0.012/0.012	NO
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(VAR vNonEmpty:S x:S)
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	b -> c | b ->* c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Inlining of Conditions Processor [STERN17]:
0.012/0.012	
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(VAR vNonEmpty:S x:S)
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	b -> c | b ->* c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Clean CTRS Processor:
0.012/0.012	
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	
0.012/0.012	CRule InfChecker Info:
0.012/0.012	a -> b
0.012/0.012	Rule remains
0.012/0.012	Proof:
0.012/0.012	NO_CONDS
0.012/0.012	
0.012/0.012	CRule InfChecker Info:
0.012/0.012	a -> c
0.012/0.012	Rule remains
0.012/0.012	Proof:
0.012/0.012	NO_CONDS
0.012/0.012	
0.012/0.012	CRule InfChecker Info:
0.012/0.012	b -> c | b ->* c
0.012/0.012	Rule deleted
0.012/0.012	Proof:
0.012/0.012	YES
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Infeasibility Problem:
0.012/0.012	[(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	b -> c | b ->* c
0.012/0.012	)]
0.012/0.012	
0.012/0.012	Infeasibility Conditions:
0.012/0.012	b ->* c
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Obtaining a model using Mace4:
0.012/0.012	
0.012/0.012	 -> Usable Rules:
0.012/0.012	b -> c | b ->* c
0.012/0.012	
0.012/0.012	 -> Mace4 Output:
0.012/0.012	============================== Mace4 =================================
0.012/0.012	Mace4 (64) version 2009-11A, November 2009.
0.012/0.012	Process 101776 was started by ubuntu on ubuntu,
0.012/0.012	Fri Jul 16 14:39:28 2021
0.012/0.012	The command was "./mace4 -c -f /tmp/mace4101763-2.in".
0.012/0.012	============================== end of head ===========================
0.012/0.012	
0.012/0.012	============================== INPUT =================================
0.012/0.012	
0.012/0.012	% Reading from file /tmp/mace4101763-2.in
0.012/0.012	
0.012/0.012	assign(max_seconds,10).
0.012/0.012	
0.012/0.012	formulas(assumptions).
0.012/0.012	->*(b,c) -> ->(b,c) # label(replacement).
0.012/0.012	->*(x,x) # label(reflexivity).
0.012/0.012	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
0.012/0.012	end_of_list.
0.012/0.012	
0.012/0.012	formulas(goals).
0.012/0.012	->*(b,c) # label(goal).
0.012/0.012	end_of_list.
0.012/0.012	
0.012/0.012	============================== end of input ==========================
0.012/0.012	
0.012/0.012	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.012/0.012	
0.012/0.012	% Formulas that are not ordinary clauses:
0.012/0.012	1 ->*(b,c) -> ->(b,c) # label(replacement) # label(non_clause).  [assumption].
0.012/0.012	2 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
0.012/0.012	3 ->*(b,c) # label(goal) # label(non_clause) # label(goal).  [goal].
0.012/0.012	
0.012/0.012	============================== end of process non-clausal formulas ===
0.012/0.012	
0.012/0.012	============================== CLAUSES FOR SEARCH ====================
0.012/0.012	
0.012/0.012	formulas(mace4_clauses).
0.012/0.012	-->*(b,c) | ->(b,c) # label(replacement).
0.012/0.012	->*(x,x) # label(reflexivity).
0.012/0.012	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
0.012/0.012	-->*(b,c) # label(goal).
0.012/0.012	end_of_list.
0.012/0.012	
0.012/0.012	============================== end of clauses for search =============
0.012/0.012	
0.012/0.012	% There are no natural numbers in the input.
0.012/0.012	
0.012/0.012	============================== DOMAIN SIZE 2 =========================
0.012/0.012	
0.012/0.012	============================== MODEL =================================
0.012/0.012	
0.012/0.012	interpretation( 2, [number=1, seconds=0], [
0.012/0.012	
0.012/0.012	        function(b, [ 0 ]),
0.012/0.012	
0.012/0.012	        function(c, [ 1 ]),
0.012/0.012	
0.012/0.012	        relation(->*(_,_), [
0.012/0.012				   1, 0,
0.012/0.012				   0, 1 ]),
0.012/0.012	
0.012/0.012	        relation(->(_,_), [
0.012/0.012				   0, 0,
0.012/0.012				   0, 0 ])
0.012/0.012	]).
0.012/0.012	
0.012/0.012	============================== end of model ==========================
0.012/0.012	
0.012/0.012	============================== STATISTICS ============================
0.012/0.012	
0.012/0.012	For domain size 2.
0.012/0.012	
0.012/0.012	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.012/0.012	Ground clauses: seen=12, kept=8.
0.012/0.012	Selections=4, assignments=4, propagations=6, current_models=1.
0.012/0.012	Rewrite_terms=6, rewrite_bools=12, indexes=2.
0.012/0.012	Rules_from_neg_clauses=1, cross_offs=1.
0.012/0.012	
0.012/0.012	============================== end of statistics =====================
0.012/0.012	
0.012/0.012	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.012/0.012	
0.012/0.012	Exiting with 1 model.
0.012/0.012	
0.012/0.012	Process 101776 exit (max_models) Fri Jul 16 14:39:28 2021
0.012/0.012	The process finished Fri Jul 16 14:39:28 2021
0.012/0.012	
0.012/0.012	
0.012/0.012	Mace4 cooked interpretation:
0.012/0.012	
0.012/0.012	
0.012/0.012	
0.012/0.012	The problem is infeasible.
0.012/0.012	
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Transform No Conds CTRS Processor:
0.012/0.012	
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Resulting R:
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	)
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	CleanTRS Processor:
0.012/0.012	
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	
0.012/0.012	Modular Confluence Combinations Decomposition Processor:
0.012/0.012	
0.012/0.012	No usable combinations
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	Confluence Problem:
0.012/0.012	(STRATEGY CONTEXTSENSITIVE
0.012/0.012	(a)
0.012/0.012	(b)
0.012/0.012	(c)
0.012/0.012	(fSNonEmpty)
0.012/0.012	)
0.012/0.012	(RULES
0.012/0.012	a -> b
0.012/0.012	a -> c
0.012/0.012	)
0.012/0.012	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.012/0.012	
0.012/0.012	Huet Levy Processor:
0.012/0.012	-> Rules:
0.012/0.012	 a -> b
0.012/0.012	 a -> c
0.012/0.012	-> Vars:
0.012/0.012	
0.012/0.012	-> FVars:
0.012/0.012	
0.012/0.012	-> PVars:
0.012/0.012	
0.012/0.012	
0.012/0.012	-> Rlps:
0.012/0.012	 (rule: a -> b, id: 1, possubterms: a->[])
0.012/0.012	 (rule: a -> c, id: 2, possubterms: a->[])
0.012/0.012	
0.012/0.012	-> Unifications:
0.012/0.012	(R2 unifies with R1 at p: [], l: a, lp: a, sig: {}, l': a, r: c, r': b)
0.012/0.012	
0.012/0.012	-> Critical pairs info:
0.012/0.012	<b,c>   =>  Not trivial, Overlay, N1
0.012/0.012	
0.012/0.012	-> Problem conclusions:
0.012/0.012	 Left linear, Right linear, Linear
0.012/0.012	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.012/0.012	 Not Huet-Levy confluent, Not Newman confluent
0.012/0.012	 R is a TRS
0.012/0.012	
0.012/0.012	
0.012/0.012	Problem 1:
0.012/0.012	Different Normal CP Terms Processor:
0.012/0.012	<b,c>   =>  Not trivial, Overlay, N1, Normal and not trivial cp
0.012/0.012	
0.012/0.012	The problem is not joinable.
0.012/0.012	0.08user 0.03system 0:00.12elapsed 99%CPU (0avgtext+0avgdata 33120maxresident)k
0.012/0.012	8inputs+0outputs (0major+11083minor)pagefaults 0swaps