8.27/3.62	NO
10.03/4.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.03/4.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.03/4.11	
10.03/4.11	
10.03/4.11	H-Termination with start terms of the given HASKELL could be disproven:
10.03/4.11	
10.03/4.11	(0) HASKELL
10.03/4.11	(1) BR [EQUIVALENT, 0 ms]
10.03/4.11	(2) HASKELL
10.03/4.11	(3) COR [EQUIVALENT, 0 ms]
10.03/4.11	(4) HASKELL
10.03/4.11	(5) Narrow [COMPLETE, 0 ms]
10.03/4.11	(6) QDP
10.03/4.11	(7) NonTerminationLoopProof [COMPLETE, 0 ms]
10.03/4.11	(8) NO
10.03/4.11	
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(0)
10.03/4.11	Obligation:
10.03/4.11	mainModule Main 
10.03/4.11	module Main where {
10.03/4.11	import qualified Prelude;
10.03/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.03/4.11	
10.03/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.03/4.11	
10.03/4.11	maxBoundMyInt :: MyInt;
10.03/4.11	maxBoundMyInt = primMaxInt;
10.03/4.11	
10.03/4.11	primMaxInt :: MyInt;
10.03/4.11	primMaxInt = primMaxInt;
10.03/4.11	
10.03/4.11	}
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(1) BR (EQUIVALENT)
10.03/4.11	Replaced joker patterns by fresh variables and removed binding patterns.
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(2)
10.03/4.11	Obligation:
10.03/4.11	mainModule Main 
10.03/4.11	module Main where {
10.03/4.11	import qualified Prelude;
10.03/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.03/4.11	
10.03/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.03/4.11	
10.03/4.11	maxBoundMyInt :: MyInt;
10.03/4.11	maxBoundMyInt = primMaxInt;
10.03/4.11	
10.03/4.11	primMaxInt :: MyInt;
10.03/4.11	primMaxInt = primMaxInt;
10.03/4.11	
10.03/4.11	}
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(3) COR (EQUIVALENT)
10.03/4.11	Cond Reductions:
10.03/4.11	The following Function with conditions
10.03/4.11	"undefined |Falseundefined;
10.03/4.11	"
10.03/4.11	is transformed to
10.03/4.11	"undefined  = undefined1;
10.03/4.11	"
10.03/4.11	"undefined0 True = undefined;
10.03/4.11	"
10.03/4.11	"undefined1  = undefined0 False;
10.03/4.11	"
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(4)
10.03/4.11	Obligation:
10.03/4.11	mainModule Main 
10.03/4.11	module Main where {
10.03/4.11	import qualified Prelude;
10.03/4.11	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
10.03/4.11	
10.03/4.11	data Main.Nat = Succ Main.Nat  | Zero ;
10.03/4.11	
10.03/4.11	maxBoundMyInt :: MyInt;
10.03/4.11	maxBoundMyInt = primMaxInt;
10.03/4.11	
10.03/4.11	primMaxInt :: MyInt;
10.03/4.11	primMaxInt = primMaxInt;
10.03/4.11	
10.03/4.11	}
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(5) Narrow (COMPLETE)
10.03/4.11	Haskell To QDPs
10.03/4.11	
10.03/4.11	digraph dp_graph {
10.03/4.11	node [outthreshold=100, inthreshold=100];1[label="maxBoundMyInt",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
10.03/4.11	3[label="primMaxInt",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.03/4.11	4 -> 3[label="",style="dashed", color="red", weight=0];
10.03/4.11	4[label="primMaxInt",fontsize=16,color="magenta"];}
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(6)
10.03/4.11	Obligation:
10.03/4.11	Q DP problem:
10.03/4.11	The TRS P consists of the following rules:
10.03/4.11	
10.03/4.11	   new_primMaxInt([]) -> new_primMaxInt([])
10.03/4.11	
10.03/4.11	R is empty.
10.03/4.11	Q is empty.
10.03/4.11	We have to consider all (P,Q,R)-chains.
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(7) NonTerminationLoopProof (COMPLETE)
10.03/4.11	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
10.03/4.11	Found a loop by semiunifying a rule from P directly.
10.03/4.11	
10.03/4.11	s = new_primMaxInt([]) evaluates to  t =new_primMaxInt([])
10.03/4.11	
10.03/4.11	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
10.03/4.11	* Matcher: [ ]
10.03/4.11	* Semiunifier: [ ]
10.03/4.11	
10.03/4.11	--------------------------------------------------------------------------------
10.03/4.11	Rewriting sequence
10.03/4.11	
10.03/4.11	The DP semiunifies directly so there is only one rewrite step from new_primMaxInt([]) to new_primMaxInt([]).
10.03/4.11	
10.03/4.11	
10.03/4.11	
10.03/4.11	
10.03/4.11	----------------------------------------
10.03/4.11	
10.03/4.11	(8)
10.03/4.11	NO
10.17/4.20	EOF