7.55/3.52 YES 9.59/4.03 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.59/4.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.59/4.03 9.59/4.03 9.59/4.03 H-Termination with start terms of the given HASKELL could be proven: 9.59/4.03 9.59/4.03 (0) HASKELL 9.59/4.03 (1) LR [EQUIVALENT, 0 ms] 9.59/4.03 (2) HASKELL 9.59/4.03 (3) BR [EQUIVALENT, 0 ms] 9.59/4.03 (4) HASKELL 9.59/4.03 (5) COR [EQUIVALENT, 0 ms] 9.59/4.03 (6) HASKELL 9.59/4.03 (7) Narrow [SOUND, 0 ms] 9.59/4.03 (8) QDP 9.59/4.03 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.59/4.03 (10) YES 9.59/4.03 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (0) 9.59/4.03 Obligation: 9.59/4.03 mainModule Main 9.59/4.03 module Main where { 9.59/4.03 import qualified Prelude; 9.59/4.03 } 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (1) LR (EQUIVALENT) 9.59/4.03 Lambda Reductions: 9.59/4.03 The following Lambda expression 9.59/4.03 "\xs->return (x : xs)" 9.59/4.03 is transformed to 9.59/4.03 "sequence0 x xs = return (x : xs); 9.59/4.03 " 9.59/4.03 The following Lambda expression 9.59/4.03 "\x->sequence cs >>= sequence0 x" 9.59/4.03 is transformed to 9.59/4.03 "sequence1 cs x = sequence cs >>= sequence0 x; 9.59/4.03 " 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (2) 9.59/4.03 Obligation: 9.59/4.03 mainModule Main 9.59/4.03 module Main where { 9.59/4.03 import qualified Prelude; 9.59/4.03 } 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (3) BR (EQUIVALENT) 9.59/4.03 Replaced joker patterns by fresh variables and removed binding patterns. 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (4) 9.59/4.03 Obligation: 9.59/4.03 mainModule Main 9.59/4.03 module Main where { 9.59/4.03 import qualified Prelude; 9.59/4.03 } 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (5) COR (EQUIVALENT) 9.59/4.03 Cond Reductions: 9.59/4.03 The following Function with conditions 9.59/4.03 "undefined |Falseundefined; 9.59/4.03 " 9.59/4.03 is transformed to 9.59/4.03 "undefined = undefined1; 9.59/4.03 " 9.59/4.03 "undefined0 True = undefined; 9.59/4.03 " 9.59/4.03 "undefined1 = undefined0 False; 9.59/4.03 " 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (6) 9.59/4.03 Obligation: 9.59/4.03 mainModule Main 9.59/4.03 module Main where { 9.59/4.03 import qualified Prelude; 9.59/4.03 } 9.59/4.03 9.59/4.03 ---------------------------------------- 9.59/4.03 9.59/4.03 (7) Narrow (SOUND) 9.59/4.03 Haskell To QDPs 9.59/4.03 9.59/4.03 digraph dp_graph { 9.59/4.03 node [outthreshold=100, inthreshold=100];1[label="sequence",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.59/4.03 3[label="sequence vx3",fontsize=16,color="burlywood",shape="triangle"];35[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 35[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 35 -> 4[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 36[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 36[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 36 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 4[label="sequence (vx30 : vx31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 9.59/4.04 5[label="sequence []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.59/4.04 6[label="vx30 >>= sequence1 vx31",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.59/4.04 7[label="return []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 9.59/4.04 8[label="primbindIO vx30 (sequence1 vx31)",fontsize=16,color="burlywood",shape="box"];37[label="vx30/IO vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 37[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 37 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 38[label="vx30/AProVE_IO vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 38 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 39[label="vx30/AProVE_Exception vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 39 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 40[label="vx30/AProVE_Error vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 40[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 40 -> 13[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 9[label="primretIO []",fontsize=16,color="black",shape="box"];9 -> 14[label="",style="solid", color="black", weight=3]; 9.59/4.04 10[label="primbindIO (IO vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3]; 9.59/4.04 11[label="primbindIO (AProVE_IO vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3]; 9.59/4.04 12[label="primbindIO (AProVE_Exception vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];12 -> 17[label="",style="solid", color="black", weight=3]; 9.59/4.04 13[label="primbindIO (AProVE_Error vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];13 -> 18[label="",style="solid", color="black", weight=3]; 9.59/4.04 14[label="AProVE_IO []",fontsize=16,color="green",shape="box"];15[label="error []",fontsize=16,color="red",shape="box"];16[label="sequence1 vx31 vx300",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3]; 9.59/4.04 17[label="AProVE_Exception vx300",fontsize=16,color="green",shape="box"];18[label="AProVE_Error vx300",fontsize=16,color="green",shape="box"];19 -> 20[label="",style="dashed", color="red", weight=0]; 9.59/4.04 19[label="sequence vx31 >>= sequence0 vx300",fontsize=16,color="magenta"];19 -> 21[label="",style="dashed", color="magenta", weight=3]; 9.59/4.04 21 -> 3[label="",style="dashed", color="red", weight=0]; 9.59/4.04 21[label="sequence vx31",fontsize=16,color="magenta"];21 -> 22[label="",style="dashed", color="magenta", weight=3]; 9.59/4.04 20[label="vx4 >>= sequence0 vx300",fontsize=16,color="black",shape="triangle"];20 -> 23[label="",style="solid", color="black", weight=3]; 9.59/4.04 22[label="vx31",fontsize=16,color="green",shape="box"];23[label="primbindIO vx4 (sequence0 vx300)",fontsize=16,color="burlywood",shape="box"];41[label="vx4/IO vx40",fontsize=10,color="white",style="solid",shape="box"];23 -> 41[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 41 -> 24[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 42[label="vx4/AProVE_IO vx40",fontsize=10,color="white",style="solid",shape="box"];23 -> 42[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 42 -> 25[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 43[label="vx4/AProVE_Exception vx40",fontsize=10,color="white",style="solid",shape="box"];23 -> 43[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 43 -> 26[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 44[label="vx4/AProVE_Error vx40",fontsize=10,color="white",style="solid",shape="box"];23 -> 44[label="",style="solid", color="burlywood", weight=9]; 9.59/4.04 44 -> 27[label="",style="solid", color="burlywood", weight=3]; 9.59/4.04 24[label="primbindIO (IO vx40) (sequence0 vx300)",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 9.59/4.04 25[label="primbindIO (AProVE_IO vx40) (sequence0 vx300)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 9.59/4.04 26[label="primbindIO (AProVE_Exception vx40) (sequence0 vx300)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 9.59/4.04 27[label="primbindIO (AProVE_Error vx40) (sequence0 vx300)",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 9.59/4.04 28[label="error []",fontsize=16,color="red",shape="box"];29[label="sequence0 vx300 vx40",fontsize=16,color="black",shape="box"];29 -> 32[label="",style="solid", color="black", weight=3]; 9.59/4.04 30[label="AProVE_Exception vx40",fontsize=16,color="green",shape="box"];31[label="AProVE_Error vx40",fontsize=16,color="green",shape="box"];32[label="return (vx300 : vx40)",fontsize=16,color="black",shape="box"];32 -> 33[label="",style="solid", color="black", weight=3]; 9.59/4.04 33[label="primretIO (vx300 : vx40)",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3]; 9.59/4.04 34[label="AProVE_IO (vx300 : vx40)",fontsize=16,color="green",shape="box"];} 9.59/4.04 9.59/4.04 ---------------------------------------- 9.59/4.04 9.59/4.04 (8) 9.59/4.04 Obligation: 9.59/4.04 Q DP problem: 9.59/4.04 The TRS P consists of the following rules: 9.59/4.04 9.59/4.04 new_sequence(:(AProVE_IO(vx300), vx31), h) -> new_sequence(vx31, h) 9.59/4.04 9.59/4.04 R is empty. 9.59/4.04 Q is empty. 9.59/4.04 We have to consider all minimal (P,Q,R)-chains. 9.59/4.04 ---------------------------------------- 9.59/4.04 9.59/4.04 (9) QDPSizeChangeProof (EQUIVALENT) 9.59/4.04 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. 9.59/4.04 9.59/4.04 From the DPs we obtained the following set of size-change graphs: 9.59/4.04 *new_sequence(:(AProVE_IO(vx300), vx31), h) -> new_sequence(vx31, h) 9.59/4.04 The graph contains the following edges 1 > 1, 2 >= 2 9.59/4.04 9.59/4.04 9.59/4.04 ---------------------------------------- 9.59/4.04 9.59/4.04 (10) 9.59/4.04 YES 9.74/4.15 EOF