20.037/20.037	YES
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR vNonEmpty x y)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> x
20.037/20.037	tc(x) -> y | pin(x) ->* pout(z), tc(z) ->* y
20.037/20.037	)
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Inlining of Conditions Processor [STERN17]:
20.037/20.037	
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR vNonEmpty x y)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> tc(z) | pin(x) ->* pout(z)
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Clean CTRS Processor:
20.037/20.037	
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR x)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	CRule InfChecker Info:
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	Rule remains
20.037/20.037	Proof:
20.037/20.037	NO_CONDS
20.037/20.037	
20.037/20.037	CRule InfChecker Info:
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	Rule remains
20.037/20.037	Proof:
20.037/20.037	NO_CONDS
20.037/20.037	
20.037/20.037	CRule InfChecker Info:
20.037/20.037	tc(x) -> tc(z) | pin(x) ->* pout(z)
20.037/20.037	Rule deleted
20.037/20.037	Proof:
20.037/20.037	YES
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Infeasibility Problem:
20.037/20.037	[(VAR vNonEmpty x y vNonEmpty x)
20.037/20.037	(STRATEGY CONTEXTSENSITIVE
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> tc(z) | pin(x) ->* pout(z)
20.037/20.037	tc(x) -> x
20.037/20.037	)]
20.037/20.037	
20.037/20.037	Infeasibility Conditions:
20.037/20.037	pin(x) ->* pout(z)
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Obtaining a model using Mace4:
20.037/20.037	
20.037/20.037	 -> Usable Rules:
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> tc(z) | pin(x) ->* pout(z)
20.037/20.037	tc(x) -> x
20.037/20.037	
20.037/20.037	 -> Mace4 Output:
20.037/20.037	============================== Mace4 =================================
20.037/20.037	Mace4 (64) version 2009-11A, November 2009.
20.037/20.037	Process 8755 was started by ubuntu on ubuntu,
20.037/20.037	Wed Mar  9 09:09:04 2022
20.037/20.037	The command was "./mace4 -c -f /tmp/mace48742-2.in".
20.037/20.037	============================== end of head ===========================
20.037/20.037	
20.037/20.037	============================== INPUT =================================
20.037/20.037	
20.037/20.037	% Reading from file /tmp/mace48742-2.in
20.037/20.037	
20.037/20.037	assign(max_seconds,20).
20.037/20.037	
20.037/20.037	formulas(assumptions).
20.037/20.037	->(x1,y) -> ->(pin(x1),pin(y)) # label(congruence).
20.037/20.037	->(x1,y) -> ->(tc(x1),tc(y)) # label(congruence).
20.037/20.037	->(x1,y) -> ->(pout(x1),pout(y)) # label(congruence).
20.037/20.037	->(pin(a),pout(b)) # label(replacement).
20.037/20.037	->(pin(b),pout(c)) # label(replacement).
20.037/20.037	->*(pin(x1),pout(z)) -> ->(tc(x1),tc(z)) # label(replacement).
20.037/20.037	->(tc(x1),x1) # label(replacement).
20.037/20.037	->*(x,x) # label(reflexivity).
20.037/20.037	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.037/20.037	end_of_list.
20.037/20.037	
20.037/20.037	formulas(goals).
20.037/20.037	(exists x4 ->*(pin(x4),pout(z))) # label(goal).
20.037/20.037	end_of_list.
20.037/20.037	
20.037/20.037	============================== end of input ==========================
20.037/20.037	
20.037/20.037	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.037/20.037	
20.037/20.037	% Formulas that are not ordinary clauses:
20.037/20.037	1 ->(x1,y) -> ->(pin(x1),pin(y)) # label(congruence) # label(non_clause).  [assumption].
20.037/20.037	2 ->(x1,y) -> ->(tc(x1),tc(y)) # label(congruence) # label(non_clause).  [assumption].
20.037/20.037	3 ->(x1,y) -> ->(pout(x1),pout(y)) # label(congruence) # label(non_clause).  [assumption].
20.037/20.037	4 ->*(pin(x1),pout(z)) -> ->(tc(x1),tc(z)) # label(replacement) # label(non_clause).  [assumption].
20.037/20.037	5 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.037/20.037	6 (exists x4 ->*(pin(x4),pout(z))) # label(goal) # label(non_clause) # label(goal).  [goal].
20.037/20.037	
20.037/20.037	============================== end of process non-clausal formulas ===
20.037/20.037	
20.037/20.037	============================== CLAUSES FOR SEARCH ====================
20.037/20.037	
20.037/20.037	formulas(mace4_clauses).
20.037/20.037	-->(x,y) | ->(pin(x),pin(y)) # label(congruence).
20.037/20.037	-->(x,y) | ->(tc(x),tc(y)) # label(congruence).
20.037/20.037	-->(x,y) | ->(pout(x),pout(y)) # label(congruence).
20.037/20.037	->(pin(a),pout(b)) # label(replacement).
20.037/20.037	->(pin(b),pout(c)) # label(replacement).
20.037/20.037	-->*(pin(x),pout(z)) | ->(tc(x),tc(z)) # label(replacement).
20.037/20.037	->(tc(x),x) # label(replacement).
20.037/20.037	->*(x,x) # label(reflexivity).
20.037/20.037	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.037/20.037	-->*(pin(x),pout(z)) # label(goal).
20.037/20.037	end_of_list.
20.037/20.037	
20.037/20.037	============================== end of clauses for search =============
20.037/20.037	
20.037/20.037	% There are no natural numbers in the input.
20.037/20.037	
20.037/20.037	============================== DOMAIN SIZE 2 =========================
20.037/20.037	
20.037/20.037	============================== MODEL =================================
20.037/20.037	
20.037/20.037	interpretation( 2, [number=1, seconds=0], [
20.037/20.037	
20.037/20.037	        function(a, [ 0 ]),
20.037/20.037	
20.037/20.037	        function(b, [ 0 ]),
20.037/20.037	
20.037/20.037	        function(c, [ 0 ]),
20.037/20.037	
20.037/20.037	        function(z, [ 1 ]),
20.037/20.037	
20.037/20.037	        function(pin(_), [ 0, 0 ]),
20.037/20.037	
20.037/20.037	        function(tc(_), [ 0, 1 ]),
20.037/20.037	
20.037/20.037	        function(pout(_), [ 0, 1 ]),
20.037/20.037	
20.037/20.037	        relation(->*(_,_), [
20.037/20.037				   1, 0,
20.037/20.037				   0, 1 ]),
20.037/20.037	
20.037/20.037	        relation(->(_,_), [
20.037/20.037				   1, 0,
20.037/20.037				   0, 1 ])
20.037/20.037	]).
20.037/20.037	
20.037/20.037	============================== end of model ==========================
20.037/20.037	
20.037/20.037	============================== STATISTICS ============================
20.037/20.037	
20.037/20.037	For domain size 2.
20.037/20.037	
20.037/20.037	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.037/20.037	Ground clauses: seen=30, kept=26.
20.037/20.037	Selections=8, assignments=10, propagations=17, current_models=1.
20.037/20.037	Rewrite_terms=94, rewrite_bools=40, indexes=37.
20.037/20.037	Rules_from_neg_clauses=6, cross_offs=6.
20.037/20.037	
20.037/20.037	============================== end of statistics =====================
20.037/20.037	
20.037/20.037	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.037/20.037	
20.037/20.037	Exiting with 1 model.
20.037/20.037	
20.037/20.037	Process 8755 exit (max_models) Wed Mar  9 09:09:04 2022
20.037/20.037	The process finished Wed Mar  9 09:09:04 2022
20.037/20.037	
20.037/20.037	
20.037/20.037	Mace4 cooked interpretation:
20.037/20.037	
20.037/20.037	
20.037/20.037	
20.037/20.037	The problem is infeasible.
20.037/20.037	
20.037/20.037	
20.037/20.037	CRule InfChecker Info:
20.037/20.037	tc(x) -> x
20.037/20.037	Rule remains
20.037/20.037	Proof:
20.037/20.037	NO_CONDS
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Transform No Conds CTRS Processor:
20.037/20.037	
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR x)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Resulting R:
20.037/20.037	(VAR x)
20.037/20.037	(STRATEGY CONTEXTSENSITIVE
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	CleanTRS Processor:
20.037/20.037	
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR x)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(tc 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(fSNonEmpty)
20.037/20.037	(pout 1)
20.037/20.037	(z)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	
20.037/20.037	Problem 1:
20.037/20.037	
20.037/20.037	Modular Confluence Combinations Decomposition Processor:
20.037/20.037	
20.037/20.037	TRS combination:
20.037/20.037	{pin(a) -> pout(b)
20.037/20.037	 pin(b) -> pout(c)}
20.037/20.037	{tc(x) -> x}
20.037/20.037	Disjoint
20.037/20.037	Constructor-sharing
20.037/20.037	Left linear
20.037/20.037	Not layer-preserving
20.037/20.037	TRS1
20.037/20.037	Just (STRATEGY CONTEXTSENSITIVE
20.037/20.037	(pin 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(pout 1)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	)
20.037/20.037	
20.037/20.037	TRS2
20.037/20.037	Just (VAR x)
20.037/20.037	(STRATEGY CONTEXTSENSITIVE
20.037/20.037	(tc 1)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	
20.037/20.037	
20.037/20.037	The problem is decomposed in 2 subproblems.
20.037/20.037	
20.037/20.037	Problem 1.1:
20.037/20.037	Linearity Processor:
20.037/20.037	Linear?
20.037/20.037	YES
20.037/20.037	Problem 1.1.1:
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(pin 1)
20.037/20.037	(a)
20.037/20.037	(b)
20.037/20.037	(c)
20.037/20.037	(pout 1)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	pin(a) -> pout(b)
20.037/20.037	pin(b) -> pout(c)
20.037/20.037	)
20.037/20.037	Linear:YES
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	Huet Levy Processor:
20.037/20.037	-> Rules:
20.037/20.037	 pin(a) -> pout(b)
20.037/20.037	 pin(b) -> pout(c)
20.037/20.037	-> Vars:
20.037/20.037	
20.037/20.037	
20.037/20.037	-> Rlps:
20.037/20.037	 (rule: pin(a) -> pout(b), id: 1, possubterms: pin(a)->[], a->[1])
20.037/20.037	 (rule: pin(b) -> pout(c), id: 2, possubterms: pin(b)->[], b->[1])
20.037/20.037	
20.037/20.037	-> Unifications:
20.037/20.037	
20.037/20.037	
20.037/20.037	-> Critical pairs info:
20.037/20.037	
20.037/20.037	
20.037/20.037	-> Problem conclusions:
20.037/20.037	 Left linear, Right linear, Linear
20.037/20.037	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.037/20.037	 Huet-Levy confluent, Not Newman confluent
20.037/20.037	 R is a TRS
20.037/20.037	
20.037/20.037	
20.037/20.037	The problem is joinable.
20.037/20.037	
20.037/20.037	Problem 1.2:
20.037/20.037	Linearity Processor:
20.037/20.037	Linear?
20.037/20.037	YES
20.037/20.037	Problem 1.2.1:
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	Confluence Problem:
20.037/20.037	(VAR x)
20.037/20.037	(REPLACEMENT-MAP
20.037/20.037	(tc 1)
20.037/20.037	)
20.037/20.037	(RULES
20.037/20.037	tc(x) -> x
20.037/20.037	)
20.037/20.037	Linear:YES
20.037/20.037	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.037/20.037	
20.037/20.037	Huet Levy Processor:
20.037/20.037	-> Rules:
20.037/20.037	 tc(x) -> x
20.037/20.037	-> Vars:
20.037/20.037	 x
20.037/20.037	
20.037/20.037	-> Rlps:
20.037/20.037	 (rule: tc(x) -> x, id: 1, possubterms: tc(x)->[])
20.037/20.037	
20.037/20.037	-> Unifications:
20.037/20.037	
20.037/20.037	
20.037/20.037	-> Critical pairs info:
20.037/20.037	
20.037/20.037	
20.037/20.037	-> Problem conclusions:
20.037/20.037	 Left linear, Right linear, Linear
20.037/20.037	 Weakly orthogonal, Almost orthogonal, Orthogonal
20.037/20.037	 Huet-Levy confluent, Not Newman confluent
20.037/20.037	 R is a TRS
20.037/20.037	
20.037/20.037	
20.037/20.037	The problem is joinable.
20.037/20.037	24.38user 0.67system 0:20.37elapsed 123%CPU (0avgtext+0avgdata 135852maxresident)k
20.037/20.037	8inputs+0outputs (0major+72411minor)pagefaults 0swaps