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 y: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 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(false)
0.001/0.001	(s 1)
0.001/0.001	(true)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(false,x:S,y:S) -> y:S
0.001/0.001	if(true,x:S,y:S) -> x:S
0.001/0.001	isZero(0) -> true
0.001/0.001	isZero(s(x:S)) -> false
0.001/0.001	p(s(x:S)) -> x:S
0.001/0.001	plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y: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 y: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 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(false)
0.001/0.001	(s 1)
0.001/0.001	(true)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(false,x:S,y:S) -> y:S
0.001/0.001	if(true,x:S,y:S) -> x:S
0.001/0.001	isZero(0) -> true
0.001/0.001	isZero(s(x:S)) -> false
0.001/0.001	p(s(x:S)) -> x:S
0.001/0.001	plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y: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	CS-TRS Processor:
0.001/0.001	R is a CS-TRS
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 y: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 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(false)
0.001/0.001	(s 1)
0.001/0.001	(true)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(false,x:S,y:S) -> y:S
0.001/0.001	if(true,x:S,y:S) -> x:S
0.001/0.001	isZero(0) -> true
0.001/0.001	isZero(s(x:S)) -> false
0.001/0.001	p(s(x:S)) -> x:S
0.001/0.001	plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Extended u-Critical Pairs NonLHRV Processor [JLAMP21]:
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => plus(x9:S,x10:S) -> if(isZero(x9:S),x10:S,s(plus(p(x9:S),x10:S)))
0.001/0.001	 Rule 6 (l' :-> r') => plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))
0.001/0.001	 Var => x9:S
0.001/0.001	 Pos x9:S in l => [1]
0.001/0.001	 Sigma => {x9:S -> plus(x:S,y:S)}
0.001/0.001	 s => if(isZero(plus(x:S,y:S)),x10:S,s(plus(p(plus(x:S,y:S)),x10:S)))
0.001/0.001	 t => plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),x10:S)
0.001/0.001	 NW => 0
0.001/0.001	
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 y: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 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(false)
0.001/0.001	(s 1)
0.001/0.001	(true)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	if(false,x:S,y:S) -> y:S
0.001/0.001	if(true,x:S,y:S) -> x:S
0.001/0.001	isZero(0) -> true
0.001/0.001	isZero(s(x:S)) -> false
0.001/0.001	p(s(x:S)) -> x:S
0.001/0.001	plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))
0.001/0.001	)
0.001/0.001	Critical Pairs:
0.001/0.001	<if(isZero(plus(x:S,y:S)),x10:S,s(plus(p(plus(x:S,y:S)),x10:S))),plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),x10:S)>   =>  Not trivial, Not overlay, NW0, N1
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(false,x:S,y:S) -> y:S
0.001/0.001	 if(true,x:S,y:S) -> x:S
0.001/0.001	 isZero(0) -> true
0.001/0.001	 isZero(s(x:S)) -> false
0.001/0.001	 p(s(x:S)) -> x:S
0.001/0.001	 plus(x:S,y:S) -> if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))
0.001/0.001	-> Vars:
0.001/0.001	 x, y, x, y, x, x, x, y
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [y], UV-LFrozen: [x, y], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x, y], 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: [x], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [x], UV-RActive: [x], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [x, y], UV-RActive: [x], UV-LFrozen: [], UV-RFrozen: [x, y])
0.001/0.001	-> FVars:
0.001/0.001	 x3, x4, x5, x6, x7, x8, x9, x10
0.001/0.001	-> PVars:
0.001/0.001	 x: [x3, x5, x7, x8, x9], y: [x4, x6, x10]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: if(false,x3:S,x4:S) -> x4:S, id: 1, possubterms: if(false,x3:S,x4:S)->[], false->[1])
0.001/0.001	 (rule: if(true,x5:S,x6:S) -> x5:S, id: 2, possubterms: if(true,x5:S,x6:S)->[], true->[1])
0.001/0.001	 (rule: isZero(0) -> true, id: 3, possubterms: isZero(0)->[], 0->[1])
0.001/0.001	 (rule: isZero(s(x7:S)) -> false, id: 4, possubterms: isZero(s(x7:S))->[], s(x7:S)->[1])
0.001/0.001	 (rule: p(s(x8:S)) -> x8:S, id: 5, possubterms: p(s(x8:S))->[], s(x8:S)->[1])
0.001/0.001	 (rule: plus(x9:S,x10:S) -> if(isZero(x9:S),x10:S,s(plus(p(x9:S),x10:S))), id: 6, possubterms: plus(x9:S,x10: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	<if(isZero(plus(x:S,y:S)),y:S,s(plus(p(plus(x:S,y:S)),y:S))),plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),y:S)>   =>  Not trivial, Not overlay, NW0, N1
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	 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, Not 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: if(isZero(plus(x:S,y:S)),y:S,s(plus(p(plus(x:S,y:S)),y:S)))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('if(isZero(plus(x:S,y:S)),y:S,s(plus(p(plus(x:S,y:S)),y:S)))', D0)
0.001/0.001	ID: 1 => ('if(isZero(if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))),y:S,s(plus(p(plus(x:S,y:S)),y:S)))', D1, R6, P[1, 1], S{x9:S -> x:S, x10:S -> y:S}), NR: 'if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))'
0.001/0.001	t: plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),y:S)
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),y:S)', D0)
0.001/0.001	ID: 1 => ('if(isZero(if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))),y:S,s(plus(p(if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))),y:S)))', D1, R6, P[], S{x9:S -> if(isZero(x:S),y:S,s(plus(p(x:S),y:S))), x10:S -> y:S}), NR: 'if(isZero(if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))),y:S,s(plus(p(if(isZero(x:S),y:S,s(plus(p(x:S),y:S)))),y:S)))'
0.001/0.001	if(isZero(plus(x:S,y:S)),y:S,s(plus(p(plus(x:S,y:S)),y:S))) ->* no union *<- plus(if(isZero(x:S),y:S,s(plus(p(x:S),y:S))),y: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 69%CPU (0avgtext+0avgdata 10004maxresident)k
0.001/0.001	0inputs+0outputs (0major+827minor)pagefaults 0swaps