20.018/20.018	YES
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR vNonEmpty:S x:S)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(a)
20.018/20.018	(f 1)
20.018/20.018	(b)
20.018/20.018	(fSNonEmpty)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	a -> b
20.018/20.018	f(x:S) -> x:S | x:S ->* a, b ->* x:S
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Inlining of Conditions Processor [STERN17]:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR vNonEmpty:S x:S)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(a)
20.018/20.018	(f 1)
20.018/20.018	(b)
20.018/20.018	(fSNonEmpty)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	a -> b
20.018/20.018	f(x:S) -> x:S | b ->* x:S, x:S ->* a
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Clean CTRS Processor:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(a)
20.018/20.018	(f 1)
20.018/20.018	(b)
20.018/20.018	(fSNonEmpty)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	a -> b
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	a -> b
20.018/20.018	Rule remains
20.018/20.018	Proof:
20.018/20.018	NO_CONDS
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	f(x:S) -> x:S | b ->* x:S, x:S ->* a
20.018/20.018	Rule deleted
20.018/20.018	Proof:
20.018/20.018	YES
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Infeasibility Problem:
20.018/20.018	[(VAR vNonEmpty:S vNonEmpty:S:S x:S:S)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(a)
20.018/20.018	(f 1)
20.018/20.018	(b)
20.018/20.018	(fSNonEmpty)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	a -> b
20.018/20.018	f(x:S:S) -> x:S:S | b ->* x:S:S, x:S:S ->* a
20.018/20.018	)]
20.018/20.018	
20.018/20.018	Infeasibility Conditions:
20.018/20.018	b ->* x:S:S, x:S:S ->* a
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Obtaining a model using Mace4:
20.018/20.018	
20.018/20.018	 -> Usable Rules:
20.018/20.018	a -> b
20.018/20.018	f(x:S:S) -> x:S:S | b ->* x:S:S, x:S:S ->* a
20.018/20.018	
20.018/20.018	 -> Mace4 Output:
20.018/20.018	============================== Mace4 =================================
20.018/20.018	Mace4 (64) version 2009-11A, November 2009.
20.018/20.018	Process 39702 was started by ubuntu on ubuntu,
20.018/20.018	Wed Jul 14 10:12:57 2021
20.018/20.018	The command was "./mace4 -c -f /tmp/mace439689-2.in".
20.018/20.018	============================== end of head ===========================
20.018/20.018	
20.018/20.018	============================== INPUT =================================
20.018/20.018	
20.018/20.018	% Reading from file /tmp/mace439689-2.in
20.018/20.018	
20.018/20.018	assign(max_seconds,20).
20.018/20.018	
20.018/20.018	formulas(assumptions).
20.018/20.018	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.018/20.018	->(a,b) # label(replacement).
20.018/20.018	->*(b,x2) & ->*(x2,a) -> ->(f(x2),x2) # label(replacement).
20.018/20.018	->*(x,x) # label(reflexivity).
20.018/20.018	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	formulas(goals).
20.018/20.018	(exists x2 (->*(b,x2) & ->*(x2,a))) # label(goal).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	============================== end of input ==========================
20.018/20.018	
20.018/20.018	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.018/20.018	
20.018/20.018	% Formulas that are not ordinary clauses:
20.018/20.018	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	2 ->*(b,x2) & ->*(x2,a) -> ->(f(x2),x2) # label(replacement) # label(non_clause).  [assumption].
20.018/20.018	3 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.018/20.018	4 (exists x2 (->*(b,x2) & ->*(x2,a))) # label(goal) # label(non_clause) # label(goal).  [goal].
20.018/20.018	
20.018/20.018	============================== end of process non-clausal formulas ===
20.018/20.018	
20.018/20.018	============================== CLAUSES FOR SEARCH ====================
20.018/20.018	
20.018/20.018	formulas(mace4_clauses).
20.018/20.018	-->(x,y) | ->(f(x),f(y)) # label(congruence).
20.018/20.018	->(a,b) # label(replacement).
20.018/20.018	-->*(b,x) | -->*(x,a) | ->(f(x),x) # label(replacement).
20.018/20.018	->*(x,x) # label(reflexivity).
20.018/20.018	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.018/20.018	-->*(b,x) | -->*(x,a) # label(goal).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	============================== end of clauses for search =============
20.018/20.018	
20.018/20.018	% There are no natural numbers in the input.
20.018/20.018	
20.018/20.018	============================== DOMAIN SIZE 2 =========================
20.018/20.018	
20.018/20.018	============================== MODEL =================================
20.018/20.018	
20.018/20.018	interpretation( 2, [number=1, seconds=0], [
20.018/20.018	
20.018/20.018	        function(a, [ 0 ]),
20.018/20.018	
20.018/20.018	        function(b, [ 1 ]),
20.018/20.018	
20.018/20.018	        function(f(_), [ 0, 1 ]),
20.018/20.018	
20.018/20.018	        relation(->*(_,_), [
20.018/20.018				   1, 1,
20.018/20.018				   0, 1 ]),
20.018/20.018	
20.018/20.018	        relation(->(_,_), [
20.018/20.018				   0, 1,
20.018/20.018				   0, 0 ])
20.018/20.018	]).
20.018/20.018	
20.018/20.018	============================== end of model ==========================
20.018/20.018	
20.018/20.018	============================== STATISTICS ============================
20.018/20.018	
20.018/20.018	For domain size 2.
20.018/20.018	
20.018/20.018	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.018/20.018	Ground clauses: seen=19, kept=15.
20.018/20.018	Selections=4, assignments=4, propagations=8, current_models=1.
20.018/20.018	Rewrite_terms=20, rewrite_bools=25, indexes=7.
20.018/20.018	Rules_from_neg_clauses=2, cross_offs=2.
20.018/20.018	
20.018/20.018	============================== end of statistics =====================
20.018/20.018	
20.018/20.018	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.018/20.018	
20.018/20.018	Exiting with 1 model.
20.018/20.018	
20.018/20.018	Process 39702 exit (max_models) Wed Jul 14 10:12:57 2021
20.018/20.018	The process finished Wed Jul 14 10:12:57 2021
20.018/20.018	
20.018/20.018	
20.018/20.018	Mace4 cooked interpretation:
20.018/20.018	
20.018/20.018	
20.018/20.018	
20.018/20.018	The problem is infeasible.
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(a)
20.018/20.018	(f 1)
20.018/20.018	(b)
20.018/20.018	(fSNonEmpty)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	a -> b
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	Critical Pairs Processor:
20.018/20.018	-> Rules:
20.018/20.018	a -> b
20.018/20.018	-> Vars:
20.018/20.018	
20.018/20.018	-> FVars:
20.018/20.018	
20.018/20.018	-> PVars:
20.018/20.018	
20.018/20.018	
20.018/20.018	-> Rlps:
20.018/20.018	crule: a -> b, id: 1, possubterms: a-> []
20.018/20.018	
20.018/20.018	-> Unifications:
20.018/20.018	
20.018/20.018	
20.018/20.018	-> Critical pairs info:
20.018/20.018	
20.018/20.018	
20.018/20.018	-> Problem conclusions:
20.018/20.018	 Left linear, Right linear, Linear
20.018/20.018	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.018/20.018	 CTRS Type: 1
20.018/20.018	 Deterministic, Strongly deterministic
20.018/20.018	 Oriented CTRS, Properly oriented CTRS, Join CTRS
20.018/20.018	 Maybe right-stable CTRS, Overlay CTRS
20.018/20.018	 Normal CTRS, Almost normal CTRS
20.018/20.018	 Maybe terminating CTRS, Joinable CCPs
20.018/20.018	 Level confluent
20.018/20.018	 Confluent
20.018/20.018	
20.018/20.018	The problem is joinable.
20.018/20.018	22.60user 0.25system 0:20.18elapsed 113%CPU (0avgtext+0avgdata 80768maxresident)k
20.018/20.018	0inputs+0outputs (0major+47812minor)pagefaults 0swaps