25.008/25.008	YES
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	
25.008/25.008	
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	Confluence Problem:
25.008/25.008	(VAR vNonEmpty:S x:S)
25.008/25.008	(STRATEGY CONTEXTSENSITIVE
25.008/25.008	(a)
25.008/25.008	(f 1)
25.008/25.008	(b)
25.008/25.008	(fSNonEmpty)
25.008/25.008	(g 1)
25.008/25.008	)
25.008/25.008	(RULES
25.008/25.008	a -> a
25.008/25.008	f(x:S) -> g(a) | g(x:S) ->* x:S
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	)
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	
25.008/25.008	Inlining of Conditions Processor [STERN17]:
25.008/25.008	
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	Confluence Problem:
25.008/25.008	(VAR vNonEmpty:S x:S)
25.008/25.008	(STRATEGY CONTEXTSENSITIVE
25.008/25.008	(a)
25.008/25.008	(f 1)
25.008/25.008	(b)
25.008/25.008	(fSNonEmpty)
25.008/25.008	(g 1)
25.008/25.008	)
25.008/25.008	(RULES
25.008/25.008	a -> a
25.008/25.008	f(x:S) -> g(a) | g(x:S) ->* x:S
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	)
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	
25.008/25.008	Clean CTRS Processor:
25.008/25.008	
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	Confluence Problem:
25.008/25.008	(VAR x:S)
25.008/25.008	(STRATEGY CONTEXTSENSITIVE
25.008/25.008	(a)
25.008/25.008	(f 1)
25.008/25.008	(b)
25.008/25.008	(fSNonEmpty)
25.008/25.008	(g 1)
25.008/25.008	)
25.008/25.008	(RULES
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	)
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	
25.008/25.008	CRule InfChecker Info:
25.008/25.008	a -> a
25.008/25.008	Rule deleted
25.008/25.008	Proof:
25.008/25.008	SAME_LHS_AND_RHS
25.008/25.008	
25.008/25.008	CRule InfChecker Info:
25.008/25.008	f(x:S) -> g(a) | g(x:S) ->* x:S
25.008/25.008	Rule deleted
25.008/25.008	Proof:
25.008/25.008	YES
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	
25.008/25.008	Infeasibility Problem:
25.008/25.008	[(VAR vNonEmpty:S x:S:S)
25.008/25.008	(STRATEGY CONTEXTSENSITIVE
25.008/25.008	(f 1)
25.008/25.008	(a)
25.008/25.008	(b)
25.008/25.008	(fSNonEmpty)
25.008/25.008	(g 1)
25.008/25.008	)
25.008/25.008	(RULES
25.008/25.008	f(x:S:S) -> g(a) | g(x:S:S) ->* x:S:S
25.008/25.008	f(x:S:S) -> g(b)
25.008/25.008	)]
25.008/25.008	
25.008/25.008	Infeasibility Conditions:
25.008/25.008	g(x:S:S) ->* x:S:S
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	
25.008/25.008	Obtaining a model using Mace4:
25.008/25.008	
25.008/25.008	 -> Usable Rules:
25.008/25.008	f(x:S:S) -> g(a) | g(x:S:S) ->* x:S:S
25.008/25.008	f(x:S:S) -> g(b)
25.008/25.008	
25.008/25.008	 -> Mace4 Output:
25.008/25.008	============================== Mace4 =================================
25.008/25.008	Mace4 (64) version 2009-11A, November 2009.
25.008/25.008	Process 31717 was started by ubuntu on ubuntu,
25.008/25.008	Wed Jul 14 09:39:29 2021
25.008/25.008	The command was "./mace4 -c -f /tmp/mace431705-2.in".
25.008/25.008	============================== end of head ===========================
25.008/25.008	
25.008/25.008	============================== INPUT =================================
25.008/25.008	
25.008/25.008	% Reading from file /tmp/mace431705-2.in
25.008/25.008	
25.008/25.008	assign(max_seconds,20).
25.008/25.008	
25.008/25.008	formulas(assumptions).
25.008/25.008	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
25.008/25.008	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
25.008/25.008	->*(g(x1),x1) -> ->(f(x1),g(a)) # label(replacement).
25.008/25.008	->(f(x1),g(b)) # label(replacement).
25.008/25.008	->*(x,x) # label(reflexivity).
25.008/25.008	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
25.008/25.008	end_of_list.
25.008/25.008	
25.008/25.008	formulas(goals).
25.008/25.008	(exists x1 ->*(g(x1),x1)) # label(goal).
25.008/25.008	end_of_list.
25.008/25.008	
25.008/25.008	============================== end of input ==========================
25.008/25.008	
25.008/25.008	============================== PROCESS NON-CLAUSAL FORMULAS ==========
25.008/25.008	
25.008/25.008	% Formulas that are not ordinary clauses:
25.008/25.008	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
25.008/25.008	2 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
25.008/25.008	3 ->*(g(x1),x1) -> ->(f(x1),g(a)) # label(replacement) # label(non_clause).  [assumption].
25.008/25.008	4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
25.008/25.008	5 (exists x1 ->*(g(x1),x1)) # label(goal) # label(non_clause) # label(goal).  [goal].
25.008/25.008	
25.008/25.008	============================== end of process non-clausal formulas ===
25.008/25.008	
25.008/25.008	============================== CLAUSES FOR SEARCH ====================
25.008/25.008	
25.008/25.008	formulas(mace4_clauses).
25.008/25.008	-->(x,y) | ->(f(x),f(y)) # label(congruence).
25.008/25.008	-->(x,y) | ->(g(x),g(y)) # label(congruence).
25.008/25.008	-->*(g(x),x) | ->(f(x),g(a)) # label(replacement).
25.008/25.008	->(f(x),g(b)) # label(replacement).
25.008/25.008	->*(x,x) # label(reflexivity).
25.008/25.008	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
25.008/25.008	-->*(g(x),x) # label(goal).
25.008/25.008	end_of_list.
25.008/25.008	
25.008/25.008	============================== end of clauses for search =============
25.008/25.008	
25.008/25.008	% There are no natural numbers in the input.
25.008/25.008	
25.008/25.008	============================== DOMAIN SIZE 2 =========================
25.008/25.008	
25.008/25.008	============================== MODEL =================================
25.008/25.008	
25.008/25.008	interpretation( 2, [number=1, seconds=0], [
25.008/25.008	
25.008/25.008	        function(a, [ 0 ]),
25.008/25.008	
25.008/25.008	        function(b, [ 0 ]),
25.008/25.008	
25.008/25.008	        function(f(_), [ 1, 1 ]),
25.008/25.008	
25.008/25.008	        function(g(_), [ 1, 0 ]),
25.008/25.008	
25.008/25.008	        relation(->*(_,_), [
25.008/25.008				   1, 0,
25.008/25.008				   0, 1 ]),
25.008/25.008	
25.008/25.008	        relation(->(_,_), [
25.008/25.008				   1, 0,
25.008/25.008				   0, 1 ])
25.008/25.008	]).
25.008/25.008	
25.008/25.008	============================== end of model ==========================
25.008/25.008	
25.008/25.008	============================== STATISTICS ============================
25.008/25.008	
25.008/25.008	For domain size 2.
25.008/25.008	
25.008/25.008	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
25.008/25.008	Ground clauses: seen=24, kept=20.
25.008/25.008	Selections=2, assignments=2, propagations=12, current_models=1.
25.008/25.008	Rewrite_terms=32, rewrite_bools=26, indexes=6.
25.008/25.008	Rules_from_neg_clauses=4, cross_offs=4.
25.008/25.008	
25.008/25.008	============================== end of statistics =====================
25.008/25.008	
25.008/25.008	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
25.008/25.008	
25.008/25.008	Exiting with 1 model.
25.008/25.008	
25.008/25.008	Process 31717 exit (max_models) Wed Jul 14 09:39:29 2021
25.008/25.008	The process finished Wed Jul 14 09:39:29 2021
25.008/25.008	
25.008/25.008	
25.008/25.008	Mace4 cooked interpretation:
25.008/25.008	
25.008/25.008	
25.008/25.008	
25.008/25.008	The problem is infeasible.
25.008/25.008	
25.008/25.008	
25.008/25.008	CRule InfChecker Info:
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	Rule remains
25.008/25.008	Proof:
25.008/25.008	NO_CONDS
25.008/25.008	
25.008/25.008	Problem 1:
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	Confluence Problem:
25.008/25.008	(VAR x:S)
25.008/25.008	(STRATEGY CONTEXTSENSITIVE
25.008/25.008	(a)
25.008/25.008	(f 1)
25.008/25.008	(b)
25.008/25.008	(fSNonEmpty)
25.008/25.008	(g 1)
25.008/25.008	)
25.008/25.008	(RULES
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	)
25.008/25.008	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.008/25.008	
25.008/25.008	Critical Pairs Processor:
25.008/25.008	-> Rules:
25.008/25.008	f(x:S) -> g(b)
25.008/25.008	-> Vars:
25.008/25.008	"x"
25.008/25.008	-> FVars:
25.008/25.008	"x2"
25.008/25.008	-> PVars:
25.008/25.008	"x": ["x2"]
25.008/25.008	
25.008/25.008	-> Rlps:
25.008/25.008	crule: f(x2:S) -> g(b), id: 1, possubterms: f(x2:S)-> []
25.008/25.008	
25.008/25.008	-> Unifications:
25.008/25.008	
25.008/25.008	
25.008/25.008	-> Critical pairs info:
25.008/25.008	
25.008/25.008	
25.008/25.008	-> Problem conclusions:
25.008/25.008	 Left linear, Right linear, Linear
25.008/25.008	 Weakly orthogonal, Almost orthogonal, Orthogonal
25.008/25.008	 CTRS Type: 1
25.008/25.008	 Deterministic, Strongly deterministic
25.008/25.008	 Oriented CTRS, Properly oriented CTRS, Join CTRS
25.008/25.008	 Maybe right-stable CTRS, Overlay CTRS
25.008/25.008	 Normal CTRS, Almost normal CTRS
25.008/25.008	 Maybe terminating CTRS, Joinable CCPs
25.008/25.008	 Level confluent
25.008/25.008	 Confluent
25.008/25.008	
25.008/25.008	The problem is joinable.
25.008/25.008	24.50user 0.41system 0:25.08elapsed 99%CPU (0avgtext+0avgdata 211224maxresident)k
25.008/25.008	0inputs+0outputs (0major+119173minor)pagefaults 0swaps