7.67/3.51 YES 9.54/3.98 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.54/3.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.54/3.98 9.54/3.98 9.54/3.98 H-Termination with start terms of the given HASKELL could be proven: 9.54/3.98 9.54/3.98 (0) HASKELL 9.54/3.98 (1) BR [EQUIVALENT, 0 ms] 9.54/3.98 (2) HASKELL 9.54/3.98 (3) COR [EQUIVALENT, 0 ms] 9.54/3.98 (4) HASKELL 9.54/3.98 (5) Narrow [SOUND, 0 ms] 9.54/3.98 (6) QDP 9.54/3.98 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.54/3.98 (8) YES 9.54/3.98 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (0) 9.54/3.98 Obligation: 9.54/3.98 mainModule Main 9.54/3.98 module Main where { 9.54/3.98 import qualified Prelude; 9.54/3.98 } 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (1) BR (EQUIVALENT) 9.54/3.98 Replaced joker patterns by fresh variables and removed binding patterns. 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (2) 9.54/3.98 Obligation: 9.54/3.98 mainModule Main 9.54/3.98 module Main where { 9.54/3.98 import qualified Prelude; 9.54/3.98 } 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (3) COR (EQUIVALENT) 9.54/3.98 Cond Reductions: 9.54/3.98 The following Function with conditions 9.54/3.98 "undefined |Falseundefined; 9.54/3.98 " 9.54/3.98 is transformed to 9.54/3.98 "undefined = undefined1; 9.54/3.98 " 9.54/3.98 "undefined0 True = undefined; 9.54/3.98 " 9.54/3.98 "undefined1 = undefined0 False; 9.54/3.98 " 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (4) 9.54/3.98 Obligation: 9.54/3.98 mainModule Main 9.54/3.98 module Main where { 9.54/3.98 import qualified Prelude; 9.54/3.98 } 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (5) Narrow (SOUND) 9.54/3.98 Haskell To QDPs 9.54/3.98 9.54/3.98 digraph dp_graph { 9.54/3.98 node [outthreshold=100, inthreshold=100];1[label="(/=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.54/3.98 3[label="(/=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.54/3.98 4[label="(/=) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.54/3.98 5[label="not (vx3 == vx4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.54/3.98 6[label="not (primEqChar vx3 vx4)",fontsize=16,color="burlywood",shape="box"];24[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 24 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 7[label="not (primEqChar (Char vx30) vx4)",fontsize=16,color="burlywood",shape="box"];25[label="vx4/Char vx40",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 25 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 8[label="not (primEqChar (Char vx30) (Char vx40))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9.54/3.98 9[label="not (primEqNat vx30 vx40)",fontsize=16,color="burlywood",shape="triangle"];26[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];9 -> 26[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 26 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 27[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 27[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 27 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 10[label="not (primEqNat (Succ vx300) vx40)",fontsize=16,color="burlywood",shape="box"];28[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];10 -> 28[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 28 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 29[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 29[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 29 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 11[label="not (primEqNat Zero vx40)",fontsize=16,color="burlywood",shape="box"];30[label="vx40/Succ vx400",fontsize=10,color="white",style="solid",shape="box"];11 -> 30[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 30 -> 14[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 31[label="vx40/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 31[label="",style="solid", color="burlywood", weight=9]; 9.54/3.98 31 -> 15[label="",style="solid", color="burlywood", weight=3]; 9.54/3.98 12[label="not (primEqNat (Succ vx300) (Succ vx400))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 9.54/3.98 13[label="not (primEqNat (Succ vx300) Zero)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 9.54/3.98 14[label="not (primEqNat Zero (Succ vx400))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 9.54/3.98 15[label="not (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.54/3.98 16 -> 9[label="",style="dashed", color="red", weight=0]; 9.54/3.98 16[label="not (primEqNat vx300 vx400)",fontsize=16,color="magenta"];16 -> 20[label="",style="dashed", color="magenta", weight=3]; 9.54/3.98 16 -> 21[label="",style="dashed", color="magenta", weight=3]; 9.54/3.98 17[label="not False",fontsize=16,color="black",shape="triangle"];17 -> 22[label="",style="solid", color="black", weight=3]; 9.54/3.98 18 -> 17[label="",style="dashed", color="red", weight=0]; 9.54/3.98 18[label="not False",fontsize=16,color="magenta"];19[label="not True",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 9.54/3.98 20[label="vx400",fontsize=16,color="green",shape="box"];21[label="vx300",fontsize=16,color="green",shape="box"];22[label="True",fontsize=16,color="green",shape="box"];23[label="False",fontsize=16,color="green",shape="box"];} 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (6) 9.54/3.98 Obligation: 9.54/3.98 Q DP problem: 9.54/3.98 The TRS P consists of the following rules: 9.54/3.98 9.54/3.98 new_not(Succ(vx300), Succ(vx400)) -> new_not(vx300, vx400) 9.54/3.98 9.54/3.98 R is empty. 9.54/3.98 Q is empty. 9.54/3.98 We have to consider all minimal (P,Q,R)-chains. 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (7) QDPSizeChangeProof (EQUIVALENT) 9.54/3.98 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. 9.54/3.98 9.54/3.98 From the DPs we obtained the following set of size-change graphs: 9.54/3.98 *new_not(Succ(vx300), Succ(vx400)) -> new_not(vx300, vx400) 9.54/3.98 The graph contains the following edges 1 > 1, 2 > 2 9.54/3.98 9.54/3.98 9.54/3.98 ---------------------------------------- 9.54/3.98 9.54/3.98 (8) 9.54/3.98 YES 9.54/4.02 EOF