20.029/20.029	YES
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR vNonEmpty x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	c -> c
20.029/20.029	g(x) -> a | h(x) ->* b
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Inlining of Conditions Processor [STERN17]:
20.029/20.029	
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR vNonEmpty x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	c -> c
20.029/20.029	g(x) -> a | h(x) ->* b
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Clean CTRS Processor:
20.029/20.029	
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	CRule InfChecker Info:
20.029/20.029	c -> c
20.029/20.029	Rule deleted
20.029/20.029	Proof:
20.029/20.029	SAME_LHS_AND_RHS
20.029/20.029	
20.029/20.029	CRule InfChecker Info:
20.029/20.029	g(x) -> a | h(x) ->* b
20.029/20.029	Rule deleted
20.029/20.029	Proof:
20.029/20.029	YES
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Infeasibility Problem:
20.029/20.029	[(VAR vNonEmpty x vNonEmpty x)
20.029/20.029	(STRATEGY CONTEXTSENSITIVE
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> a | h(x) ->* b
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)]
20.029/20.029	
20.029/20.029	Infeasibility Conditions:
20.029/20.029	h(x) ->* b
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Obtaining a model using Mace4:
20.029/20.029	
20.029/20.029	 -> Usable Rules:
20.029/20.029	g(x) -> a | h(x) ->* b
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	
20.029/20.029	 -> Mace4 Output:
20.029/20.029	============================== Mace4 =================================
20.029/20.029	Mace4 (64) version 2009-11A, November 2009.
20.029/20.029	Process 75439 was started by ubuntu on ubuntu,
20.029/20.029	Wed Mar  9 10:10:52 2022
20.029/20.029	The command was "./mace4 -c -f /tmp/mace475426-2.in".
20.029/20.029	============================== end of head ===========================
20.029/20.029	
20.029/20.029	============================== INPUT =================================
20.029/20.029	
20.029/20.029	% Reading from file /tmp/mace475426-2.in
20.029/20.029	
20.029/20.029	assign(max_seconds,20).
20.029/20.029	
20.029/20.029	formulas(assumptions).
20.029/20.029	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
20.029/20.029	->(x1,y) -> ->(h(x1),h(y)) # label(congruence).
20.029/20.029	->*(h(x1),b) -> ->(g(x1),a) # label(replacement).
20.029/20.029	->(g(x1),x1) # label(replacement).
20.029/20.029	->(h(x1),a) # label(replacement).
20.029/20.029	->*(x,x) # label(reflexivity).
20.029/20.029	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.029/20.029	end_of_list.
20.029/20.029	
20.029/20.029	formulas(goals).
20.029/20.029	(exists x3 ->*(h(x3),b)) # label(goal).
20.029/20.029	end_of_list.
20.029/20.029	
20.029/20.029	============================== end of input ==========================
20.029/20.029	
20.029/20.029	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.029/20.029	
20.029/20.029	% Formulas that are not ordinary clauses:
20.029/20.029	1 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
20.029/20.029	2 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause).  [assumption].
20.029/20.029	3 ->*(h(x1),b) -> ->(g(x1),a) # label(replacement) # label(non_clause).  [assumption].
20.029/20.029	4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.029/20.029	5 (exists x3 ->*(h(x3),b)) # label(goal) # label(non_clause) # label(goal).  [goal].
20.029/20.029	
20.029/20.029	============================== end of process non-clausal formulas ===
20.029/20.029	
20.029/20.029	============================== CLAUSES FOR SEARCH ====================
20.029/20.029	
20.029/20.029	formulas(mace4_clauses).
20.029/20.029	-->(x,y) | ->(g(x),g(y)) # label(congruence).
20.029/20.029	-->(x,y) | ->(h(x),h(y)) # label(congruence).
20.029/20.029	-->*(h(x),b) | ->(g(x),a) # label(replacement).
20.029/20.029	->(g(x),x) # label(replacement).
20.029/20.029	->(h(x),a) # label(replacement).
20.029/20.029	->*(x,x) # label(reflexivity).
20.029/20.029	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.029/20.029	-->*(h(x),b) # label(goal).
20.029/20.029	end_of_list.
20.029/20.029	
20.029/20.029	============================== end of clauses for search =============
20.029/20.029	
20.029/20.029	% There are no natural numbers in the input.
20.029/20.029	
20.029/20.029	============================== DOMAIN SIZE 2 =========================
20.029/20.029	
20.029/20.029	============================== MODEL =================================
20.029/20.029	
20.029/20.029	interpretation( 2, [number=1, seconds=0], [
20.029/20.029	
20.029/20.029	        function(a, [ 0 ]),
20.029/20.029	
20.029/20.029	        function(b, [ 1 ]),
20.029/20.029	
20.029/20.029	        function(g(_), [ 0, 1 ]),
20.029/20.029	
20.029/20.029	        function(h(_), [ 0, 0 ]),
20.029/20.029	
20.029/20.029	        relation(->*(_,_), [
20.029/20.029				   1, 0,
20.029/20.029				   0, 1 ]),
20.029/20.029	
20.029/20.029	        relation(->(_,_), [
20.029/20.029				   1, 0,
20.029/20.029				   0, 1 ])
20.029/20.029	]).
20.029/20.029	
20.029/20.029	============================== end of model ==========================
20.029/20.029	
20.029/20.029	============================== STATISTICS ============================
20.029/20.029	
20.029/20.029	For domain size 2.
20.029/20.029	
20.029/20.029	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.029/20.029	Ground clauses: seen=26, kept=22.
20.029/20.029	Selections=4, assignments=5, propagations=13, current_models=1.
20.029/20.029	Rewrite_terms=45, rewrite_bools=34, indexes=8.
20.029/20.029	Rules_from_neg_clauses=4, cross_offs=4.
20.029/20.029	
20.029/20.029	============================== end of statistics =====================
20.029/20.029	
20.029/20.029	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.029/20.029	
20.029/20.029	Exiting with 1 model.
20.029/20.029	
20.029/20.029	Process 75439 exit (max_models) Wed Mar  9 10:10:52 2022
20.029/20.029	The process finished Wed Mar  9 10:10:52 2022
20.029/20.029	
20.029/20.029	
20.029/20.029	Mace4 cooked interpretation:
20.029/20.029	
20.029/20.029	
20.029/20.029	
20.029/20.029	The problem is infeasible.
20.029/20.029	
20.029/20.029	
20.029/20.029	CRule InfChecker Info:
20.029/20.029	g(x) -> x
20.029/20.029	Rule remains
20.029/20.029	Proof:
20.029/20.029	NO_CONDS
20.029/20.029	
20.029/20.029	CRule InfChecker Info:
20.029/20.029	h(x) -> a
20.029/20.029	Rule remains
20.029/20.029	Proof:
20.029/20.029	NO_CONDS
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Transform No Conds CTRS Processor:
20.029/20.029	
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Resulting R:
20.029/20.029	(VAR x)
20.029/20.029	(STRATEGY CONTEXTSENSITIVE
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	CleanTRS Processor:
20.029/20.029	
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(c)
20.029/20.029	(g 1)
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	(b)
20.029/20.029	(fSNonEmpty)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	
20.029/20.029	Problem 1:
20.029/20.029	
20.029/20.029	Modular Confluence Combinations Decomposition Processor:
20.029/20.029	
20.029/20.029	TRS combination:
20.029/20.029	{g(x) -> x}
20.029/20.029	{h(x) -> a}
20.029/20.029	Disjoint
20.029/20.029	Constructor-sharing
20.029/20.029	Left linear
20.029/20.029	Not layer-preserving
20.029/20.029	TRS1
20.029/20.029	Just (VAR x)
20.029/20.029	(STRATEGY CONTEXTSENSITIVE
20.029/20.029	(g 1)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	)
20.029/20.029	
20.029/20.029	TRS2
20.029/20.029	Just (VAR x)
20.029/20.029	(STRATEGY CONTEXTSENSITIVE
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	
20.029/20.029	
20.029/20.029	The problem is decomposed in 2 subproblems.
20.029/20.029	
20.029/20.029	Problem 1.1:
20.029/20.029	Linearity Processor:
20.029/20.029	Linear?
20.029/20.029	YES
20.029/20.029	Problem 1.1.1:
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(g 1)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	g(x) -> x
20.029/20.029	)
20.029/20.029	Linear:YES
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	Huet Levy Processor:
20.029/20.029	-> Rules:
20.029/20.029	 g(x) -> x
20.029/20.029	-> Vars:
20.029/20.029	 x
20.029/20.029	
20.029/20.029	-> Rlps:
20.029/20.029	 (rule: g(x) -> x, id: 1, possubterms: g(x)->[])
20.029/20.029	
20.029/20.029	-> Unifications:
20.029/20.029	
20.029/20.029	
20.029/20.029	-> Critical pairs info:
20.029/20.029	
20.029/20.029	
20.029/20.029	-> Problem conclusions:
20.029/20.029	 Left linear, Right linear, Linear
20.029/20.029	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.029/20.029	 Huet-Levy confluent, Not Newman confluent
20.029/20.029	 R is a TRS
20.029/20.029	
20.029/20.029	
20.029/20.029	The problem is joinable.
20.029/20.029	
20.029/20.029	Problem 1.2:
20.029/20.029	Linearity Processor:
20.029/20.029	Linear?
20.029/20.029	YES
20.029/20.029	Problem 1.2.1:
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	Confluence Problem:
20.029/20.029	(VAR x)
20.029/20.029	(REPLACEMENT-MAP
20.029/20.029	(h 1)
20.029/20.029	(a)
20.029/20.029	)
20.029/20.029	(RULES
20.029/20.029	h(x) -> a
20.029/20.029	)
20.029/20.029	Linear:YES
20.029/20.029	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.029/20.029	
20.029/20.029	Huet Levy Processor:
20.029/20.029	-> Rules:
20.029/20.029	 h(x) -> a
20.029/20.029	-> Vars:
20.029/20.029	 x
20.029/20.029	
20.029/20.029	-> Rlps:
20.029/20.029	 (rule: h(x) -> a, id: 1, possubterms: h(x)->[])
20.029/20.029	
20.029/20.029	-> Unifications:
20.029/20.029	
20.029/20.029	
20.029/20.029	-> Critical pairs info:
20.029/20.029	
20.029/20.029	
20.029/20.029	-> Problem conclusions:
20.029/20.029	 Left linear, Right linear, Linear
20.029/20.029	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.029/20.029	 Huet-Levy confluent, Not Newman confluent
20.029/20.029	 R is a TRS
20.029/20.029	
20.029/20.029	
20.029/20.029	The problem is joinable.
20.029/20.029	23.47user 0.46system 0:20.29elapsed 117%CPU (0avgtext+0avgdata 135504maxresident)k
20.029/20.029	8inputs+0outputs (0major+60364minor)pagefaults 0swaps