8.03/3.65	NO
10.02/4.20	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.02/4.20	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.02/4.20	
10.02/4.20	
10.02/4.20	H-Termination with start terms of the given HASKELL could be disproven:
10.02/4.20	
10.02/4.20	(0) HASKELL
10.02/4.20	(1) LR [EQUIVALENT, 0 ms]
10.02/4.20	(2) HASKELL
10.02/4.20	(3) CR [EQUIVALENT, 0 ms]
10.02/4.20	(4) HASKELL
10.02/4.20	(5) BR [EQUIVALENT, 0 ms]
10.02/4.20	(6) HASKELL
10.02/4.20	(7) COR [EQUIVALENT, 0 ms]
10.02/4.20	(8) HASKELL
10.02/4.20	(9) Narrow [COMPLETE, 0 ms]
10.02/4.20	(10) AND
10.02/4.20	    (11) QDP
10.02/4.20	        (12) NonTerminationLoopProof [COMPLETE, 0 ms]
10.02/4.20	        (13) NO
10.02/4.20	    (14) QDP
10.02/4.20	
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(0)
10.02/4.20	Obligation:
10.02/4.20	mainModule Main 
10.02/4.20	module Main where {
10.02/4.20	import qualified Prelude;
10.02/4.20	}
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(1) LR (EQUIVALENT)
10.02/4.20	Lambda Reductions:
10.02/4.20	The following Lambda expression
10.02/4.20	"\e->case k e of {
10.02/4.20	IO k'  -> k' f s}
10.02/4.20	"
10.02/4.20	is transformed to
10.02/4.20	"catchHugsException0 k f s e = case k e of {
10.02/4.20	IO k'  -> k' f s}
10.02/4.20	;
10.02/4.20	"
10.02/4.20	The following Lambda expression
10.02/4.20	"\fs->Hugs_Catch (m Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 k f s) f (s . fromObj)"
10.02/4.20	is transformed to
10.02/4.20	"catchHugsException1 m k f s = Hugs_Catch (m Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 k f s) f (s . fromObj);
10.02/4.20	"
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(2)
10.02/4.20	Obligation:
10.02/4.20	mainModule Main 
10.02/4.20	module Main where {
10.02/4.20	import qualified Prelude;
10.02/4.20	}
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(3) CR (EQUIVALENT)
10.02/4.20	Case Reductions:
10.02/4.20	The following Case expression
10.02/4.20	"case k e of {
10.02/4.20	IO k'  -> k' f s}
10.02/4.20	"
10.02/4.20	is transformed to
10.02/4.20	"catchHugsException00 f s (IO k') = k' f s;
10.02/4.20	"
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(4)
10.02/4.20	Obligation:
10.02/4.20	mainModule Main 
10.02/4.20	module Main where {
10.02/4.20	import qualified Prelude;
10.02/4.20	}
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(5) BR (EQUIVALENT)
10.02/4.20	Replaced joker patterns by fresh variables and removed binding patterns.
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(6)
10.02/4.20	Obligation:
10.02/4.20	mainModule Main 
10.02/4.20	module Main where {
10.02/4.20	import qualified Prelude;
10.02/4.20	}
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(7) COR (EQUIVALENT)
10.02/4.20	Cond Reductions:
10.02/4.20	The following Function with conditions
10.02/4.20	"undefined |Falseundefined;
10.02/4.20	"
10.02/4.20	is transformed to
10.02/4.20	"undefined  = undefined1;
10.02/4.20	"
10.02/4.20	"undefined0 True = undefined;
10.02/4.20	"
10.02/4.20	"undefined1  = undefined0 False;
10.02/4.20	"
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(8)
10.02/4.20	Obligation:
10.02/4.20	mainModule Main 
10.02/4.20	module Main where {
10.02/4.20	import qualified Prelude;
10.02/4.20	}
10.02/4.20	
10.02/4.20	----------------------------------------
10.02/4.20	
10.02/4.20	(9) Narrow (COMPLETE)
10.02/4.20	Haskell To QDPs
10.02/4.20	
10.02/4.20	digraph dp_graph {
10.02/4.20	node [outthreshold=100, inthreshold=100];1[label="catchHugsException",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.02/4.20	3[label="catchHugsException vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.02/4.20	4[label="catchHugsException vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];47[label="vx3/IO vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 47[label="",style="solid", color="burlywood", weight=9];
10.02/4.20	47 -> 5[label="",style="solid", color="burlywood", weight=3];
10.02/4.20	48[label="vx3/AProVE_IO vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 48[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	48 -> 6[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	49[label="vx3/AProVE_Exception vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 49[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	49 -> 7[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	50[label="vx3/AProVE_Error vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 50[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	50 -> 8[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	5[label="catchHugsException (IO vx30) vx4",fontsize=16,color="black",shape="box"];5 -> 9[label="",style="solid", color="black", weight=3];
10.02/4.21	6[label="catchHugsException (AProVE_IO vx30) vx4",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3];
10.02/4.21	7[label="catchHugsException (AProVE_Exception vx30) vx4",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
10.02/4.21	8[label="catchHugsException (AProVE_Error vx30) vx4",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
10.02/4.21	9[label="(IO $ catchHugsException1 vx30 vx4)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10.02/4.21	10[label="error []",fontsize=16,color="red",shape="box"];11[label="error []",fontsize=16,color="red",shape="box"];12[label="error []",fontsize=16,color="red",shape="box"];13[label="IO (catchHugsException1 vx30 vx4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3];
10.02/4.21	14[label="catchHugsException1 vx30 vx4",fontsize=16,color="grey",shape="box"];14 -> 15[label="",style="dashed", color="grey", weight=3];
10.02/4.21	15[label="catchHugsException1 vx30 vx4 vx5",fontsize=16,color="grey",shape="box"];15 -> 16[label="",style="dashed", color="grey", weight=3];
10.02/4.21	16[label="catchHugsException1 vx30 vx4 vx5 vx6",fontsize=16,color="black",shape="triangle"];16 -> 17[label="",style="solid", color="black", weight=3];
10.02/4.21	17[label="Hugs_Catch (vx30 Hugs_Error (Hugs_Return . toObj)) (catchHugsException0 vx4 vx5 vx6) vx5 (vx6 . fromObj)",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3];
10.02/4.21	17 -> 19[label="",style="dashed", color="green", weight=3];
10.02/4.21	17 -> 20[label="",style="dashed", color="green", weight=3];
10.02/4.21	18[label="vx30 Hugs_Error (Hugs_Return . toObj)",fontsize=16,color="green",shape="box"];18 -> 21[label="",style="dashed", color="green", weight=3];
10.02/4.21	18 -> 22[label="",style="dashed", color="green", weight=3];
10.02/4.21	19[label="catchHugsException0 vx4 vx5 vx6",fontsize=16,color="grey",shape="box"];19 -> 23[label="",style="dashed", color="grey", weight=3];
10.02/4.21	20[label="vx6 . fromObj",fontsize=16,color="grey",shape="box"];20 -> 24[label="",style="dashed", color="grey", weight=3];
10.02/4.21	21[label="Hugs_Error",fontsize=16,color="green",shape="box"];22[label="Hugs_Return . toObj",fontsize=16,color="grey",shape="box"];22 -> 25[label="",style="dashed", color="grey", weight=3];
10.02/4.21	23[label="catchHugsException0 vx4 vx5 vx6 vx7",fontsize=16,color="black",shape="triangle"];23 -> 26[label="",style="solid", color="black", weight=3];
10.02/4.21	24[label="vx6 . fromObj",fontsize=16,color="black",shape="triangle"];24 -> 27[label="",style="solid", color="black", weight=3];
10.02/4.21	25[label="Hugs_Return . toObj",fontsize=16,color="black",shape="triangle"];25 -> 28[label="",style="solid", color="black", weight=3];
10.02/4.21	26 -> 29[label="",style="dashed", color="red", weight=0];
10.02/4.21	26[label="catchHugsException00 vx5 vx6 (vx4 vx7)",fontsize=16,color="magenta"];26 -> 30[label="",style="dashed", color="magenta", weight=3];
10.02/4.21	27[label="vx6 (fromObj vx8)",fontsize=16,color="green",shape="box"];27 -> 31[label="",style="dashed", color="green", weight=3];
10.02/4.21	28[label="Hugs_Return (toObj vx9)",fontsize=16,color="green",shape="box"];28 -> 32[label="",style="dashed", color="green", weight=3];
10.02/4.21	30[label="vx4 vx7",fontsize=16,color="green",shape="box"];30 -> 38[label="",style="dashed", color="green", weight=3];
10.02/4.21	29[label="catchHugsException00 vx5 vx6 vx10",fontsize=16,color="burlywood",shape="triangle"];51[label="vx10/IO vx100",fontsize=10,color="white",style="solid",shape="box"];29 -> 51[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	51 -> 34[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	52[label="vx10/AProVE_IO vx100",fontsize=10,color="white",style="solid",shape="box"];29 -> 52[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	52 -> 35[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	53[label="vx10/AProVE_Exception vx100",fontsize=10,color="white",style="solid",shape="box"];29 -> 53[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	53 -> 36[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	54[label="vx10/AProVE_Error vx100",fontsize=10,color="white",style="solid",shape="box"];29 -> 54[label="",style="solid", color="burlywood", weight=9];
10.02/4.21	54 -> 37[label="",style="solid", color="burlywood", weight=3];
10.02/4.21	31[label="fromObj vx8",fontsize=16,color="black",shape="triangle"];31 -> 39[label="",style="solid", color="black", weight=3];
10.02/4.21	32[label="toObj vx9",fontsize=16,color="black",shape="triangle"];32 -> 40[label="",style="solid", color="black", weight=3];
10.02/4.21	38[label="vx7",fontsize=16,color="green",shape="box"];34[label="catchHugsException00 vx5 vx6 (IO vx100)",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
10.02/4.21	35[label="catchHugsException00 vx5 vx6 (AProVE_IO vx100)",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
10.02/4.21	36[label="catchHugsException00 vx5 vx6 (AProVE_Exception vx100)",fontsize=16,color="black",shape="box"];36 -> 43[label="",style="solid", color="black", weight=3];
10.02/4.21	37[label="catchHugsException00 vx5 vx6 (AProVE_Error vx100)",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
10.02/4.21	39 -> 31[label="",style="dashed", color="red", weight=0];
10.02/4.21	39[label="fromObj vx8",fontsize=16,color="magenta"];40 -> 32[label="",style="dashed", color="red", weight=0];
10.02/4.21	40[label="toObj vx9",fontsize=16,color="magenta"];41[label="vx100 vx5 vx6",fontsize=16,color="green",shape="box"];41 -> 45[label="",style="dashed", color="green", weight=3];
10.02/4.21	41 -> 46[label="",style="dashed", color="green", weight=3];
10.02/4.21	42[label="error []",fontsize=16,color="red",shape="box"];43[label="error []",fontsize=16,color="red",shape="box"];44[label="error []",fontsize=16,color="red",shape="box"];45[label="vx5",fontsize=16,color="green",shape="box"];46[label="vx6",fontsize=16,color="green",shape="box"];}
10.02/4.21	
10.02/4.21	----------------------------------------
10.02/4.21	
10.02/4.21	(10)
10.02/4.21	Complex Obligation (AND)
10.02/4.21	
10.02/4.21	----------------------------------------
10.02/4.21	
10.02/4.21	(11)
10.02/4.21	Obligation:
10.02/4.21	Q DP problem:
10.02/4.21	The TRS P consists of the following rules:
10.02/4.21	
10.02/4.21	   new_fromObj(vx8, h, []) -> new_fromObj(vx8, h, [])
10.02/4.21	
10.02/4.21	R is empty.
10.02/4.21	Q is empty.
10.02/4.21	We have to consider all (P,Q,R)-chains.
10.02/4.21	----------------------------------------
10.02/4.21	
10.02/4.21	(12) NonTerminationLoopProof (COMPLETE)
10.02/4.21	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
10.02/4.21	Found a loop by semiunifying a rule from P directly.
10.02/4.21	
10.02/4.21	s = new_fromObj(vx8, h, []) evaluates to  t =new_fromObj(vx8, h, [])
10.02/4.21	
10.02/4.21	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
10.02/4.21	* Matcher: [ ]
10.02/4.21	* Semiunifier: [ ]
10.02/4.21	
10.02/4.21	--------------------------------------------------------------------------------
10.02/4.21	Rewriting sequence
10.02/4.21	
10.02/4.21	The DP semiunifies directly so there is only one rewrite step from new_fromObj(vx8, h, []) to new_fromObj(vx8, h, []).
10.02/4.21	
10.02/4.21	
10.02/4.21	
10.02/4.21	
10.02/4.21	----------------------------------------
10.02/4.21	
10.02/4.21	(13)
10.02/4.21	NO
10.02/4.21	
10.02/4.21	----------------------------------------
10.02/4.21	
10.02/4.21	(14)
10.02/4.21	Obligation:
10.02/4.21	Q DP problem:
10.02/4.21	The TRS P consists of the following rules:
10.02/4.21	
10.02/4.21	   new_toObj(vx9, h, []) -> new_toObj(vx9, h, [])
10.02/4.21	
10.02/4.21	R is empty.
10.02/4.21	Q is empty.
10.02/4.21	We have to consider all (P,Q,R)-chains.
10.02/4.26	EOF