0.001/0.001	NO
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(g_1(x:S)) -> *top*_0(f_0(g_1(x:S)))
0.001/0.001	f_0(g_1(x:S)) -> f_1(f_0(g_1(x:S)))
0.001/0.001	f_1(f_0(x:S)) -> b_0
0.001/0.001	f_1(f_1(x:S)) -> b_0
0.001/0.001	f_1(g_1(a_0)) -> a_0
0.001/0.001	g_1(x:S) -> f_1(g_1(x:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	CleanTRS Processor:
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(g_1(x:S)) -> *top*_0(f_0(g_1(x:S)))
0.001/0.001	f_0(g_1(x:S)) -> f_1(f_0(g_1(x:S)))
0.001/0.001	f_1(f_0(x:S)) -> b_0
0.001/0.001	f_1(f_1(x:S)) -> b_0
0.001/0.001	f_1(g_1(a_0)) -> a_0
0.001/0.001	g_1(x:S) -> f_1(g_1(x:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	Modular Confluence Combinations Decomposition Processor:
0.001/0.001	It is a CTRS -> No modular confluence
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	Left-Homogeneous u-Replacing Variables Processor:
0.001/0.001	R satisfies LHRV condition
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(g_1(x:S)) -> *top*_0(f_0(g_1(x:S)))
0.001/0.001	f_0(g_1(x:S)) -> f_1(f_0(g_1(x:S)))
0.001/0.001	f_1(f_0(x:S)) -> b_0
0.001/0.001	f_1(f_1(x:S)) -> b_0
0.001/0.001	f_1(g_1(a_0)) -> a_0
0.001/0.001	g_1(x:S) -> f_1(g_1(x:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Huet Levy Processor:
0.001/0.001	-> Rules:
0.001/0.001	 *top*_0(g_1(x:S)) -> *top*_0(f_0(g_1(x:S)))
0.001/0.001	 f_0(g_1(x:S)) -> f_1(f_0(g_1(x:S)))
0.001/0.001	 f_1(f_0(x:S)) -> b_0
0.001/0.001	 f_1(f_1(x:S)) -> b_0
0.001/0.001	 f_1(g_1(a_0)) -> a_0
0.001/0.001	 g_1(x:S) -> f_1(g_1(x:S))
0.001/0.001	-> Vars:
0.001/0.001	 x, x, x, x, x
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	-> FVars:
0.001/0.001	 x2, x3, x4, x5, x6
0.001/0.001	-> PVars:
0.001/0.001	 x: [x2, x3, x4, x5, x6]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: *top*_0(g_1(x2:S)) -> *top*_0(f_0(g_1(x2:S))), id: 1, possubterms: *top*_0(g_1(x2:S))->[], g_1(x2:S)->[1])
0.001/0.001	 (rule: f_0(g_1(x3:S)) -> f_1(f_0(g_1(x3:S))), id: 2, possubterms: f_0(g_1(x3:S))->[], g_1(x3:S)->[1])
0.001/0.001	 (rule: f_1(f_0(x4:S)) -> b_0, id: 3, possubterms: f_1(f_0(x4:S))->[])
0.001/0.001	 (rule: f_1(f_1(x5:S)) -> b_0, id: 4, possubterms: f_1(f_1(x5:S))->[])
0.001/0.001	 (rule: f_1(g_1(a_0)) -> a_0, id: 5, possubterms: f_1(g_1(a_0))->[])
0.001/0.001	 (rule: g_1(x6:S) -> f_1(g_1(x6:S)), id: 6, possubterms: g_1(x6:S)->[])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	(R1 unifies with R6 at p: [1], l: *top*_0(g_1(x2:S)), lp: g_1(x2:S), sig: {x2:S -> x:S}, l': g_1(x:S), r: *top*_0(f_0(g_1(x2:S))), r': f_1(g_1(x:S)))
0.001/0.001	(R2 unifies with R6 at p: [1], l: f_0(g_1(x3:S)), lp: g_1(x3:S), sig: {x3:S -> x:S}, l': g_1(x:S), r: f_1(f_0(g_1(x3:S))), r': f_1(g_1(x:S)))
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	<f_0(f_1(g_1(x:S))),f_1(f_0(g_1(x:S)))>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	<*top*_0(f_1(g_1(x:S))),*top*_0(f_0(g_1(x:S)))>   =>  Not trivial, Not overlay, NW0, N2
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Left linear, Right linear, Linear
0.001/0.001	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.001/0.001	 Not Huet-Levy confluent, Not Newman confluent
0.001/0.001	 R is a CS-TRS, Left-homogeneous u-replacing variables
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	No Convergence Brute Force Processor:
0.001/0.001	-> Rewritings:
0.001/0.001	s: f_0(f_1(g_1(x:S)))
0.001/0.001	Nodes: [0]
0.001/0.001	Edges: []
0.001/0.001	ID: 0 => ('f_0(f_1(g_1(x:S)))', D0)
0.001/0.001	t: f_1(f_0(g_1(x:S)))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('f_1(f_0(g_1(x:S)))', D0)
0.001/0.001	ID: 1 => ('b_0', D1, R3, P[], S{x4:S -> g_1(x:S)}), NR: 'b_0'
0.001/0.001	f_0(f_1(g_1(x:S))) ->* no union *<- f_1(f_0(g_1(x:S)))
0.001/0.001	"Not joinable"
0.001/0.001	
0.001/0.001	The problem is not joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 50%CPU (0avgtext+0avgdata 8972maxresident)k
0.001/0.001	0inputs+0outputs (0major+691minor)pagefaults 0swaps