh variables and removed binding patterns. 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (2) 10.38/4.19 Obligation: 10.38/4.19 mainModule Main 10.38/4.19 module Main where { 10.38/4.19 import qualified Prelude; 10.38/4.19 } 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (3) COR (EQUIVALENT) 10.38/4.19 Cond Reductions: 10.38/4.19 The following Function with conditions 10.38/4.19 "undefined |Falseundefined; 10.38/4.19 " 10.38/4.19 is transformed to 10.38/4.19 "undefined = undefined1; 10.38/4.19 " 10.38/4.19 "undefined0 True = undefined; 10.38/4.19 " 10.38/4.19 "undefined1 = undefined0 False; 10.38/4.19 " 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (4) 10.38/4.19 Obligation: 10.38/4.19 mainModule Main 10.38/4.19 module Main where { 10.38/4.19 import qualified Prelude; 10.38/4.19 } 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (5) NumRed (SOUND) 10.38/4.19 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (6) 10.38/4.19 Obligation: 10.38/4.19 mainModule Main 10.38/4.19 module Main where { 10.38/4.19 import qualified Prelude; 10.38/4.19 } 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (7) Narrow (SOUND) 10.38/4.19 Haskell To QDPs 10.38/4.19 10.38/4.19 digraph dp_graph { 10.38/4.19 node [outthreshold=100, inthreshold=100];1[label="product",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.38/4.19 3[label="product vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.38/4.19 4[label="foldl' (*) (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];94[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 94[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 94 -> 5[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 95[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 95[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 95 -> 6[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 5[label="foldl' (*) (fromInt (Pos (Succ Zero))) (vx30 : vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 10.38/4.19 6[label="foldl' (*) (fromInt (Pos (Succ Zero))) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 10.38/4.19 7[label="(foldl' (*) $! (*) fromInt (Pos (Succ Zero)) vx30)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 10.38/4.19 8[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];8 -> 10[label="",style="solid", color="black", weight=3]; 10.38/4.19 9 -> 11[label="",style="dashed", color="red", weight=0]; 10.38/4.19 9[label="((*) fromInt (Pos (Succ Zero)) vx30 `seq` foldl' (*) ((*) fromInt (Pos (Succ Zero)) vx30))",fontsize=16,color="magenta"];9 -> 12[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 9 -> 13[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 10[label="primIntToFloat (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 10.38/4.19 12 -> 8[label="",style="dashed", color="red", weight=0]; 10.38/4.19 12[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];13 -> 8[label="",style="dashed", color="red", weight=0]; 10.38/4.19 13[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];11[label="((*) vx4 vx30 `seq` foldl' (*) ((*) vx5 vx30))",fontsize=16,color="black",shape="triangle"];11 -> 15[label="",style="solid", color="black", weight=3]; 10.38/4.19 14[label="Float (Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];15[label="enforceWHNF (WHNF ((*) vx4 vx30)) (foldl' (*) ((*) vx5 vx30)) vx31",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 10.38/4.19 16[label="enforceWHNF (WHNF (primMulFloat vx4 vx30)) (foldl' primMulFloat (primMulFloat vx5 vx30)) vx31",fontsize=16,color="burlywood",shape="triangle"];96[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];16 -> 96[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 96 -> 17[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 17[label="enforceWHNF (WHNF (primMulFloat (Float vx40 vx41) vx30)) (foldl' primMulFloat (primMulFloat vx5 vx30)) vx31",fontsize=16,color="burlywood",shape="box"];97[label="vx30/Float vx300 vx301",fontsize=10,color="white",style="solid",shape="box"];17 -> 97[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 97 -> 18[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 18[label="enforceWHNF (WHNF (primMulFloat (Float vx40 vx41) (Float vx300 vx301))) (foldl' primMulFloat (primMulFloat vx5 (Float vx300 vx301))) vx31",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 10.38/4.19 19[label="enforceWHNF (WHNF (Float (vx40 * vx300) (vx41 * vx301))) (foldl' primMulFloat (Float (vx40 * vx300) (vx41 * vx301))) vx31",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 10.38/4.19 20[label="foldl' primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx31",fontsize=16,color="burlywood",shape="box"];98[label="vx31/vx310 : vx311",fontsize=10,color="white",style="solid",shape="box"];20 -> 98[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 98 -> 21[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 99[label="vx31/[]",fontsize=10,color="white",style="solid",shape="box"];20 -> 99[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 99 -> 22[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 21[label="foldl' primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) (vx310 : vx311)",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 10.38/4.19 22[label="foldl' primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) []",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 10.38/4.19 23[label="(foldl' primMulFloat $! primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx310)",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 10.38/4.19 24[label="Float (vx40 * vx300) (vx41 * vx301)",fontsize=16,color="green",shape="box"];24 -> 26[label="",style="dashed", color="green", weight=3]; 10.38/4.19 24 -> 27[label="",style="dashed", color="green", weight=3]; 10.38/4.19 25[label="(primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx310 `seq` foldl' primMulFloat (primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx310))",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3]; 10.38/4.19 26[label="vx40 * vx300",fontsize=16,color="black",shape="triangle"];26 -> 29[label="",style="solid", color="black", weight=3]; 10.38/4.19 27 -> 26[label="",style="dashed", color="red", weight=0]; 10.38/4.19 27[label="vx41 * vx301",fontsize=16,color="magenta"];27 -> 30[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 27 -> 31[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 28 -> 16[label="",style="dashed", color="red", weight=0]; 10.38/4.19 28[label="enforceWHNF (WHNF (primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx310)) (foldl' primMulFloat (primMulFloat (Float (vx40 * vx300) (vx41 * vx301)) vx310)) vx311",fontsize=16,color="magenta"];28 -> 32[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 28 -> 33[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 28 -> 34[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 28 -> 35[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 29[label="primMulInt vx40 vx300",fontsize=16,color="burlywood",shape="box"];100[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];29 -> 100[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 100 -> 36[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 101[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];29 -> 101[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 101 -> 37[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 30[label="vx301",fontsize=16,color="green",shape="box"];31[label="vx41",fontsize=16,color="green",shape="box"];32[label="vx310",fontsize=16,color="green",shape="box"];33[label="Float (vx40 * vx300) (vx41 * vx301)",fontsize=16,color="green",shape="box"];33 -> 38[label="",style="dashed", color="green", weight=3]; 10.38/4.19 33 -> 39[label="",style="dashed", color="green", weight=3]; 10.38/4.19 34[label="Float (vx40 * vx300) (vx41 * vx301)",fontsize=16,color="green",shape="box"];34 -> 40[label="",style="dashed", color="green", weight=3]; 10.38/4.19 34 -> 41[label="",style="dashed", color="green", weight=3]; 10.38/4.19 35[label="vx311",fontsize=16,color="green",shape="box"];36[label="primMulInt (Pos vx400) vx300",fontsize=16,color="burlywood",shape="box"];102[label="vx300/Pos vx3000",fontsize=10,color="white",style="solid",shape="box"];36 -> 102[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 102 -> 42[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 103[label="vx300/Neg vx3000",fontsize=10,color="white",style="solid",shape="box"];36 -> 103[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 103 -> 43[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 37[label="primMulInt (Neg vx400) vx300",fontsize=16,color="burlywood",shape="box"];104[label="vx300/Pos vx3000",fontsize=10,color="white",style="solid",shape="box"];37 -> 104[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 104 -> 44[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 105[label="vx300/Neg vx3000",fontsize=10,color="white",style="solid",shape="box"];37 -> 105[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 105 -> 45[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 38 -> 26[label="",style="dashed", color="red", weight=0]; 10.38/4.19 38[label="vx40 * vx300",fontsize=16,color="magenta"];39 -> 26[label="",style="dashed", color="red", weight=0]; 10.38/4.19 39[label="vx41 * vx301",fontsize=16,color="magenta"];39 -> 46[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 39 -> 47[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 40 -> 26[label="",style="dashed", color="red", weight=0]; 10.38/4.19 40[label="vx40 * vx300",fontsize=16,color="magenta"];41 -> 26[label="",style="dashed", color="red", weight=0]; 10.38/4.19 41[label="vx41 * vx301",fontsize=16,color="magenta"];41 -> 48[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 41 -> 49[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 42[label="primMulInt (Pos vx400) (Pos vx3000)",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 10.38/4.19 43[label="primMulInt (Pos vx400) (Neg vx3000)",fontsize=16,color="black",shape="box"];43 -> 51[label="",style="solid", color="black", weight=3]; 10.38/4.19 44[label="primMulInt (Neg vx400) (Pos vx3000)",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3]; 10.38/4.19 45[label="primMulInt (Neg vx400) (Neg vx3000)",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3]; 10.38/4.19 46[label="vx301",fontsize=16,color="green",shape="box"];47[label="vx41",fontsize=16,color="green",shape="box"];48[label="vx301",fontsize=16,color="green",shape="box"];49[label="vx41",fontsize=16,color="green",shape="box"];50[label="Pos (primMulNat vx400 vx3000)",fontsize=16,color="green",shape="box"];50 -> 54[label="",style="dashed", color="green", weight=3]; 10.38/4.19 51[label="Neg (primMulNat vx400 vx3000)",fontsize=16,color="green",shape="box"];51 -> 55[label="",style="dashed", color="green", weight=3]; 10.38/4.19 52[label="Neg (primMulNat vx400 vx3000)",fontsize=16,color="green",shape="box"];52 -> 56[label="",style="dashed", color="green", weight=3]; 10.38/4.19 53[label="Pos (primMulNat vx400 vx3000)",fontsize=16,color="green",shape="box"];53 -> 57[label="",style="dashed", color="green", weight=3]; 10.38/4.19 54[label="primMulNat vx400 vx3000",fontsize=16,color="burlywood",shape="triangle"];106[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];54 -> 106[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 106 -> 58[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 107[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 107[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 107 -> 59[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 55 -> 54[label="",style="dashed", color="red", weight=0]; 10.38/4.19 55[label="primMulNat vx400 vx3000",fontsize=16,color="magenta"];55 -> 60[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 56 -> 54[label="",style="dashed", color="red", weight=0]; 10.38/4.19 56[label="primMulNat vx400 vx3000",fontsize=16,color="magenta"];56 -> 61[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 57 -> 54[label="",style="dashed", color="red", weight=0]; 10.38/4.19 57[label="primMulNat vx400 vx3000",fontsize=16,color="magenta"];57 -> 62[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 57 -> 63[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 58[label="primMulNat (Succ vx4000) vx3000",fontsize=16,color="burlywood",shape="box"];108[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];58 -> 108[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 108 -> 64[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 109[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];58 -> 109[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 109 -> 65[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 59[label="primMulNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];110[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];59 -> 110[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 110 -> 66[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 111[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 111[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 111 -> 67[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 60[label="vx3000",fontsize=16,color="green",shape="box"];61[label="vx400",fontsize=16,color="green",shape="box"];62[label="vx3000",fontsize=16,color="green",shape="box"];63[label="vx400",fontsize=16,color="green",shape="box"];64[label="primMulNat (Succ vx4000) (Succ vx30000)",fontsize=16,color="black",shape="box"];64 -> 68[label="",style="solid", color="black", weight=3]; 10.38/4.19 65[label="primMulNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];65 -> 69[label="",style="solid", color="black", weight=3]; 10.38/4.19 66[label="primMulNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];66 -> 70[label="",style="solid", color="black", weight=3]; 10.38/4.19 67[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3]; 10.38/4.19 68 -> 72[label="",style="dashed", color="red", weight=0]; 10.38/4.19 68[label="primPlusNat (primMulNat vx4000 (Succ vx30000)) (Succ vx30000)",fontsize=16,color="magenta"];68 -> 73[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 69[label="Zero",fontsize=16,color="green",shape="box"];70[label="Zero",fontsize=16,color="green",shape="box"];71[label="Zero",fontsize=16,color="green",shape="box"];73 -> 54[label="",style="dashed", color="red", weight=0]; 10.38/4.19 73[label="primMulNat vx4000 (Succ vx30000)",fontsize=16,color="magenta"];73 -> 74[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 73 -> 75[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 72[label="primPlusNat vx6 (Succ vx30000)",fontsize=16,color="burlywood",shape="triangle"];112[label="vx6/Succ vx60",fontsize=10,color="white",style="solid",shape="box"];72 -> 112[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 112 -> 76[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 113[label="vx6/Zero",fontsize=10,color="white",style="solid",shape="box"];72 -> 113[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 113 -> 77[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 74[label="Succ vx30000",fontsize=16,color="green",shape="box"];75[label="vx4000",fontsize=16,color="green",shape="box"];76[label="primPlusNat (Succ vx60) (Succ vx30000)",fontsize=16,color="black",shape="box"];76 -> 78[label="",style="solid", color="black", weight=3]; 10.38/4.19 77[label="primPlusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];77 -> 79[label="",style="solid", color="black", weight=3]; 10.38/4.19 78[label="Succ (Succ (primPlusNat vx60 vx30000))",fontsize=16,color="green",shape="box"];78 -> 80[label="",style="dashed", color="green", weight=3]; 10.38/4.19 79[label="Succ vx30000",fontsize=16,color="green",shape="box"];80[label="primPlusNat vx60 vx30000",fontsize=16,color="burlywood",shape="triangle"];114[label="vx60/Succ vx600",fontsize=10,color="white",style="solid",shape="box"];80 -> 114[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 114 -> 81[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 115[label="vx60/Zero",fontsize=10,color="white",style="solid",shape="box"];80 -> 115[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 115 -> 82[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 81[label="primPlusNat (Succ vx600) vx30000",fontsize=16,color="burlywood",shape="box"];116[label="vx30000/Succ vx300000",fontsize=10,color="white",style="solid",shape="box"];81 -> 116[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 116 -> 83[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 117[label="vx30000/Zero",fontsize=10,color="white",style="solid",shape="box"];81 -> 117[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 117 -> 84[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 82[label="primPlusNat Zero vx30000",fontsize=16,color="burlywood",shape="box"];118[label="vx30000/Succ vx300000",fontsize=10,color="white",style="solid",shape="box"];82 -> 118[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 118 -> 85[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 119[label="vx30000/Zero",fontsize=10,color="white",style="solid",shape="box"];82 -> 119[label="",style="solid", color="burlywood", weight=9]; 10.38/4.19 119 -> 86[label="",style="solid", color="burlywood", weight=3]; 10.38/4.19 83[label="primPlusNat (Succ vx600) (Succ vx300000)",fontsize=16,color="black",shape="box"];83 -> 87[label="",style="solid", color="black", weight=3]; 10.38/4.19 84[label="primPlusNat (Succ vx600) Zero",fontsize=16,color="black",shape="box"];84 -> 88[label="",style="solid", color="black", weight=3]; 10.38/4.19 85[label="primPlusNat Zero (Succ vx300000)",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3]; 10.38/4.19 86[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];86 -> 90[label="",style="solid", color="black", weight=3]; 10.38/4.19 87[label="Succ (Succ (primPlusNat vx600 vx300000))",fontsize=16,color="green",shape="box"];87 -> 91[label="",style="dashed", color="green", weight=3]; 10.38/4.19 88[label="Succ vx600",fontsize=16,color="green",shape="box"];89[label="Succ vx300000",fontsize=16,color="green",shape="box"];90[label="Zero",fontsize=16,color="green",shape="box"];91 -> 80[label="",style="dashed", color="red", weight=0]; 10.38/4.19 91[label="primPlusNat vx600 vx300000",fontsize=16,color="magenta"];91 -> 92[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 91 -> 93[label="",style="dashed", color="magenta", weight=3]; 10.38/4.19 92[label="vx600",fontsize=16,color="green",shape="box"];93[label="vx300000",fontsize=16,color="green",shape="box"];} 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (8) 10.38/4.19 Complex Obligation (AND) 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (9) 10.38/4.19 Obligation: 10.38/4.19 Q DP problem: 10.38/4.19 The TRS P consists of the following rules: 10.38/4.19 10.38/4.19 new_enforceWHNF(Float(vx40, vx41), Float(vx300, vx301), vx5, :(vx310, vx311)) -> new_enforceWHNF(Float(new_sr(vx40, vx300), new_sr(vx41, vx301)), vx310, Float(new_sr(vx40, vx300), new_sr(vx41, vx301)), vx311) 10.38/4.19 10.38/4.19 The TRS R consists of the following rules: 10.38/4.19 10.38/4.19 new_primPlusNat1(Succ(vx600), Zero) -> Succ(vx600) 10.38/4.19 new_primPlusNat1(Zero, Succ(vx300000)) -> Succ(vx300000) 10.38/4.19 new_sr(Pos(vx400), Neg(vx3000)) -> Neg(new_primMulNat0(vx400, vx3000)) 10.38/4.19 new_sr(Neg(vx400), Pos(vx3000)) -> Neg(new_primMulNat0(vx400, vx3000)) 10.38/4.19 new_primMulNat0(Zero, Zero) -> Zero 10.38/4.19 new_primPlusNat1(Succ(vx600), Succ(vx300000)) -> Succ(Succ(new_primPlusNat1(vx600, vx300000))) 10.38/4.19 new_primPlusNat1(Zero, Zero) -> Zero 10.38/4.19 new_primMulNat0(Succ(vx4000), Zero) -> Zero 10.38/4.19 new_primMulNat0(Zero, Succ(vx30000)) -> Zero 10.38/4.19 new_sr(Pos(vx400), Pos(vx3000)) -> Pos(new_primMulNat0(vx400, vx3000)) 10.38/4.19 new_primPlusNat0(Zero, vx30000) -> Succ(vx30000) 10.38/4.19 new_primMulNat0(Succ(vx4000), Succ(vx30000)) -> new_primPlusNat0(new_primMulNat0(vx4000, Succ(vx30000)), vx30000) 10.38/4.19 new_primPlusNat0(Succ(vx60), vx30000) -> Succ(Succ(new_primPlusNat1(vx60, vx30000))) 10.38/4.19 new_sr(Neg(vx400), Neg(vx3000)) -> Pos(new_primMulNat0(vx400, vx3000)) 10.38/4.19 10.38/4.19 The set Q consists of the following terms: 10.38/4.19 10.38/4.19 new_primPlusNat1(Succ(x0), Zero) 10.38/4.19 new_primMulNat0(Zero, Succ(x0)) 10.38/4.19 new_sr(Pos(x0), Pos(x1)) 10.38/4.19 new_primMulNat0(Zero, Zero) 10.38/4.19 new_primPlusNat1(Zero, Zero) 10.38/4.19 new_primPlusNat1(Succ(x0), Succ(x1)) 10.38/4.19 new_primPlusNat0(Zero, x0) 10.38/4.19 new_primPlusNat1(Zero, Succ(x0)) 10.38/4.19 new_primMulNat0(Succ(x0), Succ(x1)) 10.38/4.19 new_primMulNat0(Succ(x0), Zero) 10.38/4.19 new_primPlusNat0(Succ(x0), x1) 10.38/4.19 new_sr(Pos(x0), Neg(x1)) 10.38/4.19 new_sr(Neg(x0), Pos(x1)) 10.38/4.19 new_sr(Neg(x0), Neg(x1)) 10.38/4.19 10.38/4.19 We have to consider all minimal (P,Q,R)-chains. 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (10) QDPSizeChangeProof (EQUIVALENT) 10.38/4.19 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. 10.38/4.19 10.38/4.19 From the DPs we obtained the following set of size-change graphs: 10.38/4.19 *new_enforceWHNF(Float(vx40, vx41), Float(vx300, vx301), vx5, :(vx310, vx311)) -> new_enforceWHNF(Float(new_sr(vx40, vx300), new_sr(vx41, vx301)), vx310, Float(new_sr(vx40, vx300), new_sr(vx41, vx301)), vx311) 10.38/4.19 The graph contains the following edges 4 > 2, 4 > 4 10.38/4.19 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (11) 10.38/4.19 YES 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (12) 10.38/4.19 Obligation: 10.38/4.19 Q DP problem: 10.38/4.19 The TRS P consists of the following rules: 10.38/4.19 10.38/4.19 new_primMulNat(Succ(vx4000), Succ(vx30000)) -> new_primMulNat(vx4000, Succ(vx30000)) 10.38/4.19 10.38/4.19 R is empty. 10.38/4.19 Q is empty. 10.38/4.19 We have to consider all minimal (P,Q,R)-chains. 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (13) QDPSizeChangeProof (EQUIVALENT) 10.38/4.19 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. 10.38/4.19 10.38/4.19 From the DPs we obtained the following set of size-change graphs: 10.38/4.19 *new_primMulNat(Succ(vx4000), Succ(vx30000)) -> new_primMulNat(vx4000, Succ(vx30000)) 10.38/4.19 The graph contains the following edges 1 > 1, 2 >= 2 10.38/4.19 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (14) 10.38/4.19 YES 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (15) 10.38/4.19 Obligation: 10.38/4.19 Q DP problem: 10.38/4.19 The TRS P consists of the following rules: 10.38/4.19 10.38/4.19 new_primPlusNat(Succ(vx600), Succ(vx300000)) -> new_primPlusNat(vx600, vx300000) 10.38/4.19 10.38/4.19 R is empty. 10.38/4.19 Q is empty. 10.38/4.19 We have to consider all minimal (P,Q,R)-chains. 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (16) QDPSizeChangeProof (EQUIVALENT) 10.38/4.19 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. 10.38/4.19 10.38/4.19 From the DPs we obtained the following set of size-change graphs: 10.38/4.19 *new_primPlusNat(Succ(vx600), Succ(vx300000)) -> new_primPlusNat(vx600, vx300000) 10.38/4.19 The graph contains the following edges 1 > 1, 2 > 2 10.38/4.19 10.38/4.19 10.38/4.19 ---------------------------------------- 10.38/4.19 10.38/4.19 (17) 10.38/4.19 YES 10.38/4.22 EOF