7.38/3.50 YES 9.03/3.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.03/3.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.03/3.99 9.03/3.99 9.03/3.99 H-Termination with start terms of the given HASKELL could be proven: 9.03/3.99 9.03/3.99 (0) HASKELL 9.03/3.99 (1) BR [EQUIVALENT, 0 ms] 9.03/3.99 (2) HASKELL 9.03/3.99 (3) COR [EQUIVALENT, 0 ms] 9.03/3.99 (4) HASKELL 9.03/3.99 (5) Narrow [EQUIVALENT, 0 ms] 9.03/3.99 (6) YES 9.03/3.99 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (0) 9.03/3.99 Obligation: 9.03/3.99 mainModule Main 9.03/3.99 module Main where { 9.03/3.99 import qualified Prelude; 9.03/3.99 data MyBool = MyTrue | MyFalse ; 9.03/3.99 9.03/3.99 ltEsMyBool :: MyBool -> MyBool -> MyBool; 9.03/3.99 ltEsMyBool MyFalse MyFalse = MyTrue; 9.03/3.99 ltEsMyBool MyFalse MyTrue = MyTrue; 9.03/3.99 ltEsMyBool MyTrue MyFalse = MyFalse; 9.03/3.99 ltEsMyBool MyTrue MyTrue = MyTrue; 9.03/3.99 9.03/3.99 } 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (1) BR (EQUIVALENT) 9.03/3.99 Replaced joker patterns by fresh variables and removed binding patterns. 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (2) 9.03/3.99 Obligation: 9.03/3.99 mainModule Main 9.03/3.99 module Main where { 9.03/3.99 import qualified Prelude; 9.03/3.99 data MyBool = MyTrue | MyFalse ; 9.03/3.99 9.03/3.99 ltEsMyBool :: MyBool -> MyBool -> MyBool; 9.03/3.99 ltEsMyBool MyFalse MyFalse = MyTrue; 9.03/3.99 ltEsMyBool MyFalse MyTrue = MyTrue; 9.03/3.99 ltEsMyBool MyTrue MyFalse = MyFalse; 9.03/3.99 ltEsMyBool MyTrue MyTrue = MyTrue; 9.03/3.99 9.03/3.99 } 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (3) COR (EQUIVALENT) 9.03/3.99 Cond Reductions: 9.03/3.99 The following Function with conditions 9.03/3.99 "undefined |Falseundefined; 9.03/3.99 " 9.03/3.99 is transformed to 9.03/3.99 "undefined = undefined1; 9.03/3.99 " 9.03/3.99 "undefined0 True = undefined; 9.03/3.99 " 9.03/3.99 "undefined1 = undefined0 False; 9.03/3.99 " 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (4) 9.03/3.99 Obligation: 9.03/3.99 mainModule Main 9.03/3.99 module Main where { 9.03/3.99 import qualified Prelude; 9.03/3.99 data MyBool = MyTrue | MyFalse ; 9.03/3.99 9.03/3.99 ltEsMyBool :: MyBool -> MyBool -> MyBool; 9.03/3.99 ltEsMyBool MyFalse MyFalse = MyTrue; 9.03/3.99 ltEsMyBool MyFalse MyTrue = MyTrue; 9.03/3.99 ltEsMyBool MyTrue MyFalse = MyFalse; 9.03/3.99 ltEsMyBool MyTrue MyTrue = MyTrue; 9.03/3.99 9.03/3.99 } 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (5) Narrow (EQUIVALENT) 9.03/3.99 Haskell To QDPs 9.03/3.99 9.03/3.99 digraph dp_graph { 9.03/3.99 node [outthreshold=100, inthreshold=100];1[label="ltEsMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.03/3.99 3[label="ltEsMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.03/3.99 4[label="ltEsMyBool vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];15[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 15 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 16[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 16 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 5[label="ltEsMyBool MyTrue vx4",fontsize=16,color="burlywood",shape="box"];17[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 17 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 18[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 18 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 6[label="ltEsMyBool MyFalse vx4",fontsize=16,color="burlywood",shape="box"];19[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 19 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 20[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9]; 9.03/3.99 20 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.03/3.99 7[label="ltEsMyBool MyTrue MyTrue",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3]; 9.03/3.99 8[label="ltEsMyBool MyTrue MyFalse",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3]; 9.03/3.99 9[label="ltEsMyBool MyFalse MyTrue",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 9.03/3.99 10[label="ltEsMyBool MyFalse MyFalse",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 9.03/3.99 11[label="MyTrue",fontsize=16,color="green",shape="box"];12[label="MyFalse",fontsize=16,color="green",shape="box"];13[label="MyTrue",fontsize=16,color="green",shape="box"];14[label="MyTrue",fontsize=16,color="green",shape="box"];} 9.03/3.99 9.03/3.99 ---------------------------------------- 9.03/3.99 9.03/3.99 (6) 9.03/3.99 YES 9.03/4.02 EOF