7.69/3.46 YES 9.33/3.91 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.33/3.91 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.33/3.91 9.33/3.91 9.33/3.91 H-Termination with start terms of the given HASKELL could be proven: 9.33/3.91 9.33/3.91 (0) HASKELL 9.33/3.91 (1) BR [EQUIVALENT, 0 ms] 9.33/3.91 (2) HASKELL 9.33/3.91 (3) COR [EQUIVALENT, 0 ms] 9.33/3.91 (4) HASKELL 9.33/3.91 (5) Narrow [SOUND, 0 ms] 9.33/3.91 (6) QDP 9.33/3.91 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.33/3.91 (8) YES 9.33/3.91 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (0) 9.33/3.91 Obligation: 9.33/3.91 mainModule Main 9.33/3.91 module Main where { 9.33/3.91 import qualified Prelude; 9.33/3.91 } 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (1) BR (EQUIVALENT) 9.33/3.91 Replaced joker patterns by fresh variables and removed binding patterns. 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (2) 9.33/3.91 Obligation: 9.33/3.91 mainModule Main 9.33/3.91 module Main where { 9.33/3.91 import qualified Prelude; 9.33/3.91 } 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (3) COR (EQUIVALENT) 9.33/3.91 Cond Reductions: 9.33/3.91 The following Function with conditions 9.33/3.91 "undefined |Falseundefined; 9.33/3.91 " 9.33/3.91 is transformed to 9.33/3.91 "undefined = undefined1; 9.33/3.91 " 9.33/3.91 "undefined0 True = undefined; 9.33/3.91 " 9.33/3.91 "undefined1 = undefined0 False; 9.33/3.91 " 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (4) 9.33/3.91 Obligation: 9.33/3.91 mainModule Main 9.33/3.91 module Main where { 9.33/3.91 import qualified Prelude; 9.33/3.91 } 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (5) Narrow (SOUND) 9.33/3.91 Haskell To QDPs 9.33/3.91 9.33/3.91 digraph dp_graph { 9.33/3.91 node [outthreshold=100, inthreshold=100];1[label="and",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.33/3.91 3[label="and vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.33/3.91 4[label="foldr (&&) True vx3",fontsize=16,color="burlywood",shape="triangle"];16[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9]; 9.33/3.91 16 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.33/3.91 17[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9]; 9.33/3.91 17 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.33/3.91 5[label="foldr (&&) True (vx30 : vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.33/3.91 6[label="foldr (&&) True []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.33/3.91 7 -> 9[label="",style="dashed", color="red", weight=0]; 9.33/3.91 7[label="(&&) vx30 foldr (&&) True vx31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 9.33/3.91 8[label="True",fontsize=16,color="green",shape="box"];10 -> 4[label="",style="dashed", color="red", weight=0]; 9.33/3.91 10[label="foldr (&&) True vx31",fontsize=16,color="magenta"];10 -> 11[label="",style="dashed", color="magenta", weight=3]; 9.33/3.91 9[label="(&&) vx30 vx4",fontsize=16,color="burlywood",shape="triangle"];18[label="vx30/False",fontsize=10,color="white",style="solid",shape="box"];9 -> 18[label="",style="solid", color="burlywood", weight=9]; 9.33/3.91 18 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.33/3.91 19[label="vx30/True",fontsize=10,color="white",style="solid",shape="box"];9 -> 19[label="",style="solid", color="burlywood", weight=9]; 9.33/3.91 19 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.33/3.91 11[label="vx31",fontsize=16,color="green",shape="box"];12[label="(&&) False vx4",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 9.33/3.91 13[label="(&&) True vx4",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 9.33/3.91 14[label="False",fontsize=16,color="green",shape="box"];15[label="vx4",fontsize=16,color="green",shape="box"];} 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (6) 9.33/3.91 Obligation: 9.33/3.91 Q DP problem: 9.33/3.91 The TRS P consists of the following rules: 9.33/3.91 9.33/3.91 new_foldr(:(vx30, vx31)) -> new_foldr(vx31) 9.33/3.91 9.33/3.91 R is empty. 9.33/3.91 Q is empty. 9.33/3.91 We have to consider all minimal (P,Q,R)-chains. 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (7) QDPSizeChangeProof (EQUIVALENT) 9.33/3.91 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 9.33/3.91 9.33/3.91 From the DPs we obtained the following set of size-change graphs: 9.33/3.91 *new_foldr(:(vx30, vx31)) -> new_foldr(vx31) 9.33/3.91 The graph contains the following edges 1 > 1 9.33/3.91 9.33/3.91 9.33/3.91 ---------------------------------------- 9.33/3.91 9.33/3.91 (8) 9.33/3.91 YES 9.33/3.95 EOF