0.00/0.06	YES
0.00/0.06	
0.00/0.06	Problem 1: 
0.00/0.06	
0.00/0.06	(VAR v_NonEmpty:S x:S y:S)
0.00/0.06	(RULES
0.00/0.06	pin(a) -> pout(b)
0.00/0.06	pin(b) -> pout(c)
0.00/0.06	tc(x:S) -> x:S
0.00/0.06	tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	)
0.00/0.06	
0.00/0.06	Problem 1: 
0.00/0.06	Valid CTRS Processor:
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	-> The system is a deterministic 3-CTRS.
0.00/0.06	
0.00/0.06	Problem 1: 
0.00/0.06	
0.00/0.06	Dependency Pairs Processor:
0.00/0.06	
0.00/0.06	Conditional Termination Problem 1:
0.00/0.06	-> Pairs:
0.00/0.06	 Empty
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	
0.00/0.06	Conditional Termination Problem 2:
0.00/0.06	-> Pairs:
0.00/0.06	 TC(x:S) -> PIN(x:S)
0.00/0.06	 TC(x:S) -> TC(z) | pin(x:S) ->* pout(z)
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	
0.00/0.06	
0.00/0.06	The problem is decomposed in 2 subproblems.
0.00/0.06	
0.00/0.06	Problem 1.1: 
0.00/0.06	
0.00/0.06	SCC Processor:
0.00/0.06	-> Pairs:
0.00/0.06	 Empty
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	->Strongly Connected Components:
0.00/0.06	 There is no strongly connected component
0.00/0.06	
0.00/0.06	The problem is finite.
0.00/0.06	
0.00/0.06	Problem 1.2: 
0.00/0.06	
0.00/0.06	SCC Processor:
0.00/0.06	-> Pairs:
0.00/0.06	 TC(x:S) -> PIN(x:S)
0.00/0.06	 TC(x:S) -> TC(z) | pin(x:S) ->* pout(z)
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	->Strongly Connected Components:
0.00/0.06	->->Cycle:
0.00/0.06	->->-> Pairs:
0.00/0.06	 TC(x:S) -> TC(z) | pin(x:S) ->* pout(z)
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	->->-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	
0.00/0.06	Problem 1.2: 
0.00/0.06	
0.00/0.06	Reduction Pair Processor:
0.00/0.06	-> Pairs:
0.00/0.06	 TC(x:S) -> TC(z) | pin(x:S) ->* pout(z)
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	-> Needed rules:
0.00/0.06	 Empty
0.00/0.06	-> Usable rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	->Mace4 Output:
0.00/0.06	 ============================== Mace4 =================================
0.00/0.06	Mace4 (64) version 2009-11A, November 2009.
0.00/0.06	Process 64907 was started by sandbox on n155.star.cs.uiowa.edu,
0.00/0.06	Fri Mar 29 01:49:27 2019
0.00/0.06	The command was "./mace4 -c -f /tmp/mace41957747793424238335.in".
0.00/0.06	============================== end of head ===========================
0.00/0.06	
0.00/0.06	============================== INPUT =================================
0.00/0.06	
0.00/0.06	% Reading from file /tmp/mace41957747793424238335.in
0.00/0.06	
0.00/0.06	assign(max_seconds,20).
0.00/0.06	
0.00/0.06	formulas(assumptions).
0.00/0.06	arrowStar_s0(x,x) # label(reflexivity).
0.00/0.06	arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility).
0.00/0.06	gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.06	succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
0.00/0.06	gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
0.00/0.06	arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence).
0.00/0.06	arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence).
0.00/0.06	arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence).
0.00/0.06	arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
0.00/0.06	arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f13(x1),f13(y)) # label(congruence).
0.00/0.06	arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
0.00/0.06	arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
0.00/0.06	arrow_s0(f2(f4),f8(f5)) # label(replacement).
0.00/0.06	arrow_s0(f2(f5),f8(f6)) # label(replacement).
0.00/0.06	arrow_s0(f14(x3,x4),x3) # label(replacement).
0.00/0.06	arrow_s0(f14(x3,x4),x4) # label(replacement).
0.00/0.06	arrowN_s0(f14(x3,x4),x3) # label(replacement).
0.00/0.06	arrowN_s0(f14(x3,x4),x4) # label(replacement).
0.00/0.06	arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
0.00/0.06	arrowStar_s0(f2(x1),f8(f9)) -> sqsupset_s0(f13(x1),f13(f9)) # label(replacement).
0.00/0.06	sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.06	sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.06	end_of_list.
0.00/0.06	
0.00/0.06	formulas(goals).
0.00/0.06	(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
0.00/0.06	end_of_list.
0.00/0.06	
0.00/0.06	============================== end of input ==========================
0.00/0.06	
0.00/0.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.00/0.06	
0.00/0.06	% Formulas that are not ordinary clauses:
0.00/0.06	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.06	2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.06	3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.06	4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.06	5 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	7 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	8 arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	9 arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	10 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	12 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	13 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	14 arrowN_s0(x1,y) -> arrowN_s0(f13(x1),f13(y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	15 arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	16 arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
0.00/0.06	17 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.06	18 arrowStar_s0(f2(x1),f8(f9)) -> sqsupset_s0(f13(x1),f13(f9)) # label(replacement) # label(non_clause).  [assumption].
0.00/0.06	19 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
0.00/0.06	20 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
0.00/0.06	21 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].
0.00/0.06	
0.00/0.06	============================== end of process non-clausal formulas ===
0.00/0.06	
0.00/0.06	============================== CLAUSES FOR SEARCH ====================
0.00/0.06	
0.00/0.06	formulas(mace4_clauses).
0.00/0.06	arrowStar_s0(x,x) # label(reflexivity).
0.00/0.06	-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility).
0.00/0.06	-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.06	-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
0.00/0.06	-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
0.00/0.06	-arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence).
0.00/0.06	-arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).
0.00/0.06	-arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence).
0.00/0.06	-arrow_s0(x,y) | arrow_s0(f14(x,z),f14(y,z)) # label(congruence).
0.00/0.06	-arrow_s0(x,y) | arrow_s0(f14(z,x),f14(z,y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f2(x),f2(y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f13(x),f13(y)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f14(x,z),f14(y,z)) # label(congruence).
0.00/0.06	-arrowN_s0(x,y) | arrowN_s0(f14(z,x),f14(z,y)) # label(congruence).
0.00/0.06	arrow_s0(f2(f4),f8(f5)) # label(replacement).
0.00/0.06	arrow_s0(f2(f5),f8(f6)) # label(replacement).
0.00/0.06	arrow_s0(f14(x,y),x) # label(replacement).
0.00/0.06	arrow_s0(f14(x,y),y) # label(replacement).
0.00/0.06	arrowN_s0(f14(x,y),x) # label(replacement).
0.00/0.06	arrowN_s0(f14(x,y),y) # label(replacement).
0.00/0.06	-arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
0.00/0.06	-arrowStar_s0(f2(x),f8(f9)) | sqsupset_s0(f13(x),f13(f9)) # label(replacement).
0.00/0.06	-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
0.00/0.06	-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
0.00/0.06	-sqsupsetStar_s0(x,x) # label(wellfoundedness).
0.00/0.06	end_of_list.
0.00/0.06	
0.00/0.06	============================== end of clauses for search =============
0.00/0.06	
0.00/0.06	% There are no natural numbers in the input.
0.00/0.06	
0.00/0.06	============================== DOMAIN SIZE 2 =========================
0.00/0.06	
0.00/0.06	============================== MODEL =================================
0.00/0.06	
0.00/0.06	interpretation( 2, [number=1, seconds=0], [
0.00/0.06	
0.00/0.06	        function(f4, [ 0 ]),
0.00/0.06	
0.00/0.06	        function(f5, [ 0 ]),
0.00/0.06	
0.00/0.06	        function(f6, [ 0 ]),
0.00/0.06	
0.00/0.06	        function(f9, [ 1 ]),
0.00/0.06	
0.00/0.06	        function(f12(_), [ 0, 0 ]),
0.00/0.06	
0.00/0.06	        function(f13(_), [ 0, 0 ]),
0.00/0.06	
0.00/0.06	        function(f2(_), [ 0, 0 ]),
0.00/0.06	
0.00/0.06	        function(f3(_), [ 0, 0 ]),
0.00/0.06	
0.00/0.06	        function(f8(_), [ 0, 1 ]),
0.00/0.06	
0.00/0.06	        function(f14(_,_), [
0.00/0.06				   0, 1,
0.00/0.06				   1, 1 ]),
0.00/0.06	
0.00/0.06	        relation(arrowN_s0(_,_), [
0.00/0.06				   1, 0,
0.00/0.06				   1, 1 ]),
0.00/0.06	
0.00/0.06	        relation(arrowStar_s0(_,_), [
0.00/0.06				   1, 0,
0.00/0.06				   1, 1 ]),
0.00/0.06	
0.00/0.06	        relation(arrow_s0(_,_), [
0.00/0.06				   1, 0,
0.00/0.06				   1, 1 ]),
0.00/0.06	
0.00/0.06	        relation(gtrsim_s0(_,_), [
0.00/0.06				   1, 0,
0.00/0.06				   1, 1 ]),
0.00/0.06	
0.00/0.06	        relation(sqsupsetStar_s0(_,_), [
0.00/0.06				   0, 0,
0.00/0.06				   0, 0 ]),
0.00/0.06	
0.00/0.06	        relation(sqsupset_s0(_,_), [
0.00/0.06				   0, 0,
0.00/0.06				   0, 0 ]),
0.00/0.06	
0.00/0.06	        relation(succeq_s0(_,_), [
0.00/0.06				   0, 0,
0.00/0.06				   0, 0 ])
0.00/0.06	]).
0.00/0.06	
0.00/0.06	============================== end of model ==========================
0.00/0.06	
0.00/0.06	============================== STATISTICS ============================
0.00/0.06	
0.00/0.06	For domain size 2.
0.00/0.06	
0.00/0.06	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
0.00/0.06	Ground clauses: seen=136, kept=132.
0.00/0.06	Selections=27, assignments=35, propagations=50, current_models=1.
0.00/0.06	Rewrite_terms=388, rewrite_bools=277, indexes=88.
0.00/0.06	Rules_from_neg_clauses=13, cross_offs=13.
0.00/0.06	
0.00/0.06	============================== end of statistics =====================
0.00/0.06	
0.00/0.06	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
0.00/0.06	
0.00/0.06	Exiting with 1 model.
0.00/0.06	
0.00/0.06	Process 64907 exit (max_models) Fri Mar 29 01:49:27 2019
0.00/0.06	The process finished Fri Mar 29 01:49:27 2019
0.00/0.06	
0.00/0.06	
0.00/0.06	Mace4 cooked interpretation:
0.00/0.06	
0.00/0.06	% number = 1
0.00/0.06	% seconds = 0
0.00/0.06	
0.00/0.06	% Interpretation of size 2
0.00/0.06	
0.00/0.06	f4 = 0.
0.00/0.06	
0.00/0.06	f5 = 0.
0.00/0.06	
0.00/0.06	f6 = 0.
0.00/0.06	
0.00/0.06	f9 = 1.
0.00/0.06	
0.00/0.06	f12(0) = 0.
0.00/0.06	f12(1) = 0.
0.00/0.06	
0.00/0.06	f13(0) = 0.
0.00/0.06	f13(1) = 0.
0.00/0.06	
0.00/0.06	f2(0) = 0.
0.00/0.06	f2(1) = 0.
0.00/0.06	
0.00/0.06	f3(0) = 0.
0.00/0.06	f3(1) = 0.
0.00/0.06	
0.00/0.06	f8(0) = 0.
0.00/0.06	f8(1) = 1.
0.00/0.06	
0.00/0.06	f14(0,0) = 0.
0.00/0.06	f14(0,1) = 1.
0.00/0.06	f14(1,0) = 1.
0.00/0.06	f14(1,1) = 1.
0.00/0.06	
0.00/0.06	  arrowN_s0(0,0).
0.00/0.06	- arrowN_s0(0,1).
0.00/0.06	  arrowN_s0(1,0).
0.00/0.06	  arrowN_s0(1,1).
0.00/0.06	
0.00/0.06	  arrowStar_s0(0,0).
0.00/0.06	- arrowStar_s0(0,1).
0.00/0.06	  arrowStar_s0(1,0).
0.00/0.06	  arrowStar_s0(1,1).
0.00/0.06	
0.00/0.06	  arrow_s0(0,0).
0.00/0.06	- arrow_s0(0,1).
0.00/0.06	  arrow_s0(1,0).
0.00/0.06	  arrow_s0(1,1).
0.00/0.06	
0.00/0.06	  gtrsim_s0(0,0).
0.00/0.06	- gtrsim_s0(0,1).
0.00/0.06	  gtrsim_s0(1,0).
0.00/0.06	  gtrsim_s0(1,1).
0.00/0.06	
0.00/0.06	- sqsupsetStar_s0(0,0).
0.00/0.06	- sqsupsetStar_s0(0,1).
0.00/0.06	- sqsupsetStar_s0(1,0).
0.00/0.06	- sqsupsetStar_s0(1,1).
0.00/0.06	
0.00/0.06	- sqsupset_s0(0,0).
0.00/0.06	- sqsupset_s0(0,1).
0.00/0.06	- sqsupset_s0(1,0).
0.00/0.06	- sqsupset_s0(1,1).
0.00/0.06	
0.00/0.06	- succeq_s0(0,0).
0.00/0.06	- succeq_s0(0,1).
0.00/0.06	- succeq_s0(1,0).
0.00/0.06	- succeq_s0(1,1).
0.00/0.06	
0.00/0.06	
0.00/0.06	Problem 1.2: 
0.00/0.06	
0.00/0.06	SCC Processor:
0.00/0.06	-> Pairs:
0.00/0.06	 Empty
0.00/0.06	-> QPairs:
0.00/0.06	 Empty
0.00/0.06	-> Rules:
0.00/0.06	 pin(a) -> pout(b)
0.00/0.06	 pin(b) -> pout(c)
0.00/0.06	 tc(x:S) -> x:S
0.00/0.06	 tc(x:S) -> y:S | pin(x:S) ->* pout(z), tc(z) ->* y:S
0.00/0.06	->Strongly Connected Components:
0.00/0.06	 There is no strongly connected component
0.00/0.06	
0.00/0.06	The problem is finite.
0.00/0.07	EOF