20.024/20.024	NO
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(VAR vNonEmpty x y)
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	f(x) -> c(x,y) | g(x) ->* y, y ->* h(x)
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Inlining of Conditions Processor [STERN17]:
20.024/20.024	
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(VAR vNonEmpty x y)
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	f(x) -> c(x,g(x)) | g(x) ->* h(x)
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Clean CTRS Processor:
20.024/20.024	
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	
20.024/20.024	CRule InfChecker Info:
20.024/20.024	a -> b
20.024/20.024	Rule remains
20.024/20.024	Proof:
20.024/20.024	NO_CONDS
20.024/20.024	
20.024/20.024	CRule InfChecker Info:
20.024/20.024	f(x) -> c(x,g(x)) | g(x) ->* h(x)
20.024/20.024	Rule deleted
20.024/20.024	Proof:
20.024/20.024	YES
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Infeasibility Problem:
20.024/20.024	[(VAR vNonEmpty x y vNonEmpty x)
20.024/20.024	(STRATEGY CONTEXTSENSITIVE
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	f(x) -> c(x,g(x)) | g(x) ->* h(x)
20.024/20.024	g(a) -> h(b)
20.024/20.024	)]
20.024/20.024	
20.024/20.024	Infeasibility Conditions:
20.024/20.024	g(x) ->* h(x)
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Obtaining a model using Mace4:
20.024/20.024	
20.024/20.024	 -> Usable Rules:
20.024/20.024	a -> b
20.024/20.024	f(x) -> c(x,g(x)) | g(x) ->* h(x)
20.024/20.024	g(a) -> h(b)
20.024/20.024	
20.024/20.024	 -> Mace4 Output:
20.024/20.024	============================== Mace4 =================================
20.024/20.024	Mace4 (64) version 2009-11A, November 2009.
20.024/20.024	Process 12273 was started by ubuntu on ubuntu,
20.024/20.024	Wed Mar  9 09:19:23 2022
20.024/20.024	The command was "./mace4 -c -f /tmp/mace412260-2.in".
20.024/20.024	============================== end of head ===========================
20.024/20.024	
20.024/20.024	============================== INPUT =================================
20.024/20.024	
20.024/20.024	% Reading from file /tmp/mace412260-2.in
20.024/20.024	
20.024/20.024	assign(max_seconds,20).
20.024/20.024	
20.024/20.024	formulas(assumptions).
20.024/20.024	->(x1,y) -> ->(f(x1),f(y)) # label(congruence).
20.024/20.024	->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
20.024/20.024	->(x1,y) -> ->(c(x1,x2),c(y,x2)) # label(congruence).
20.024/20.024	->(x2,y) -> ->(c(x1,x2),c(x1,y)) # label(congruence).
20.024/20.024	->(x1,y) -> ->(h(x1),h(y)) # label(congruence).
20.024/20.024	->(a,b) # label(replacement).
20.024/20.024	->*(g(x1),h(x1)) -> ->(f(x1),c(x1,g(x1))) # label(replacement).
20.024/20.024	->(g(a),h(b)) # label(replacement).
20.024/20.024	->*(x,x) # label(reflexivity).
20.024/20.024	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.024/20.024	end_of_list.
20.024/20.024	
20.024/20.024	formulas(goals).
20.024/20.024	(exists x4 ->*(g(x4),h(x4))) # label(goal).
20.024/20.024	end_of_list.
20.024/20.024	
20.024/20.024	============================== end of input ==========================
20.024/20.024	
20.024/20.024	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.024/20.024	
20.024/20.024	% Formulas that are not ordinary clauses:
20.024/20.024	1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause).  [assumption].
20.024/20.024	2 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
20.024/20.024	3 ->(x1,y) -> ->(c(x1,x2),c(y,x2)) # label(congruence) # label(non_clause).  [assumption].
20.024/20.024	4 ->(x2,y) -> ->(c(x1,x2),c(x1,y)) # label(congruence) # label(non_clause).  [assumption].
20.024/20.024	5 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause).  [assumption].
20.024/20.024	6 ->*(g(x1),h(x1)) -> ->(f(x1),c(x1,g(x1))) # label(replacement) # label(non_clause).  [assumption].
20.024/20.024	7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.024/20.024	8 (exists x4 ->*(g(x4),h(x4))) # label(goal) # label(non_clause) # label(goal).  [goal].
20.024/20.024	
20.024/20.024	============================== end of process non-clausal formulas ===
20.024/20.024	
20.024/20.024	============================== CLAUSES FOR SEARCH ====================
20.024/20.024	
20.024/20.024	formulas(mace4_clauses).
20.024/20.024	-->(x,y) | ->(f(x),f(y)) # label(congruence).
20.024/20.024	-->(x,y) | ->(g(x),g(y)) # label(congruence).
20.024/20.024	-->(x,y) | ->(c(x,z),c(y,z)) # label(congruence).
20.024/20.024	-->(x,y) | ->(c(z,x),c(z,y)) # label(congruence).
20.024/20.024	-->(x,y) | ->(h(x),h(y)) # label(congruence).
20.024/20.024	->(a,b) # label(replacement).
20.024/20.024	-->*(g(x),h(x)) | ->(f(x),c(x,g(x))) # label(replacement).
20.024/20.024	->(g(a),h(b)) # label(replacement).
20.024/20.024	->*(x,x) # label(reflexivity).
20.024/20.024	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.024/20.024	-->*(g(x),h(x)) # label(goal).
20.024/20.024	end_of_list.
20.024/20.024	
20.024/20.024	============================== end of clauses for search =============
20.024/20.024	
20.024/20.024	% There are no natural numbers in the input.
20.024/20.024	
20.024/20.024	============================== DOMAIN SIZE 2 =========================
20.024/20.024	
20.024/20.024	============================== STATISTICS ============================
20.024/20.024	
20.024/20.024	For domain size 2.
20.024/20.024	
20.024/20.024	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.024/20.024	Ground clauses: seen=44, kept=40.
20.024/20.024	Selections=8, assignments=15, propagations=35, current_models=0.
20.024/20.024	Rewrite_terms=149, rewrite_bools=113, indexes=38.
20.024/20.024	Rules_from_neg_clauses=13, cross_offs=13.
20.024/20.024	
20.024/20.024	============================== end of statistics =====================
20.024/20.024	
20.024/20.024	============================== DOMAIN SIZE 3 =========================
20.024/20.024	
20.024/20.024	============================== MODEL =================================
20.024/20.024	
20.024/20.024	interpretation( 3, [number=1, seconds=0], [
20.024/20.024	
20.024/20.024	        function(a, [ 0 ]),
20.024/20.024	
20.024/20.024	        function(b, [ 1 ]),
20.024/20.024	
20.024/20.024	        function(f(_), [ 0, 0, 0 ]),
20.024/20.024	
20.024/20.024	        function(g(_), [ 0, 1, 0 ]),
20.024/20.024	
20.024/20.024	        function(h(_), [ 2, 0, 2 ]),
20.024/20.024	
20.024/20.024	        function(c(_,_), [
20.024/20.024				   0, 0, 0,
20.024/20.024				   0, 0, 0,
20.024/20.024				   0, 0, 0 ]),
20.024/20.024	
20.024/20.024	        relation(->*(_,_), [
20.024/20.024				   1, 1, 0,
20.024/20.024				   0, 1, 0,
20.024/20.024				   1, 1, 1 ]),
20.024/20.024	
20.024/20.024	        relation(->(_,_), [
20.024/20.024				   1, 1, 0,
20.024/20.024				   0, 0, 0,
20.024/20.024				   1, 0, 1 ])
20.024/20.024	]).
20.024/20.024	
20.024/20.024	============================== end of model ==========================
20.024/20.024	
20.024/20.024	============================== STATISTICS ============================
20.024/20.024	
20.024/20.024	For domain size 3.
20.024/20.024	
20.024/20.024	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.024/20.024	Ground clauses: seen=119, kept=110.
20.024/20.024	Selections=24, assignments=39, propagations=49, current_models=1.
20.024/20.024	Rewrite_terms=355, rewrite_bools=323, indexes=50.
20.024/20.024	Rules_from_neg_clauses=7, cross_offs=27.
20.024/20.024	
20.024/20.024	============================== end of statistics =====================
20.024/20.024	
20.024/20.024	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.024/20.024	
20.024/20.024	Exiting with 1 model.
20.024/20.024	
20.024/20.024	Process 12273 exit (max_models) Wed Mar  9 09:19:23 2022
20.024/20.024	The process finished Wed Mar  9 09:19:23 2022
20.024/20.024	
20.024/20.024	
20.024/20.024	Mace4 cooked interpretation:
20.024/20.024	
20.024/20.024	
20.024/20.024	
20.024/20.024	The problem is infeasible.
20.024/20.024	
20.024/20.024	
20.024/20.024	CRule InfChecker Info:
20.024/20.024	g(a) -> h(b)
20.024/20.024	Rule remains
20.024/20.024	Proof:
20.024/20.024	NO_CONDS
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Transform No Conds CTRS Processor:
20.024/20.024	
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Resulting R:
20.024/20.024	(STRATEGY CONTEXTSENSITIVE
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	CleanTRS Processor:
20.024/20.024	
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	
20.024/20.024	Modular Confluence Combinations Decomposition Processor:
20.024/20.024	
20.024/20.024	No usable combinations
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	Confluence Problem:
20.024/20.024	(REPLACEMENT-MAP
20.024/20.024	(a)
20.024/20.024	(f 1)
20.024/20.024	(g 1)
20.024/20.024	(b)
20.024/20.024	(c 1, 2)
20.024/20.024	(fSNonEmpty)
20.024/20.024	(h 1)
20.024/20.024	)
20.024/20.024	(RULES
20.024/20.024	a -> b
20.024/20.024	g(a) -> h(b)
20.024/20.024	)
20.024/20.024	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.024/20.024	
20.024/20.024	Huet Levy Processor:
20.024/20.024	-> Rules:
20.024/20.024	 a -> b
20.024/20.024	 g(a) -> h(b)
20.024/20.024	-> Vars:
20.024/20.024	
20.024/20.024	
20.024/20.024	-> Rlps:
20.024/20.024	 (rule: a -> b, id: 1, possubterms: a->[])
20.024/20.024	 (rule: g(a) -> h(b), id: 2, possubterms: g(a)->[], a->[1])
20.024/20.024	
20.024/20.024	-> Unifications:
20.024/20.024	(R2 unifies with R1 at p: [1], l: g(a), lp: a, sig: {}, l': a, r: h(b), r': b)
20.024/20.024	
20.024/20.024	-> Critical pairs info:
20.024/20.024	<g(b),h(b)>   =>  Not trivial, Not overlay, NW0, N1
20.024/20.024	
20.024/20.024	-> Problem conclusions:
20.024/20.024	 Left linear, Right linear, Linear
20.024/20.024	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
20.024/20.024	 Not Huet-Levy confluent, Not Newman confluent
20.024/20.024	 R is a TRS
20.024/20.024	
20.024/20.024	
20.024/20.024	Problem 1:
20.024/20.024	Different Normal CP Terms Processor:
20.024/20.024	<g(b),h(b)>   =>  Not trivial, Not overlay, NW0, N1, Normal and not trivial cp
20.024/20.024	
20.024/20.024	The problem is not joinable.
20.024/20.024	19.45user 0.86system 0:20.24elapsed 100%CPU (0avgtext+0avgdata 62112maxresident)k
20.024/20.024	8inputs+0outputs (0major+29323minor)pagefaults 0swaps