0.009/0.009	NO
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(VAR vNonEmpty x)
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	b -> c | b ->* c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Inlining of Conditions Processor [STERN17]:
0.009/0.009	
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(VAR vNonEmpty x)
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	b -> c | b ->* c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Clean CTRS Processor:
0.009/0.009	
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	
0.009/0.009	CRule InfChecker Info:
0.009/0.009	a -> b
0.009/0.009	Rule remains
0.009/0.009	Proof:
0.009/0.009	NO_CONDS
0.009/0.009	
0.009/0.009	CRule InfChecker Info:
0.009/0.009	a -> c
0.009/0.009	Rule remains
0.009/0.009	Proof:
0.009/0.009	NO_CONDS
0.009/0.009	
0.009/0.009	CRule InfChecker Info:
0.009/0.009	b -> c | b ->* c
0.009/0.009	Rule deleted
0.009/0.009	Proof:
0.009/0.009	YES
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Infeasibility Problem:
0.009/0.009	[(VAR vNonEmpty x vNonEmpty)
0.009/0.009	(STRATEGY CONTEXTSENSITIVE
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	b -> c | b ->* c
0.009/0.009	)]
0.009/0.009	
0.009/0.009	Infeasibility Conditions:
0.009/0.009	b ->* c
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Obtaining a model using Mace4:
0.009/0.009	
0.009/0.009	 -> Usable Rules:
0.009/0.009	b -> c | b ->* c
0.009/0.009	
0.009/0.009	 -> Mace4 Output:
0.009/0.009	============================== Mace4 =================================
0.009/0.009	Mace4 (64) version 2009-11A, November 2009.
0.009/0.009	Process 10193 was started by ubuntu on ubuntu,
0.009/0.009	Wed Mar  9 09:12:52 2022
0.009/0.009	The command was "./mace4 -c -f /tmp/mace410180-2.in".
0.009/0.009	============================== end of head ===========================
0.009/0.009	
0.009/0.009	============================== INPUT =================================
0.009/0.009	
0.009/0.009	% Reading from file /tmp/mace410180-2.in
0.009/0.009	
0.009/0.009	assign(max_seconds,20).
0.009/0.009	
0.009/0.009	formulas(assumptions).
0.009/0.009	->*(b,c) -> ->(b,c) # label(replacement).
0.009/0.009	->*(x,x) # label(reflexivity).
0.009/0.009	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
0.009/0.009	end_of_list.
0.009/0.009	
0.009/0.009	formulas(goals).
0.009/0.009	->*(b,c) # label(goal).
0.009/0.009	end_of_list.
0.009/0.009	
0.009/0.009	============================== end of input ==========================
0.009/0.009	
0.009/0.009	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.009/0.009	
0.009/0.009	% Formulas that are not ordinary clauses:
0.009/0.009	1 ->*(b,c) -> ->(b,c) # label(replacement) # label(non_clause).  [assumption].
0.009/0.009	2 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
0.009/0.009	3 ->*(b,c) # label(goal) # label(non_clause) # label(goal).  [goal].
0.009/0.009	
0.009/0.009	============================== end of process non-clausal formulas ===
0.009/0.009	
0.009/0.009	============================== CLAUSES FOR SEARCH ====================
0.009/0.009	
0.009/0.009	formulas(mace4_clauses).
0.009/0.009	-->*(b,c) | ->(b,c) # label(replacement).
0.009/0.009	->*(x,x) # label(reflexivity).
0.009/0.009	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
0.009/0.009	-->*(b,c) # label(goal).
0.009/0.009	end_of_list.
0.009/0.009	
0.009/0.009	============================== end of clauses for search =============
0.009/0.009	
0.009/0.009	% There are no natural numbers in the input.
0.009/0.009	
0.009/0.009	============================== DOMAIN SIZE 2 =========================
0.009/0.009	
0.009/0.009	============================== MODEL =================================
0.009/0.009	
0.009/0.009	interpretation( 2, [number=1, seconds=0], [
0.009/0.009	
0.009/0.009	        function(b, [ 0 ]),
0.009/0.009	
0.009/0.009	        function(c, [ 1 ]),
0.009/0.009	
0.009/0.009	        relation(->*(_,_), [
0.009/0.009				   1, 0,
0.009/0.009				   0, 1 ]),
0.009/0.009	
0.009/0.009	        relation(->(_,_), [
0.009/0.009				   0, 0,
0.009/0.009				   0, 0 ])
0.009/0.009	]).
0.009/0.009	
0.009/0.009	============================== end of model ==========================
0.009/0.009	
0.009/0.009	============================== STATISTICS ============================
0.009/0.009	
0.009/0.009	For domain size 2.
0.009/0.009	
0.009/0.009	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.009/0.009	Ground clauses: seen=12, kept=8.
0.009/0.009	Selections=4, assignments=4, propagations=6, current_models=1.
0.009/0.009	Rewrite_terms=6, rewrite_bools=12, indexes=2.
0.009/0.009	Rules_from_neg_clauses=1, cross_offs=1.
0.009/0.009	
0.009/0.009	============================== end of statistics =====================
0.009/0.009	
0.009/0.009	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.009/0.009	
0.009/0.009	Exiting with 1 model.
0.009/0.009	
0.009/0.009	Process 10193 exit (max_models) Wed Mar  9 09:12:52 2022
0.009/0.009	The process finished Wed Mar  9 09:12:52 2022
0.009/0.009	
0.009/0.009	
0.009/0.009	Mace4 cooked interpretation:
0.009/0.009	
0.009/0.009	
0.009/0.009	
0.009/0.009	The problem is infeasible.
0.009/0.009	
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Transform No Conds CTRS Processor:
0.009/0.009	
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Resulting R:
0.009/0.009	(STRATEGY CONTEXTSENSITIVE
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	)
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	CleanTRS Processor:
0.009/0.009	
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	
0.009/0.009	Modular Confluence Combinations Decomposition Processor:
0.009/0.009	
0.009/0.009	No usable combinations
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	Confluence Problem:
0.009/0.009	(REPLACEMENT-MAP
0.009/0.009	(a)
0.009/0.009	(b)
0.009/0.009	(c)
0.009/0.009	(fSNonEmpty)
0.009/0.009	)
0.009/0.009	(RULES
0.009/0.009	a -> b
0.009/0.009	a -> c
0.009/0.009	)
0.009/0.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.009/0.009	
0.009/0.009	Huet Levy Processor:
0.009/0.009	-> Rules:
0.009/0.009	 a -> b
0.009/0.009	 a -> c
0.009/0.009	-> Vars:
0.009/0.009	
0.009/0.009	
0.009/0.009	-> Rlps:
0.009/0.009	 (rule: a -> b, id: 1, possubterms: a->[])
0.009/0.009	 (rule: a -> c, id: 2, possubterms: a->[])
0.009/0.009	
0.009/0.009	-> Unifications:
0.009/0.009	(R2 unifies with R1 at p: [], l: a, lp: a, sig: {}, l': a, r: c, r': b)
0.009/0.009	
0.009/0.009	-> Critical pairs info:
0.009/0.009	<b,c>   =>  Not trivial, Overlay, NW0, N1
0.009/0.009	
0.009/0.009	-> Problem conclusions:
0.009/0.009	 Left linear, Right linear, Linear
0.009/0.009	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.009/0.009	 Not Huet-Levy confluent, Not Newman confluent
0.009/0.009	 R is a TRS
0.009/0.009	
0.009/0.009	
0.009/0.009	Problem 1:
0.009/0.009	Different Normal CP Terms Processor:
0.009/0.009	<b,c>   =>  Not trivial, Overlay, NW0, N1, Normal and not trivial cp
0.009/0.009	
0.009/0.009	The problem is not joinable.
0.009/0.009	0.06user 0.02system 0:00.09elapsed 94%CPU (0avgtext+0avgdata 20700maxresident)k
0.009/0.009	8inputs+0outputs (0major+8085minor)pagefaults 0swaps