YES
by ACP
The rewrite relation of the following TRS is considered.
foo(0(x)) | → | 0(s(p(p(p(s(s(s(p(s(x)))))))))) |
foo(s(x)) | → | p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x)))))))))))))))))))))))))) |
bar(0(x)) | → | 0(p(s(s(s(x))))) |
bar(s(x)) | → | p(s(p(p(s(s(foo(s(p(p(s(s(x)))))))))))) |
p(p(s(x))) | → | p(x) |
p(s(x)) | → | x |
p(0(x)) | → | 0(s(s(s(s(x))))) |
ACP