7.80/3.50 YES 9.18/3.93 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.18/3.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.18/3.93 9.18/3.93 9.18/3.93 H-Termination with start terms of the given HASKELL could be proven: 9.18/3.93 9.18/3.93 (0) HASKELL 9.18/3.93 (1) BR [EQUIVALENT, 0 ms] 9.18/3.93 (2) HASKELL 9.18/3.93 (3) COR [EQUIVALENT, 0 ms] 9.18/3.93 (4) HASKELL 9.18/3.93 (5) Narrow [SOUND, 0 ms] 9.18/3.93 (6) QDP 9.18/3.93 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.18/3.93 (8) YES 9.18/3.93 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (0) 9.18/3.93 Obligation: 9.18/3.93 mainModule Main 9.18/3.93 module Main where { 9.18/3.93 import qualified Prelude; 9.18/3.93 } 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (1) BR (EQUIVALENT) 9.18/3.93 Replaced joker patterns by fresh variables and removed binding patterns. 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (2) 9.18/3.93 Obligation: 9.18/3.93 mainModule Main 9.18/3.93 module Main where { 9.18/3.93 import qualified Prelude; 9.18/3.93 } 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (3) COR (EQUIVALENT) 9.18/3.93 Cond Reductions: 9.18/3.93 The following Function with conditions 9.18/3.93 "undefined |Falseundefined; 9.18/3.93 " 9.18/3.93 is transformed to 9.18/3.93 "undefined = undefined1; 9.18/3.93 " 9.18/3.93 "undefined0 True = undefined; 9.18/3.93 " 9.18/3.93 "undefined1 = undefined0 False; 9.18/3.93 " 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (4) 9.18/3.93 Obligation: 9.18/3.93 mainModule Main 9.18/3.93 module Main where { 9.18/3.93 import qualified Prelude; 9.18/3.93 } 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (5) Narrow (SOUND) 9.18/3.93 Haskell To QDPs 9.18/3.93 9.18/3.93 digraph dp_graph { 9.18/3.93 node [outthreshold=100, inthreshold=100];1[label="last",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.18/3.93 3[label="last vy3",fontsize=16,color="burlywood",shape="triangle"];12[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 12[label="",style="solid", color="burlywood", weight=9]; 9.18/3.93 12 -> 4[label="",style="solid", color="burlywood", weight=3]; 9.18/3.93 13[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 13[label="",style="solid", color="burlywood", weight=9]; 9.18/3.93 13 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.18/3.93 4[label="last (vy30 : vy31)",fontsize=16,color="burlywood",shape="box"];14[label="vy31/vy310 : vy311",fontsize=10,color="white",style="solid",shape="box"];4 -> 14[label="",style="solid", color="burlywood", weight=9]; 9.18/3.93 14 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.18/3.93 15[label="vy31/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9]; 9.18/3.93 15 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.18/3.93 5[label="last []",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3]; 9.18/3.93 6[label="last (vy30 : vy310 : vy311)",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 9.18/3.93 7[label="last (vy30 : [])",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 9.18/3.93 8[label="error []",fontsize=16,color="red",shape="box"];9 -> 3[label="",style="dashed", color="red", weight=0]; 9.18/3.93 9[label="last (vy310 : vy311)",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3]; 9.18/3.93 10[label="vy30",fontsize=16,color="green",shape="box"];11[label="vy310 : vy311",fontsize=16,color="green",shape="box"];} 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (6) 9.18/3.93 Obligation: 9.18/3.93 Q DP problem: 9.18/3.93 The TRS P consists of the following rules: 9.18/3.93 9.18/3.93 new_last(:(vy30, :(vy310, vy311)), h) -> new_last(:(vy310, vy311), h) 9.18/3.93 9.18/3.93 R is empty. 9.18/3.93 Q is empty. 9.18/3.93 We have to consider all minimal (P,Q,R)-chains. 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (7) QDPSizeChangeProof (EQUIVALENT) 9.18/3.93 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. 9.18/3.93 9.18/3.93 From the DPs we obtained the following set of size-change graphs: 9.18/3.93 *new_last(:(vy30, :(vy310, vy311)), h) -> new_last(:(vy310, vy311), h) 9.18/3.93 The graph contains the following edges 1 > 1, 2 >= 2 9.18/3.93 9.18/3.93 9.18/3.93 ---------------------------------------- 9.18/3.93 9.18/3.93 (8) 9.18/3.93 YES 9.42/3.97 EOF