0.00/0.05	YES
0.00/0.05	
0.00/0.05	# Compositional parallel rule labeling (Shintani and Hirokawa 2022).
0.00/0.05	
0.00/0.05	Consider the left-linear TRS R:
0.00/0.05	
0.00/0.05	  b(a(b(b(x)))) -> b(b(b(a(b(x)))))
0.00/0.05	  b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
0.00/0.05	  b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))
0.00/0.05	
0.00/0.05	Let C be the following subset of R:
0.00/0.05	
0.00/0.05	  (empty)
0.00/0.05	
0.00/0.05	All parallel critical peaks (except C's) are decreasing wrt rule labeling:
0.00/0.05	
0.00/0.05	  phi(b(a(b(b(x)))) -> b(b(b(a(b(x)))))) = 1
0.00/0.05	  phi(b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))) = 1
0.00/0.05	  phi(b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))) = 1
0.00/0.05	
0.00/0.05	  psi(b(a(b(b(x)))) -> b(b(b(a(b(x)))))) = 1
0.00/0.05	  psi(b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))) = 1
0.00/0.05	  psi(b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))) = 1
0.00/0.05	
0.00/0.05	
0.00/0.05	Therefore, the confluence of R follows from that of C.
0.00/0.05	
0.00/0.05	# Compositional parallel critical pair system (Shintani and Hirokawa 2022).
0.00/0.05	
0.00/0.05	Consider the left-linear TRS R:
0.00/0.05	
0.00/0.05	  (empty)
0.00/0.05	
0.00/0.05	Let C be the following subset of R:
0.00/0.05	
0.00/0.05	  (empty)
0.00/0.05	
0.00/0.05	The parallel critical pair system PCPS(R,C) is:
0.00/0.05	
0.00/0.05	  (empty)
0.00/0.05	
0.00/0.05	The TRS R is locally confluent and PCPS(R,C)/R is terminating.
0.00/0.05	Therefore, the confluence of R follows from that of C.
0.00/0.05	
0.00/0.05	# Emptiness.
0.00/0.05	
0.00/0.05	The empty TRS is confluent.
0.00/0.05	
0.00/0.05	EOF