7.94/3.53 MAYBE 9.77/4.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.77/4.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.77/4.05 9.77/4.05 9.77/4.05 H-Termination with start terms of the given HASKELL could not be shown: 9.77/4.05 9.77/4.05 (0) HASKELL 9.77/4.05 (1) IFR [EQUIVALENT, 0 ms] 9.77/4.05 (2) HASKELL 9.77/4.05 (3) BR [EQUIVALENT, 0 ms] 9.77/4.05 (4) HASKELL 9.77/4.05 (5) COR [EQUIVALENT, 0 ms] 9.77/4.05 (6) HASKELL 9.77/4.05 (7) Narrow [SOUND, 0 ms] 9.77/4.05 (8) QDP 9.77/4.05 (9) NonTerminationLoopProof [COMPLETE, 0 ms] 9.77/4.05 (10) NO 9.77/4.05 (11) Narrow [COMPLETE, 0 ms] 9.77/4.05 (12) QDP 9.77/4.05 (13) PisEmptyProof [EQUIVALENT, 0 ms] 9.77/4.05 (14) YES 9.77/4.05 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (0) 9.77/4.05 Obligation: 9.77/4.05 mainModule Main 9.77/4.05 module Main where { 9.77/4.05 import qualified Prelude; 9.77/4.05 } 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (1) IFR (EQUIVALENT) 9.77/4.05 If Reductions: 9.77/4.05 The following If expression 9.77/4.05 "if p x then x else until p f (f x)" 9.77/4.05 is transformed to 9.77/4.05 "until0 x p f True = x; 9.77/4.05 until0 x p f False = until p f (f x); 9.77/4.05 " 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (2) 9.77/4.05 Obligation: 9.77/4.05 mainModule Main 9.77/4.05 module Main where { 9.77/4.05 import qualified Prelude; 9.77/4.05 } 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (3) BR (EQUIVALENT) 9.77/4.05 Replaced joker patterns by fresh variables and removed binding patterns. 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (4) 9.77/4.05 Obligation: 9.77/4.05 mainModule Main 9.77/4.05 module Main where { 9.77/4.05 import qualified Prelude; 9.77/4.05 } 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (5) COR (EQUIVALENT) 9.77/4.05 Cond Reductions: 9.77/4.05 The following Function with conditions 9.77/4.05 "undefined |Falseundefined; 9.77/4.05 " 9.77/4.05 is transformed to 9.77/4.05 "undefined = undefined1; 9.77/4.05 " 9.77/4.05 "undefined0 True = undefined; 9.77/4.05 " 9.77/4.05 "undefined1 = undefined0 False; 9.77/4.05 " 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (6) 9.77/4.05 Obligation: 9.77/4.05 mainModule Main 9.77/4.05 module Main where { 9.77/4.05 import qualified Prelude; 9.77/4.05 } 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (7) Narrow (SOUND) 9.77/4.05 Haskell To QDPs 9.77/4.05 9.77/4.05 digraph dp_graph { 9.77/4.05 node [outthreshold=100, inthreshold=100];1[label="until",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 3[label="until vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 4[label="until vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 5[label="until vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.77/4.05 6 -> 7[label="",style="dashed", color="red", weight=0]; 9.77/4.05 6[label="until0 vx5 vx3 vx4 (vx3 vx5)",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 9.77/4.05 8[label="vx3 vx5",fontsize=16,color="green",shape="box"];8 -> 12[label="",style="dashed", color="green", weight=3]; 9.77/4.05 7[label="until0 vx5 vx3 vx4 vx6",fontsize=16,color="burlywood",shape="triangle"];17[label="vx6/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 17[label="",style="solid", color="burlywood", weight=9]; 9.77/4.05 17 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.77/4.05 18[label="vx6/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 18[label="",style="solid", color="burlywood", weight=9]; 9.77/4.05 18 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.77/4.05 12[label="vx5",fontsize=16,color="green",shape="box"];10[label="until0 vx5 vx3 vx4 False",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 9.77/4.05 11[label="until0 vx5 vx3 vx4 True",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 9.77/4.05 13 -> 5[label="",style="dashed", color="red", weight=0]; 9.77/4.05 13[label="until vx3 vx4 (vx4 vx5)",fontsize=16,color="magenta"];13 -> 15[label="",style="dashed", color="magenta", weight=3]; 9.77/4.05 14[label="vx5",fontsize=16,color="green",shape="box"];15[label="vx4 vx5",fontsize=16,color="green",shape="box"];15 -> 16[label="",style="dashed", color="green", weight=3]; 9.77/4.05 16[label="vx5",fontsize=16,color="green",shape="box"];} 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (8) 9.77/4.05 Obligation: 9.77/4.05 Q DP problem: 9.77/4.05 The TRS P consists of the following rules: 9.77/4.05 9.77/4.05 new_until(vx3, vx4, h) -> new_until0(vx3, vx4, h) 9.77/4.05 new_until0(vx3, vx4, h) -> new_until(vx3, vx4, h) 9.77/4.05 9.77/4.05 R is empty. 9.77/4.05 Q is empty. 9.77/4.05 We have to consider all minimal (P,Q,R)-chains. 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (9) NonTerminationLoopProof (COMPLETE) 9.77/4.05 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 9.77/4.05 Found a loop by narrowing to the left: 9.77/4.05 9.77/4.05 s = new_until0(vx3', vx4', h') evaluates to t =new_until0(vx3', vx4', h') 9.77/4.05 9.77/4.05 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 9.77/4.05 * Matcher: [ ] 9.77/4.05 * Semiunifier: [ ] 9.77/4.05 9.77/4.05 -------------------------------------------------------------------------------- 9.77/4.05 Rewriting sequence 9.77/4.05 9.77/4.05 new_until0(vx3', vx4', h') -> new_until(vx3', vx4', h') 9.77/4.05 with rule new_until0(vx3'', vx4'', h'') -> new_until(vx3'', vx4'', h'') at position [] and matcher [vx3'' / vx3', vx4'' / vx4', h'' / h'] 9.77/4.05 9.77/4.05 new_until(vx3', vx4', h') -> new_until0(vx3', vx4', h') 9.77/4.05 with rule new_until(vx3, vx4, h) -> new_until0(vx3, vx4, h) 9.77/4.05 9.77/4.05 Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence 9.77/4.05 9.77/4.05 9.77/4.05 All these steps are and every following step will be a correct step w.r.t to Q. 9.77/4.05 9.77/4.05 9.77/4.05 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (10) 9.77/4.05 NO 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (11) Narrow (COMPLETE) 9.77/4.05 Haskell To QDPs 9.77/4.05 9.77/4.05 digraph dp_graph { 9.77/4.05 node [outthreshold=100, inthreshold=100];1[label="until",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 3[label="until vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 4[label="until vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 9.77/4.05 5[label="until vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.77/4.05 6 -> 7[label="",style="dashed", color="red", weight=0]; 9.77/4.05 6[label="until0 vx5 vx3 vx4 (vx3 vx5)",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 9.77/4.05 8[label="vx3 vx5",fontsize=16,color="green",shape="box"];8 -> 12[label="",style="dashed", color="green", weight=3]; 9.77/4.05 7[label="until0 vx5 vx3 vx4 vx6",fontsize=16,color="burlywood",shape="triangle"];17[label="vx6/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 17[label="",style="solid", color="burlywood", weight=9]; 9.77/4.05 17 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.77/4.05 18[label="vx6/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 18[label="",style="solid", color="burlywood", weight=9]; 9.77/4.05 18 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.77/4.05 12[label="vx5",fontsize=16,color="green",shape="box"];10[label="until0 vx5 vx3 vx4 False",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 9.77/4.05 11[label="until0 vx5 vx3 vx4 True",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 9.77/4.05 13 -> 5[label="",style="dashed", color="red", weight=0]; 9.77/4.05 13[label="until vx3 vx4 (vx4 vx5)",fontsize=16,color="magenta"];13 -> 15[label="",style="dashed", color="magenta", weight=3]; 9.77/4.05 14[label="vx5",fontsize=16,color="green",shape="box"];15[label="vx4 vx5",fontsize=16,color="green",shape="box"];15 -> 16[label="",style="dashed", color="green", weight=3]; 9.77/4.05 16[label="vx5",fontsize=16,color="green",shape="box"];} 9.77/4.05 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (12) 9.77/4.05 Obligation: 9.77/4.05 Q DP problem: 9.77/4.05 P is empty. 9.77/4.05 R is empty. 9.77/4.05 Q is empty. 9.77/4.05 We have to consider all (P,Q,R)-chains. 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (13) PisEmptyProof (EQUIVALENT) 9.77/4.05 The TRS P is empty. Hence, there is no (P,Q,R) chain. 9.77/4.05 ---------------------------------------- 9.77/4.05 9.77/4.05 (14) 9.77/4.05 YES 9.94/4.10 EOF