8.05/3.54	YES
9.98/4.06	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.98/4.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.98/4.06	
9.98/4.06	
9.98/4.06	H-Termination with start terms of the given HASKELL could be proven:
9.98/4.06	
9.98/4.06	(0) HASKELL
9.98/4.06	(1) LR [EQUIVALENT, 0 ms]
9.98/4.06	(2) HASKELL
9.98/4.06	(3) BR [EQUIVALENT, 0 ms]
9.98/4.06	(4) HASKELL
9.98/4.06	(5) COR [EQUIVALENT, 0 ms]
9.98/4.06	(6) HASKELL
9.98/4.06	(7) Narrow [SOUND, 0 ms]
9.98/4.06	(8) AND
9.98/4.06	    (9) QDP
9.98/4.06	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.98/4.06	        (11) YES
9.98/4.06	    (12) QDP
9.98/4.06	        (13) DependencyGraphProof [EQUIVALENT, 0 ms]
9.98/4.06	        (14) AND
9.98/4.06	            (15) QDP
9.98/4.06	                (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.98/4.06	                (17) YES
9.98/4.06	            (18) QDP
9.98/4.06	                (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.98/4.06	                (20) YES
9.98/4.06	            (21) QDP
9.98/4.06	                (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.98/4.06	                (23) YES
9.98/4.06	    (24) QDP
9.98/4.06	        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
9.98/4.06	        (26) YES
9.98/4.06	
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(0)
9.98/4.06	Obligation:
9.98/4.06	mainModule Main 
9.98/4.06	module Main where {
9.98/4.06	import qualified Prelude;
9.98/4.06	}
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(1) LR (EQUIVALENT)
9.98/4.06	Lambda Reductions:
9.98/4.06	The following Lambda expression
9.98/4.06	"\xs->return (x : xs)"
9.98/4.06	is transformed to
9.98/4.06	"sequence0 x xs = return (x : xs);
9.98/4.06	"
9.98/4.06	The following Lambda expression
9.98/4.06	"\x->sequence cs >>= sequence0 x"
9.98/4.06	is transformed to
9.98/4.06	"sequence1 cs x = sequence cs >>= sequence0 x;
9.98/4.06	"
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(2)
9.98/4.06	Obligation:
9.98/4.06	mainModule Main 
9.98/4.06	module Main where {
9.98/4.06	import qualified Prelude;
9.98/4.06	}
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(3) BR (EQUIVALENT)
9.98/4.06	Replaced joker patterns by fresh variables and removed binding patterns.
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(4)
9.98/4.06	Obligation:
9.98/4.06	mainModule Main 
9.98/4.06	module Main where {
9.98/4.06	import qualified Prelude;
9.98/4.06	}
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(5) COR (EQUIVALENT)
9.98/4.06	Cond Reductions:
9.98/4.06	The following Function with conditions
9.98/4.06	"undefined |Falseundefined;
9.98/4.06	"
9.98/4.06	is transformed to
9.98/4.06	"undefined  = undefined1;
9.98/4.06	"
9.98/4.06	"undefined0 True = undefined;
9.98/4.06	"
9.98/4.06	"undefined1  = undefined0 False;
9.98/4.06	"
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(6)
9.98/4.06	Obligation:
9.98/4.06	mainModule Main 
9.98/4.06	module Main where {
9.98/4.06	import qualified Prelude;
9.98/4.06	}
9.98/4.06	
9.98/4.06	----------------------------------------
9.98/4.06	
9.98/4.06	(7) Narrow (SOUND)
9.98/4.06	Haskell To QDPs
9.98/4.06	
9.98/4.06	digraph dp_graph {
9.98/4.06	node [outthreshold=100, inthreshold=100];1[label="sequence",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.98/4.06	3[label="sequence vx3",fontsize=16,color="burlywood",shape="triangle"];96[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 96[label="",style="solid", color="burlywood", weight=9];
9.98/4.06	96 -> 4[label="",style="solid", color="burlywood", weight=3];
9.98/4.06	97[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 97[label="",style="solid", color="burlywood", weight=9];
9.98/4.06	97 -> 5[label="",style="solid", color="burlywood", weight=3];
9.98/4.06	4[label="sequence (vx30 : vx31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
9.98/4.06	5[label="sequence []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.98/4.07	6[label="vx30 >>= sequence1 vx31",fontsize=16,color="blue",shape="box"];98[label=">>= :: (IO a) -> (a -> IO ([] a)) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];6 -> 98[label="",style="solid", color="blue", weight=9];
9.98/4.07	98 -> 8[label="",style="solid", color="blue", weight=3];
9.98/4.07	99[label=">>= :: ([] a) -> (a -> [] ([] a)) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];6 -> 99[label="",style="solid", color="blue", weight=9];
9.98/4.07	99 -> 9[label="",style="solid", color="blue", weight=3];
9.98/4.07	100[label=">>= :: (Maybe a) -> (a -> Maybe ([] a)) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];6 -> 100[label="",style="solid", color="blue", weight=9];
9.98/4.07	100 -> 10[label="",style="solid", color="blue", weight=3];
9.98/4.07	7[label="return []",fontsize=16,color="blue",shape="box"];101[label="return :: ([] a) -> IO ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 101[label="",style="solid", color="blue", weight=9];
9.98/4.07	101 -> 11[label="",style="solid", color="blue", weight=3];
9.98/4.07	102[label="return :: ([] a) -> [] ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 102[label="",style="solid", color="blue", weight=9];
9.98/4.07	102 -> 12[label="",style="solid", color="blue", weight=3];
9.98/4.07	103[label="return :: ([] a) -> Maybe ([] a)",fontsize=10,color="white",style="solid",shape="box"];7 -> 103[label="",style="solid", color="blue", weight=9];
9.98/4.07	103 -> 13[label="",style="solid", color="blue", weight=3];
9.98/4.07	8[label="vx30 >>= sequence1 vx31",fontsize=16,color="black",shape="box"];8 -> 14[label="",style="solid", color="black", weight=3];
9.98/4.07	9[label="vx30 >>= sequence1 vx31",fontsize=16,color="burlywood",shape="triangle"];104[label="vx30/vx300 : vx301",fontsize=10,color="white",style="solid",shape="box"];9 -> 104[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	104 -> 15[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	105[label="vx30/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 105[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	105 -> 16[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	10[label="vx30 >>= sequence1 vx31",fontsize=16,color="burlywood",shape="box"];106[label="vx30/Nothing",fontsize=10,color="white",style="solid",shape="box"];10 -> 106[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	106 -> 17[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	107[label="vx30/Just vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 107[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	107 -> 18[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	11[label="return []",fontsize=16,color="black",shape="box"];11 -> 19[label="",style="solid", color="black", weight=3];
9.98/4.07	12[label="return []",fontsize=16,color="black",shape="box"];12 -> 20[label="",style="solid", color="black", weight=3];
9.98/4.07	13[label="return []",fontsize=16,color="black",shape="box"];13 -> 21[label="",style="solid", color="black", weight=3];
9.98/4.07	14[label="primbindIO vx30 (sequence1 vx31)",fontsize=16,color="burlywood",shape="box"];108[label="vx30/IO vx300",fontsize=10,color="white",style="solid",shape="box"];14 -> 108[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	108 -> 22[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	109[label="vx30/AProVE_IO vx300",fontsize=10,color="white",style="solid",shape="box"];14 -> 109[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	109 -> 23[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	110[label="vx30/AProVE_Exception vx300",fontsize=10,color="white",style="solid",shape="box"];14 -> 110[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	110 -> 24[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	111[label="vx30/AProVE_Error vx300",fontsize=10,color="white",style="solid",shape="box"];14 -> 111[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	111 -> 25[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	15[label="vx300 : vx301 >>= sequence1 vx31",fontsize=16,color="black",shape="box"];15 -> 26[label="",style="solid", color="black", weight=3];
9.98/4.07	16[label="[] >>= sequence1 vx31",fontsize=16,color="black",shape="box"];16 -> 27[label="",style="solid", color="black", weight=3];
9.98/4.07	17[label="Nothing >>= sequence1 vx31",fontsize=16,color="black",shape="box"];17 -> 28[label="",style="solid", color="black", weight=3];
9.98/4.07	18[label="Just vx300 >>= sequence1 vx31",fontsize=16,color="black",shape="box"];18 -> 29[label="",style="solid", color="black", weight=3];
9.98/4.07	19[label="primretIO []",fontsize=16,color="black",shape="box"];19 -> 30[label="",style="solid", color="black", weight=3];
9.98/4.07	20[label="[] : []",fontsize=16,color="green",shape="box"];21[label="Just []",fontsize=16,color="green",shape="box"];22[label="primbindIO (IO vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.98/4.07	23[label="primbindIO (AProVE_IO vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.98/4.07	24[label="primbindIO (AProVE_Exception vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.98/4.07	25[label="primbindIO (AProVE_Error vx300) (sequence1 vx31)",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.98/4.07	26 -> 35[label="",style="dashed", color="red", weight=0];
9.98/4.07	26[label="sequence1 vx31 vx300 ++ (vx301 >>= sequence1 vx31)",fontsize=16,color="magenta"];26 -> 36[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	27[label="[]",fontsize=16,color="green",shape="box"];28[label="Nothing",fontsize=16,color="green",shape="box"];29[label="sequence1 vx31 vx300",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3];
9.98/4.07	30[label="AProVE_IO []",fontsize=16,color="green",shape="box"];31[label="error []",fontsize=16,color="red",shape="box"];32[label="sequence1 vx31 vx300",fontsize=16,color="black",shape="box"];32 -> 38[label="",style="solid", color="black", weight=3];
9.98/4.07	33[label="AProVE_Exception vx300",fontsize=16,color="green",shape="box"];34[label="AProVE_Error vx300",fontsize=16,color="green",shape="box"];36 -> 9[label="",style="dashed", color="red", weight=0];
9.98/4.07	36[label="vx301 >>= sequence1 vx31",fontsize=16,color="magenta"];36 -> 39[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	35[label="sequence1 vx31 vx300 ++ vx4",fontsize=16,color="black",shape="triangle"];35 -> 40[label="",style="solid", color="black", weight=3];
9.98/4.07	37 -> 41[label="",style="dashed", color="red", weight=0];
9.98/4.07	37[label="sequence vx31 >>= sequence0 vx300",fontsize=16,color="magenta"];37 -> 42[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	38 -> 43[label="",style="dashed", color="red", weight=0];
9.98/4.07	38[label="sequence vx31 >>= sequence0 vx300",fontsize=16,color="magenta"];38 -> 44[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	39[label="vx301",fontsize=16,color="green",shape="box"];40 -> 45[label="",style="dashed", color="red", weight=0];
9.98/4.07	40[label="(sequence vx31 >>= sequence0 vx300) ++ vx4",fontsize=16,color="magenta"];40 -> 46[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	42 -> 3[label="",style="dashed", color="red", weight=0];
9.98/4.07	42[label="sequence vx31",fontsize=16,color="magenta"];42 -> 47[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	41[label="vx5 >>= sequence0 vx300",fontsize=16,color="burlywood",shape="triangle"];112[label="vx5/Nothing",fontsize=10,color="white",style="solid",shape="box"];41 -> 112[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	112 -> 48[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	113[label="vx5/Just vx50",fontsize=10,color="white",style="solid",shape="box"];41 -> 113[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	113 -> 49[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	44 -> 3[label="",style="dashed", color="red", weight=0];
9.98/4.07	44[label="sequence vx31",fontsize=16,color="magenta"];44 -> 50[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	43[label="vx6 >>= sequence0 vx300",fontsize=16,color="black",shape="triangle"];43 -> 51[label="",style="solid", color="black", weight=3];
9.98/4.07	46 -> 3[label="",style="dashed", color="red", weight=0];
9.98/4.07	46[label="sequence vx31",fontsize=16,color="magenta"];46 -> 52[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	45[label="(vx7 >>= sequence0 vx300) ++ vx4",fontsize=16,color="burlywood",shape="triangle"];114[label="vx7/vx70 : vx71",fontsize=10,color="white",style="solid",shape="box"];45 -> 114[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	114 -> 53[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	115[label="vx7/[]",fontsize=10,color="white",style="solid",shape="box"];45 -> 115[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	115 -> 54[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	47[label="vx31",fontsize=16,color="green",shape="box"];48[label="Nothing >>= sequence0 vx300",fontsize=16,color="black",shape="box"];48 -> 55[label="",style="solid", color="black", weight=3];
9.98/4.07	49[label="Just vx50 >>= sequence0 vx300",fontsize=16,color="black",shape="box"];49 -> 56[label="",style="solid", color="black", weight=3];
9.98/4.07	50[label="vx31",fontsize=16,color="green",shape="box"];51[label="primbindIO vx6 (sequence0 vx300)",fontsize=16,color="burlywood",shape="box"];116[label="vx6/IO vx60",fontsize=10,color="white",style="solid",shape="box"];51 -> 116[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	116 -> 57[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	117[label="vx6/AProVE_IO vx60",fontsize=10,color="white",style="solid",shape="box"];51 -> 117[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	117 -> 58[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	118[label="vx6/AProVE_Exception vx60",fontsize=10,color="white",style="solid",shape="box"];51 -> 118[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	118 -> 59[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	119[label="vx6/AProVE_Error vx60",fontsize=10,color="white",style="solid",shape="box"];51 -> 119[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	119 -> 60[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	52[label="vx31",fontsize=16,color="green",shape="box"];53[label="(vx70 : vx71 >>= sequence0 vx300) ++ vx4",fontsize=16,color="black",shape="box"];53 -> 61[label="",style="solid", color="black", weight=3];
9.98/4.07	54[label="([] >>= sequence0 vx300) ++ vx4",fontsize=16,color="black",shape="box"];54 -> 62[label="",style="solid", color="black", weight=3];
9.98/4.07	55[label="Nothing",fontsize=16,color="green",shape="box"];56[label="sequence0 vx300 vx50",fontsize=16,color="black",shape="box"];56 -> 63[label="",style="solid", color="black", weight=3];
9.98/4.07	57[label="primbindIO (IO vx60) (sequence0 vx300)",fontsize=16,color="black",shape="box"];57 -> 64[label="",style="solid", color="black", weight=3];
9.98/4.07	58[label="primbindIO (AProVE_IO vx60) (sequence0 vx300)",fontsize=16,color="black",shape="box"];58 -> 65[label="",style="solid", color="black", weight=3];
9.98/4.07	59[label="primbindIO (AProVE_Exception vx60) (sequence0 vx300)",fontsize=16,color="black",shape="box"];59 -> 66[label="",style="solid", color="black", weight=3];
9.98/4.07	60[label="primbindIO (AProVE_Error vx60) (sequence0 vx300)",fontsize=16,color="black",shape="box"];60 -> 67[label="",style="solid", color="black", weight=3];
9.98/4.07	61[label="(sequence0 vx300 vx70 ++ (vx71 >>= sequence0 vx300)) ++ vx4",fontsize=16,color="black",shape="box"];61 -> 68[label="",style="solid", color="black", weight=3];
9.98/4.07	62[label="[] ++ vx4",fontsize=16,color="black",shape="triangle"];62 -> 69[label="",style="solid", color="black", weight=3];
9.98/4.07	63[label="return (vx300 : vx50)",fontsize=16,color="black",shape="box"];63 -> 70[label="",style="solid", color="black", weight=3];
9.98/4.07	64[label="error []",fontsize=16,color="red",shape="box"];65[label="sequence0 vx300 vx60",fontsize=16,color="black",shape="box"];65 -> 71[label="",style="solid", color="black", weight=3];
9.98/4.07	66[label="AProVE_Exception vx60",fontsize=16,color="green",shape="box"];67[label="AProVE_Error vx60",fontsize=16,color="green",shape="box"];68[label="(return (vx300 : vx70) ++ (vx71 >>= sequence0 vx300)) ++ vx4",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
9.98/4.07	69[label="vx4",fontsize=16,color="green",shape="box"];70[label="Just (vx300 : vx50)",fontsize=16,color="green",shape="box"];71[label="return (vx300 : vx60)",fontsize=16,color="black",shape="box"];71 -> 73[label="",style="solid", color="black", weight=3];
9.98/4.07	72[label="(((vx300 : vx70) : []) ++ (vx71 >>= sequence0 vx300)) ++ vx4",fontsize=16,color="black",shape="box"];72 -> 74[label="",style="solid", color="black", weight=3];
9.98/4.07	73[label="primretIO (vx300 : vx60)",fontsize=16,color="black",shape="box"];73 -> 75[label="",style="solid", color="black", weight=3];
9.98/4.07	74 -> 76[label="",style="dashed", color="red", weight=0];
9.98/4.07	74[label="((vx300 : vx70) : [] ++ (vx71 >>= sequence0 vx300)) ++ vx4",fontsize=16,color="magenta"];74 -> 77[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	75[label="AProVE_IO (vx300 : vx60)",fontsize=16,color="green",shape="box"];77 -> 62[label="",style="dashed", color="red", weight=0];
9.98/4.07	77[label="[] ++ (vx71 >>= sequence0 vx300)",fontsize=16,color="magenta"];77 -> 78[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	76[label="((vx300 : vx70) : vx8) ++ vx4",fontsize=16,color="black",shape="triangle"];76 -> 79[label="",style="solid", color="black", weight=3];
9.98/4.07	78[label="vx71 >>= sequence0 vx300",fontsize=16,color="burlywood",shape="triangle"];120[label="vx71/vx710 : vx711",fontsize=10,color="white",style="solid",shape="box"];78 -> 120[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	120 -> 80[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	121[label="vx71/[]",fontsize=10,color="white",style="solid",shape="box"];78 -> 121[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	121 -> 81[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	79[label="(vx300 : vx70) : vx8 ++ vx4",fontsize=16,color="green",shape="box"];79 -> 82[label="",style="dashed", color="green", weight=3];
9.98/4.07	80[label="vx710 : vx711 >>= sequence0 vx300",fontsize=16,color="black",shape="box"];80 -> 83[label="",style="solid", color="black", weight=3];
9.98/4.07	81[label="[] >>= sequence0 vx300",fontsize=16,color="black",shape="box"];81 -> 84[label="",style="solid", color="black", weight=3];
9.98/4.07	82[label="vx8 ++ vx4",fontsize=16,color="burlywood",shape="triangle"];122[label="vx8/vx80 : vx81",fontsize=10,color="white",style="solid",shape="box"];82 -> 122[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	122 -> 85[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	123[label="vx8/[]",fontsize=10,color="white",style="solid",shape="box"];82 -> 123[label="",style="solid", color="burlywood", weight=9];
9.98/4.07	123 -> 86[label="",style="solid", color="burlywood", weight=3];
9.98/4.07	83 -> 82[label="",style="dashed", color="red", weight=0];
9.98/4.07	83[label="sequence0 vx300 vx710 ++ (vx711 >>= sequence0 vx300)",fontsize=16,color="magenta"];83 -> 87[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	83 -> 88[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	84[label="[]",fontsize=16,color="green",shape="box"];85[label="(vx80 : vx81) ++ vx4",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3];
9.98/4.07	86[label="[] ++ vx4",fontsize=16,color="black",shape="box"];86 -> 90[label="",style="solid", color="black", weight=3];
9.98/4.07	87 -> 78[label="",style="dashed", color="red", weight=0];
9.98/4.07	87[label="vx711 >>= sequence0 vx300",fontsize=16,color="magenta"];87 -> 91[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	88[label="sequence0 vx300 vx710",fontsize=16,color="black",shape="box"];88 -> 92[label="",style="solid", color="black", weight=3];
9.98/4.07	89[label="vx80 : vx81 ++ vx4",fontsize=16,color="green",shape="box"];89 -> 93[label="",style="dashed", color="green", weight=3];
9.98/4.07	90[label="vx4",fontsize=16,color="green",shape="box"];91[label="vx711",fontsize=16,color="green",shape="box"];92[label="return (vx300 : vx710)",fontsize=16,color="black",shape="box"];92 -> 94[label="",style="solid", color="black", weight=3];
9.98/4.07	93 -> 82[label="",style="dashed", color="red", weight=0];
9.98/4.07	93[label="vx81 ++ vx4",fontsize=16,color="magenta"];93 -> 95[label="",style="dashed", color="magenta", weight=3];
9.98/4.07	94[label="(vx300 : vx710) : []",fontsize=16,color="green",shape="box"];95[label="vx81",fontsize=16,color="green",shape="box"];}
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(8)
9.98/4.07	Complex Obligation (AND)
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(9)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_gtGtEs(:(vx710, vx711), vx300, h) -> new_gtGtEs(vx711, vx300, h)
9.98/4.07	
9.98/4.07	R is empty.
9.98/4.07	Q is empty.
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(10) QDPSizeChangeProof (EQUIVALENT)
9.98/4.07	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. 
9.98/4.07	
9.98/4.07	From the DPs we obtained the following set of size-change graphs:
9.98/4.07	*new_gtGtEs(:(vx710, vx711), vx300, h) -> new_gtGtEs(vx711, vx300, h)
9.98/4.07	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(11)
9.98/4.07	YES
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(12)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	   new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	   new_sequence(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_sequence(vx31, ty_IO, h)
9.98/4.07	   new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_psPs0(vx31, vx300, vx4, h) -> new_sequence(vx31, ty_[], h)
9.98/4.07	   new_sequence(:(Just(vx300), vx31), ty_Maybe, h) -> new_sequence(vx31, ty_Maybe, h)
9.98/4.07	
9.98/4.07	The TRS R consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs4(vx4, h) -> vx4
9.98/4.07	   new_gtGtEs0([], vx31, h) -> []
9.98/4.07	   new_sequence0(:(AProVE_Exception(vx300), vx31), ty_IO, h) -> AProVE_Exception(vx300)
9.98/4.07	   new_sequence0(:(Just(vx300), vx31), ty_Maybe, h) -> new_gtGtEs3(new_sequence0(vx31, ty_Maybe, h), vx300, h)
9.98/4.07	   new_gtGtEs0(:(vx300, vx301), vx31, h) -> new_psPs1(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_sequence0([], ty_[], h) -> :([], [])
9.98/4.07	   new_sequence0(:(IO(vx300), vx31), ty_IO, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_IO(vx60), vx300, h) -> AProVE_IO(:(vx300, vx60))
9.98/4.07	   new_sequence0(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_gtGtEs2(new_sequence0(vx31, ty_IO, h), vx300, h)
9.98/4.07	   new_sequence0([], ty_Maybe, h) -> Just([])
9.98/4.07	   new_gtGtEs4([], vx300, h) -> []
9.98/4.07	   new_sequence0(:(Nothing, vx31), ty_Maybe, h) -> Nothing
9.98/4.07	   new_gtGtEs2(AProVE_Error(vx60), vx300, h) -> AProVE_Error(vx60)
9.98/4.07	   new_psPs1(vx31, vx300, vx4, h) -> new_psPs2(new_sequence0(vx31, ty_[], h), vx300, vx4, h)
9.98/4.07	   new_gtGtEs2(IO(vx60), vx300, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_Exception(vx60), vx300, h) -> AProVE_Exception(vx60)
9.98/4.07	   new_sequence0(:(AProVE_Error(vx300), vx31), ty_IO, h) -> AProVE_Error(vx300)
9.98/4.07	   new_psPs2([], vx300, vx4, h) -> new_psPs4(vx4, h)
9.98/4.07	   new_psPs3(vx300, vx70, vx8, vx4, h) -> :(:(vx300, vx70), new_psPs5(vx8, vx4, h))
9.98/4.07	   new_psPs2(:(vx70, vx71), vx300, vx4, h) -> new_psPs3(vx300, vx70, new_psPs4(new_gtGtEs4(vx71, vx300, h), h), vx4, h)
9.98/4.07	   new_psPs5(:(vx80, vx81), vx4, h) -> :(vx80, new_psPs5(vx81, vx4, h))
9.98/4.07	   new_gtGtEs4(:(vx710, vx711), vx300, h) -> new_psPs5(:(:(vx300, vx710), []), new_gtGtEs4(vx711, vx300, h), h)
9.98/4.07	   new_psPs5([], vx4, h) -> vx4
9.98/4.07	   new_gtGtEs3(Nothing, vx300, h) -> Nothing
9.98/4.07	   new_sequence0(:(vx30, vx31), ty_[], h) -> new_gtGtEs0(vx30, vx31, h)
9.98/4.07	   new_sequence0([], ty_IO, h) -> AProVE_IO([])
9.98/4.07	   new_gtGtEs3(Just(vx50), vx300, h) -> Just(:(vx300, vx50))
9.98/4.07	
9.98/4.07	The set Q consists of the following terms:
9.98/4.07	
9.98/4.07	   new_gtGtEs3(Just(x0), x1, x2)
9.98/4.07	   new_gtGtEs2(AProVE_IO(x0), x1, x2)
9.98/4.07	   new_psPs4(x0, x1)
9.98/4.07	   new_gtGtEs2(AProVE_Exception(x0), x1, x2)
9.98/4.07	   new_sequence0([], ty_IO, x0)
9.98/4.07	   new_psPs1(x0, x1, x2, x3)
9.98/4.07	   new_gtGtEs4(:(x0, x1), x2, x3)
9.98/4.07	   new_psPs2(:(x0, x1), x2, x3, x4)
9.98/4.07	   new_sequence0(:(AProVE_IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs2(IO(x0), x1, x2)
9.98/4.07	   new_gtGtEs0(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(AProVE_Error(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs3(Nothing, x0, x1)
9.98/4.07	   new_psPs5(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(Nothing, x0), ty_Maybe, x1)
9.98/4.07	   new_sequence0(:(Just(x0), x1), ty_Maybe, x2)
9.98/4.07	   new_gtGtEs0([], x0, x1)
9.98/4.07	   new_gtGtEs4([], x0, x1)
9.98/4.07	   new_sequence0([], ty_[], x0)
9.98/4.07	   new_sequence0([], ty_Maybe, x0)
9.98/4.07	   new_sequence0(:(x0, x1), ty_[], x2)
9.98/4.07	   new_gtGtEs2(AProVE_Error(x0), x1, x2)
9.98/4.07	   new_psPs2([], x0, x1, x2)
9.98/4.07	   new_sequence0(:(IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_psPs3(x0, x1, x2, x3, x4)
9.98/4.07	   new_psPs5([], x0, x1)
9.98/4.07	   new_sequence0(:(AProVE_Exception(x0), x1), ty_IO, x2)
9.98/4.07	
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(13) DependencyGraphProof (EQUIVALENT)
9.98/4.07	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(14)
9.98/4.07	Complex Obligation (AND)
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(15)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_sequence(:(Just(vx300), vx31), ty_Maybe, h) -> new_sequence(vx31, ty_Maybe, h)
9.98/4.07	
9.98/4.07	The TRS R consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs4(vx4, h) -> vx4
9.98/4.07	   new_gtGtEs0([], vx31, h) -> []
9.98/4.07	   new_sequence0(:(AProVE_Exception(vx300), vx31), ty_IO, h) -> AProVE_Exception(vx300)
9.98/4.07	   new_sequence0(:(Just(vx300), vx31), ty_Maybe, h) -> new_gtGtEs3(new_sequence0(vx31, ty_Maybe, h), vx300, h)
9.98/4.07	   new_gtGtEs0(:(vx300, vx301), vx31, h) -> new_psPs1(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_sequence0([], ty_[], h) -> :([], [])
9.98/4.07	   new_sequence0(:(IO(vx300), vx31), ty_IO, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_IO(vx60), vx300, h) -> AProVE_IO(:(vx300, vx60))
9.98/4.07	   new_sequence0(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_gtGtEs2(new_sequence0(vx31, ty_IO, h), vx300, h)
9.98/4.07	   new_sequence0([], ty_Maybe, h) -> Just([])
9.98/4.07	   new_gtGtEs4([], vx300, h) -> []
9.98/4.07	   new_sequence0(:(Nothing, vx31), ty_Maybe, h) -> Nothing
9.98/4.07	   new_gtGtEs2(AProVE_Error(vx60), vx300, h) -> AProVE_Error(vx60)
9.98/4.07	   new_psPs1(vx31, vx300, vx4, h) -> new_psPs2(new_sequence0(vx31, ty_[], h), vx300, vx4, h)
9.98/4.07	   new_gtGtEs2(IO(vx60), vx300, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_Exception(vx60), vx300, h) -> AProVE_Exception(vx60)
9.98/4.07	   new_sequence0(:(AProVE_Error(vx300), vx31), ty_IO, h) -> AProVE_Error(vx300)
9.98/4.07	   new_psPs2([], vx300, vx4, h) -> new_psPs4(vx4, h)
9.98/4.07	   new_psPs3(vx300, vx70, vx8, vx4, h) -> :(:(vx300, vx70), new_psPs5(vx8, vx4, h))
9.98/4.07	   new_psPs2(:(vx70, vx71), vx300, vx4, h) -> new_psPs3(vx300, vx70, new_psPs4(new_gtGtEs4(vx71, vx300, h), h), vx4, h)
9.98/4.07	   new_psPs5(:(vx80, vx81), vx4, h) -> :(vx80, new_psPs5(vx81, vx4, h))
9.98/4.07	   new_gtGtEs4(:(vx710, vx711), vx300, h) -> new_psPs5(:(:(vx300, vx710), []), new_gtGtEs4(vx711, vx300, h), h)
9.98/4.07	   new_psPs5([], vx4, h) -> vx4
9.98/4.07	   new_gtGtEs3(Nothing, vx300, h) -> Nothing
9.98/4.07	   new_sequence0(:(vx30, vx31), ty_[], h) -> new_gtGtEs0(vx30, vx31, h)
9.98/4.07	   new_sequence0([], ty_IO, h) -> AProVE_IO([])
9.98/4.07	   new_gtGtEs3(Just(vx50), vx300, h) -> Just(:(vx300, vx50))
9.98/4.07	
9.98/4.07	The set Q consists of the following terms:
9.98/4.07	
9.98/4.07	   new_gtGtEs3(Just(x0), x1, x2)
9.98/4.07	   new_gtGtEs2(AProVE_IO(x0), x1, x2)
9.98/4.07	   new_psPs4(x0, x1)
9.98/4.07	   new_gtGtEs2(AProVE_Exception(x0), x1, x2)
9.98/4.07	   new_sequence0([], ty_IO, x0)
9.98/4.07	   new_psPs1(x0, x1, x2, x3)
9.98/4.07	   new_gtGtEs4(:(x0, x1), x2, x3)
9.98/4.07	   new_psPs2(:(x0, x1), x2, x3, x4)
9.98/4.07	   new_sequence0(:(AProVE_IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs2(IO(x0), x1, x2)
9.98/4.07	   new_gtGtEs0(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(AProVE_Error(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs3(Nothing, x0, x1)
9.98/4.07	   new_psPs5(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(Nothing, x0), ty_Maybe, x1)
9.98/4.07	   new_sequence0(:(Just(x0), x1), ty_Maybe, x2)
9.98/4.07	   new_gtGtEs0([], x0, x1)
9.98/4.07	   new_gtGtEs4([], x0, x1)
9.98/4.07	   new_sequence0([], ty_[], x0)
9.98/4.07	   new_sequence0([], ty_Maybe, x0)
9.98/4.07	   new_sequence0(:(x0, x1), ty_[], x2)
9.98/4.07	   new_gtGtEs2(AProVE_Error(x0), x1, x2)
9.98/4.07	   new_psPs2([], x0, x1, x2)
9.98/4.07	   new_sequence0(:(IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_psPs3(x0, x1, x2, x3, x4)
9.98/4.07	   new_psPs5([], x0, x1)
9.98/4.07	   new_sequence0(:(AProVE_Exception(x0), x1), ty_IO, x2)
9.98/4.07	
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(16) QDPSizeChangeProof (EQUIVALENT)
9.98/4.07	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. 
9.98/4.07	
9.98/4.07	From the DPs we obtained the following set of size-change graphs:
9.98/4.07	*new_sequence(:(Just(vx300), vx31), ty_Maybe, h) -> new_sequence(vx31, ty_Maybe, h)
9.98/4.07	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(17)
9.98/4.07	YES
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(18)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_sequence(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_sequence(vx31, ty_IO, h)
9.98/4.07	
9.98/4.07	The TRS R consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs4(vx4, h) -> vx4
9.98/4.07	   new_gtGtEs0([], vx31, h) -> []
9.98/4.07	   new_sequence0(:(AProVE_Exception(vx300), vx31), ty_IO, h) -> AProVE_Exception(vx300)
9.98/4.07	   new_sequence0(:(Just(vx300), vx31), ty_Maybe, h) -> new_gtGtEs3(new_sequence0(vx31, ty_Maybe, h), vx300, h)
9.98/4.07	   new_gtGtEs0(:(vx300, vx301), vx31, h) -> new_psPs1(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_sequence0([], ty_[], h) -> :([], [])
9.98/4.07	   new_sequence0(:(IO(vx300), vx31), ty_IO, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_IO(vx60), vx300, h) -> AProVE_IO(:(vx300, vx60))
9.98/4.07	   new_sequence0(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_gtGtEs2(new_sequence0(vx31, ty_IO, h), vx300, h)
9.98/4.07	   new_sequence0([], ty_Maybe, h) -> Just([])
9.98/4.07	   new_gtGtEs4([], vx300, h) -> []
9.98/4.07	   new_sequence0(:(Nothing, vx31), ty_Maybe, h) -> Nothing
9.98/4.07	   new_gtGtEs2(AProVE_Error(vx60), vx300, h) -> AProVE_Error(vx60)
9.98/4.07	   new_psPs1(vx31, vx300, vx4, h) -> new_psPs2(new_sequence0(vx31, ty_[], h), vx300, vx4, h)
9.98/4.07	   new_gtGtEs2(IO(vx60), vx300, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_Exception(vx60), vx300, h) -> AProVE_Exception(vx60)
9.98/4.07	   new_sequence0(:(AProVE_Error(vx300), vx31), ty_IO, h) -> AProVE_Error(vx300)
9.98/4.07	   new_psPs2([], vx300, vx4, h) -> new_psPs4(vx4, h)
9.98/4.07	   new_psPs3(vx300, vx70, vx8, vx4, h) -> :(:(vx300, vx70), new_psPs5(vx8, vx4, h))
9.98/4.07	   new_psPs2(:(vx70, vx71), vx300, vx4, h) -> new_psPs3(vx300, vx70, new_psPs4(new_gtGtEs4(vx71, vx300, h), h), vx4, h)
9.98/4.07	   new_psPs5(:(vx80, vx81), vx4, h) -> :(vx80, new_psPs5(vx81, vx4, h))
9.98/4.07	   new_gtGtEs4(:(vx710, vx711), vx300, h) -> new_psPs5(:(:(vx300, vx710), []), new_gtGtEs4(vx711, vx300, h), h)
9.98/4.07	   new_psPs5([], vx4, h) -> vx4
9.98/4.07	   new_gtGtEs3(Nothing, vx300, h) -> Nothing
9.98/4.07	   new_sequence0(:(vx30, vx31), ty_[], h) -> new_gtGtEs0(vx30, vx31, h)
9.98/4.07	   new_sequence0([], ty_IO, h) -> AProVE_IO([])
9.98/4.07	   new_gtGtEs3(Just(vx50), vx300, h) -> Just(:(vx300, vx50))
9.98/4.07	
9.98/4.07	The set Q consists of the following terms:
9.98/4.07	
9.98/4.07	   new_gtGtEs3(Just(x0), x1, x2)
9.98/4.07	   new_gtGtEs2(AProVE_IO(x0), x1, x2)
9.98/4.07	   new_psPs4(x0, x1)
9.98/4.07	   new_gtGtEs2(AProVE_Exception(x0), x1, x2)
9.98/4.07	   new_sequence0([], ty_IO, x0)
9.98/4.07	   new_psPs1(x0, x1, x2, x3)
9.98/4.07	   new_gtGtEs4(:(x0, x1), x2, x3)
9.98/4.07	   new_psPs2(:(x0, x1), x2, x3, x4)
9.98/4.07	   new_sequence0(:(AProVE_IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs2(IO(x0), x1, x2)
9.98/4.07	   new_gtGtEs0(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(AProVE_Error(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs3(Nothing, x0, x1)
9.98/4.07	   new_psPs5(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(Nothing, x0), ty_Maybe, x1)
9.98/4.07	   new_sequence0(:(Just(x0), x1), ty_Maybe, x2)
9.98/4.07	   new_gtGtEs0([], x0, x1)
9.98/4.07	   new_gtGtEs4([], x0, x1)
9.98/4.07	   new_sequence0([], ty_[], x0)
9.98/4.07	   new_sequence0([], ty_Maybe, x0)
9.98/4.07	   new_sequence0(:(x0, x1), ty_[], x2)
9.98/4.07	   new_gtGtEs2(AProVE_Error(x0), x1, x2)
9.98/4.07	   new_psPs2([], x0, x1, x2)
9.98/4.07	   new_sequence0(:(IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_psPs3(x0, x1, x2, x3, x4)
9.98/4.07	   new_psPs5([], x0, x1)
9.98/4.07	   new_sequence0(:(AProVE_Exception(x0), x1), ty_IO, x2)
9.98/4.07	
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(19) QDPSizeChangeProof (EQUIVALENT)
9.98/4.07	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. 
9.98/4.07	
9.98/4.07	From the DPs we obtained the following set of size-change graphs:
9.98/4.07	*new_sequence(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_sequence(vx31, ty_IO, h)
9.98/4.07	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(20)
9.98/4.07	YES
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(21)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs0(vx31, vx300, vx4, h) -> new_sequence(vx31, ty_[], h)
9.98/4.07	   new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	   new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	   new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	
9.98/4.07	The TRS R consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs4(vx4, h) -> vx4
9.98/4.07	   new_gtGtEs0([], vx31, h) -> []
9.98/4.07	   new_sequence0(:(AProVE_Exception(vx300), vx31), ty_IO, h) -> AProVE_Exception(vx300)
9.98/4.07	   new_sequence0(:(Just(vx300), vx31), ty_Maybe, h) -> new_gtGtEs3(new_sequence0(vx31, ty_Maybe, h), vx300, h)
9.98/4.07	   new_gtGtEs0(:(vx300, vx301), vx31, h) -> new_psPs1(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	   new_sequence0([], ty_[], h) -> :([], [])
9.98/4.07	   new_sequence0(:(IO(vx300), vx31), ty_IO, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_IO(vx60), vx300, h) -> AProVE_IO(:(vx300, vx60))
9.98/4.07	   new_sequence0(:(AProVE_IO(vx300), vx31), ty_IO, h) -> new_gtGtEs2(new_sequence0(vx31, ty_IO, h), vx300, h)
9.98/4.07	   new_sequence0([], ty_Maybe, h) -> Just([])
9.98/4.07	   new_gtGtEs4([], vx300, h) -> []
9.98/4.07	   new_sequence0(:(Nothing, vx31), ty_Maybe, h) -> Nothing
9.98/4.07	   new_gtGtEs2(AProVE_Error(vx60), vx300, h) -> AProVE_Error(vx60)
9.98/4.07	   new_psPs1(vx31, vx300, vx4, h) -> new_psPs2(new_sequence0(vx31, ty_[], h), vx300, vx4, h)
9.98/4.07	   new_gtGtEs2(IO(vx60), vx300, h) -> error([])
9.98/4.07	   new_gtGtEs2(AProVE_Exception(vx60), vx300, h) -> AProVE_Exception(vx60)
9.98/4.07	   new_sequence0(:(AProVE_Error(vx300), vx31), ty_IO, h) -> AProVE_Error(vx300)
9.98/4.07	   new_psPs2([], vx300, vx4, h) -> new_psPs4(vx4, h)
9.98/4.07	   new_psPs3(vx300, vx70, vx8, vx4, h) -> :(:(vx300, vx70), new_psPs5(vx8, vx4, h))
9.98/4.07	   new_psPs2(:(vx70, vx71), vx300, vx4, h) -> new_psPs3(vx300, vx70, new_psPs4(new_gtGtEs4(vx71, vx300, h), h), vx4, h)
9.98/4.07	   new_psPs5(:(vx80, vx81), vx4, h) -> :(vx80, new_psPs5(vx81, vx4, h))
9.98/4.07	   new_gtGtEs4(:(vx710, vx711), vx300, h) -> new_psPs5(:(:(vx300, vx710), []), new_gtGtEs4(vx711, vx300, h), h)
9.98/4.07	   new_psPs5([], vx4, h) -> vx4
9.98/4.07	   new_gtGtEs3(Nothing, vx300, h) -> Nothing
9.98/4.07	   new_sequence0(:(vx30, vx31), ty_[], h) -> new_gtGtEs0(vx30, vx31, h)
9.98/4.07	   new_sequence0([], ty_IO, h) -> AProVE_IO([])
9.98/4.07	   new_gtGtEs3(Just(vx50), vx300, h) -> Just(:(vx300, vx50))
9.98/4.07	
9.98/4.07	The set Q consists of the following terms:
9.98/4.07	
9.98/4.07	   new_gtGtEs3(Just(x0), x1, x2)
9.98/4.07	   new_gtGtEs2(AProVE_IO(x0), x1, x2)
9.98/4.07	   new_psPs4(x0, x1)
9.98/4.07	   new_gtGtEs2(AProVE_Exception(x0), x1, x2)
9.98/4.07	   new_sequence0([], ty_IO, x0)
9.98/4.07	   new_psPs1(x0, x1, x2, x3)
9.98/4.07	   new_gtGtEs4(:(x0, x1), x2, x3)
9.98/4.07	   new_psPs2(:(x0, x1), x2, x3, x4)
9.98/4.07	   new_sequence0(:(AProVE_IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs2(IO(x0), x1, x2)
9.98/4.07	   new_gtGtEs0(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(AProVE_Error(x0), x1), ty_IO, x2)
9.98/4.07	   new_gtGtEs3(Nothing, x0, x1)
9.98/4.07	   new_psPs5(:(x0, x1), x2, x3)
9.98/4.07	   new_sequence0(:(Nothing, x0), ty_Maybe, x1)
9.98/4.07	   new_sequence0(:(Just(x0), x1), ty_Maybe, x2)
9.98/4.07	   new_gtGtEs0([], x0, x1)
9.98/4.07	   new_gtGtEs4([], x0, x1)
9.98/4.07	   new_sequence0([], ty_[], x0)
9.98/4.07	   new_sequence0([], ty_Maybe, x0)
9.98/4.07	   new_sequence0(:(x0, x1), ty_[], x2)
9.98/4.07	   new_gtGtEs2(AProVE_Error(x0), x1, x2)
9.98/4.07	   new_psPs2([], x0, x1, x2)
9.98/4.07	   new_sequence0(:(IO(x0), x1), ty_IO, x2)
9.98/4.07	   new_psPs3(x0, x1, x2, x3, x4)
9.98/4.07	   new_psPs5([], x0, x1)
9.98/4.07	   new_sequence0(:(AProVE_Exception(x0), x1), ty_IO, x2)
9.98/4.07	
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(22) QDPSizeChangeProof (EQUIVALENT)
9.98/4.07	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. 
9.98/4.07	
9.98/4.07	From the DPs we obtained the following set of size-change graphs:
9.98/4.07	*new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	The graph contains the following edges 1 > 1, 1 > 2, 3 >= 4
9.98/4.07	
9.98/4.07	
9.98/4.07	*new_sequence(:(:(vx300, vx301), vx31), ty_[], h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	The graph contains the following edges 1 > 1, 1 > 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	*new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_psPs0(vx31, vx300, new_gtGtEs0(vx301, vx31, h), h)
9.98/4.07	The graph contains the following edges 2 >= 1, 1 > 2, 3 >= 4
9.98/4.07	
9.98/4.07	
9.98/4.07	*new_psPs0(vx31, vx300, vx4, h) -> new_sequence(vx31, ty_[], h)
9.98/4.07	The graph contains the following edges 1 >= 1, 4 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	*new_gtGtEs1(:(vx300, vx301), vx31, h) -> new_gtGtEs1(vx301, vx31, h)
9.98/4.07	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(23)
9.98/4.07	YES
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(24)
9.98/4.07	Obligation:
9.98/4.07	Q DP problem:
9.98/4.07	The TRS P consists of the following rules:
9.98/4.07	
9.98/4.07	   new_psPs(:(vx80, vx81), vx4, h) -> new_psPs(vx81, vx4, h)
9.98/4.07	
9.98/4.07	R is empty.
9.98/4.07	Q is empty.
9.98/4.07	We have to consider all minimal (P,Q,R)-chains.
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(25) QDPSizeChangeProof (EQUIVALENT)
9.98/4.07	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. 
9.98/4.07	
9.98/4.07	From the DPs we obtained the following set of size-change graphs:
9.98/4.07	*new_psPs(:(vx80, vx81), vx4, h) -> new_psPs(vx81, vx4, h)
9.98/4.07	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
9.98/4.07	
9.98/4.07	
9.98/4.07	----------------------------------------
9.98/4.07	
9.98/4.07	(26)
9.98/4.07	YES
9.98/4.11	EOF