7.80/3.72 YES 9.27/4.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.27/4.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.27/4.17 9.27/4.17 9.27/4.17 H-Termination with start terms of the given HASKELL could be proven: 9.27/4.17 9.27/4.17 (0) HASKELL 9.27/4.17 (1) BR [EQUIVALENT, 0 ms] 9.27/4.17 (2) HASKELL 9.27/4.17 (3) COR [EQUIVALENT, 0 ms] 9.27/4.17 (4) HASKELL 9.27/4.17 (5) Narrow [EQUIVALENT, 0 ms] 9.27/4.17 (6) YES 9.27/4.17 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (0) 9.27/4.17 Obligation: 9.27/4.17 mainModule Main 9.27/4.17 module Main where { 9.27/4.17 import qualified Prelude; 9.27/4.17 data List a = Cons a (List a) | Nil ; 9.27/4.17 9.27/4.17 head :: List a -> a; 9.27/4.17 head (Cons x vv) = x; 9.27/4.17 9.27/4.17 } 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (1) BR (EQUIVALENT) 9.27/4.17 Replaced joker patterns by fresh variables and removed binding patterns. 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (2) 9.27/4.17 Obligation: 9.27/4.17 mainModule Main 9.27/4.17 module Main where { 9.27/4.17 import qualified Prelude; 9.27/4.17 data List a = Cons a (List a) | Nil ; 9.27/4.17 9.27/4.17 head :: List a -> a; 9.27/4.17 head (Cons x vv) = x; 9.27/4.17 9.27/4.17 } 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (3) COR (EQUIVALENT) 9.27/4.17 Cond Reductions: 9.27/4.17 The following Function with conditions 9.27/4.17 "undefined |Falseundefined; 9.27/4.17 " 9.27/4.17 is transformed to 9.27/4.17 "undefined = undefined1; 9.27/4.17 " 9.27/4.17 "undefined0 True = undefined; 9.27/4.17 " 9.27/4.17 "undefined1 = undefined0 False; 9.27/4.17 " 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (4) 9.27/4.17 Obligation: 9.27/4.17 mainModule Main 9.27/4.17 module Main where { 9.27/4.17 import qualified Prelude; 9.27/4.17 data List a = Cons a (List a) | Nil ; 9.27/4.17 9.27/4.17 head :: List a -> a; 9.27/4.17 head (Cons x vv) = x; 9.27/4.17 9.27/4.17 } 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (5) Narrow (EQUIVALENT) 9.27/4.17 Haskell To QDPs 9.27/4.17 9.27/4.17 digraph dp_graph { 9.27/4.17 node [outthreshold=100, inthreshold=100];1[label="head",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.27/4.17 3[label="head vy3",fontsize=16,color="burlywood",shape="triangle"];8[label="vy3/Cons vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 8[label="",style="solid", color="burlywood", weight=9]; 9.27/4.17 8 -> 4[label="",style="solid", color="burlywood", weight=3]; 9.27/4.17 9[label="vy3/Nil",fontsize=10,color="white",style="solid",shape="box"];3 -> 9[label="",style="solid", color="burlywood", weight=9]; 9.27/4.17 9 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.27/4.17 4[label="head (Cons vy30 vy31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 9.27/4.17 5[label="head Nil",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.27/4.17 6[label="vy30",fontsize=16,color="green",shape="box"];7[label="error []",fontsize=16,color="red",shape="box"];} 9.27/4.17 9.27/4.17 ---------------------------------------- 9.27/4.17 9.27/4.17 (6) 9.27/4.17 YES 9.47/4.21 EOF