120.61/120.81	YES
120.61/120.81	
120.61/120.81	Problem 1: 
120.61/120.81	
120.61/120.81	(VAR v_NonEmpty:S x:S y:S)
120.61/120.81	(RULES
120.61/120.81	a -> h(b)
120.61/120.81	a -> h(c)
120.61/120.81	f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	)
120.61/120.81	
120.61/120.81	Problem 1: 
120.61/120.81	Valid CTRS Processor:
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> The system is a deterministic 3-CTRS.
120.61/120.81	
120.61/120.81	Problem 1: 
120.61/120.81	
120.61/120.81	Dependency Pairs Processor:
120.61/120.81	
120.61/120.81	Conditional Termination Problem 1:
120.61/120.81	-> Pairs:
120.61/120.81	 G(x:S,b) -> F(c) | f(b) ->* x:S, x:S ->* c
120.61/120.81	 G(x:S,b) -> G(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	
120.61/120.81	Conditional Termination Problem 2:
120.61/120.81	-> Pairs:
120.61/120.81	 F(x:S) -> A
120.61/120.81	 G(x:S,b) -> F(b)
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	
120.61/120.81	
120.61/120.81	The problem is decomposed in 2 subproblems.
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	SCC Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(x:S,b) -> F(c) | f(b) ->* x:S, x:S ->* c
120.61/120.81	 G(x:S,b) -> G(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	->Strongly Connected Components:
120.61/120.81	->->Cycle:
120.61/120.81	->->-> Pairs:
120.61/120.81	 G(x:S,b) -> G(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	->->-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	Simplification and Narrowing on Condition Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(x:S,b) -> G(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	->Narrowed Pairs:
120.61/120.81	->->Original Pair:
120.61/120.81	 G(x:S,b) -> G(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	->-> Narrowed pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(b), b ->* x3:S, x3:S ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	SCC Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(b), b ->* x3:S, x3:S ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	->Strongly Connected Components:
120.61/120.81	->->Cycle:
120.61/120.81	->->-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(b), b ->* x3:S, x3:S ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	->->-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	Reduction Pair Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(b), b ->* x3:S, x3:S ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> Needed rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	-> Usable rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	->Mace4 Output:
120.61/120.81	 ============================== Mace4 =================================
120.61/120.81	Mace4 (64) version 2009-11A, November 2009.
120.61/120.81	Process 10196 was started by sandbox2 on n124.star.cs.uiowa.edu,
120.61/120.81	Fri Mar 29 01:44:08 2019
120.61/120.81	The command was "./mace4 -c -f /tmp/mace45726603361159126505.in".
120.61/120.81	============================== end of head ===========================
120.61/120.81	
120.61/120.81	============================== INPUT =================================
120.61/120.81	
120.61/120.81	% Reading from file /tmp/mace45726603361159126505.in
120.61/120.81	
120.61/120.81	assign(max_seconds,20).
120.61/120.81	
120.61/120.81	formulas(assumptions).
120.61/120.81	arrowStar_s0(x,x) # label(reflexivity).
120.61/120.81	arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility).
120.61/120.81	gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence).
120.61/120.81	arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
120.61/120.81	arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f4(x1,x2),f4(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f4(x1,x2),f4(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
120.61/120.81	arrow_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrow_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	arrowStar_s0(f2,f8(x2)) -> arrow_s0(f3(x1),x2) # label(replacement).
120.61/120.81	arrow_s0(f14(x4,x5),x4) # label(replacement).
120.61/120.81	arrow_s0(f14(x4,x5),x5) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	arrowStar_s0(f2,f8(x2)) -> arrowN_s0(f3(x1),x2) # label(replacement).
120.61/120.81	arrowN_s0(f14(x4,x5),x4) # label(replacement).
120.61/120.81	arrowN_s0(f14(x4,x5),x5) # label(replacement).
120.61/120.81	arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
120.61/120.81	arrowStar_s0(f2,f8(f5)) & arrowStar_s0(f5,x3) & arrowStar_s0(x3,f6) -> sqsupset_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement).
120.61/120.81	arrowStar_s0(f3(f5),f6) -> succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement).
120.61/120.81	arrowStar_s0(f2,f8(f6)) & arrowStar_s0(f6,x3) & arrowStar_s0(x3,f6) -> succeq_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement).
120.61/120.81	sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
120.61/120.81	sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	formulas(goals).
120.61/120.81	(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	============================== end of input ==========================
120.61/120.81	
120.61/120.81	============================== PROCESS NON-CLAUSAL FORMULAS ==========
120.61/120.81	
120.61/120.81	% Formulas that are not ordinary clauses:
120.61/120.81	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	5 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	6 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	7 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	8 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	9 arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	10 arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	12 arrowN_s0(x1,y) -> arrowN_s0(f4(x1,x2),f4(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	13 arrowN_s0(x2,y) -> arrowN_s0(f4(x1,x2),f4(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	14 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	15 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	16 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	17 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	18 arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	19 arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	20 arrowStar_s0(f2,f8(x2)) -> arrow_s0(f3(x1),x2) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	21 arrowStar_s0(f2,f8(x2)) -> arrowN_s0(f3(x1),x2) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	22 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
120.61/120.81	23 arrowStar_s0(f2,f8(f5)) & arrowStar_s0(f5,x3) & arrowStar_s0(x3,f6) -> sqsupset_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	24 arrowStar_s0(f3(f5),f6) -> succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	25 arrowStar_s0(f2,f8(f6)) & arrowStar_s0(f6,x3) & arrowStar_s0(x3,f6) -> succeq_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	26 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
120.61/120.81	27 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	28 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].
120.61/120.81	
120.61/120.81	============================== end of process non-clausal formulas ===
120.61/120.81	
120.61/120.81	============================== CLAUSES FOR SEARCH ====================
120.61/120.81	
120.61/120.81	formulas(mace4_clauses).
120.61/120.81	arrowStar_s0(x,x) # label(reflexivity).
120.61/120.81	-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility).
120.61/120.81	-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f4(x,z),f4(y,z)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f4(z,x),f4(z,y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f14(x,z),f14(y,z)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f14(z,x),f14(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f4(x,z),f4(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f4(z,x),f4(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f14(x,z),f14(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f14(z,x),f14(z,y)) # label(congruence).
120.61/120.81	arrow_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrow_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	-arrowStar_s0(f2,f8(x)) | arrow_s0(f3(y),x) # label(replacement).
120.61/120.81	arrow_s0(f14(x,y),x) # label(replacement).
120.61/120.81	arrow_s0(f14(x,y),y) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	-arrowStar_s0(f2,f8(x)) | arrowN_s0(f3(y),x) # label(replacement).
120.61/120.81	arrowN_s0(f14(x,y),x) # label(replacement).
120.61/120.81	arrowN_s0(f14(x,y),y) # label(replacement).
120.61/120.81	-arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
120.61/120.81	-arrowStar_s0(f2,f8(f5)) | -arrowStar_s0(f5,x) | -arrowStar_s0(x,f6) | sqsupset_s0(f13(x,f5),f13(f3(f6),x)) # label(replacement).
120.61/120.81	-arrowStar_s0(f3(f5),f6) | succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement).
120.61/120.81	-arrowStar_s0(f2,f8(f6)) | -arrowStar_s0(f6,x) | -arrowStar_s0(x,f6) | succeq_s0(f13(x,f5),f13(f3(f6),x)) # label(replacement).
120.61/120.81	-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
120.61/120.81	-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
120.61/120.81	-sqsupsetStar_s0(x,x) # label(wellfoundedness).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	============================== end of clauses for search =============
120.61/120.81	
120.61/120.81	% There are no natural numbers in the input.
120.61/120.81	
120.61/120.81	============================== DOMAIN SIZE 2 =========================
120.61/120.81	
120.61/120.81	============================== MODEL =================================
120.61/120.81	
120.61/120.81	interpretation( 2, [number=1, seconds=0], [
120.61/120.81	
120.61/120.81	        function(f2, [ 0 ]),
120.61/120.81	
120.61/120.81	        function(f5, [ 0 ]),
120.61/120.81	
120.61/120.81	        function(f6, [ 1 ]),
120.61/120.81	
120.61/120.81	        function(f12(_), [ 0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f3(_), [ 1, 1 ]),
120.61/120.81	
120.61/120.81	        function(f8(_), [ 0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f13(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 1 ]),
120.61/120.81	
120.61/120.81	        function(f14(_,_), [
120.61/120.81				   0, 1,
120.61/120.81				   1, 1 ]),
120.61/120.81	
120.61/120.81	        function(f4(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(arrowN_s0(_,_), [
120.61/120.81				   1, 0,
120.61/120.81				   1, 1 ]),
120.61/120.81	
120.61/120.81	        relation(arrowStar_s0(_,_), [
120.61/120.81				   1, 0,
120.61/120.81				   1, 1 ]),
120.61/120.81	
120.61/120.81	        relation(arrow_s0(_,_), [
120.61/120.81				   1, 0,
120.61/120.81				   1, 1 ]),
120.61/120.81	
120.61/120.81	        relation(gtrsim_s0(_,_), [
120.61/120.81				   1, 1,
120.61/120.81				   1, 1 ]),
120.61/120.81	
120.61/120.81	        relation(sqsupsetStar_s0(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(sqsupset_s0(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(succeq_s0(_,_), [
120.61/120.81				   0, 1,
120.61/120.81				   0, 0 ])
120.61/120.81	]).
120.61/120.81	
120.61/120.81	============================== end of model ==========================
120.61/120.81	
120.61/120.81	============================== STATISTICS ============================
120.61/120.81	
120.61/120.81	For domain size 2.
120.61/120.81	
120.61/120.81	Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds).
120.61/120.81	Ground clauses: seen=185, kept=181.
120.61/120.81	Selections=197, assignments=374, propagations=981, current_models=1.
120.61/120.81	Rewrite_terms=4840, rewrite_bools=7708, indexes=1226.
120.61/120.81	Rules_from_neg_clauses=228, cross_offs=228.
120.61/120.81	
120.61/120.81	============================== end of statistics =====================
120.61/120.81	
120.61/120.81	User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
120.61/120.81	
120.61/120.81	Exiting with 1 model.
120.61/120.81	
120.61/120.81	Process 10196 exit (max_models) Fri Mar 29 01:44:08 2019
120.61/120.81	The process finished Fri Mar 29 01:44:08 2019
120.61/120.81	
120.61/120.81	
120.61/120.81	Mace4 cooked interpretation:
120.61/120.81	
120.61/120.81	% number = 1
120.61/120.81	% seconds = 0
120.61/120.81	
120.61/120.81	% Interpretation of size 2
120.61/120.81	
120.61/120.81	f2 = 0.
120.61/120.81	
120.61/120.81	f5 = 0.
120.61/120.81	
120.61/120.81	f6 = 1.
120.61/120.81	
120.61/120.81	f12(0) = 0.
120.61/120.81	f12(1) = 0.
120.61/120.81	
120.61/120.81	f3(0) = 1.
120.61/120.81	f3(1) = 1.
120.61/120.81	
120.61/120.81	f8(0) = 0.
120.61/120.81	f8(1) = 0.
120.61/120.81	
120.61/120.81	f13(0,0) = 0.
120.61/120.81	f13(0,1) = 0.
120.61/120.81	f13(1,0) = 0.
120.61/120.81	f13(1,1) = 1.
120.61/120.81	
120.61/120.81	f14(0,0) = 0.
120.61/120.81	f14(0,1) = 1.
120.61/120.81	f14(1,0) = 1.
120.61/120.81	f14(1,1) = 1.
120.61/120.81	
120.61/120.81	f4(0,0) = 0.
120.61/120.81	f4(0,1) = 0.
120.61/120.81	f4(1,0) = 0.
120.61/120.81	f4(1,1) = 0.
120.61/120.81	
120.61/120.81	  arrowN_s0(0,0).
120.61/120.81	- arrowN_s0(0,1).
120.61/120.81	  arrowN_s0(1,0).
120.61/120.81	  arrowN_s0(1,1).
120.61/120.81	
120.61/120.81	  arrowStar_s0(0,0).
120.61/120.81	- arrowStar_s0(0,1).
120.61/120.81	  arrowStar_s0(1,0).
120.61/120.81	  arrowStar_s0(1,1).
120.61/120.81	
120.61/120.81	  arrow_s0(0,0).
120.61/120.81	- arrow_s0(0,1).
120.61/120.81	  arrow_s0(1,0).
120.61/120.81	  arrow_s0(1,1).
120.61/120.81	
120.61/120.81	  gtrsim_s0(0,0).
120.61/120.81	  gtrsim_s0(0,1).
120.61/120.81	  gtrsim_s0(1,0).
120.61/120.81	  gtrsim_s0(1,1).
120.61/120.81	
120.61/120.81	- sqsupsetStar_s0(0,0).
120.61/120.81	- sqsupsetStar_s0(0,1).
120.61/120.81	- sqsupsetStar_s0(1,0).
120.61/120.81	- sqsupsetStar_s0(1,1).
120.61/120.81	
120.61/120.81	- sqsupset_s0(0,0).
120.61/120.81	- sqsupset_s0(0,1).
120.61/120.81	- sqsupset_s0(1,0).
120.61/120.81	- sqsupset_s0(1,1).
120.61/120.81	
120.61/120.81	- succeq_s0(0,0).
120.61/120.81	  succeq_s0(0,1).
120.61/120.81	- succeq_s0(1,0).
120.61/120.81	- succeq_s0(1,1).
120.61/120.81	
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	SCC Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	->Strongly Connected Components:
120.61/120.81	->->Cycle:
120.61/120.81	->->-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> QPairs:
120.61/120.81	 Empty
120.61/120.81	->->-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	
120.61/120.81	Problem 1.1: 
120.61/120.81	
120.61/120.81	Reduction Pair Processor:
120.61/120.81	-> Pairs:
120.61/120.81	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.81	 G(x3:S,b) -> G(f(c),x3:S) | a ->* h(c), c ->* x3:S, x3:S ->* c
120.61/120.81	-> Rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.81	-> Needed rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	-> Usable rules:
120.61/120.81	 a -> h(b)
120.61/120.81	 a -> h(c)
120.61/120.81	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.81	->Mace4 Output:
120.61/120.81	 ============================== Mace4 =================================
120.61/120.81	Mace4 (64) version 2009-11A, November 2009.
120.61/120.81	Process 10222 was started by sandbox2 on n124.star.cs.uiowa.edu,
120.61/120.81	Fri Mar 29 01:44:28 2019
120.61/120.81	The command was "./mace4 -c -f /tmp/mace41780695788709393584.in".
120.61/120.81	============================== end of head ===========================
120.61/120.81	
120.61/120.81	============================== INPUT =================================
120.61/120.81	
120.61/120.81	% Reading from file /tmp/mace41780695788709393584.in
120.61/120.81	
120.61/120.81	assign(max_seconds,20).
120.61/120.81	
120.61/120.81	formulas(assumptions).
120.61/120.81	arrowStar_s0(x,x) # label(reflexivity).
120.61/120.81	arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility).
120.61/120.81	gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence).
120.61/120.81	arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence).
120.61/120.81	arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
120.61/120.81	arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f4(x1,x2),f4(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f4(x1,x2),f4(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence).
120.61/120.81	arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence).
120.61/120.81	arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence).
120.61/120.81	arrow_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrow_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	arrowStar_s0(f2,f8(x2)) -> arrow_s0(f3(x1),x2) # label(replacement).
120.61/120.81	arrow_s0(f14(x4,x5),x4) # label(replacement).
120.61/120.81	arrow_s0(f14(x4,x5),x5) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	arrowStar_s0(f2,f8(x2)) -> arrowN_s0(f3(x1),x2) # label(replacement).
120.61/120.81	arrowN_s0(f14(x4,x5),x4) # label(replacement).
120.61/120.81	arrowN_s0(f14(x4,x5),x5) # label(replacement).
120.61/120.81	arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).
120.61/120.81	arrowStar_s0(f2,f8(f6)) & arrowStar_s0(f6,x3) & arrowStar_s0(x3,f6) -> sqsupset_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement).
120.61/120.81	arrowStar_s0(f3(f5),f6) -> succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement).
120.61/120.81	sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion).
120.61/120.81	sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	formulas(goals).
120.61/120.81	(exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	============================== end of input ==========================
120.61/120.81	
120.61/120.81	============================== PROCESS NON-CLAUSAL FORMULAS ==========
120.61/120.81	
120.61/120.81	% Formulas that are not ordinary clauses:
120.61/120.81	1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	5 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	6 arrow_s0(x1,y) -> arrow_s0(f4(x1,x2),f4(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	7 arrow_s0(x2,y) -> arrow_s0(f4(x1,x2),f4(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	8 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	9 arrow_s0(x1,y) -> arrow_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	10 arrow_s0(x2,y) -> arrow_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	12 arrowN_s0(x1,y) -> arrowN_s0(f4(x1,x2),f4(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	13 arrowN_s0(x2,y) -> arrowN_s0(f4(x1,x2),f4(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	14 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	15 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	16 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	17 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	18 arrowN_s0(x1,y) -> arrowN_s0(f14(x1,x2),f14(y,x2)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	19 arrowN_s0(x2,y) -> arrowN_s0(f14(x1,x2),f14(x1,y)) # label(congruence) # label(non_clause).  [assumption].
120.61/120.81	20 arrowStar_s0(f2,f8(x2)) -> arrow_s0(f3(x1),x2) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	21 arrowStar_s0(f2,f8(x2)) -> arrowN_s0(f3(x1),x2) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	22 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
120.61/120.81	23 arrowStar_s0(f2,f8(f6)) & arrowStar_s0(f6,x3) & arrowStar_s0(x3,f6) -> sqsupset_s0(f13(x3,f5),f13(f3(f6),x3)) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	24 arrowStar_s0(f3(f5),f6) -> succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement) # label(non_clause).  [assumption].
120.61/120.81	25 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause).  [assumption].
120.61/120.81	26 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause).  [assumption].
120.61/120.81	27 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal).  [goal].
120.61/120.81	
120.61/120.81	============================== end of process non-clausal formulas ===
120.61/120.81	
120.61/120.81	============================== CLAUSES FOR SEARCH ====================
120.61/120.81	
120.61/120.81	formulas(mace4_clauses).
120.61/120.81	arrowStar_s0(x,x) # label(reflexivity).
120.61/120.81	-arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility).
120.61/120.81	-gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	-succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility).
120.61/120.81	-gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f4(x,z),f4(y,z)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f4(z,x),f4(z,y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f14(x,z),f14(y,z)) # label(congruence).
120.61/120.81	-arrow_s0(x,y) | arrow_s0(f14(z,x),f14(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f4(x,z),f4(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f4(z,x),f4(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f14(x,z),f14(y,z)) # label(congruence).
120.61/120.81	-arrowN_s0(x,y) | arrowN_s0(f14(z,x),f14(z,y)) # label(congruence).
120.61/120.81	arrow_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrow_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	-arrowStar_s0(f2,f8(x)) | arrow_s0(f3(y),x) # label(replacement).
120.61/120.81	arrow_s0(f14(x,y),x) # label(replacement).
120.61/120.81	arrow_s0(f14(x,y),y) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f5)) # label(replacement).
120.61/120.81	arrowN_s0(f2,f8(f6)) # label(replacement).
120.61/120.81	-arrowStar_s0(f2,f8(x)) | arrowN_s0(f3(y),x) # label(replacement).
120.61/120.81	arrowN_s0(f14(x,y),x) # label(replacement).
120.61/120.81	arrowN_s0(f14(x,y),y) # label(replacement).
120.61/120.81	-arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion).
120.61/120.81	-arrowStar_s0(f2,f8(f6)) | -arrowStar_s0(f6,x) | -arrowStar_s0(x,f6) | sqsupset_s0(f13(x,f5),f13(f3(f6),x)) # label(replacement).
120.61/120.81	-arrowStar_s0(f3(f5),f6) | succeq_s0(f13(f3(f5),f5),f13(f3(f6),f3(f5))) # label(replacement).
120.61/120.81	-sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion).
120.61/120.81	-sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility).
120.61/120.81	-sqsupsetStar_s0(x,x) # label(wellfoundedness).
120.61/120.81	end_of_list.
120.61/120.81	
120.61/120.81	============================== end of clauses for search =============
120.61/120.81	
120.61/120.81	% There are no natural numbers in the input.
120.61/120.81	
120.61/120.81	============================== DOMAIN SIZE 2 =========================
120.61/120.81	
120.61/120.81	============================== MODEL =================================
120.61/120.81	
120.61/120.81	interpretation( 2, [number=1, seconds=0], [
120.61/120.81	
120.61/120.81	        function(f2, [ 0 ]),
120.61/120.81	
120.61/120.81	        function(f5, [ 0 ]),
120.61/120.81	
120.61/120.81	        function(f6, [ 1 ]),
120.61/120.81	
120.61/120.81	        function(f12(_), [ 0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f3(_), [ 0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f8(_), [ 0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f13(_,_), [
120.61/120.81				   0, 1,
120.61/120.81				   0, 1 ]),
120.61/120.81	
120.61/120.81	        function(f14(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        function(f4(_,_), [
120.61/120.81				   0, 0,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(arrowN_s0(_,_), [
120.61/120.81				   1, 1,
120.61/120.81				   0, 1 ]),
120.61/120.81	
120.61/120.81	        relation(arrowStar_s0(_,_), [
120.61/120.81				   1, 1,
120.61/120.81				   0, 1 ]),
120.61/120.81	
120.61/120.81	        relation(arrow_s0(_,_), [
120.61/120.81				   1, 1,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(gtrsim_s0(_,_), [
120.61/120.81				   1, 1,
120.61/120.81				   0, 1 ]),
120.61/120.81	
120.61/120.81	        relation(sqsupsetStar_s0(_,_), [
120.61/120.81				   0, 1,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(sqsupset_s0(_,_), [
120.61/120.81				   0, 1,
120.61/120.81				   0, 0 ]),
120.61/120.81	
120.61/120.81	        relation(succeq_s0(_,_), [
120.61/120.81				   1, 0,
120.61/120.81				   0, 0 ])
120.61/120.81	]).
120.61/120.81	
120.61/120.81	============================== end of model ==========================
120.61/120.81	
120.61/120.81	============================== STATISTICS ============================
120.61/120.82	
120.61/120.82	For domain size 2.
120.61/120.82	
120.61/120.82	Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds).
120.61/120.82	Ground clauses: seen=183, kept=179.
120.61/120.82	Selections=41, assignments=64, propagations=175, current_models=1.
120.61/120.82	Rewrite_terms=805, rewrite_bools=1456, indexes=206.
120.61/120.82	Rules_from_neg_clauses=25, cross_offs=25.
120.61/120.82	
120.61/120.82	============================== end of statistics =====================
120.61/120.82	
120.61/120.82	User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
120.61/120.82	
120.61/120.82	Exiting with 1 model.
120.61/120.82	
120.61/120.82	Process 10222 exit (max_models) Fri Mar 29 01:44:28 2019
120.61/120.82	The process finished Fri Mar 29 01:44:28 2019
120.61/120.82	
120.61/120.82	
120.61/120.82	Mace4 cooked interpretation:
120.61/120.82	
120.61/120.82	% number = 1
120.61/120.82	% seconds = 0
120.61/120.82	
120.61/120.82	% Interpretation of size 2
120.61/120.82	
120.61/120.82	f2 = 0.
120.61/120.82	
120.61/120.82	f5 = 0.
120.61/120.82	
120.61/120.82	f6 = 1.
120.61/120.82	
120.61/120.82	f12(0) = 0.
120.61/120.82	f12(1) = 0.
120.61/120.82	
120.61/120.82	f3(0) = 0.
120.61/120.82	f3(1) = 0.
120.61/120.82	
120.61/120.82	f8(0) = 0.
120.61/120.82	f8(1) = 0.
120.61/120.82	
120.61/120.82	f13(0,0) = 0.
120.61/120.82	f13(0,1) = 1.
120.61/120.82	f13(1,0) = 0.
120.61/120.82	f13(1,1) = 1.
120.61/120.82	
120.61/120.82	f14(0,0) = 0.
120.61/120.82	f14(0,1) = 0.
120.61/120.82	f14(1,0) = 0.
120.61/120.82	f14(1,1) = 0.
120.61/120.82	
120.61/120.82	f4(0,0) = 0.
120.61/120.82	f4(0,1) = 0.
120.61/120.82	f4(1,0) = 0.
120.61/120.82	f4(1,1) = 0.
120.61/120.82	
120.61/120.82	  arrowN_s0(0,0).
120.61/120.82	  arrowN_s0(0,1).
120.61/120.82	- arrowN_s0(1,0).
120.61/120.82	  arrowN_s0(1,1).
120.61/120.82	
120.61/120.82	  arrowStar_s0(0,0).
120.61/120.82	  arrowStar_s0(0,1).
120.61/120.82	- arrowStar_s0(1,0).
120.61/120.82	  arrowStar_s0(1,1).
120.61/120.82	
120.61/120.82	  arrow_s0(0,0).
120.61/120.82	  arrow_s0(0,1).
120.61/120.82	- arrow_s0(1,0).
120.61/120.82	- arrow_s0(1,1).
120.61/120.82	
120.61/120.82	  gtrsim_s0(0,0).
120.61/120.82	  gtrsim_s0(0,1).
120.61/120.82	- gtrsim_s0(1,0).
120.61/120.82	  gtrsim_s0(1,1).
120.61/120.82	
120.61/120.82	- sqsupsetStar_s0(0,0).
120.61/120.82	  sqsupsetStar_s0(0,1).
120.61/120.82	- sqsupsetStar_s0(1,0).
120.61/120.82	- sqsupsetStar_s0(1,1).
120.61/120.82	
120.61/120.82	- sqsupset_s0(0,0).
120.61/120.82	  sqsupset_s0(0,1).
120.61/120.82	- sqsupset_s0(1,0).
120.61/120.82	- sqsupset_s0(1,1).
120.61/120.82	
120.61/120.82	  succeq_s0(0,0).
120.61/120.82	- succeq_s0(0,1).
120.61/120.82	- succeq_s0(1,0).
120.61/120.82	- succeq_s0(1,1).
120.61/120.82	
120.61/120.82	
120.61/120.82	Problem 1.1: 
120.61/120.82	
120.61/120.82	SCC Processor:
120.61/120.82	-> Pairs:
120.61/120.82	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.82	-> QPairs:
120.61/120.82	 Empty
120.61/120.82	-> Rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.82	->Strongly Connected Components:
120.61/120.82	->->Cycle:
120.61/120.82	->->-> Pairs:
120.61/120.82	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.82	-> QPairs:
120.61/120.82	 Empty
120.61/120.82	->->-> Rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.82	
120.61/120.82	Problem 1.1: 
120.61/120.82	
120.61/120.82	Reduction Triple Processor:
120.61/120.82	-> Pairs:
120.61/120.82	 G(f(b),b) -> G(f(c),f(b)) | f(b) ->* c
120.61/120.82	-> QPairs:
120.61/120.82	 Empty
120.61/120.82	-> Rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.82	-> Usable rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	->Interpretation type:
120.61/120.82	 Linear
120.61/120.82	->Coefficients:
120.61/120.82	 Natural Numbers
120.61/120.82	->Dimension:
120.61/120.82	 1
120.61/120.82	->Bound:
120.61/120.82	 2
120.61/120.82	->Interpretation:
120.61/120.82	 
120.61/120.82	[a] = 2
120.61/120.82	[f](X) = 2.X + 2
120.61/120.82	[g](X1,X2) = 0
120.61/120.82	[b] = 1
120.61/120.82	[c] = 0
120.61/120.82	[fSNonEmpty] = 0
120.61/120.82	[h](X) = X + 1
120.61/120.82	[A] = 0
120.61/120.82	[F](X) = 0
120.61/120.82	[G](X1,X2) = 2.X1 + X2
120.61/120.82	
120.61/120.82	Problem 1.1: 
120.61/120.82	
120.61/120.82	SCC Processor:
120.61/120.82	-> Pairs:
120.61/120.82	 Empty
120.61/120.82	-> QPairs:
120.61/120.82	 Empty
120.61/120.82	-> Rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.82	->Strongly Connected Components:
120.61/120.82	 There is no strongly connected component
120.61/120.82	
120.61/120.82	The problem is finite.
120.61/120.82	
120.61/120.82	Problem 1.2: 
120.61/120.82	
120.61/120.82	SCC Processor:
120.61/120.82	-> Pairs:
120.61/120.82	 F(x:S) -> A
120.61/120.82	 G(x:S,b) -> F(b)
120.61/120.82	-> QPairs:
120.61/120.82	 Empty
120.61/120.82	-> Rules:
120.61/120.82	 a -> h(b)
120.61/120.82	 a -> h(c)
120.61/120.82	 f(x:S) -> y:S | a ->* h(y:S)
120.61/120.82	 g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
120.61/120.82	->Strongly Connected Components:
120.61/120.82	 There is no strongly connected component
120.61/120.82	
120.61/120.82	The problem is finite.
120.61/120.82	EOF