0.00/0.03	YES
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	(VAR v_NonEmpty:S x:S)
0.00/0.03	(RULES
0.00/0.03	a -> a | b ->* x:S, c ->* x:S
0.00/0.03	b -> d | d ->* x:S, e ->* x:S
0.00/0.03	c -> d | d ->* x:S, e ->* x:S
0.00/0.03	)
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	Valid CTRS Processor:
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	-> The system is a deterministic 3-CTRS.
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Dependency Pairs Processor:
0.00/0.03	
0.00/0.03	Conditional Termination Problem 1:
0.00/0.03	-> Pairs:
0.00/0.03	 A -> A | b ->* x:S, c ->* x:S
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	
0.00/0.03	Conditional Termination Problem 2:
0.00/0.03	-> Pairs:
0.00/0.03	 A -> B
0.00/0.03	 A -> C | b ->* x:S
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	
0.00/0.03	
0.00/0.03	The problem is decomposed in 2 subproblems.
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 A -> A | b ->* x:S, c ->* x:S
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	->Strongly Connected Components:
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 A -> A | b ->* x:S, c ->* x:S
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	->->-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	Reduction Pair Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 A -> A | b ->* x:S, c ->* x:S
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	-> Needed rules:
0.00/0.03	 Empty
0.00/0.03	-> Usable rules:
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	->Mace4 Output:
0.00/0.03	 ============================== Mace4 =================================
0.00/0.03	Mace4 (64) version 2009-11A, November 2009.
0.00/0.03	Process 62940 was started by sandbox on n014.star.cs.uiowa.edu,
0.00/0.03	Fri Mar 29 01:41:27 2019
0.00/0.03	The command was "./mace4 -c -f /tmp/mace41804289383846930886.in".
0.00/0.03	============================== end of head ===========================
0.00/0.03	
0.00/0.03	============================== INPUT =================================
0.00/0.03	
0.00/0.03	% Reading from file /tmp/mace41804289383846930886.in
0.00/0.03	
0.00/0.03	assign(max_seconds,20).
0.00/0.03	
0.00/0.03	formulas(assumptions).
0.00/0.03	arrowStar_s0(x,x) # label(reflexivity).
0.00/0.03	arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility).
0.00/0.03	gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.03	succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.03	gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
0.00/0.03	arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence).
0.00/0.03	arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence).
0.00/0.03	arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence).
0.00/0.03	arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence).
0.00/0.03	arrowStar_s0(f5,x1) & arrowStar_s0(f6,x1) -> arrow_s0(f3,f5) # label(replacement).
0.00/0.03	arrowStar_s0(f5,x1) & arrowStar_s0(f6,x1) -> arrow_s0(f4,f5) # label(replacement).
0.00/0.03	arrow_s0(f13(x2,x3),x2) # label(replacement).
0.00/0.03	arrow_s0(f13(x2,x3),x3) # label(replacement).
0.00/0.03	arrowN_s0(f13(x2,x3),x2) # label(replacement).
0.00/0.03	arrowN_s0(f13(x2,x3),x3) # label(replacement).
0.00/0.03	arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
0.00/0.03	arrowStar_s0(f3,x1) & arrowStar_s0(f4,x1) -> sqsupset_s0(f10,f10) # label(replacement).
0.00/0.03	sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.03	sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	formulas(goals).
0.00/0.03	(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	============================== end of input ==========================
0.00/0.03	
0.00/0.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.00/0.03	
0.00/0.03	% Formulas that are not ordinary clauses:
0.00/0.03	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.03	2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.03	3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.03	4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.03	5 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	6 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	7 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	8 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.03	9 arrowStar_s0(f5,x1) & arrowStar_s0(f6,x1) -> arrow_s0(f3,f5) # label(replacement) # label(non_clause).  [assumption].
0.00/0.03	10 arrowStar_s0(f5,x1) & arrowStar_s0(f6,x1) -> arrow_s0(f4,f5) # label(replacement) # label(non_clause).  [assumption].
0.00/0.03	11 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.03	12 arrowStar_s0(f3,x1) & arrowStar_s0(f4,x1) -> sqsupset_s0(f10,f10) # label(replacement) # label(non_clause).  [assumption].
0.00/0.03	13 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.03	14 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.03	15 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].
0.00/0.03	
0.00/0.03	============================== end of process non-clausal formulas ===
0.00/0.03	
0.00/0.03	============================== CLAUSES FOR SEARCH ====================
0.00/0.03	
0.00/0.03	formulas(mace4_clauses).
0.00/0.03	arrowStar_s0(x,x) # label(reflexivity).
0.00/0.03	-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility).
0.00/0.03	-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.03	-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.03	-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f13(x,z),f13(y,z)) # label(congruence).
0.00/0.03	-arrow_s0(x,y) | arrow_s0(f13(z,x),f13(z,y)) # label(congruence).
0.00/0.03	-arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence).
0.00/0.03	-arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence).
0.00/0.03	-arrowStar_s0(f5,x) | -arrowStar_s0(f6,x) | arrow_s0(f3,f5) # label(replacement).
0.00/0.03	-arrowStar_s0(f5,x) | -arrowStar_s0(f6,x) | arrow_s0(f4,f5) # label(replacement).
0.00/0.03	arrow_s0(f13(x,y),x) # label(replacement).
0.00/0.03	arrow_s0(f13(x,y),y) # label(replacement).
0.00/0.03	arrowN_s0(f13(x,y),x) # label(replacement).
0.00/0.03	arrowN_s0(f13(x,y),y) # label(replacement).
0.00/0.03	-arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
0.00/0.03	-arrowStar_s0(f3,x) | -arrowStar_s0(f4,x) | sqsupset_s0(f10,f10) # label(replacement).
0.00/0.03	-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.03	-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.03	-sqsupsetStar_s0(x,x) # label(wellfoundedness).
0.00/0.03	end_of_list.
0.00/0.03	
0.00/0.03	============================== end of clauses for search =============
0.00/0.03	
0.00/0.03	% There are no natural numbers in the input.
0.00/0.03	
0.00/0.03	============================== DOMAIN SIZE 2 =========================
0.00/0.03	
0.00/0.03	============================== STATISTICS ============================
0.00/0.03	
0.00/0.03	For domain size 2.
0.00/0.03	
0.00/0.03	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.00/0.03	Ground clauses: seen=106, kept=102.
0.00/0.03	Selections=2, assignments=3, propagations=28, current_models=0.
0.00/0.03	Rewrite_terms=60, rewrite_bools=88, indexes=12.
0.00/0.03	Rules_from_neg_clauses=8, cross_offs=8.
0.00/0.03	
0.00/0.03	============================== end of statistics =====================
0.00/0.03	
0.00/0.03	============================== DOMAIN SIZE 3 =========================
0.00/0.03	
0.00/0.03	============================== MODEL =================================
0.00/0.03	
0.00/0.03	interpretation( 3, [number=1, seconds=0], [
0.00/0.03	
0.00/0.03	        function(f10, [ 0 ]),
0.00/0.03	
0.00/0.03	        function(f3, [ 0 ]),
0.00/0.03	
0.00/0.03	        function(f4, [ 1 ]),
0.00/0.03	
0.00/0.03	        function(f5, [ 0 ]),
0.00/0.03	
0.00/0.03	        function(f6, [ 1 ]),
0.00/0.03	
0.00/0.03	        function(f13(_,_), [
0.00/0.03				   0, 2, 2,
0.00/0.03				   2, 1, 2,
0.00/0.03				   2, 2, 2 ]),
0.00/0.03	
0.00/0.03	        relation(arrowN_s0(_,_), [
0.00/0.03				   1, 0, 0,
0.00/0.03				   0, 1, 0,
0.00/0.03				   1, 1, 1 ]),
0.00/0.03	
0.00/0.03	        relation(arrowStar_s0(_,_), [
0.00/0.03				   1, 0, 0,
0.00/0.03				   0, 1, 0,
0.00/0.03				   1, 1, 1 ]),
0.00/0.03	
0.00/0.03	        relation(arrow_s0(_,_), [
0.00/0.03				   1, 0, 0,
0.00/0.03				   0, 1, 0,
0.00/0.03				   1, 1, 1 ]),
0.00/0.03	
0.00/0.03	        relation(gtrsim_s0(_,_), [
0.00/0.03				   1, 0, 0,
0.00/0.03				   0, 1, 0,
0.00/0.03				   1, 1, 1 ]),
0.00/0.03	
0.00/0.03	        relation(sqsupsetStar_s0(_,_), [
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0 ]),
0.00/0.03	
0.00/0.03	        relation(sqsupset_s0(_,_), [
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0 ]),
0.00/0.03	
0.00/0.03	        relation(succeq_s0(_,_), [
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0,
0.00/0.03				   0, 0, 0 ])
0.00/0.03	]).
0.00/0.03	
0.00/0.03	============================== end of model ==========================
0.00/0.03	
0.00/0.03	============================== STATISTICS ============================
0.00/0.03	
0.00/0.03	For domain size 3.
0.00/0.03	
0.00/0.03	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.00/0.03	Ground clauses: seen=312, kept=303.
0.00/0.03	Selections=27, assignments=29, propagations=51, current_models=1.
0.00/0.03	Rewrite_terms=294, rewrite_bools=443, indexes=33.
0.00/0.03	Rules_from_neg_clauses=8, cross_offs=19.
0.00/0.03	
0.00/0.03	============================== end of statistics =====================
0.00/0.03	
0.00/0.03	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.00/0.03	
0.00/0.03	Exiting with 1 model.
0.00/0.03	
0.00/0.03	Process 62940 exit (max_models) Fri Mar 29 01:41:27 2019
0.00/0.03	The process finished Fri Mar 29 01:41:27 2019
0.00/0.03	
0.00/0.03	
0.00/0.03	Mace4 cooked interpretation:
0.00/0.03	
0.00/0.03	% number = 1
0.00/0.03	% seconds = 0
0.00/0.03	
0.00/0.03	% Interpretation of size 3
0.00/0.03	
0.00/0.03	f10 = 0.
0.00/0.03	
0.00/0.03	f3 = 0.
0.00/0.03	
0.00/0.03	f4 = 1.
0.00/0.03	
0.00/0.03	f5 = 0.
0.00/0.03	
0.00/0.03	f6 = 1.
0.00/0.03	
0.00/0.03	f13(0,0) = 0.
0.00/0.03	f13(0,1) = 2.
0.00/0.03	f13(0,2) = 2.
0.00/0.03	f13(1,0) = 2.
0.00/0.03	f13(1,1) = 1.
0.00/0.03	f13(1,2) = 2.
0.00/0.03	f13(2,0) = 2.
0.00/0.03	f13(2,1) = 2.
0.00/0.03	f13(2,2) = 2.
0.00/0.03	
0.00/0.03	  arrowN_s0(0,0).
0.00/0.03	- arrowN_s0(0,1).
0.00/0.03	- arrowN_s0(0,2).
0.00/0.03	- arrowN_s0(1,0).
0.00/0.03	  arrowN_s0(1,1).
0.00/0.03	- arrowN_s0(1,2).
0.00/0.03	  arrowN_s0(2,0).
0.00/0.03	  arrowN_s0(2,1).
0.00/0.03	  arrowN_s0(2,2).
0.00/0.03	
0.00/0.03	  arrowStar_s0(0,0).
0.00/0.03	- arrowStar_s0(0,1).
0.00/0.03	- arrowStar_s0(0,2).
0.00/0.03	- arrowStar_s0(1,0).
0.00/0.03	  arrowStar_s0(1,1).
0.00/0.03	- arrowStar_s0(1,2).
0.00/0.03	  arrowStar_s0(2,0).
0.00/0.03	  arrowStar_s0(2,1).
0.00/0.03	  arrowStar_s0(2,2).
0.00/0.03	
0.00/0.03	  arrow_s0(0,0).
0.00/0.03	- arrow_s0(0,1).
0.00/0.03	- arrow_s0(0,2).
0.00/0.03	- arrow_s0(1,0).
0.00/0.03	  arrow_s0(1,1).
0.00/0.03	- arrow_s0(1,2).
0.00/0.03	  arrow_s0(2,0).
0.00/0.03	  arrow_s0(2,1).
0.00/0.03	  arrow_s0(2,2).
0.00/0.03	
0.00/0.03	  gtrsim_s0(0,0).
0.00/0.03	- gtrsim_s0(0,1).
0.00/0.03	- gtrsim_s0(0,2).
0.00/0.03	- gtrsim_s0(1,0).
0.00/0.03	  gtrsim_s0(1,1).
0.00/0.03	- gtrsim_s0(1,2).
0.00/0.03	  gtrsim_s0(2,0).
0.00/0.03	  gtrsim_s0(2,1).
0.00/0.03	  gtrsim_s0(2,2).
0.00/0.03	
0.00/0.03	- sqsupsetStar_s0(0,0).
0.00/0.03	- sqsupsetStar_s0(0,1).
0.00/0.03	- sqsupsetStar_s0(0,2).
0.00/0.03	- sqsupsetStar_s0(1,0).
0.00/0.03	- sqsupsetStar_s0(1,1).
0.00/0.03	- sqsupsetStar_s0(1,2).
0.00/0.03	- sqsupsetStar_s0(2,0).
0.00/0.03	- sqsupsetStar_s0(2,1).
0.00/0.03	- sqsupsetStar_s0(2,2).
0.00/0.03	
0.00/0.03	- sqsupset_s0(0,0).
0.00/0.03	- sqsupset_s0(0,1).
0.00/0.03	- sqsupset_s0(0,2).
0.00/0.03	- sqsupset_s0(1,0).
0.00/0.03	- sqsupset_s0(1,1).
0.00/0.03	- sqsupset_s0(1,2).
0.00/0.03	- sqsupset_s0(2,0).
0.00/0.03	- sqsupset_s0(2,1).
0.00/0.03	- sqsupset_s0(2,2).
0.00/0.03	
0.00/0.03	- succeq_s0(0,0).
0.00/0.03	- succeq_s0(0,1).
0.00/0.03	- succeq_s0(0,2).
0.00/0.03	- succeq_s0(1,0).
0.00/0.03	- succeq_s0(1,1).
0.00/0.03	- succeq_s0(1,2).
0.00/0.03	- succeq_s0(2,0).
0.00/0.03	- succeq_s0(2,1).
0.00/0.03	- succeq_s0(2,2).
0.00/0.03	
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 Empty
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	
0.00/0.03	Problem 1.2: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 A -> B
0.00/0.03	 A -> C | b ->* x:S
0.00/0.03	-> QPairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 a -> a | b ->* x:S, c ->* x:S
0.00/0.03	 b -> d | d ->* x:S, e ->* x:S
0.00/0.03	 c -> d | d ->* x:S, e ->* x:S
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	EOF