0.00/0.14	YES
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	(VAR v_NonEmpty:S x:S)
0.00/0.14	(RULES
0.00/0.14	f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	g(x:S) -> s(x:S)
0.00/0.14	) 
0.00/0.14	(STRATEGY INNERMOST)
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Dependency Pairs Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 F(x:S,x:S) -> F(g(x:S),x:S)
0.00/0.14	 F(x:S,x:S) -> G(x:S)
0.00/0.14	-> Rules:
0.00/0.14	 f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 F(x:S,x:S) -> F(g(x:S),x:S)
0.00/0.14	 F(x:S,x:S) -> G(x:S)
0.00/0.14	-> Rules:
0.00/0.14	 f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	->Strongly Connected Components:
0.00/0.14	->->Cycle:
0.00/0.14	->->-> Pairs:
0.00/0.14	 F(x:S,x:S) -> F(g(x:S),x:S)
0.00/0.14	->->-> Rules:
0.00/0.14	 f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Reduction Pair Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 F(x:S,x:S) -> F(g(x:S),x:S)
0.00/0.14	-> Rules:
0.00/0.14	 f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	-> Usable rules:
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	->Mace4 Output:
0.00/0.14	 ============================== Mace4 =================================
0.00/0.14	Mace4 (64) version 2009-11A, November 2009.
0.00/0.14	Process 38208 was started by sandbox2 on n069.star.cs.uiowa.edu,
0.00/0.14	Thu Mar 28 22:22:14 2019
0.00/0.14	The command was "./mace4 -c -f /tmp/mace4336465782861021530.in".
0.00/0.14	============================== end of head ===========================
0.00/0.14	
0.00/0.14	============================== INPUT =================================
0.00/0.14	
0.00/0.14	% Reading from file /tmp/mace4336465782861021530.in
0.00/0.14	
0.00/0.14	assign(max_seconds,20).
0.00/0.14	
0.00/0.14	formulas(assumptions).
0.00/0.14	gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.14	succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.14	gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
0.00/0.14	arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence).
0.00/0.14	arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence).
0.00/0.14	arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence).
0.00/0.14	arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence).
0.00/0.14	arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence).
0.00/0.14	arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence).
0.00/0.14	arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence).
0.00/0.14	arrow_s0(f3(x1),f5(x1)) # label(replacement).
0.00/0.14	arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
0.00/0.14	sqsupset_s0(f7(x1,x1),f7(f3(x1),x1)) # label(replacement).
0.00/0.14	sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.14	sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.14	end_of_list.
0.00/0.14	
0.00/0.14	formulas(goals).
0.00/0.14	(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
0.00/0.14	end_of_list.
0.00/0.14	
0.00/0.14	============================== end of input ==========================
0.00/0.14	
0.00/0.14	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.00/0.14	
0.00/0.14	% Formulas that are not ordinary clauses:
0.00/0.14	1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.14	2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.14	3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.14	4 arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	5 arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	7 arrow_s0(x1,y) -> arrow_s0(f5(x1),f5(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	8 arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	9 arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	10 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.14	11 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.14	12 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.14	13 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.14	14 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].
0.00/0.14	
0.00/0.14	============================== end of process non-clausal formulas ===
0.00/0.14	
0.00/0.14	============================== CLAUSES FOR SEARCH ====================
0.00/0.14	
0.00/0.14	formulas(mace4_clauses).
0.00/0.14	-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.14	-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.14	-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f2(x,z),f2(y,z)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f2(z,x),f2(z,y)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f5(x),f5(y)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f7(x,z),f7(y,z)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f7(z,x),f7(z,y)) # label(congruence).
0.00/0.14	-arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence).
0.00/0.14	arrow_s0(f3(x),f5(x)) # label(replacement).
0.00/0.14	-arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
0.00/0.14	sqsupset_s0(f7(x,x),f7(f3(x),x)) # label(replacement).
0.00/0.14	-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.14	-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.14	-sqsupsetStar_s0(x,x) # label(wellfoundedness).
0.00/0.14	end_of_list.
0.00/0.14	
0.00/0.14	============================== end of clauses for search =============
0.00/0.14	
0.00/0.14	% There are no natural numbers in the input.
0.00/0.14	
0.00/0.14	============================== DOMAIN SIZE 2 =========================
0.00/0.14	
0.00/0.14	============================== MODEL =================================
0.00/0.14	
0.00/0.14	interpretation( 2, [number=1, seconds=0], [
0.00/0.14	
0.00/0.14	        function(f3(_), [ 1, 0 ]),
0.00/0.14	
0.00/0.14	        function(f5(_), [ 1, 0 ]),
0.00/0.14	
0.00/0.14	        function(f8(_), [ 0, 0 ]),
0.00/0.14	
0.00/0.14	        function(f2(_,_), [
0.00/0.14				   0, 0,
0.00/0.14				   0, 0 ]),
0.00/0.14	
0.00/0.14	        function(f7(_,_), [
0.00/0.14				   0, 1,
0.00/0.14				   1, 0 ]),
0.00/0.14	
0.00/0.14	        relation(arrow_s0(_,_), [
0.00/0.14				   1, 0,
0.00/0.14				   0, 1 ]),
0.00/0.14	
0.00/0.14	        relation(gtrsim_s0(_,_), [
0.00/0.14				   1, 0,
0.00/0.14				   0, 1 ]),
0.00/0.14	
0.00/0.14	        relation(sqsupsetStar_s0(_,_), [
0.00/0.14				   0, 1,
0.00/0.14				   0, 0 ]),
0.00/0.14	
0.00/0.14	        relation(sqsupset_s0(_,_), [
0.00/0.14				   0, 1,
0.00/0.14				   0, 0 ]),
0.00/0.14	
0.00/0.14	        relation(succeq_s0(_,_), [
0.00/0.14				   0, 0,
0.00/0.14				   0, 0 ])
0.00/0.14	]).
0.00/0.14	
0.00/0.14	============================== end of model ==========================
0.00/0.14	
0.00/0.14	============================== STATISTICS ============================
0.00/0.14	
0.00/0.14	For domain size 2.
0.00/0.14	
0.00/0.14	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.00/0.14	Ground clauses: seen=90, kept=90.
0.00/0.14	Selections=68, assignments=125, propagations=56, current_models=1.
0.00/0.14	Rewrite_terms=664, rewrite_bools=445, indexes=98.
0.00/0.14	Rules_from_neg_clauses=16, cross_offs=16.
0.00/0.14	
0.00/0.14	============================== end of statistics =====================
0.00/0.14	
0.00/0.14	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.00/0.14	
0.00/0.14	Exiting with 1 model.
0.00/0.14	
0.00/0.14	Process 38208 exit (max_models) Thu Mar 28 22:22:14 2019
0.00/0.14	The process finished Thu Mar 28 22:22:14 2019
0.00/0.14	
0.00/0.14	
0.00/0.14	Mace4 cooked interpretation:
0.00/0.14	
0.00/0.14	% number = 1
0.00/0.14	% seconds = 0
0.00/0.14	
0.00/0.14	% Interpretation of size 2
0.00/0.14	
0.00/0.14	f3(0) = 1.
0.00/0.14	f3(1) = 0.
0.00/0.14	
0.00/0.14	f5(0) = 1.
0.00/0.14	f5(1) = 0.
0.00/0.14	
0.00/0.14	f8(0) = 0.
0.00/0.14	f8(1) = 0.
0.00/0.14	
0.00/0.14	f2(0,0) = 0.
0.00/0.14	f2(0,1) = 0.
0.00/0.14	f2(1,0) = 0.
0.00/0.14	f2(1,1) = 0.
0.00/0.14	
0.00/0.14	f7(0,0) = 0.
0.00/0.14	f7(0,1) = 1.
0.00/0.14	f7(1,0) = 1.
0.00/0.14	f7(1,1) = 0.
0.00/0.14	
0.00/0.14	  arrow_s0(0,0).
0.00/0.14	- arrow_s0(0,1).
0.00/0.14	- arrow_s0(1,0).
0.00/0.14	  arrow_s0(1,1).
0.00/0.14	
0.00/0.14	  gtrsim_s0(0,0).
0.00/0.14	- gtrsim_s0(0,1).
0.00/0.14	- gtrsim_s0(1,0).
0.00/0.14	  gtrsim_s0(1,1).
0.00/0.14	
0.00/0.14	- sqsupsetStar_s0(0,0).
0.00/0.14	  sqsupsetStar_s0(0,1).
0.00/0.14	- sqsupsetStar_s0(1,0).
0.00/0.14	- sqsupsetStar_s0(1,1).
0.00/0.14	
0.00/0.14	- sqsupset_s0(0,0).
0.00/0.14	  sqsupset_s0(0,1).
0.00/0.14	- sqsupset_s0(1,0).
0.00/0.14	- sqsupset_s0(1,1).
0.00/0.14	
0.00/0.14	- succeq_s0(0,0).
0.00/0.14	- succeq_s0(0,1).
0.00/0.14	- succeq_s0(1,0).
0.00/0.14	- succeq_s0(1,1).
0.00/0.14	
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 Empty
0.00/0.14	-> Rules:
0.00/0.14	 f(x:S,x:S) -> f(g(x:S),x:S)
0.00/0.14	 g(x:S) -> s(x:S)
0.00/0.14	->Strongly Connected Components:
0.00/0.14	 There is no strongly connected component
0.00/0.14	
0.00/0.14	The problem is finite.
0.00/0.14	EOF