YES
by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| a(b(x0)) | → | x0 | 
| a(c(x0)) | → | c(c(x0)) | 
| b(c(x0)) | → | a(b(a(b(x0)))) | 
| b#(c(x0)) | → | b#(x0) | 
| b#(c(x0)) | → | a#(b(x0)) | 
| b#(c(x0)) | → | b#(a(b(x0))) | 
| b#(c(x0)) | → | a#(b(a(b(x0)))) | 
The dependency pairs are split into 1 component.
| b#(c(x0)) | → | b#(a(b(x0))) | 
| b#(c(x0)) | → | b#(x0) | 
| [b#(x1)] | = | 1 · x1 + -∞ | 
| [a(x1)] | = | 1 · x1 + 5 | 
| [b(x1)] | = | -1 · x1 + 3 | 
| [c(x1)] | = | 1 · x1 + 8 | 
| a(b(x0)) | → | x0 | 
| a(c(x0)) | → | c(c(x0)) | 
| b(c(x0)) | → | a(b(a(b(x0)))) | 
There are no pairs anymore.