8.90/3.92	YES
11.16/4.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.16/4.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.16/4.47	
11.16/4.47	
11.16/4.47	H-Termination with start terms of the given HASKELL could be proven:
11.16/4.47	
11.16/4.47	(0) HASKELL
11.16/4.47	(1) LR [EQUIVALENT, 0 ms]
11.16/4.47	(2) HASKELL
11.16/4.47	(3) BR [EQUIVALENT, 0 ms]
11.16/4.47	(4) HASKELL
11.16/4.47	(5) COR [EQUIVALENT, 0 ms]
11.16/4.47	(6) HASKELL
11.16/4.47	(7) Narrow [EQUIVALENT, 17 ms]
11.16/4.47	(8) YES
11.16/4.47	
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(0)
11.16/4.47	Obligation:
11.16/4.47	mainModule Main 
11.16/4.47	module Maybe where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Main where {
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Monad where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Prelude;
11.16/4.47	liftM3 :: Monad e => (c  ->  a  ->  d  ->  b)  ->  e c  ->  e a  ->  e d  ->  e b;
11.16/4.47	liftM3 f m1 m2 m3 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->return (f x1 x2 x3))));
11.16/4.47	
11.16/4.47	}
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(1) LR (EQUIVALENT)
11.16/4.47	Lambda Reductions:
11.16/4.47	The following Lambda expression
11.16/4.47	"\x3->return (f x1 x2 x3)"
11.16/4.47	is transformed to
11.16/4.47	"liftM30 f x1 x2 x3 = return (f x1 x2 x3);
11.16/4.47	"
11.16/4.47	The following Lambda expression
11.16/4.47	"\x2->m3 >>= liftM30 f x1 x2"
11.16/4.47	is transformed to
11.16/4.47	"liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2;
11.16/4.47	"
11.16/4.47	The following Lambda expression
11.16/4.47	"\x1->m2 >>= liftM31 m3 f x1"
11.16/4.47	is transformed to
11.16/4.47	"liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1;
11.16/4.47	"
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(2)
11.16/4.47	Obligation:
11.16/4.47	mainModule Main 
11.16/4.47	module Maybe where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Main where {
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Monad where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Prelude;
11.16/4.47	liftM3 :: Monad e => (a  ->  c  ->  b  ->  d)  ->  e a  ->  e c  ->  e b  ->  e d;
11.16/4.47	liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f;
11.16/4.47	
11.16/4.47	liftM30 f x1 x2 x3 = return (f x1 x2 x3);
11.16/4.47	
11.16/4.47	liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2;
11.16/4.47	
11.16/4.47	liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1;
11.16/4.47	
11.16/4.47	}
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(3) BR (EQUIVALENT)
11.16/4.47	Replaced joker patterns by fresh variables and removed binding patterns.
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(4)
11.16/4.47	Obligation:
11.16/4.47	mainModule Main 
11.16/4.47	module Maybe where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Main where {
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Monad where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Prelude;
11.16/4.47	liftM3 :: Monad d => (b  ->  a  ->  c  ->  e)  ->  d b  ->  d a  ->  d c  ->  d e;
11.16/4.47	liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f;
11.16/4.47	
11.16/4.47	liftM30 f x1 x2 x3 = return (f x1 x2 x3);
11.16/4.47	
11.16/4.47	liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2;
11.16/4.47	
11.16/4.47	liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1;
11.16/4.47	
11.16/4.47	}
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(5) COR (EQUIVALENT)
11.16/4.47	Cond Reductions:
11.16/4.47	The following Function with conditions
11.16/4.47	"undefined |Falseundefined;
11.16/4.47	"
11.16/4.47	is transformed to
11.16/4.47	"undefined  = undefined1;
11.16/4.47	"
11.16/4.47	"undefined0 True = undefined;
11.16/4.47	"
11.16/4.47	"undefined1  = undefined0 False;
11.16/4.47	"
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(6)
11.16/4.47	Obligation:
11.16/4.47	mainModule Main 
11.16/4.47	module Maybe where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Main where {
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Monad;
11.16/4.47	import qualified Prelude;
11.16/4.47	}
11.16/4.47	module Monad where {
11.16/4.47	import qualified Main;
11.16/4.47	import qualified Maybe;
11.16/4.47	import qualified Prelude;
11.16/4.47	liftM3 :: Monad a => (e  ->  b  ->  d  ->  c)  ->  a e  ->  a b  ->  a d  ->  a c;
11.16/4.47	liftM3 f m1 m2 m3 = m1 >>= liftM32 m2 m3 f;
11.16/4.47	
11.16/4.47	liftM30 f x1 x2 x3 = return (f x1 x2 x3);
11.16/4.47	
11.16/4.47	liftM31 m3 f x1 x2 = m3 >>= liftM30 f x1 x2;
11.16/4.47	
11.16/4.47	liftM32 m2 m3 f x1 = m2 >>= liftM31 m3 f x1;
11.16/4.47	
11.16/4.47	}
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(7) Narrow (EQUIVALENT)
11.16/4.47	Haskell To QDPs
11.16/4.47	
11.16/4.47	digraph dp_graph {
11.16/4.47	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM3",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.16/4.47	3[label="Monad.liftM3 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.16/4.47	4[label="Monad.liftM3 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.16/4.47	5[label="Monad.liftM3 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.16/4.47	6[label="Monad.liftM3 vy3 vy4 vy5 vy6",fontsize=16,color="black",shape="triangle"];6 -> 7[label="",style="solid", color="black", weight=3];
11.16/4.47	7[label="vy4 >>= Monad.liftM32 vy5 vy6 vy3",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
11.16/4.47	8[label="primbindIO vy4 (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="burlywood",shape="box"];44[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 44[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	44 -> 9[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	45[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 45[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	45 -> 10[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	46[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 46[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	46 -> 11[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	47[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];8 -> 47[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	47 -> 12[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	9[label="primbindIO (IO vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
11.16/4.47	10[label="primbindIO (AProVE_IO vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11.16/4.47	11[label="primbindIO (AProVE_Exception vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
11.16/4.47	12[label="primbindIO (AProVE_Error vy40) (Monad.liftM32 vy5 vy6 vy3)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
11.16/4.47	13[label="error []",fontsize=16,color="red",shape="box"];14[label="Monad.liftM32 vy5 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3];
11.16/4.47	15[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];16[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];17[label="vy5 >>= Monad.liftM31 vy6 vy3 vy40",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
11.16/4.47	18[label="primbindIO vy5 (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];48[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];18 -> 48[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	48 -> 19[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	49[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];18 -> 49[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	49 -> 20[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	50[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];18 -> 50[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	50 -> 21[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	51[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];18 -> 51[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	51 -> 22[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	19[label="primbindIO (IO vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
11.16/4.47	20[label="primbindIO (AProVE_IO vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
11.16/4.47	21[label="primbindIO (AProVE_Exception vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
11.16/4.47	22[label="primbindIO (AProVE_Error vy50) (Monad.liftM31 vy6 vy3 vy40)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
11.16/4.47	23[label="error []",fontsize=16,color="red",shape="box"];24[label="Monad.liftM31 vy6 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
11.16/4.47	25[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];26[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];27[label="vy6 >>= Monad.liftM30 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
11.16/4.47	28[label="primbindIO vy6 (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];52[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];28 -> 52[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	52 -> 29[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	53[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];28 -> 53[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	53 -> 30[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	54[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];28 -> 54[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	54 -> 31[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	55[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];28 -> 55[label="",style="solid", color="burlywood", weight=9];
11.16/4.47	55 -> 32[label="",style="solid", color="burlywood", weight=3];
11.16/4.47	29[label="primbindIO (IO vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
11.16/4.47	30[label="primbindIO (AProVE_IO vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
11.16/4.47	31[label="primbindIO (AProVE_Exception vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
11.16/4.47	32[label="primbindIO (AProVE_Error vy60) (Monad.liftM30 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
11.16/4.47	33[label="error []",fontsize=16,color="red",shape="box"];34[label="Monad.liftM30 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];34 -> 37[label="",style="solid", color="black", weight=3];
11.16/4.47	35[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];36[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];37[label="return (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3];
11.16/4.47	38[label="primretIO (vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
11.16/4.47	39[label="AProVE_IO (vy3 vy40 vy50 vy60)",fontsize=16,color="green",shape="box"];39 -> 40[label="",style="dashed", color="green", weight=3];
11.16/4.47	40[label="vy3 vy40 vy50 vy60",fontsize=16,color="green",shape="box"];40 -> 41[label="",style="dashed", color="green", weight=3];
11.16/4.47	40 -> 42[label="",style="dashed", color="green", weight=3];
11.16/4.47	40 -> 43[label="",style="dashed", color="green", weight=3];
11.16/4.47	41[label="vy40",fontsize=16,color="green",shape="box"];42[label="vy50",fontsize=16,color="green",shape="box"];43[label="vy60",fontsize=16,color="green",shape="box"];}
11.16/4.47	
11.16/4.47	----------------------------------------
11.16/4.47	
11.16/4.47	(8)
11.16/4.47	YES
11.27/4.55	EOF