/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) CR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) QDP (9) NonTerminationLoopProof [COMPLETE, 0 ms] (10) NO (11) Narrow [COMPLETE, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; unfoldr :: (b -> Maybe (a,b)) -> b -> [a]; unfoldr f b = case f b of { Just (a,new_b)-> a : unfoldr f new_b; Nothing-> []; } ; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) CR (EQUIVALENT) Case Reductions: The following Case expression "case f b of { Just (a,new_b) -> a : unfoldr f new_b; Nothing -> []} " is transformed to "unfoldr0 f (Just (a,new_b)) = a : unfoldr f new_b; unfoldr0 f Nothing = []; " ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; unfoldr :: (b -> Maybe (a,b)) -> b -> [a]; unfoldr f b = unfoldr0 f (f b); unfoldr0 f (Just (a,new_b)) = a : unfoldr f new_b; unfoldr0 f Nothing = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; unfoldr :: (a -> Maybe (b,a)) -> a -> [b]; unfoldr f b = unfoldr0 f (f b); unfoldr0 f (Just (a,new_b)) = a : unfoldr f new_b; unfoldr0 f Nothing = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; unfoldr :: (b -> Maybe (a,b)) -> b -> [a]; unfoldr f b = unfoldr0 f (f b); unfoldr0 f (Just (a,new_b)) = a : unfoldr f new_b; unfoldr0 f Nothing = []; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.unfoldr",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.unfoldr vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="List.unfoldr vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5 -> 6[label="",style="dashed", color="red", weight=0]; 5[label="List.unfoldr0 vy3 (vy3 vy4)",fontsize=16,color="magenta"];5 -> 7[label="",style="dashed", color="magenta", weight=3]; 7[label="vy3 vy4",fontsize=16,color="green",shape="box"];7 -> 11[label="",style="dashed", color="green", weight=3]; 6[label="List.unfoldr0 vy3 vy5",fontsize=16,color="burlywood",shape="triangle"];17[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 17[label="",style="solid", color="burlywood", weight=9]; 17 -> 9[label="",style="solid", color="burlywood", weight=3]; 18[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];6 -> 18[label="",style="solid", color="burlywood", weight=9]; 18 -> 10[label="",style="solid", color="burlywood", weight=3]; 11[label="vy4",fontsize=16,color="green",shape="box"];9[label="List.unfoldr0 vy3 Nothing",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 10[label="List.unfoldr0 vy3 (Just vy50)",fontsize=16,color="burlywood",shape="box"];19[label="vy50/(vy500,vy501)",fontsize=10,color="white",style="solid",shape="box"];10 -> 19[label="",style="solid", color="burlywood", weight=9]; 19 -> 13[label="",style="solid", color="burlywood", weight=3]; 12[label="[]",fontsize=16,color="green",shape="box"];13[label="List.unfoldr0 vy3 (Just (vy500,vy501))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 14[label="vy500 : List.unfoldr vy3 vy501",fontsize=16,color="green",shape="box"];14 -> 15[label="",style="dashed", color="green", weight=3]; 15 -> 4[label="",style="dashed", color="red", weight=0]; 15[label="List.unfoldr vy3 vy501",fontsize=16,color="magenta"];15 -> 16[label="",style="dashed", color="magenta", weight=3]; 16[label="vy501",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_unfoldr(vy3, ba, bb) -> new_unfoldr0(vy3, ba, bb) new_unfoldr0(vy3, ba, bb) -> new_unfoldr(vy3, ba, bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by narrowing to the left: s = new_unfoldr0(vy3', ba', bb') evaluates to t =new_unfoldr0(vy3', ba', bb') Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence new_unfoldr0(vy3', ba', bb') -> new_unfoldr(vy3', ba', bb') with rule new_unfoldr0(vy3'', ba'', bb'') -> new_unfoldr(vy3'', ba'', bb'') at position [] and matcher [vy3'' / vy3', ba'' / ba', bb'' / bb'] new_unfoldr(vy3', ba', bb') -> new_unfoldr0(vy3', ba', bb') with rule new_unfoldr(vy3, ba, bb) -> new_unfoldr0(vy3, ba, bb) Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence All these steps are and every following step will be a correct step w.r.t to Q. ---------------------------------------- (10) NO ---------------------------------------- (11) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.unfoldr",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.unfoldr vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="List.unfoldr vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5 -> 6[label="",style="dashed", color="red", weight=0]; 5[label="List.unfoldr0 vy3 (vy3 vy4)",fontsize=16,color="magenta"];5 -> 7[label="",style="dashed", color="magenta", weight=3]; 7[label="vy3 vy4",fontsize=16,color="green",shape="box"];7 -> 11[label="",style="dashed", color="green", weight=3]; 6[label="List.unfoldr0 vy3 vy5",fontsize=16,color="burlywood",shape="triangle"];17[label="vy5/Nothing",fontsize=10,color="white",style="solid",shape="box"];6 -> 17[label="",style="solid", color="burlywood", weight=9]; 17 -> 9[label="",style="solid", color="burlywood", weight=3]; 18[label="vy5/Just vy50",fontsize=10,color="white",style="solid",shape="box"];6 -> 18[label="",style="solid", color="burlywood", weight=9]; 18 -> 10[label="",style="solid", color="burlywood", weight=3]; 11[label="vy4",fontsize=16,color="green",shape="box"];9[label="List.unfoldr0 vy3 Nothing",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 10[label="List.unfoldr0 vy3 (Just vy50)",fontsize=16,color="burlywood",shape="box"];19[label="vy50/(vy500,vy501)",fontsize=10,color="white",style="solid",shape="box"];10 -> 19[label="",style="solid", color="burlywood", weight=9]; 19 -> 13[label="",style="solid", color="burlywood", weight=3]; 12[label="[]",fontsize=16,color="green",shape="box"];13[label="List.unfoldr0 vy3 (Just (vy500,vy501))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 14[label="vy500 : List.unfoldr vy3 vy501",fontsize=16,color="green",shape="box"];14 -> 15[label="",style="dashed", color="green", weight=3]; 15 -> 4[label="",style="dashed", color="red", weight=0]; 15[label="List.unfoldr vy3 vy501",fontsize=16,color="magenta"];15 -> 16[label="",style="dashed", color="magenta", weight=3]; 16[label="vy501",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_unfoldr0(vy3, Just(@2(vy500, vy501)), ba, bb, []) -> new_unfoldr(vy3, vy501, ba, bb, []) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (13) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (14) TRUE