8.27/3.55 NO 10.32/4.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 10.32/4.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.32/4.09 10.32/4.09 10.32/4.09 H-Termination with start terms of the given HASKELL could be disproven: 10.32/4.09 10.32/4.09 (0) HASKELL 10.32/4.09 (1) BR [EQUIVALENT, 0 ms] 10.32/4.09 (2) HASKELL 10.32/4.09 (3) COR [EQUIVALENT, 0 ms] 10.32/4.09 (4) HASKELL 10.32/4.09 (5) LetRed [EQUIVALENT, 0 ms] 10.32/4.09 (6) HASKELL 10.32/4.09 (7) Narrow [COMPLETE, 0 ms] 10.32/4.09 (8) QDP 10.32/4.09 (9) NonTerminationLoopProof [COMPLETE, 0 ms] 10.32/4.09 (10) NO 10.32/4.09 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (0) 10.32/4.09 Obligation: 10.32/4.09 mainModule Main 10.32/4.09 module Main where { 10.32/4.09 import qualified Prelude; 10.32/4.09 } 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (1) BR (EQUIVALENT) 10.32/4.09 Replaced joker patterns by fresh variables and removed binding patterns. 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (2) 10.32/4.09 Obligation: 10.32/4.09 mainModule Main 10.32/4.09 module Main where { 10.32/4.09 import qualified Prelude; 10.32/4.09 } 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (3) COR (EQUIVALENT) 10.32/4.09 Cond Reductions: 10.32/4.09 The following Function with conditions 10.32/4.09 "undefined |Falseundefined; 10.32/4.09 " 10.32/4.09 is transformed to 10.32/4.09 "undefined = undefined1; 10.32/4.09 " 10.32/4.09 "undefined0 True = undefined; 10.32/4.09 " 10.32/4.09 "undefined1 = undefined0 False; 10.32/4.09 " 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (4) 10.32/4.09 Obligation: 10.32/4.09 mainModule Main 10.32/4.09 module Main where { 10.32/4.09 import qualified Prelude; 10.32/4.09 } 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (5) LetRed (EQUIVALENT) 10.32/4.09 Let/Where Reductions: 10.32/4.09 The bindings of the following Let/Where expression 10.32/4.09 "xs where { 10.32/4.09 xs = x : xs; 10.32/4.09 } 10.32/4.09 " 10.32/4.09 are unpacked to the following functions on top level 10.32/4.09 "repeatXs vx = vx : repeatXs vx; 10.32/4.09 " 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (6) 10.32/4.09 Obligation: 10.32/4.09 mainModule Main 10.32/4.09 module Main where { 10.32/4.09 import qualified Prelude; 10.32/4.09 } 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (7) Narrow (COMPLETE) 10.32/4.09 Haskell To QDPs 10.32/4.09 10.32/4.09 digraph dp_graph { 10.32/4.09 node [outthreshold=100, inthreshold=100];1[label="repeat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.32/4.09 3[label="repeat vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.32/4.09 4[label="repeatXs vy3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 10.32/4.09 5[label="vy3 : repeatXs vy3",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 10.32/4.09 6 -> 4[label="",style="dashed", color="red", weight=0]; 10.32/4.09 6[label="repeatXs vy3",fontsize=16,color="magenta"];} 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (8) 10.32/4.09 Obligation: 10.32/4.09 Q DP problem: 10.32/4.09 The TRS P consists of the following rules: 10.32/4.09 10.32/4.09 new_repeatXs(vy3, h, []) -> new_repeatXs(vy3, h, []) 10.32/4.09 10.32/4.09 R is empty. 10.32/4.09 Q is empty. 10.32/4.09 We have to consider all (P,Q,R)-chains. 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (9) NonTerminationLoopProof (COMPLETE) 10.32/4.09 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 10.32/4.09 Found a loop by semiunifying a rule from P directly. 10.32/4.09 10.32/4.09 s = new_repeatXs(vy3, h, []) evaluates to t =new_repeatXs(vy3, h, []) 10.32/4.09 10.32/4.09 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 10.32/4.09 * Matcher: [ ] 10.32/4.09 * Semiunifier: [ ] 10.32/4.09 10.32/4.09 -------------------------------------------------------------------------------- 10.32/4.09 Rewriting sequence 10.32/4.09 10.32/4.09 The DP semiunifies directly so there is only one rewrite step from new_repeatXs(vy3, h, []) to new_repeatXs(vy3, h, []). 10.32/4.09 10.32/4.09 10.32/4.09 10.32/4.09 10.32/4.09 ---------------------------------------- 10.32/4.09 10.32/4.09 (10) 10.32/4.09 NO 10.44/4.15 EOF