0.001/0.001	YES
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 v_NonEmpty:S:S x:S:S y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(if 1)
0.001/0.001	(isZero 1)
0.001/0.001	(p 1)
0.001/0.001	(plus)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(ffalse,x:S:S,y:S:S) -> y:S:S
0.001/0.001	if(ftrue,x:S:S,y:S:S) -> x:S:S
0.001/0.001	isZero(num0) -> ftrue
0.001/0.001	isZero(s(x:S:S)) -> ffalse
0.001/0.001	p(s(x:S:S)) -> x:S:S
0.001/0.001	plus(x:S:S,y:S:S) -> if(isZero(x:S:S),y:S:S,s(plus(p(x:S:S),y:S: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 v_NonEmpty:S:S x:S:S y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(if 1)
0.001/0.001	(isZero 1)
0.001/0.001	(p 1)
0.001/0.001	(plus)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(ffalse,x:S:S,y:S:S) -> y:S:S
0.001/0.001	if(ftrue,x:S:S,y:S:S) -> x:S:S
0.001/0.001	isZero(num0) -> ftrue
0.001/0.001	isZero(s(x:S:S)) -> ffalse
0.001/0.001	p(s(x:S:S)) -> x:S:S
0.001/0.001	plus(x:S:S,y:S:S) -> if(isZero(x:S:S),y:S:S,s(plus(p(x:S:S),y:S: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 v_NonEmpty:S:S x:S:S y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(if 1)
0.001/0.001	(isZero 1)
0.001/0.001	(p 1)
0.001/0.001	(plus)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(ffalse,x:S:S,y:S:S) -> y:S:S
0.001/0.001	if(ftrue,x:S:S,y:S:S) -> x:S:S
0.001/0.001	isZero(num0) -> ftrue
0.001/0.001	isZero(s(x:S:S)) -> ffalse
0.001/0.001	p(s(x:S:S)) -> x:S:S
0.001/0.001	plus(x:S:S,y:S:S) -> if(isZero(x:S:S),y:S:S,s(plus(p(x:S:S),y:S: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	 if(ffalse,x:S:S,y:S:S) -> y:S:S
0.001/0.001	 if(ftrue,x:S:S,y:S:S) -> x:S:S
0.001/0.001	 isZero(num0) -> ftrue
0.001/0.001	 isZero(s(x:S:S)) -> ffalse
0.001/0.001	 p(s(x:S:S)) -> x:S:S
0.001/0.001	 plus(x:S:S,y:S:S) -> if(isZero(x:S:S),y:S:S,s(plus(p(x:S:S),y:S:S)))
0.001/0.001	-> Vars:
0.001/0.001	 x:S, y:S, x:S, y:S, x:S, x:S, x:S, y:S
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [y:S], UV-LFrozen: [x:S, y:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S, y:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S, y:S], UV-RFrozen: [x:S, y:S])
0.001/0.001	-> FVars:
0.001/0.001	 x4, x5, x6, x7, x8, x9, x10, x11
0.001/0.001	-> PVars:
0.001/0.001	 x:S: [x4, x6, x8, x9, x10], y:S: [x5, x7, x11]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: if(ffalse,x4:S,x5:S) -> x5:S, id: 1, possubterms: if(ffalse,x4:S,x5:S)->[], ffalse->[1])
0.001/0.001	 (rule: if(ftrue,x6:S,x7:S) -> x6:S, id: 2, possubterms: if(ftrue,x6:S,x7:S)->[], ftrue->[1])
0.001/0.001	 (rule: isZero(num0) -> ftrue, id: 3, possubterms: isZero(num0)->[], num0->[1])
0.001/0.001	 (rule: isZero(s(x8:S)) -> ffalse, id: 4, possubterms: isZero(s(x8:S))->[], s(x8:S)->[1])
0.001/0.001	 (rule: p(s(x9:S)) -> x9:S, id: 5, possubterms: p(s(x9:S))->[], s(x9:S)->[1])
0.001/0.001	 (rule: plus(x10:S,x11:S) -> if(isZero(x10:S),x11:S,s(plus(p(x10:S),x11:S))), id: 6, possubterms: plus(x10:S,x11:S)->[])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Left linear, Not right linear, Not linear
0.001/0.001	 Weakly orthogonal, Almost orthogonal, Orthogonal
0.001/0.001	 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	The problem is joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 69%CPU (0avgtext+0avgdata 8284maxresident)k
0.001/0.001	8inputs+0outputs (0major+685minor)pagefaults 0swaps