NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(c)
(h 1, 2)
(a)
(b)
(f 1)
(fSNonEmpty)
)
(RULES
c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
h(c,f(f(c))) -> f(f(a))
h(h(c,f(f(a))),f(b)) -> a
h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

Problem 1: 
Not CS-TRS Procedure:
R is not a CS-TRS

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(c)
(h 1, 2)
(a)
(b)
(f 1)
(fSNonEmpty)
)
(RULES
c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
h(c,f(f(c))) -> f(f(a))
h(h(c,f(f(a))),f(b)) -> a
h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Ordered by Num of Vars and Symbs Procedure:
-> Rules:
 c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
 h(c,f(f(c))) -> f(f(a))
 h(h(c,f(f(a))),f(b)) -> a
 h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c
-> Vars:


-> Rlps:
 (rule: c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b)))), id: 1, possubterms: c->[])
 (rule: h(c,f(f(c))) -> f(f(a)), id: 2, possubterms: h(c,f(f(c)))->[], c->[1], f(f(c))->[2], f(c)->[2, 1], c->[2, 1, 1])
 (rule: h(h(c,f(f(a))),f(b)) -> a, id: 3, possubterms: h(h(c,f(f(a))),f(b))->[], h(c,f(f(a)))->[1], c->[1, 1], f(f(a))->[1, 2], f(a)->[1, 2, 1], a->[1, 2, 1, 1], f(b)->[2], b->[2, 1])
 (rule: h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c, id: 4, possubterms: h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c))->[], f(h(c,b))->[1], h(c,b)->[1, 1], c->[1, 1, 1], b->[1, 1, 2], h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)->[2], h(h(b,a),h(c,f(h(h(b,a),a))))->[2, 1], h(b,a)->[2, 1, 1], b->[2, 1, 1, 1], a->[2, 1, 1, 2], h(c,f(h(h(b,a),a)))->[2, 1, 2], c->[2, 1, 2, 1], f(h(h(b,a),a))->[2, 1, 2, 2], h(h(b,a),a)->[2, 1, 2, 2, 1], h(b,a)->[2, 1, 2, 2, 1, 1], b->[2, 1, 2, 2, 1, 1, 1], a->[2, 1, 2, 2, 1, 1, 2], a->[2, 1, 2, 2, 1, 2], c->[2, 2])

-> Unifications:
(R2 unifies with R1 at p: [1], l: h(c,f(f(c))), lp: c, sig: {}, l': c, r: f(f(a)), r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))
(R2 unifies with R1 at p: [2,1,1], l: h(c,f(f(c))), lp: c, sig: {}, l': c, r: f(f(a)), r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))
(R3 unifies with R1 at p: [1,1], l: h(h(c,f(f(a))),f(b)), lp: c, sig: {}, l': c, r: a, r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))
(R4 unifies with R1 at p: [1,1,1], l: h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)), lp: c, sig: {}, l': c, r: c, r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))
(R4 unifies with R1 at p: [2,1,2,1], l: h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)), lp: c, sig: {}, l': c, r: c, r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))
(R4 unifies with R1 at p: [2,2], l: h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)), lp: c, sig: {}, l': c, r: c, r': h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))

-> Critical pairs info:
<h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
<h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))),c>   =>  Not trivial, Not overlay, Proper, NW0, N2
<h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)),c>   =>  Not trivial, Not overlay, Proper, NW0, N3
<h(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(a))),f(b)),a>   =>  Not trivial, Not overlay, Proper, NW0, N4
<h(c,f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))),f(f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N5
<h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(c))),f(f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N6

-> Problem conclusions:
 Left linear, Right linear, Linear
 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
 Not Huet-Levy confluent, Not Newman confluent
 R is a TRS 


Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(REPLACEMENT-MAP
(c)
(h 1, 2)
(a)
(b)
(f 1)
(fSNonEmpty)
)
(RULES
c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
h(c,f(f(c))) -> f(f(a))
h(h(c,f(f(a))),f(b)) -> a
h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c
)
Critical Pairs:
<h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

No Convergence InfChecker Procedure:
Infeasible convergence?
YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty vNonEmpty z0)
(STRATEGY CONTEXTSENSITIVE
(c)
(h 1 2)
(a)
(b)
(f 1)
(fSNonEmpty)
)
(RULES
c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
h(c,f(f(c))) -> f(f(a))
h(h(c,f(f(a))),f(b)) -> a
h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c
)]
Infeasibility Conditions:
h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)) ->* z0, c ->* z0

Problem 1: 

Obtaining a model using AGES:

 -> Theory (Usable Rules):
c -> h(a,h(f(f(f(f(c)))),h(a,h(b,b))))
h(c,f(f(c))) -> f(f(a))
h(h(c,f(f(a))),f(b)) -> a
h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c

 -> AGES Output:




The problem is infeasible.


The problem is not confluent.