20.018/20.018	NO
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR vNonEmpty x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	r(x) -> r(h(x)) | s(x) ->* 0
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Inlining of Conditions Processor [STERN17]:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR vNonEmpty x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	r(x) -> r(h(x)) | s(x) ->* 0
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Clean CTRS Processor:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	Rule remains
20.018/20.018	Proof:
20.018/20.018	NO_CONDS
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	Rule remains
20.018/20.018	Proof:
20.018/20.018	NO_CONDS
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	r(x) -> r(h(x)) | s(x) ->* 0
20.018/20.018	Rule deleted
20.018/20.018	Proof:
20.018/20.018	YES
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Infeasibility Problem:
20.018/20.018	[(VAR vNonEmpty x vNonEmpty x)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	r(x) -> r(h(x)) | s(x) ->* 0
20.018/20.018	s(x) -> 1
20.018/20.018	)]
20.018/20.018	
20.018/20.018	Infeasibility Conditions:
20.018/20.018	s(x) ->* 0
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Obtaining a model using Mace4:
20.018/20.018	
20.018/20.018	 -> Usable Rules:
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	r(x) -> r(h(x)) | s(x) ->* 0
20.018/20.018	s(x) -> 1
20.018/20.018	
20.018/20.018	 -> Mace4 Output:
20.018/20.018	============================== Mace4 =================================
20.018/20.018	Mace4 (64) version 2009-11A, November 2009.
20.018/20.018	Process 6508 was started by ubuntu on ubuntu,
20.018/20.018	Wed Mar  9 08:57:19 2022
20.018/20.018	The command was "./mace4 -c -f /tmp/mace46495-2.in".
20.018/20.018	============================== end of head ===========================
20.018/20.018	
20.018/20.018	============================== INPUT =================================
20.018/20.018	
20.018/20.018	% Reading from file /tmp/mace46495-2.in
20.018/20.018	
20.018/20.018	assign(max_seconds,20).
20.018/20.018	
20.018/20.018	formulas(assumptions).
20.018/20.018	->(x1,y) -> ->(p(x1),p(y)) # label(congruence).
20.018/20.018	->(x1,y) -> ->(q(x1),q(y)) # label(congruence).
20.018/20.018	->(x1,y) -> ->(r(x1),r(y)) # label(congruence).
20.018/20.018	->(x1,y) -> ->(s(x1),s(y)) # label(congruence).
20.018/20.018	->(x1,y) -> ->(h(x1),h(y)) # label(congruence).
20.018/20.018	->(p(q(x1)),p(r(x1))) # label(replacement).
20.018/20.018	->(q(h(x1)),r(x1)) # label(replacement).
20.018/20.018	->*(s(x1),0) -> ->(r(x1),r(h(x1))) # label(replacement).
20.018/20.018	->(s(x1),1) # label(replacement).
20.018/20.018	->*(x,x) # label(reflexivity).
20.018/20.018	->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	formulas(goals).
20.018/20.018	(exists x3 ->*(s(x3),0)) # label(goal).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	============================== end of input ==========================
20.018/20.018	
20.018/20.018	============================== PROCESS NON-CLAUSAL FORMULAS ==========
20.018/20.018	
20.018/20.018	% Formulas that are not ordinary clauses:
20.018/20.018	1 ->(x1,y) -> ->(p(x1),p(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	2 ->(x1,y) -> ->(q(x1),q(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	3 ->(x1,y) -> ->(r(x1),r(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	5 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause).  [assumption].
20.018/20.018	6 ->*(s(x1),0) -> ->(r(x1),r(h(x1))) # label(replacement) # label(non_clause).  [assumption].
20.018/20.018	7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
20.018/20.018	8 (exists x3 ->*(s(x3),0)) # label(goal) # label(non_clause) # label(goal).  [goal].
20.018/20.018	
20.018/20.018	============================== end of process non-clausal formulas ===
20.018/20.018	
20.018/20.018	============================== CLAUSES FOR SEARCH ====================
20.018/20.018	
20.018/20.018	formulas(mace4_clauses).
20.018/20.018	-->(x,y) | ->(p(x),p(y)) # label(congruence).
20.018/20.018	-->(x,y) | ->(q(x),q(y)) # label(congruence).
20.018/20.018	-->(x,y) | ->(r(x),r(y)) # label(congruence).
20.018/20.018	-->(x,y) | ->(s(x),s(y)) # label(congruence).
20.018/20.018	-->(x,y) | ->(h(x),h(y)) # label(congruence).
20.018/20.018	->(p(q(x)),p(r(x))) # label(replacement).
20.018/20.018	->(q(h(x)),r(x)) # label(replacement).
20.018/20.018	-->*(s(x),0) | ->(r(x),r(h(x))) # label(replacement).
20.018/20.018	->(s(x),1) # label(replacement).
20.018/20.018	->*(x,x) # label(reflexivity).
20.018/20.018	-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
20.018/20.018	-->*(s(x),0) # label(goal).
20.018/20.018	end_of_list.
20.018/20.018	
20.018/20.018	============================== end of clauses for search =============
20.018/20.018	
20.018/20.018	% There are no natural numbers in the input.
20.018/20.018	
20.018/20.018	============================== DOMAIN SIZE 2 =========================
20.018/20.018	
20.018/20.018	============================== MODEL =================================
20.018/20.018	
20.018/20.018	interpretation( 2, [number=1, seconds=0], [
20.018/20.018	
20.018/20.018	        function(0, [ 0 ]),
20.018/20.018	
20.018/20.018	        function(1, [ 1 ]),
20.018/20.018	
20.018/20.018	        function(p(_), [ 0, 0 ]),
20.018/20.018	
20.018/20.018	        function(q(_), [ 0, 0 ]),
20.018/20.018	
20.018/20.018	        function(r(_), [ 0, 0 ]),
20.018/20.018	
20.018/20.018	        function(s(_), [ 1, 1 ]),
20.018/20.018	
20.018/20.018	        function(h(_), [ 0, 0 ]),
20.018/20.018	
20.018/20.018	        relation(->*(_,_), [
20.018/20.018				   1, 0,
20.018/20.018				   0, 1 ]),
20.018/20.018	
20.018/20.018	        relation(->(_,_), [
20.018/20.018				   1, 0,
20.018/20.018				   0, 1 ])
20.018/20.018	]).
20.018/20.018	
20.018/20.018	============================== end of model ==========================
20.018/20.018	
20.018/20.018	============================== STATISTICS ============================
20.018/20.018	
20.018/20.018	For domain size 2.
20.018/20.018	
20.018/20.018	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
20.018/20.018	Ground clauses: seen=40, kept=36.
20.018/20.018	Selections=10, assignments=10, propagations=10, current_models=1.
20.018/20.018	Rewrite_terms=72, rewrite_bools=47, indexes=6.
20.018/20.018	Rules_from_neg_clauses=3, cross_offs=3.
20.018/20.018	
20.018/20.018	============================== end of statistics =====================
20.018/20.018	
20.018/20.018	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
20.018/20.018	
20.018/20.018	Exiting with 1 model.
20.018/20.018	
20.018/20.018	Process 6508 exit (max_models) Wed Mar  9 08:57:19 2022
20.018/20.018	The process finished Wed Mar  9 08:57:19 2022
20.018/20.018	
20.018/20.018	
20.018/20.018	Mace4 cooked interpretation:
20.018/20.018	
20.018/20.018	
20.018/20.018	
20.018/20.018	The problem is infeasible.
20.018/20.018	
20.018/20.018	
20.018/20.018	CRule InfChecker Info:
20.018/20.018	s(x) -> 1
20.018/20.018	Rule remains
20.018/20.018	Proof:
20.018/20.018	NO_CONDS
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Transform No Conds CTRS Processor:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Resulting R:
20.018/20.018	(VAR x)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	CleanTRS Processor:
20.018/20.018	
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(s 1)
20.018/20.018	(0)
20.018/20.018	(1)
20.018/20.018	(fSNonEmpty)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	
20.018/20.018	Modular Confluence Combinations Decomposition Processor:
20.018/20.018	
20.018/20.018	TRS combination:
20.018/20.018	{p(q(x)) -> p(r(x))
20.018/20.018	 q(h(x)) -> r(x)}
20.018/20.018	{s(x) -> 1}
20.018/20.018	Disjoint
20.018/20.018	Constructor-sharing
20.018/20.018	Left linear
20.018/20.018	Layer-preserving
20.018/20.018	TRS1
20.018/20.018	Just (VAR x)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	)
20.018/20.018	
20.018/20.018	TRS2
20.018/20.018	Just (VAR x)
20.018/20.018	(STRATEGY CONTEXTSENSITIVE
20.018/20.018	(s 1)
20.018/20.018	(1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	s(x) -> 1
20.018/20.018	)
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	Confluence Problem:
20.018/20.018	(VAR x)
20.018/20.018	(REPLACEMENT-MAP
20.018/20.018	(p 1)
20.018/20.018	(q 1)
20.018/20.018	(r 1)
20.018/20.018	(h 1)
20.018/20.018	)
20.018/20.018	(RULES
20.018/20.018	p(q(x)) -> p(r(x))
20.018/20.018	q(h(x)) -> r(x)
20.018/20.018	)
20.018/20.018	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
20.018/20.018	
20.018/20.018	Huet Levy Processor:
20.018/20.018	-> Rules:
20.018/20.018	 p(q(x)) -> p(r(x))
20.018/20.018	 q(h(x)) -> r(x)
20.018/20.018	-> Vars:
20.018/20.018	 x, x
20.018/20.018	
20.018/20.018	-> Rlps:
20.018/20.018	 (rule: p(q(x)) -> p(r(x)), id: 1, possubterms: p(q(x))->[], q(x)->[1])
20.018/20.018	 (rule: q(h(x)) -> r(x), id: 2, possubterms: q(h(x))->[], h(x)->[1])
20.018/20.018	
20.018/20.018	-> Unifications:
20.018/20.018	(R1 unifies with R2 at p: [1], l: p(q(x)), lp: q(x), sig: {x -> h(x')}, l': q(h(x')), r: p(r(x)), r': r(x'))
20.018/20.018	
20.018/20.018	-> Critical pairs info:
20.018/20.018	<p(r(x')),p(r(h(x')))>   =>  Not trivial, Not overlay, NW0, N1
20.018/20.018	
20.018/20.018	-> Problem conclusions:
20.018/20.018	 Left linear, Right linear, Linear
20.018/20.018	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
20.018/20.018	 Not Huet-Levy confluent, Not Newman confluent
20.018/20.018	 R is a TRS
20.018/20.018	
20.018/20.018	
20.018/20.018	Problem 1:
20.018/20.018	Different Normal CP Terms Processor:
20.018/20.018	<p(r(x')),p(r(h(x')))>   =>  Not trivial, Not overlay, NW0, N1, Normal and not trivial cp
20.018/20.018	
20.018/20.018	The problem is not joinable.
20.018/20.018	19.94user 0.29system 0:20.18elapsed 100%CPU (0avgtext+0avgdata 62384maxresident)k
20.018/20.018	184inputs+0outputs (0major+27353minor)pagefaults 0swaps