Term Rewriting System R:
[x]
a(b(x)) -> b(a(a(x)))
a(u(x)) -> x
b(c(x)) -> c(b(b(x)))
b(v(x)) -> x
c(a(x)) -> a(c(c(x)))
c(w(x)) -> x
u(a(x)) -> x
v(b(x)) -> x
w(c(x)) -> x

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

A(b(x)) -> B(a(a(x)))
A(b(x)) -> A(a(x))
A(b(x)) -> A(x)
B(c(x)) -> C(b(b(x)))
B(c(x)) -> B(b(x))
B(c(x)) -> B(x)
C(a(x)) -> A(c(c(x)))
C(a(x)) -> C(c(x))
C(a(x)) -> C(x)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

B(c(x)) -> B(x)
B(c(x)) -> B(b(x))
C(a(x)) -> C(x)
C(a(x)) -> C(c(x))
A(b(x)) -> A(x)
A(b(x)) -> A(a(x))
C(a(x)) -> A(c(c(x)))
B(c(x)) -> C(b(b(x)))
A(b(x)) -> B(a(a(x)))

Rules:

a(b(x)) -> b(a(a(x)))
a(u(x)) -> x
b(c(x)) -> c(b(b(x)))
b(v(x)) -> x
c(a(x)) -> a(c(c(x)))
c(w(x)) -> x
u(a(x)) -> x
v(b(x)) -> x
w(c(x)) -> x

Strategy:

innermost

Innermost Termination of R could not be shown.
Duration:
0:02 minutes