25.018/25.018	NO
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(VAR vNonEmpty:S x:S y:S)
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	f(x:S) -> c(x:S,y:S) | g(x:S) ->* y:S, y:S ->* h(x:S)
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Inlining of Conditions Processor [STERN17]:
25.018/25.018	
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(VAR vNonEmpty:S x:S y:S)
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	f(x:S) -> c(x:S,g(x:S)) | g(x:S) ->* h(x:S)
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Clean CTRS Processor:
25.018/25.018	
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	
25.018/25.018	CRule InfChecker Info:
25.018/25.018	a -> b
25.018/25.018	Rule remains
25.018/25.018	Proof:
25.018/25.018	NO_CONDS
25.018/25.018	
25.018/25.018	CRule InfChecker Info:
25.018/25.018	f(x:S) -> c(x:S,g(x:S)) | g(x:S) ->* h(x:S)
25.018/25.018	Rule deleted
25.018/25.018	Proof:
25.018/25.018	YES
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Infeasibility Problem:
25.018/25.018	[(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S)
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	f(x:S:S) -> c(x:S:S,g(x:S:S)) | g(x:S:S) ->* h(x:S:S)
25.018/25.018	g(a) -> h(b)
25.018/25.018	)]
25.018/25.018	
25.018/25.018	Infeasibility Conditions:
25.018/25.018	g(x:S:S) ->* h(x:S:S)
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Obtaining a model using Mace4:
25.018/25.018	
25.018/25.018	 -> Usable Rules:
25.018/25.018	a -> b
25.018/25.018	f(x:S:S) -> c(x:S:S,g(x:S:S)) | g(x:S:S) ->* h(x:S:S)
25.018/25.018	g(a) -> h(b)
25.018/25.018	
25.018/25.018	 -> Mace4 Output:
25.018/25.018	============================== Mace4 =================================
25.018/25.018	Mace4 (64) version 2009-11A, November 2009.
25.018/25.018	Process 103291 was started by ubuntu on ubuntu,
25.018/25.018	Fri Jul 16 14:44:23 2021
25.018/25.018	The command was "./mace4 -c -f /tmp/mace4103278-2.in".
25.018/25.018	============================== end of head ===========================
25.018/25.018	
25.018/25.018	============================== INPUT =================================
25.018/25.018	
25.018/25.018	% Reading from file /tmp/mace4103278-2.in
25.018/25.018	
25.018/25.018	assign(max_seconds,10).
25.018/25.018	
25.018/25.018	formulas(assumptions).
25.018/25.018	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
25.018/25.018	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
25.018/25.018	->(x1,y) -> ->(c(x1,x2),c(y,x2)) # label(congruence).
25.018/25.018	->(x2,y) -> ->(c(x1,x2),c(x1,y)) # label(congruence).
25.018/25.018	->(x1,y) -> ->(h(x1),h(y)) # label(congruence).
25.018/25.018	->(a,b) # label(replacement).
25.018/25.018	->*(g(x2),h(x2)) -> ->(f(x2),c(x2,g(x2))) # label(replacement).
25.018/25.018	->(g(a),h(b)) # label(replacement).
25.018/25.018	->*(x,x) # label(reflexivity).
25.018/25.018	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
25.018/25.018	end_of_list.
25.018/25.018	
25.018/25.018	formulas(goals).
25.018/25.018	(exists x2 ->*(g(x2),h(x2))) # label(goal).
25.018/25.018	end_of_list.
25.018/25.018	
25.018/25.018	============================== end of input ==========================
25.018/25.018	
25.018/25.018	============================== PROCESS NON-CLAUSAL FORMULAS ==========
25.018/25.018	
25.018/25.018	% Formulas that are not ordinary clauses:
25.018/25.018	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
25.018/25.018	2 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
25.018/25.018	3 ->(x1,y) -> ->(c(x1,x2),c(y,x2)) # label(congruence) # label(non_clause).  [assumption].
25.018/25.018	4 ->(x2,y) -> ->(c(x1,x2),c(x1,y)) # label(congruence) # label(non_clause).  [assumption].
25.018/25.018	5 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause).  [assumption].
25.018/25.018	6 ->*(g(x2),h(x2)) -> ->(f(x2),c(x2,g(x2))) # label(replacement) # label(non_clause).  [assumption].
25.018/25.018	7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
25.018/25.018	8 (exists x2 ->*(g(x2),h(x2))) # label(goal) # label(non_clause) # label(goal).  [goal].
25.018/25.018	
25.018/25.018	============================== end of process non-clausal formulas ===
25.018/25.018	
25.018/25.018	============================== CLAUSES FOR SEARCH ====================
25.018/25.018	
25.018/25.018	formulas(mace4_clauses).
25.018/25.018	-->(x,y) | ->(f(x),f(y)) # label(congruence).
25.018/25.018	-->(x,y) | ->(g(x),g(y)) # label(congruence).
25.018/25.018	-->(x,y) | ->(c(x,z),c(y,z)) # label(congruence).
25.018/25.018	-->(x,y) | ->(c(z,x),c(z,y)) # label(congruence).
25.018/25.018	-->(x,y) | ->(h(x),h(y)) # label(congruence).
25.018/25.018	->(a,b) # label(replacement).
25.018/25.018	-->*(g(x),h(x)) | ->(f(x),c(x,g(x))) # label(replacement).
25.018/25.018	->(g(a),h(b)) # label(replacement).
25.018/25.018	->*(x,x) # label(reflexivity).
25.018/25.018	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
25.018/25.018	-->*(g(x),h(x)) # label(goal).
25.018/25.018	end_of_list.
25.018/25.018	
25.018/25.018	============================== end of clauses for search =============
25.018/25.018	
25.018/25.018	% There are no natural numbers in the input.
25.018/25.018	
25.018/25.018	============================== DOMAIN SIZE 2 =========================
25.018/25.018	
25.018/25.018	============================== STATISTICS ============================
25.018/25.018	
25.018/25.018	For domain size 2.
25.018/25.018	
25.018/25.018	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
25.018/25.018	Ground clauses: seen=44, kept=40.
25.018/25.018	Selections=8, assignments=15, propagations=35, current_models=0.
25.018/25.018	Rewrite_terms=149, rewrite_bools=113, indexes=38.
25.018/25.018	Rules_from_neg_clauses=13, cross_offs=13.
25.018/25.018	
25.018/25.018	============================== end of statistics =====================
25.018/25.018	
25.018/25.018	============================== DOMAIN SIZE 3 =========================
25.018/25.018	
25.018/25.018	============================== MODEL =================================
25.018/25.018	
25.018/25.018	interpretation( 3, [number=1, seconds=0], [
25.018/25.018	
25.018/25.018	        function(a, [ 0 ]),
25.018/25.018	
25.018/25.018	        function(b, [ 1 ]),
25.018/25.018	
25.018/25.018	        function(f(_), [ 0, 0, 0 ]),
25.018/25.018	
25.018/25.018	        function(g(_), [ 0, 1, 0 ]),
25.018/25.018	
25.018/25.018	        function(h(_), [ 2, 0, 2 ]),
25.018/25.018	
25.018/25.018	        function(c(_,_), [
25.018/25.018				   0, 0, 0,
25.018/25.018				   0, 0, 0,
25.018/25.018				   0, 0, 0 ]),
25.018/25.018	
25.018/25.018	        relation(->*(_,_), [
25.018/25.018				   1, 1, 0,
25.018/25.018				   0, 1, 0,
25.018/25.018				   1, 1, 1 ]),
25.018/25.018	
25.018/25.018	        relation(->(_,_), [
25.018/25.018				   1, 1, 0,
25.018/25.018				   0, 0, 0,
25.018/25.018				   1, 0, 1 ])
25.018/25.018	]).
25.018/25.018	
25.018/25.018	============================== end of model ==========================
25.018/25.018	
25.018/25.018	============================== STATISTICS ============================
25.018/25.018	
25.018/25.018	For domain size 3.
25.018/25.018	
25.018/25.018	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
25.018/25.018	Ground clauses: seen=119, kept=110.
25.018/25.018	Selections=24, assignments=39, propagations=49, current_models=1.
25.018/25.018	Rewrite_terms=355, rewrite_bools=323, indexes=50.
25.018/25.018	Rules_from_neg_clauses=7, cross_offs=27.
25.018/25.018	
25.018/25.018	============================== end of statistics =====================
25.018/25.018	
25.018/25.018	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
25.018/25.018	
25.018/25.018	Exiting with 1 model.
25.018/25.018	
25.018/25.018	Process 103291 exit (max_models) Fri Jul 16 14:44:23 2021
25.018/25.018	The process finished Fri Jul 16 14:44:23 2021
25.018/25.018	
25.018/25.018	
25.018/25.018	Mace4 cooked interpretation:
25.018/25.018	
25.018/25.018	
25.018/25.018	
25.018/25.018	The problem is infeasible.
25.018/25.018	
25.018/25.018	
25.018/25.018	CRule InfChecker Info:
25.018/25.018	g(a) -> h(b)
25.018/25.018	Rule remains
25.018/25.018	Proof:
25.018/25.018	NO_CONDS
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Transform No Conds CTRS Processor:
25.018/25.018	
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Resulting R:
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	CleanTRS Processor:
25.018/25.018	
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	
25.018/25.018	Modular Confluence Combinations Decomposition Processor:
25.018/25.018	
25.018/25.018	No usable combinations
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	Confluence Problem:
25.018/25.018	(STRATEGY CONTEXTSENSITIVE
25.018/25.018	(a)
25.018/25.018	(f 1)
25.018/25.018	(g 1)
25.018/25.018	(b)
25.018/25.018	(c 1 2)
25.018/25.018	(fSNonEmpty)
25.018/25.018	(h 1)
25.018/25.018	)
25.018/25.018	(RULES
25.018/25.018	a -> b
25.018/25.018	g(a) -> h(b)
25.018/25.018	)
25.018/25.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
25.018/25.018	
25.018/25.018	Huet Levy Processor:
25.018/25.018	-> Rules:
25.018/25.018	 a -> b
25.018/25.018	 g(a) -> h(b)
25.018/25.018	-> Vars:
25.018/25.018	
25.018/25.018	-> FVars:
25.018/25.018	
25.018/25.018	-> PVars:
25.018/25.018	
25.018/25.018	
25.018/25.018	-> Rlps:
25.018/25.018	 (rule: a -> b, id: 1, possubterms: a->[])
25.018/25.018	 (rule: g(a) -> h(b), id: 2, possubterms: g(a)->[], a->[1])
25.018/25.018	
25.018/25.018	-> Unifications:
25.018/25.018	(R2 unifies with R1 at p: [1], l: g(a), lp: a, sig: {}, l': a, r: h(b), r': b)
25.018/25.018	
25.018/25.018	-> Critical pairs info:
25.018/25.018	<g(b),h(b)>   =>  Not trivial, Not overlay, N1
25.018/25.018	
25.018/25.018	-> Problem conclusions:
25.018/25.018	 Left linear, Right linear, Linear
25.018/25.018	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
25.018/25.018	 Not Huet-Levy confluent, Not Newman confluent
25.018/25.018	 R is a TRS
25.018/25.018	
25.018/25.018	
25.018/25.018	Problem 1:
25.018/25.018	Different Normal CP Terms Processor:
25.018/25.018	<g(b),h(b)>   =>  Not trivial, Not overlay, N1, Normal and not trivial cp
25.018/25.018	
25.018/25.018	The problem is not joinable.
25.018/25.018	19.80user 0.99system 0:25.18elapsed 82%CPU (0avgtext+0avgdata 72332maxresident)k
25.018/25.018	8inputs+0outputs (0major+41179minor)pagefaults 0swaps