Confluence Problems (Cops)

(VAR x y)
(RULES
  f(x,y) -> x
  f(x,y) -> f(x,g(y))
  g(x) -> h(x)
  F(g(x),x) -> F(x,g(x))
  F(h(x),x) -> F(x,h(x))
)
(COMMENT Example 6 of \cite{AT97})

(VAR x y)
(RULES
  f(x,y) -> f(g(x),g(x))
  g(x) -> h(x)
  F(g(x),x) -> F(x,g(x))
  F(h(x),x) -> F(x,h(x))
)
(COMMENT Example 1 of \cite{AT97b})

(VAR x y)
(RULES
  f(a(x), x) -> f(x,a(x))
  f(b(x), x) -> f(x,b(x))
  g(b(x),y) -> g(a(a(x)),y) 
  g(c(x),y) -> y
  a(x) -> b(x) 
)
(COMMENT Example 1 of cite{AYT09})

(VAR x y)
(RULES
  or(true,true) -> true
  or(x,y) -> or(y,x)
)
(COMMENT Exercise 6.17 of \cite{BN98})

(VAR x y)
(RULES
  f(g(x,a,b)) -> x
  p(a) -> c
  g(f(h(c,d)),x,y) -> h(p(x),q(x))
  q(b) -> d
)
(COMMENT Exercise 6.18 of \cite{BN98})

(VAR x y z x1)
(RULES
  f(f(x,y),z) -> f(x,f(y,z))
  f(i(x1),x1) -> e
)
(COMMENT Example 6.2.2 of \cite{BN98})

(VAR x)
(RULES
  f(f(x)) -> g(x)
)
(COMMENT Example 6.2.7 of \cite{BN98})

(VAR x y)
(RULES
  +(s(x),y) -> s(+(x,y))
  +(x,s(y)) -> s(+(x,y))
  +(x,y) -> +(y,x)
)
(COMMENT Example 6.3.4 of \cite{BN98})

(VAR x)
(RULES
  f(g(f(x))) -> g(x)
)
(COMMENT Exercise 6.4 of \cite{BN98})

(VAR x)
(RULES
  f(g(f(x))) -> x
  f(g(x)) -> g(f(x))
)
(COMMENT Exercise 6.5(a) of \cite{BN98})