7.88/3.56 YES 9.87/4.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.87/4.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.87/4.10 9.87/4.10 9.87/4.10 H-Termination with start terms of the given HASKELL could be proven: 9.87/4.10 9.87/4.10 (0) HASKELL 9.87/4.10 (1) LR [EQUIVALENT, 0 ms] 9.87/4.10 (2) HASKELL 9.87/4.10 (3) BR [EQUIVALENT, 0 ms] 9.87/4.10 (4) HASKELL 9.87/4.10 (5) COR [EQUIVALENT, 0 ms] 9.87/4.10 (6) HASKELL 9.87/4.10 (7) Narrow [SOUND, 0 ms] 9.87/4.10 (8) AND 9.87/4.10 (9) QDP 9.87/4.10 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.87/4.10 (11) YES 9.87/4.10 (12) QDP 9.87/4.10 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 9.87/4.10 (14) AND 9.87/4.10 (15) QDP 9.87/4.10 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.87/4.10 (17) YES 9.87/4.10 (18) QDP 9.87/4.10 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.87/4.10 (20) YES 9.87/4.10 (21) QDP 9.87/4.10 (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.87/4.10 (23) YES 9.87/4.10 (24) QDP 9.87/4.10 (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.87/4.10 (26) YES 9.87/4.10 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (0) 9.87/4.10 Obligation: 9.87/4.10 mainModule Main 9.87/4.10 module Main where { 9.87/4.10 import qualified Prelude; 9.87/4.10 } 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (1) LR (EQUIVALENT) 9.87/4.10 Lambda Reductions: 9.87/4.10 The following Lambda expression 9.87/4.10 "\_->q" 9.87/4.10 is transformed to 9.87/4.10 "gtGt0 q _ = q; 9.87/4.10 " 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (2) 9.87/4.10 Obligation: 9.87/4.10 mainModule Main 9.87/4.10 module Main where { 9.87/4.10 import qualified Prelude; 9.87/4.10 } 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (3) BR (EQUIVALENT) 9.87/4.10 Replaced joker patterns by fresh variables and removed binding patterns. 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (4) 9.87/4.10 Obligation: 9.87/4.10 mainModule Main 9.87/4.10 module Main where { 9.87/4.10 import qualified Prelude; 9.87/4.10 } 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (5) COR (EQUIVALENT) 9.87/4.10 Cond Reductions: 9.87/4.10 The following Function with conditions 9.87/4.10 "undefined |Falseundefined; 9.87/4.10 " 9.87/4.10 is transformed to 9.87/4.10 "undefined = undefined1; 9.87/4.10 " 9.87/4.10 "undefined0 True = undefined; 9.87/4.10 " 9.87/4.10 "undefined1 = undefined0 False; 9.87/4.10 " 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (6) 9.87/4.10 Obligation: 9.87/4.10 mainModule Main 9.87/4.10 module Main where { 9.87/4.10 import qualified Prelude; 9.87/4.10 } 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (7) Narrow (SOUND) 9.87/4.10 Haskell To QDPs 9.87/4.10 9.87/4.10 digraph dp_graph { 9.87/4.10 node [outthreshold=100, inthreshold=100];1[label="sequence_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.87/4.10 3[label="sequence_ vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.87/4.10 4[label="foldr (>>) (return ()) vy3",fontsize=16,color="burlywood",shape="triangle"];63[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 63[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 63 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 64[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 64[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 64 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 5[label="foldr (>>) (return ()) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.87/4.10 6[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.87/4.10 7[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="blue",shape="box"];65[label=">> :: (IO a) -> (IO ()) -> IO ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 65[label="",style="solid", color="blue", weight=9]; 9.87/4.10 65 -> 21[label="",style="solid", color="blue", weight=3]; 9.87/4.10 66[label=">> :: (Maybe a) -> (Maybe ()) -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 66[label="",style="solid", color="blue", weight=9]; 9.87/4.10 66 -> 22[label="",style="solid", color="blue", weight=3]; 9.87/4.10 67[label=">> :: ([] a) -> ([] ()) -> [] ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 67[label="",style="solid", color="blue", weight=9]; 9.87/4.10 67 -> 23[label="",style="solid", color="blue", weight=3]; 9.87/4.10 8[label="return ()",fontsize=16,color="blue",shape="box"];68[label="return :: () -> IO ()",fontsize=10,color="white",style="solid",shape="box"];8 -> 68[label="",style="solid", color="blue", weight=9]; 9.87/4.10 68 -> 11[label="",style="solid", color="blue", weight=3]; 9.87/4.10 69[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];8 -> 69[label="",style="solid", color="blue", weight=9]; 9.87/4.10 69 -> 12[label="",style="solid", color="blue", weight=3]; 9.87/4.10 70[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];8 -> 70[label="",style="solid", color="blue", weight=9]; 9.87/4.10 70 -> 13[label="",style="solid", color="blue", weight=3]; 9.87/4.10 21 -> 15[label="",style="dashed", color="red", weight=0]; 9.87/4.10 21[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];21 -> 28[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 22 -> 16[label="",style="dashed", color="red", weight=0]; 9.87/4.10 22[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];22 -> 29[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 23 -> 17[label="",style="dashed", color="red", weight=0]; 9.87/4.10 23[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];23 -> 30[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 11[label="return ()",fontsize=16,color="black",shape="box"];11 -> 18[label="",style="solid", color="black", weight=3]; 9.87/4.10 12[label="return ()",fontsize=16,color="black",shape="box"];12 -> 19[label="",style="solid", color="black", weight=3]; 9.87/4.10 13[label="return ()",fontsize=16,color="black",shape="box"];13 -> 20[label="",style="solid", color="black", weight=3]; 9.87/4.10 28 -> 4[label="",style="dashed", color="red", weight=0]; 9.87/4.10 28[label="foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];28 -> 36[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 15[label="(>>) vy30 vy4",fontsize=16,color="black",shape="triangle"];15 -> 24[label="",style="solid", color="black", weight=3]; 9.87/4.10 29 -> 4[label="",style="dashed", color="red", weight=0]; 9.87/4.10 29[label="foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];29 -> 37[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 16[label="(>>) vy30 vy4",fontsize=16,color="black",shape="triangle"];16 -> 25[label="",style="solid", color="black", weight=3]; 9.87/4.10 30 -> 4[label="",style="dashed", color="red", weight=0]; 9.87/4.10 30[label="foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];30 -> 38[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 17[label="(>>) vy30 vy4",fontsize=16,color="black",shape="triangle"];17 -> 26[label="",style="solid", color="black", weight=3]; 9.87/4.10 18[label="primretIO ()",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3]; 9.87/4.10 19[label="Just ()",fontsize=16,color="green",shape="box"];20[label="() : []",fontsize=16,color="green",shape="box"];36[label="vy31",fontsize=16,color="green",shape="box"];24[label="vy30 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];24 -> 31[label="",style="solid", color="black", weight=3]; 9.87/4.10 37[label="vy31",fontsize=16,color="green",shape="box"];25[label="vy30 >>= gtGt0 vy4",fontsize=16,color="burlywood",shape="box"];71[label="vy30/Nothing",fontsize=10,color="white",style="solid",shape="box"];25 -> 71[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 71 -> 32[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 72[label="vy30/Just vy300",fontsize=10,color="white",style="solid",shape="box"];25 -> 72[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 72 -> 33[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 38[label="vy31",fontsize=16,color="green",shape="box"];26[label="vy30 >>= gtGt0 vy4",fontsize=16,color="burlywood",shape="triangle"];73[label="vy30/vy300 : vy301",fontsize=10,color="white",style="solid",shape="box"];26 -> 73[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 73 -> 34[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 74[label="vy30/[]",fontsize=10,color="white",style="solid",shape="box"];26 -> 74[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 74 -> 35[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 27[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];31[label="primbindIO vy30 (gtGt0 vy4)",fontsize=16,color="burlywood",shape="box"];75[label="vy30/IO vy300",fontsize=10,color="white",style="solid",shape="box"];31 -> 75[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 75 -> 39[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 76[label="vy30/AProVE_IO vy300",fontsize=10,color="white",style="solid",shape="box"];31 -> 76[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 76 -> 40[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 77[label="vy30/AProVE_Exception vy300",fontsize=10,color="white",style="solid",shape="box"];31 -> 77[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 77 -> 41[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 78[label="vy30/AProVE_Error vy300",fontsize=10,color="white",style="solid",shape="box"];31 -> 78[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 78 -> 42[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 32[label="Nothing >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];32 -> 43[label="",style="solid", color="black", weight=3]; 9.87/4.10 33[label="Just vy300 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];33 -> 44[label="",style="solid", color="black", weight=3]; 9.87/4.10 34[label="vy300 : vy301 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];34 -> 45[label="",style="solid", color="black", weight=3]; 9.87/4.10 35[label="[] >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];35 -> 46[label="",style="solid", color="black", weight=3]; 9.87/4.10 39[label="primbindIO (IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];39 -> 47[label="",style="solid", color="black", weight=3]; 9.87/4.10 40[label="primbindIO (AProVE_IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];40 -> 48[label="",style="solid", color="black", weight=3]; 9.87/4.10 41[label="primbindIO (AProVE_Exception vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];41 -> 49[label="",style="solid", color="black", weight=3]; 9.87/4.10 42[label="primbindIO (AProVE_Error vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];42 -> 50[label="",style="solid", color="black", weight=3]; 9.87/4.10 43[label="Nothing",fontsize=16,color="green",shape="box"];44[label="gtGt0 vy4 vy300",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3]; 9.87/4.10 45 -> 52[label="",style="dashed", color="red", weight=0]; 9.87/4.10 45[label="gtGt0 vy4 vy300 ++ (vy301 >>= gtGt0 vy4)",fontsize=16,color="magenta"];45 -> 53[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 46[label="[]",fontsize=16,color="green",shape="box"];47[label="error []",fontsize=16,color="red",shape="box"];48[label="gtGt0 vy4 vy300",fontsize=16,color="black",shape="box"];48 -> 54[label="",style="solid", color="black", weight=3]; 9.87/4.10 49[label="AProVE_Exception vy300",fontsize=16,color="green",shape="box"];50[label="AProVE_Error vy300",fontsize=16,color="green",shape="box"];51[label="vy4",fontsize=16,color="green",shape="box"];53 -> 26[label="",style="dashed", color="red", weight=0]; 9.87/4.10 53[label="vy301 >>= gtGt0 vy4",fontsize=16,color="magenta"];53 -> 55[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 52[label="gtGt0 vy4 vy300 ++ vy5",fontsize=16,color="black",shape="triangle"];52 -> 56[label="",style="solid", color="black", weight=3]; 9.87/4.10 54[label="vy4",fontsize=16,color="green",shape="box"];55[label="vy301",fontsize=16,color="green",shape="box"];56[label="vy4 ++ vy5",fontsize=16,color="burlywood",shape="triangle"];79[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];56 -> 79[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 79 -> 57[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 80[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];56 -> 80[label="",style="solid", color="burlywood", weight=9]; 9.87/4.10 80 -> 58[label="",style="solid", color="burlywood", weight=3]; 9.87/4.10 57[label="(vy40 : vy41) ++ vy5",fontsize=16,color="black",shape="box"];57 -> 59[label="",style="solid", color="black", weight=3]; 9.87/4.10 58[label="[] ++ vy5",fontsize=16,color="black",shape="box"];58 -> 60[label="",style="solid", color="black", weight=3]; 9.87/4.10 59[label="vy40 : vy41 ++ vy5",fontsize=16,color="green",shape="box"];59 -> 61[label="",style="dashed", color="green", weight=3]; 9.87/4.10 60[label="vy5",fontsize=16,color="green",shape="box"];61 -> 56[label="",style="dashed", color="red", weight=0]; 9.87/4.10 61[label="vy41 ++ vy5",fontsize=16,color="magenta"];61 -> 62[label="",style="dashed", color="magenta", weight=3]; 9.87/4.10 62[label="vy41",fontsize=16,color="green",shape="box"];} 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (8) 9.87/4.10 Complex Obligation (AND) 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (9) 9.87/4.10 Obligation: 9.87/4.10 Q DP problem: 9.87/4.10 The TRS P consists of the following rules: 9.87/4.10 9.87/4.10 new_gtGtEs(:(vy300, vy301), vy4, h) -> new_gtGtEs(vy301, vy4, h) 9.87/4.10 9.87/4.10 R is empty. 9.87/4.10 Q is empty. 9.87/4.10 We have to consider all minimal (P,Q,R)-chains. 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (10) QDPSizeChangeProof (EQUIVALENT) 9.87/4.10 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. 9.87/4.10 9.87/4.10 From the DPs we obtained the following set of size-change graphs: 9.87/4.10 *new_gtGtEs(:(vy300, vy301), vy4, h) -> new_gtGtEs(vy301, vy4, h) 9.87/4.10 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 9.87/4.10 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (11) 9.87/4.10 YES 9.87/4.10 9.87/4.10 ---------------------------------------- 9.87/4.10 9.87/4.10 (12) 9.87/4.10 Obligation: 9.87/4.11 Q DP problem: 9.87/4.11 The TRS P consists of the following rules: 9.87/4.11 9.87/4.11 new_foldr(:(vy30, vy31), ty_[], h) -> new_foldr(vy31, ty_[], h) 9.87/4.11 new_foldr(:(vy30, vy31), ty_Maybe, h) -> new_foldr(vy31, ty_Maybe, h) 9.87/4.11 new_foldr(:(vy30, vy31), ty_IO, h) -> new_foldr(vy31, ty_IO, h) 9.87/4.11 9.87/4.11 R is empty. 9.87/4.11 Q is empty. 9.87/4.11 We have to consider all minimal (P,Q,R)-chains. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (13) DependencyGraphProof (EQUIVALENT) 9.87/4.11 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (14) 9.87/4.11 Complex Obligation (AND) 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (15) 9.87/4.11 Obligation: 9.87/4.11 Q DP problem: 9.87/4.11 The TRS P consists of the following rules: 9.87/4.11 9.87/4.11 new_foldr(:(vy30, vy31), ty_IO, h) -> new_foldr(vy31, ty_IO, h) 9.87/4.11 9.87/4.11 R is empty. 9.87/4.11 Q is empty. 9.87/4.11 We have to consider all minimal (P,Q,R)-chains. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (16) QDPSizeChangeProof (EQUIVALENT) 9.87/4.11 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. 9.87/4.11 9.87/4.11 From the DPs we obtained the following set of size-change graphs: 9.87/4.11 *new_foldr(:(vy30, vy31), ty_IO, h) -> new_foldr(vy31, ty_IO, h) 9.87/4.11 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 9.87/4.11 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (17) 9.87/4.11 YES 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (18) 9.87/4.11 Obligation: 9.87/4.11 Q DP problem: 9.87/4.11 The TRS P consists of the following rules: 9.87/4.11 9.87/4.11 new_foldr(:(vy30, vy31), ty_Maybe, h) -> new_foldr(vy31, ty_Maybe, h) 9.87/4.11 9.87/4.11 R is empty. 9.87/4.11 Q is empty. 9.87/4.11 We have to consider all minimal (P,Q,R)-chains. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (19) QDPSizeChangeProof (EQUIVALENT) 9.87/4.11 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. 9.87/4.11 9.87/4.11 From the DPs we obtained the following set of size-change graphs: 9.87/4.11 *new_foldr(:(vy30, vy31), ty_Maybe, h) -> new_foldr(vy31, ty_Maybe, h) 9.87/4.11 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 9.87/4.11 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (20) 9.87/4.11 YES 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (21) 9.87/4.11 Obligation: 9.87/4.11 Q DP problem: 9.87/4.11 The TRS P consists of the following rules: 9.87/4.11 9.87/4.11 new_foldr(:(vy30, vy31), ty_[], h) -> new_foldr(vy31, ty_[], h) 9.87/4.11 9.87/4.11 R is empty. 9.87/4.11 Q is empty. 9.87/4.11 We have to consider all minimal (P,Q,R)-chains. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (22) QDPSizeChangeProof (EQUIVALENT) 9.87/4.11 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. 9.87/4.11 9.87/4.11 From the DPs we obtained the following set of size-change graphs: 9.87/4.11 *new_foldr(:(vy30, vy31), ty_[], h) -> new_foldr(vy31, ty_[], h) 9.87/4.11 The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 9.87/4.11 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (23) 9.87/4.11 YES 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (24) 9.87/4.11 Obligation: 9.87/4.11 Q DP problem: 9.87/4.11 The TRS P consists of the following rules: 9.87/4.11 9.87/4.11 new_psPs(:(vy40, vy41), vy5) -> new_psPs(vy41, vy5) 9.87/4.11 9.87/4.11 R is empty. 9.87/4.11 Q is empty. 9.87/4.11 We have to consider all minimal (P,Q,R)-chains. 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (25) QDPSizeChangeProof (EQUIVALENT) 9.87/4.11 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. 9.87/4.11 9.87/4.11 From the DPs we obtained the following set of size-change graphs: 9.87/4.11 *new_psPs(:(vy40, vy41), vy5) -> new_psPs(vy41, vy5) 9.87/4.11 The graph contains the following edges 1 > 1, 2 >= 2 9.87/4.11 9.87/4.11 9.87/4.11 ---------------------------------------- 9.87/4.11 9.87/4.11 (26) 9.87/4.11 YES 10.05/4.17 EOF