20.035/20.035	YES
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(VAR vNonEmpty x)
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	g(x) -> x | x ->* a, b ->* x
20.035/20.035	)
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Inlining of Conditions Processor [STERN17]:
20.035/20.035	
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(VAR vNonEmpty x)
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	g(x) -> x | b ->* x, x ->* a
20.035/20.035	)
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Clean CTRS Processor:
20.035/20.035	
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	)
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	
20.035/20.035	CRule InfChecker Info:
20.035/20.035	g(x) -> x | b ->* x, x ->* a
20.035/20.035	Rule deleted
20.035/20.035	Proof:
20.035/20.035	YES
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Infeasibility Problem:
20.035/20.035	[(VAR vNonEmpty x vNonEmpty x)
20.035/20.035	(STRATEGY CONTEXTSENSITIVE
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	g(x) -> x | b ->* x, x ->* a
20.035/20.035	)]
20.035/20.035	
20.035/20.035	Infeasibility Conditions:
20.035/20.035	b ->* x, x ->* a
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Obtaining a model using Mace4:
20.035/20.035	
20.035/20.035	 -> Usable Rules:
20.035/20.035	g(x) -> x | b ->* x, x ->* a
20.035/20.035	
20.035/20.035	 -> Mace4 Output:
20.035/20.035	============================== Mace4 =================================
20.035/20.035	Mace4 (64) version 2009-11A, November 2009.
20.035/20.035	Process 77085 was started by ubuntu on ubuntu,
20.035/20.035	Wed Mar  9 10:17:39 2022
20.035/20.035	The command was "./mace4 -c -f /tmp/mace477072-2.in".
20.035/20.035	============================== end of head ===========================
20.035/20.035	
20.035/20.035	============================== INPUT =================================
20.035/20.035	
20.035/20.035	% Reading from file /tmp/mace477072-2.in
20.035/20.035	
20.035/20.035	assign(max_seconds,20).
20.035/20.035	
20.035/20.035	formulas(assumptions).
20.035/20.035	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
20.035/20.035	->*(b,x1) & ->*(x1,a) -> ->(g(x1),x1) # label(replacement).
20.035/20.035	->*(x,x) # label(reflexivity).
20.035/20.035	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.035/20.035	end_of_list.
20.035/20.035	
20.035/20.035	formulas(goals).
20.035/20.035	(exists x3 (->*(b,x3) & ->*(x3,a))) # label(goal).
20.035/20.035	end_of_list.
20.035/20.035	
20.035/20.035	============================== end of input ==========================
20.035/20.035	
20.035/20.035	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.035/20.035	
20.035/20.035	% Formulas that are not ordinary clauses:
20.035/20.035	1 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
20.035/20.035	2 ->*(b,x1) & ->*(x1,a) -> ->(g(x1),x1) # label(replacement) # label(non_clause).  [assumption].
20.035/20.035	3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.035/20.035	4 (exists x3 (->*(b,x3) & ->*(x3,a))) # label(goal) # label(non_clause) # label(goal).  [goal].
20.035/20.035	
20.035/20.035	============================== end of process non-clausal formulas ===
20.035/20.035	
20.035/20.035	============================== CLAUSES FOR SEARCH ====================
20.035/20.035	
20.035/20.035	formulas(mace4_clauses).
20.035/20.035	-->(x,y) | ->(g(x),g(y)) # label(congruence).
20.035/20.035	-->*(b,x) | -->*(x,a) | ->(g(x),x) # label(replacement).
20.035/20.035	->*(x,x) # label(reflexivity).
20.035/20.035	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.035/20.035	-->*(b,x) | -->*(x,a) # label(goal).
20.035/20.035	end_of_list.
20.035/20.035	
20.035/20.035	============================== end of clauses for search =============
20.035/20.035	
20.035/20.035	% There are no natural numbers in the input.
20.035/20.035	
20.035/20.035	============================== DOMAIN SIZE 2 =========================
20.035/20.035	
20.035/20.035	============================== MODEL =================================
20.035/20.035	
20.035/20.035	interpretation( 2, [number=1, seconds=0], [
20.035/20.035	
20.035/20.035	        function(a, [ 0 ]),
20.035/20.035	
20.035/20.035	        function(b, [ 1 ]),
20.035/20.035	
20.035/20.035	        function(g(_), [ 0, 0 ]),
20.035/20.035	
20.035/20.035	        relation(->*(_,_), [
20.035/20.035				   1, 0,
20.035/20.035				   0, 1 ]),
20.035/20.035	
20.035/20.035	        relation(->(_,_), [
20.035/20.035				   0, 0,
20.035/20.035				   0, 0 ])
20.035/20.035	]).
20.035/20.035	
20.035/20.035	============================== end of model ==========================
20.035/20.035	
20.035/20.035	============================== STATISTICS ============================
20.035/20.035	
20.035/20.035	For domain size 2.
20.035/20.035	
20.035/20.035	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.035/20.035	Ground clauses: seen=18, kept=14.
20.035/20.035	Selections=5, assignments=5, propagations=7, current_models=1.
20.035/20.035	Rewrite_terms=18, rewrite_bools=23, indexes=5.
20.035/20.035	Rules_from_neg_clauses=1, cross_offs=1.
20.035/20.035	
20.035/20.035	============================== end of statistics =====================
20.035/20.035	
20.035/20.035	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.035/20.035	
20.035/20.035	Exiting with 1 model.
20.035/20.035	
20.035/20.035	Process 77085 exit (max_models) Wed Mar  9 10:17:39 2022
20.035/20.035	The process finished Wed Mar  9 10:17:39 2022
20.035/20.035	
20.035/20.035	
20.035/20.035	Mace4 cooked interpretation:
20.035/20.035	
20.035/20.035	
20.035/20.035	
20.035/20.035	The problem is infeasible.
20.035/20.035	
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Transform No Conds CTRS Processor:
20.035/20.035	
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	)
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Resulting R:
20.035/20.035	(STRATEGY CONTEXTSENSITIVE
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	)
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	CleanTRS Processor:
20.035/20.035	
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	)
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	
20.035/20.035	Modular Confluence Combinations Decomposition Processor:
20.035/20.035	
20.035/20.035	No usable combinations
20.035/20.035	
20.035/20.035	Problem 1:
20.035/20.035	Linearity Processor:
20.035/20.035	Linear?
20.035/20.035	YES
20.035/20.035	Problem 1.1:
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	Confluence Problem:
20.035/20.035	(REPLACEMENT-MAP
20.035/20.035	(g 1)
20.035/20.035	(a)
20.035/20.035	(b)
20.035/20.035	(fSNonEmpty)
20.035/20.035	)
20.035/20.035	(RULES
20.035/20.035	)
20.035/20.035	Linear:YES
20.035/20.035	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.035/20.035	
20.035/20.035	Huet Levy Processor:
20.035/20.035	-> Rules:
20.035/20.035	
20.035/20.035	-> Vars:
20.035/20.035	
20.035/20.035	
20.035/20.035	-> Rlps:
20.035/20.035	
20.035/20.035	
20.035/20.035	-> Unifications:
20.035/20.035	
20.035/20.035	
20.035/20.035	-> Critical pairs info:
20.035/20.035	
20.035/20.035	
20.035/20.035	-> Problem conclusions:
20.035/20.035	 Left linear, Right linear, Linear
20.035/20.035	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.035/20.035	 Huet-Levy confluent, Not Newman confluent
20.035/20.035	 R is a TRS
20.035/20.035	
20.035/20.035	
20.035/20.035	The problem is joinable.
20.035/20.035	21.39user 0.27system 0:20.35elapsed 106%CPU (0avgtext+0avgdata 135984maxresident)k
20.035/20.035	8inputs+0outputs (0major+57567minor)pagefaults 0swaps