20.009/20.009	YES
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR vNonEmpty x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(a) | g(x) ->* x
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Inlining of Conditions Processor [STERN17]:
20.009/20.009	
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR vNonEmpty x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(a) | g(x) ->* x
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Clean CTRS Processor:
20.009/20.009	
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	
20.009/20.009	CRule InfChecker Info:
20.009/20.009	f(x) -> g(a) | g(x) ->* x
20.009/20.009	Rule deleted
20.009/20.009	Proof:
20.009/20.009	YES
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Infeasibility Problem:
20.009/20.009	[(VAR vNonEmpty x vNonEmpty x)
20.009/20.009	(STRATEGY CONTEXTSENSITIVE
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(a) | g(x) ->* x
20.009/20.009	f(x) -> g(b)
20.009/20.009	)]
20.009/20.009	
20.009/20.009	Infeasibility Conditions:
20.009/20.009	g(x) ->* x
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Obtaining a model using Mace4:
20.009/20.009	
20.009/20.009	 -> Usable Rules:
20.009/20.009	f(x) -> g(a) | g(x) ->* x
20.009/20.009	f(x) -> g(b)
20.009/20.009	
20.009/20.009	 -> Mace4 Output:
20.009/20.009	============================== Mace4 =================================
20.009/20.009	Mace4 (64) version 2009-11A, November 2009.
20.009/20.009	Process 82129 was started by ubuntu on ubuntu,
20.009/20.009	Wed Mar  9 10:30:39 2022
20.009/20.009	The command was "./mace4 -c -f /tmp/mace482116-2.in".
20.009/20.009	============================== end of head ===========================
20.009/20.009	
20.009/20.009	============================== INPUT =================================
20.009/20.009	
20.009/20.009	% Reading from file /tmp/mace482116-2.in
20.009/20.009	
20.009/20.009	assign(max_seconds,20).
20.009/20.009	
20.009/20.009	formulas(assumptions).
20.009/20.009	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.009/20.009	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
20.009/20.009	->*(g(x1),x1) -> ->(f(x1),g(a)) # label(replacement).
20.009/20.009	->(f(x1),g(b)) # label(replacement).
20.009/20.009	->*(x,x) # label(reflexivity).
20.009/20.009	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.009/20.009	end_of_list.
20.009/20.009	
20.009/20.009	formulas(goals).
20.009/20.009	(exists x3 ->*(g(x3),x3)) # label(goal).
20.009/20.009	end_of_list.
20.009/20.009	
20.009/20.009	============================== end of input ==========================
20.009/20.009	
20.009/20.009	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.009/20.009	
20.009/20.009	% Formulas that are not ordinary clauses:
20.009/20.009	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
20.009/20.009	2 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
20.009/20.009	3 ->*(g(x1),x1) -> ->(f(x1),g(a)) # label(replacement) # label(non_clause).  [assumption].
20.009/20.009	4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.009/20.009	5 (exists x3 ->*(g(x3),x3)) # label(goal) # label(non_clause) # label(goal).  [goal].
20.009/20.009	
20.009/20.009	============================== end of process non-clausal formulas ===
20.009/20.009	
20.009/20.009	============================== CLAUSES FOR SEARCH ====================
20.009/20.009	
20.009/20.009	formulas(mace4_clauses).
20.009/20.009	-->(x,y) | ->(f(x),f(y)) # label(congruence).
20.009/20.009	-->(x,y) | ->(g(x),g(y)) # label(congruence).
20.009/20.009	-->*(g(x),x) | ->(f(x),g(a)) # label(replacement).
20.009/20.009	->(f(x),g(b)) # label(replacement).
20.009/20.009	->*(x,x) # label(reflexivity).
20.009/20.009	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.009/20.009	-->*(g(x),x) # label(goal).
20.009/20.009	end_of_list.
20.009/20.009	
20.009/20.009	============================== end of clauses for search =============
20.009/20.009	
20.009/20.009	% There are no natural numbers in the input.
20.009/20.009	
20.009/20.009	============================== DOMAIN SIZE 2 =========================
20.009/20.009	
20.009/20.009	============================== MODEL =================================
20.009/20.009	
20.009/20.009	interpretation( 2, [number=1, seconds=0], [
20.009/20.009	
20.009/20.009	        function(a, [ 0 ]),
20.009/20.009	
20.009/20.009	        function(b, [ 0 ]),
20.009/20.009	
20.009/20.009	        function(f(_), [ 1, 1 ]),
20.009/20.009	
20.009/20.009	        function(g(_), [ 1, 0 ]),
20.009/20.009	
20.009/20.009	        relation(->*(_,_), [
20.009/20.009				   1, 0,
20.009/20.009				   0, 1 ]),
20.009/20.009	
20.009/20.009	        relation(->(_,_), [
20.009/20.009				   1, 0,
20.009/20.009				   0, 1 ])
20.009/20.009	]).
20.009/20.009	
20.009/20.009	============================== end of model ==========================
20.009/20.009	
20.009/20.009	============================== STATISTICS ============================
20.009/20.009	
20.009/20.009	For domain size 2.
20.009/20.009	
20.009/20.009	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.009/20.009	Ground clauses: seen=24, kept=20.
20.009/20.009	Selections=2, assignments=2, propagations=12, current_models=1.
20.009/20.009	Rewrite_terms=32, rewrite_bools=26, indexes=6.
20.009/20.009	Rules_from_neg_clauses=4, cross_offs=4.
20.009/20.009	
20.009/20.009	============================== end of statistics =====================
20.009/20.009	
20.009/20.009	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.009/20.009	
20.009/20.009	Exiting with 1 model.
20.009/20.009	
20.009/20.009	Process 82129 exit (max_models) Wed Mar  9 10:30:39 2022
20.009/20.009	The process finished Wed Mar  9 10:30:39 2022
20.009/20.009	
20.009/20.009	
20.009/20.009	Mace4 cooked interpretation:
20.009/20.009	
20.009/20.009	
20.009/20.009	
20.009/20.009	The problem is infeasible.
20.009/20.009	
20.009/20.009	
20.009/20.009	CRule InfChecker Info:
20.009/20.009	f(x) -> g(b)
20.009/20.009	Rule remains
20.009/20.009	Proof:
20.009/20.009	NO_CONDS
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Transform No Conds CTRS Processor:
20.009/20.009	
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Resulting R:
20.009/20.009	(VAR x)
20.009/20.009	(STRATEGY CONTEXTSENSITIVE
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	CleanTRS Processor:
20.009/20.009	
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	
20.009/20.009	Modular Confluence Combinations Decomposition Processor:
20.009/20.009	
20.009/20.009	No usable combinations
20.009/20.009	
20.009/20.009	Problem 1:
20.009/20.009	Linearity Processor:
20.009/20.009	Linear?
20.009/20.009	YES
20.009/20.009	Problem 1.1:
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	Confluence Problem:
20.009/20.009	(VAR x)
20.009/20.009	(REPLACEMENT-MAP
20.009/20.009	(f 1)
20.009/20.009	(a)
20.009/20.009	(b)
20.009/20.009	(fSNonEmpty)
20.009/20.009	(g 1)
20.009/20.009	)
20.009/20.009	(RULES
20.009/20.009	f(x) -> g(b)
20.009/20.009	)
20.009/20.009	Linear:YES
20.009/20.009	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.009/20.009	
20.009/20.009	Huet Levy Processor:
20.009/20.009	-> Rules:
20.009/20.009	 f(x) -> g(b)
20.009/20.009	-> Vars:
20.009/20.009	 x
20.009/20.009	
20.009/20.009	-> Rlps:
20.009/20.009	 (rule: f(x) -> g(b), id: 1, possubterms: f(x)->[])
20.009/20.009	
20.009/20.009	-> Unifications:
20.009/20.009	
20.009/20.009	
20.009/20.009	-> Critical pairs info:
20.009/20.009	
20.009/20.009	
20.009/20.009	-> Problem conclusions:
20.009/20.009	 Left linear, Right linear, Linear
20.009/20.009	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.009/20.009	 Huet-Levy confluent, Not Newman confluent
20.009/20.009	 R is a TRS
20.009/20.009	
20.009/20.009	
20.009/20.009	The problem is joinable.
20.009/20.009	21.88user 0.29system 0:20.09elapsed 110%CPU (0avgtext+0avgdata 55152maxresident)k
20.009/20.009	8inputs+0outputs (0major+29148minor)pagefaults 0swaps