20.021/20.021	YES
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(VAR vNonEmpty x)
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	f(x) -> x | x ->* a, b ->* x
20.021/20.021	)
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Inlining of Conditions Processor [STERN17]:
20.021/20.021	
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(VAR vNonEmpty x)
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	f(x) -> x | b ->* x, x ->* a
20.021/20.021	)
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Clean CTRS Processor:
20.021/20.021	
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	)
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	
20.021/20.021	CRule InfChecker Info:
20.021/20.021	a -> b
20.021/20.021	Rule remains
20.021/20.021	Proof:
20.021/20.021	NO_CONDS
20.021/20.021	
20.021/20.021	CRule InfChecker Info:
20.021/20.021	f(x) -> x | b ->* x, x ->* a
20.021/20.021	Rule deleted
20.021/20.021	Proof:
20.021/20.021	YES
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Infeasibility Problem:
20.021/20.021	[(VAR vNonEmpty x vNonEmpty x)
20.021/20.021	(STRATEGY CONTEXTSENSITIVE
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	f(x) -> x | b ->* x, x ->* a
20.021/20.021	)]
20.021/20.021	
20.021/20.021	Infeasibility Conditions:
20.021/20.021	b ->* x, x ->* a
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Obtaining a model using Mace4:
20.021/20.021	
20.021/20.021	 -> Usable Rules:
20.021/20.021	a -> b
20.021/20.021	f(x) -> x | b ->* x, x ->* a
20.021/20.021	
20.021/20.021	 -> Mace4 Output:
20.021/20.021	============================== Mace4 =================================
20.021/20.021	Mace4 (64) version 2009-11A, November 2009.
20.021/20.021	Process 11423 was started by ubuntu on ubuntu,
20.021/20.021	Wed Mar  9 09:16:38 2022
20.021/20.021	The command was "./mace4 -c -f /tmp/mace411411-2.in".
20.021/20.021	============================== end of head ===========================
20.021/20.021	
20.021/20.021	============================== INPUT =================================
20.021/20.021	
20.021/20.021	% Reading from file /tmp/mace411411-2.in
20.021/20.021	
20.021/20.021	assign(max_seconds,20).
20.021/20.021	
20.021/20.021	formulas(assumptions).
20.021/20.021	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.021/20.021	->(a,b) # label(replacement).
20.021/20.021	->*(b,x1) & ->*(x1,a) -> ->(f(x1),x1) # label(replacement).
20.021/20.021	->*(x,x) # label(reflexivity).
20.021/20.021	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.021/20.021	end_of_list.
20.021/20.021	
20.021/20.021	formulas(goals).
20.021/20.021	(exists x3 (->*(b,x3) & ->*(x3,a))) # label(goal).
20.021/20.021	end_of_list.
20.021/20.021	
20.021/20.021	============================== end of input ==========================
20.021/20.021	
20.021/20.021	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.021/20.021	
20.021/20.021	% Formulas that are not ordinary clauses:
20.021/20.021	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
20.021/20.021	2 ->*(b,x1) & ->*(x1,a) -> ->(f(x1),x1) # label(replacement) # label(non_clause).  [assumption].
20.021/20.021	3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.021/20.021	4 (exists x3 (->*(b,x3) & ->*(x3,a))) # label(goal) # label(non_clause) # label(goal).  [goal].
20.021/20.021	
20.021/20.021	============================== end of process non-clausal formulas ===
20.021/20.021	
20.021/20.021	============================== CLAUSES FOR SEARCH ====================
20.021/20.021	
20.021/20.021	formulas(mace4_clauses).
20.021/20.021	-->(x,y) | ->(f(x),f(y)) # label(congruence).
20.021/20.021	->(a,b) # label(replacement).
20.021/20.021	-->*(b,x) | -->*(x,a) | ->(f(x),x) # label(replacement).
20.021/20.021	->*(x,x) # label(reflexivity).
20.021/20.021	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.021/20.021	-->*(b,x) | -->*(x,a) # label(goal).
20.021/20.021	end_of_list.
20.021/20.021	
20.021/20.021	============================== end of clauses for search =============
20.021/20.021	
20.021/20.021	% There are no natural numbers in the input.
20.021/20.021	
20.021/20.021	============================== DOMAIN SIZE 2 =========================
20.021/20.021	
20.021/20.021	============================== MODEL =================================
20.021/20.021	
20.021/20.021	interpretation( 2, [number=1, seconds=0], [
20.021/20.021	
20.021/20.021	        function(a, [ 0 ]),
20.021/20.021	
20.021/20.021	        function(b, [ 1 ]),
20.021/20.021	
20.021/20.021	        function(f(_), [ 0, 1 ]),
20.021/20.021	
20.021/20.021	        relation(->*(_,_), [
20.021/20.021				   1, 1,
20.021/20.021				   0, 1 ]),
20.021/20.021	
20.021/20.021	        relation(->(_,_), [
20.021/20.021				   0, 1,
20.021/20.021				   0, 0 ])
20.021/20.021	]).
20.021/20.021	
20.021/20.021	============================== end of model ==========================
20.021/20.021	
20.021/20.021	============================== STATISTICS ============================
20.021/20.021	
20.021/20.021	For domain size 2.
20.021/20.021	
20.021/20.021	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.021/20.021	Ground clauses: seen=19, kept=15.
20.021/20.021	Selections=4, assignments=4, propagations=8, current_models=1.
20.021/20.021	Rewrite_terms=20, rewrite_bools=25, indexes=7.
20.021/20.021	Rules_from_neg_clauses=2, cross_offs=2.
20.021/20.021	
20.021/20.021	============================== end of statistics =====================
20.021/20.021	
20.021/20.021	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.021/20.021	
20.021/20.021	Exiting with 1 model.
20.021/20.021	
20.021/20.021	Process 11423 exit (max_models) Wed Mar  9 09:16:38 2022
20.021/20.021	The process finished Wed Mar  9 09:16:38 2022
20.021/20.021	
20.021/20.021	
20.021/20.021	Mace4 cooked interpretation:
20.021/20.021	
20.021/20.021	
20.021/20.021	
20.021/20.021	The problem is infeasible.
20.021/20.021	
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Transform No Conds CTRS Processor:
20.021/20.021	
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	)
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Resulting R:
20.021/20.021	(STRATEGY CONTEXTSENSITIVE
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	)
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	CleanTRS Processor:
20.021/20.021	
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	)
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	
20.021/20.021	Modular Confluence Combinations Decomposition Processor:
20.021/20.021	
20.021/20.021	No usable combinations
20.021/20.021	
20.021/20.021	Problem 1:
20.021/20.021	Linearity Processor:
20.021/20.021	Linear?
20.021/20.021	YES
20.021/20.021	Problem 1.1:
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	Confluence Problem:
20.021/20.021	(REPLACEMENT-MAP
20.021/20.021	(a)
20.021/20.021	(f 1)
20.021/20.021	(b)
20.021/20.021	(fSNonEmpty)
20.021/20.021	)
20.021/20.021	(RULES
20.021/20.021	a -> b
20.021/20.021	)
20.021/20.021	Linear:YES
20.021/20.021	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.021/20.021	
20.021/20.021	Huet Levy Processor:
20.021/20.021	-> Rules:
20.021/20.021	 a -> b
20.021/20.021	-> Vars:
20.021/20.021	
20.021/20.021	
20.021/20.021	-> Rlps:
20.021/20.021	 (rule: a -> b, id: 1, possubterms: a->[])
20.021/20.021	
20.021/20.021	-> Unifications:
20.021/20.021	
20.021/20.021	
20.021/20.021	-> Critical pairs info:
20.021/20.021	
20.021/20.021	
20.021/20.021	-> Problem conclusions:
20.021/20.021	 Left linear, Right linear, Linear
20.021/20.021	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.021/20.021	 Huet-Levy confluent, Not Newman confluent
20.021/20.021	 R is a TRS
20.021/20.021	
20.021/20.021	
20.021/20.021	The problem is joinable.
20.021/20.021	21.81user 0.27system 0:20.21elapsed 109%CPU (0avgtext+0avgdata 82920maxresident)k
20.021/20.021	8inputs+0outputs (0major+56706minor)pagefaults 0swaps