8.05/3.63 MAYBE 9.97/4.13 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.97/4.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.97/4.13 9.97/4.13 9.97/4.13 H-Termination with start terms of the given HASKELL could not be shown: 9.97/4.13 9.97/4.13 (0) HASKELL 9.97/4.13 (1) BR [EQUIVALENT, 0 ms] 9.97/4.13 (2) HASKELL 9.97/4.13 (3) COR [EQUIVALENT, 0 ms] 9.97/4.13 (4) HASKELL 9.97/4.13 (5) Narrow [SOUND, 0 ms] 9.97/4.13 (6) QDP 9.97/4.13 (7) NonTerminationLoopProof [COMPLETE, 0 ms] 9.97/4.13 (8) NO 9.97/4.13 (9) Narrow [COMPLETE, 0 ms] 9.97/4.13 (10) QDP 9.97/4.13 (11) PisEmptyProof [EQUIVALENT, 0 ms] 9.97/4.13 (12) YES 9.97/4.13 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (0) 9.97/4.13 Obligation: 9.97/4.13 mainModule Main 9.97/4.13 module Main where { 9.97/4.13 import qualified Prelude; 9.97/4.13 } 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (1) BR (EQUIVALENT) 9.97/4.13 Replaced joker patterns by fresh variables and removed binding patterns. 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (2) 9.97/4.13 Obligation: 9.97/4.13 mainModule Main 9.97/4.13 module Main where { 9.97/4.13 import qualified Prelude; 9.97/4.13 } 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (3) COR (EQUIVALENT) 9.97/4.13 Cond Reductions: 9.97/4.13 The following Function with conditions 9.97/4.13 "undefined |Falseundefined; 9.97/4.13 " 9.97/4.13 is transformed to 9.97/4.13 "undefined = undefined1; 9.97/4.13 " 9.97/4.13 "undefined0 True = undefined; 9.97/4.13 " 9.97/4.13 "undefined1 = undefined0 False; 9.97/4.13 " 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (4) 9.97/4.13 Obligation: 9.97/4.13 mainModule Main 9.97/4.13 module Main where { 9.97/4.13 import qualified Prelude; 9.97/4.13 } 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (5) Narrow (SOUND) 9.97/4.13 Haskell To QDPs 9.97/4.13 9.97/4.13 digraph dp_graph { 9.97/4.13 node [outthreshold=100, inthreshold=100];1[label="iterate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.97/4.13 3[label="iterate vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.97/4.13 4[label="iterate vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.97/4.13 5[label="vx4 : iterate vx3 (vx3 vx4)",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 9.97/4.13 6 -> 4[label="",style="dashed", color="red", weight=0]; 9.97/4.13 6[label="iterate vx3 (vx3 vx4)",fontsize=16,color="magenta"];6 -> 7[label="",style="dashed", color="magenta", weight=3]; 9.97/4.13 7[label="vx3 vx4",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3]; 9.97/4.13 8[label="vx4",fontsize=16,color="green",shape="box"];} 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (6) 9.97/4.13 Obligation: 9.97/4.13 Q DP problem: 9.97/4.13 The TRS P consists of the following rules: 9.97/4.13 9.97/4.13 new_iterate(vx3, h) -> new_iterate(vx3, h) 9.97/4.13 9.97/4.13 R is empty. 9.97/4.13 Q is empty. 9.97/4.13 We have to consider all minimal (P,Q,R)-chains. 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (7) NonTerminationLoopProof (COMPLETE) 9.97/4.13 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 9.97/4.13 Found a loop by semiunifying a rule from P directly. 9.97/4.13 9.97/4.13 s = new_iterate(vx3, h) evaluates to t =new_iterate(vx3, h) 9.97/4.13 9.97/4.13 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 9.97/4.13 * Matcher: [ ] 9.97/4.13 * Semiunifier: [ ] 9.97/4.13 9.97/4.13 -------------------------------------------------------------------------------- 9.97/4.13 Rewriting sequence 9.97/4.13 9.97/4.13 The DP semiunifies directly so there is only one rewrite step from new_iterate(vx3, h) to new_iterate(vx3, h). 9.97/4.13 9.97/4.13 9.97/4.13 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (8) 9.97/4.13 NO 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (9) Narrow (COMPLETE) 9.97/4.13 Haskell To QDPs 9.97/4.13 9.97/4.13 digraph dp_graph { 9.97/4.13 node [outthreshold=100, inthreshold=100];1[label="iterate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.97/4.13 3[label="iterate vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.97/4.13 4[label="iterate vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.97/4.13 5[label="vx4 : iterate vx3 (vx3 vx4)",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 9.97/4.13 6 -> 4[label="",style="dashed", color="red", weight=0]; 9.97/4.13 6[label="iterate vx3 (vx3 vx4)",fontsize=16,color="magenta"];6 -> 7[label="",style="dashed", color="magenta", weight=3]; 9.97/4.13 7[label="vx3 vx4",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3]; 9.97/4.13 8[label="vx4",fontsize=16,color="green",shape="box"];} 9.97/4.13 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (10) 9.97/4.13 Obligation: 9.97/4.13 Q DP problem: 9.97/4.13 P is empty. 9.97/4.13 R is empty. 9.97/4.13 Q is empty. 9.97/4.13 We have to consider all (P,Q,R)-chains. 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (11) PisEmptyProof (EQUIVALENT) 9.97/4.13 The TRS P is empty. Hence, there is no (P,Q,R) chain. 9.97/4.13 ---------------------------------------- 9.97/4.13 9.97/4.13 (12) 9.97/4.13 YES 10.02/4.22 EOF