8.79/3.92	YES
11.04/4.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
11.04/4.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.04/4.50	
11.04/4.50	
11.04/4.50	H-Termination with start terms of the given HASKELL could be proven:
11.04/4.50	
11.04/4.50	(0) HASKELL
11.04/4.50	(1) LR [EQUIVALENT, 0 ms]
11.04/4.50	(2) HASKELL
11.04/4.50	(3) BR [EQUIVALENT, 0 ms]
11.04/4.50	(4) HASKELL
11.04/4.50	(5) COR [EQUIVALENT, 0 ms]
11.04/4.50	(6) HASKELL
11.04/4.50	(7) Narrow [EQUIVALENT, 17 ms]
11.04/4.50	(8) YES
11.04/4.50	
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(0)
11.04/4.50	Obligation:
11.04/4.50	mainModule Main 
11.04/4.50	module Maybe where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Main where {
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Monad where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Prelude;
11.04/4.50	liftM4 :: Monad e => (d  ->  a  ->  b  ->  c  ->  f)  ->  e d  ->  e a  ->  e b  ->  e c  ->  e f;
11.04/4.50	liftM4 f m1 m2 m3 m4 = m1 >>= (\x1 ->m2 >>= (\x2 ->m3 >>= (\x3 ->m4 >>= (\x4 ->return (f x1 x2 x3 x4)))));
11.04/4.50	
11.04/4.50	}
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(1) LR (EQUIVALENT)
11.04/4.50	Lambda Reductions:
11.04/4.50	The following Lambda expression
11.04/4.50	"\x4->return (f x1 x2 x3 x4)"
11.04/4.50	is transformed to
11.04/4.50	"liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.50	"
11.04/4.50	The following Lambda expression
11.04/4.50	"\x3->m4 >>= liftM40 f x1 x2 x3"
11.04/4.50	is transformed to
11.04/4.50	"liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.50	"
11.04/4.50	The following Lambda expression
11.04/4.50	"\x2->m3 >>= liftM41 m4 f x1 x2"
11.04/4.50	is transformed to
11.04/4.50	"liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.50	"
11.04/4.50	The following Lambda expression
11.04/4.50	"\x1->m2 >>= liftM42 m3 m4 f x1"
11.04/4.50	is transformed to
11.04/4.50	"liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.50	"
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(2)
11.04/4.50	Obligation:
11.04/4.50	mainModule Main 
11.04/4.50	module Maybe where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Main where {
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Monad where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Prelude;
11.04/4.50	liftM4 :: Monad a => (f  ->  e  ->  b  ->  c  ->  d)  ->  a f  ->  a e  ->  a b  ->  a c  ->  a d;
11.04/4.50	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.50	
11.04/4.50	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.50	
11.04/4.50	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.50	
11.04/4.50	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.50	
11.04/4.50	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.50	
11.04/4.50	}
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(3) BR (EQUIVALENT)
11.04/4.50	Replaced joker patterns by fresh variables and removed binding patterns.
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(4)
11.04/4.50	Obligation:
11.04/4.50	mainModule Main 
11.04/4.50	module Maybe where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Main where {
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Monad where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Prelude;
11.04/4.50	liftM4 :: Monad f => (b  ->  d  ->  c  ->  e  ->  a)  ->  f b  ->  f d  ->  f c  ->  f e  ->  f a;
11.04/4.50	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.50	
11.04/4.50	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.50	
11.04/4.50	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.50	
11.04/4.50	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.50	
11.04/4.50	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.50	
11.04/4.50	}
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(5) COR (EQUIVALENT)
11.04/4.50	Cond Reductions:
11.04/4.50	The following Function with conditions
11.04/4.50	"undefined |Falseundefined;
11.04/4.50	"
11.04/4.50	is transformed to
11.04/4.50	"undefined  = undefined1;
11.04/4.50	"
11.04/4.50	"undefined0 True = undefined;
11.04/4.50	"
11.04/4.50	"undefined1  = undefined0 False;
11.04/4.50	"
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(6)
11.04/4.50	Obligation:
11.04/4.50	mainModule Main 
11.04/4.50	module Maybe where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Main where {
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Monad;
11.04/4.50	import qualified Prelude;
11.04/4.50	}
11.04/4.50	module Monad where {
11.04/4.50	import qualified Main;
11.04/4.50	import qualified Maybe;
11.04/4.50	import qualified Prelude;
11.04/4.50	liftM4 :: Monad a => (e  ->  f  ->  d  ->  b  ->  c)  ->  a e  ->  a f  ->  a d  ->  a b  ->  a c;
11.04/4.50	liftM4 f m1 m2 m3 m4 = m1 >>= liftM43 m2 m3 m4 f;
11.04/4.50	
11.04/4.50	liftM40 f x1 x2 x3 x4 = return (f x1 x2 x3 x4);
11.04/4.50	
11.04/4.50	liftM41 m4 f x1 x2 x3 = m4 >>= liftM40 f x1 x2 x3;
11.04/4.50	
11.04/4.50	liftM42 m3 m4 f x1 x2 = m3 >>= liftM41 m4 f x1 x2;
11.04/4.50	
11.04/4.50	liftM43 m2 m3 m4 f x1 = m2 >>= liftM42 m3 m4 f x1;
11.04/4.50	
11.04/4.50	}
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(7) Narrow (EQUIVALENT)
11.04/4.50	Haskell To QDPs
11.04/4.50	
11.04/4.50	digraph dp_graph {
11.04/4.50	node [outthreshold=100, inthreshold=100];1[label="Monad.liftM4",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.04/4.50	3[label="Monad.liftM4 vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.04/4.50	4[label="Monad.liftM4 vy3 vy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
11.04/4.50	5[label="Monad.liftM4 vy3 vy4 vy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
11.04/4.50	6[label="Monad.liftM4 vy3 vy4 vy5 vy6",fontsize=16,color="grey",shape="box"];6 -> 7[label="",style="dashed", color="grey", weight=3];
11.04/4.50	7[label="Monad.liftM4 vy3 vy4 vy5 vy6 vy7",fontsize=16,color="black",shape="triangle"];7 -> 8[label="",style="solid", color="black", weight=3];
11.04/4.50	8[label="vy4 >>= Monad.liftM43 vy5 vy6 vy7 vy3",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
11.04/4.50	9[label="primbindIO vy4 (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="burlywood",shape="box"];56[label="vy4/IO vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 56[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	56 -> 10[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	57[label="vy4/AProVE_IO vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 57[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	57 -> 11[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	58[label="vy4/AProVE_Exception vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 58[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	58 -> 12[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	59[label="vy4/AProVE_Error vy40",fontsize=10,color="white",style="solid",shape="box"];9 -> 59[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	59 -> 13[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	10[label="primbindIO (IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11.04/4.50	11[label="primbindIO (AProVE_IO vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
11.04/4.50	12[label="primbindIO (AProVE_Exception vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
11.04/4.50	13[label="primbindIO (AProVE_Error vy40) (Monad.liftM43 vy5 vy6 vy7 vy3)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
11.04/4.50	14[label="error []",fontsize=16,color="red",shape="box"];15[label="Monad.liftM43 vy5 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
11.04/4.50	16[label="AProVE_Exception vy40",fontsize=16,color="green",shape="box"];17[label="AProVE_Error vy40",fontsize=16,color="green",shape="box"];18[label="vy5 >>= Monad.liftM42 vy6 vy7 vy3 vy40",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
11.04/4.50	19[label="primbindIO vy5 (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="burlywood",shape="box"];60[label="vy5/IO vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 60[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	60 -> 20[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	61[label="vy5/AProVE_IO vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 61[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	61 -> 21[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	62[label="vy5/AProVE_Exception vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 62[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	62 -> 22[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	63[label="vy5/AProVE_Error vy50",fontsize=10,color="white",style="solid",shape="box"];19 -> 63[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	63 -> 23[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	20[label="primbindIO (IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
11.04/4.50	21[label="primbindIO (AProVE_IO vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
11.04/4.50	22[label="primbindIO (AProVE_Exception vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
11.04/4.50	23[label="primbindIO (AProVE_Error vy50) (Monad.liftM42 vy6 vy7 vy3 vy40)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
11.04/4.50	24[label="error []",fontsize=16,color="red",shape="box"];25[label="Monad.liftM42 vy6 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
11.04/4.50	26[label="AProVE_Exception vy50",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vy50",fontsize=16,color="green",shape="box"];28[label="vy6 >>= Monad.liftM41 vy7 vy3 vy40 vy50",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
11.04/4.50	29[label="primbindIO vy6 (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="burlywood",shape="box"];64[label="vy6/IO vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 64[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	64 -> 30[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	65[label="vy6/AProVE_IO vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 65[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	65 -> 31[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	66[label="vy6/AProVE_Exception vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 66[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	66 -> 32[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	67[label="vy6/AProVE_Error vy60",fontsize=10,color="white",style="solid",shape="box"];29 -> 67[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	67 -> 33[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	30[label="primbindIO (IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
11.04/4.50	31[label="primbindIO (AProVE_IO vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
11.04/4.50	32[label="primbindIO (AProVE_Exception vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
11.04/4.50	33[label="primbindIO (AProVE_Error vy60) (Monad.liftM41 vy7 vy3 vy40 vy50)",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
11.04/4.50	34[label="error []",fontsize=16,color="red",shape="box"];35[label="Monad.liftM41 vy7 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];35 -> 38[label="",style="solid", color="black", weight=3];
11.04/4.50	36[label="AProVE_Exception vy60",fontsize=16,color="green",shape="box"];37[label="AProVE_Error vy60",fontsize=16,color="green",shape="box"];38[label="vy7 >>= Monad.liftM40 vy3 vy40 vy50 vy60",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
11.04/4.50	39[label="primbindIO vy7 (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="burlywood",shape="box"];68[label="vy7/IO vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 68[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	68 -> 40[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	69[label="vy7/AProVE_IO vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 69[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	69 -> 41[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	70[label="vy7/AProVE_Exception vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 70[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	70 -> 42[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	71[label="vy7/AProVE_Error vy70",fontsize=10,color="white",style="solid",shape="box"];39 -> 71[label="",style="solid", color="burlywood", weight=9];
11.04/4.50	71 -> 43[label="",style="solid", color="burlywood", weight=3];
11.04/4.50	40[label="primbindIO (IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
11.04/4.50	41[label="primbindIO (AProVE_IO vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
11.04/4.50	42[label="primbindIO (AProVE_Exception vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
11.04/4.50	43[label="primbindIO (AProVE_Error vy70) (Monad.liftM40 vy3 vy40 vy50 vy60)",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
11.04/4.50	44[label="error []",fontsize=16,color="red",shape="box"];45[label="Monad.liftM40 vy3 vy40 vy50 vy60 vy70",fontsize=16,color="black",shape="box"];45 -> 48[label="",style="solid", color="black", weight=3];
11.04/4.50	46[label="AProVE_Exception vy70",fontsize=16,color="green",shape="box"];47[label="AProVE_Error vy70",fontsize=16,color="green",shape="box"];48[label="return (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
11.04/4.50	49[label="primretIO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="black",shape="box"];49 -> 50[label="",style="solid", color="black", weight=3];
11.04/4.50	50[label="AProVE_IO (vy3 vy40 vy50 vy60 vy70)",fontsize=16,color="green",shape="box"];50 -> 51[label="",style="dashed", color="green", weight=3];
11.04/4.50	51[label="vy3 vy40 vy50 vy60 vy70",fontsize=16,color="green",shape="box"];51 -> 52[label="",style="dashed", color="green", weight=3];
11.04/4.50	51 -> 53[label="",style="dashed", color="green", weight=3];
11.04/4.50	51 -> 54[label="",style="dashed", color="green", weight=3];
11.04/4.50	51 -> 55[label="",style="dashed", color="green", weight=3];
11.04/4.50	52[label="vy40",fontsize=16,color="green",shape="box"];53[label="vy50",fontsize=16,color="green",shape="box"];54[label="vy60",fontsize=16,color="green",shape="box"];55[label="vy70",fontsize=16,color="green",shape="box"];}
11.04/4.50	
11.04/4.50	----------------------------------------
11.04/4.50	
11.04/4.50	(8)
11.04/4.50	YES
11.23/4.56	EOF