NO Non-Confluence Proof

Non-Confluence Proof

by Hakusan

Input

The rewrite relation of the following TRS is considered.

a(a(x)) b(c(x))
b(b(x)) c(d(x))
c(c(x)) d(d(d(x)))
d(d(d(x))) a(c(x))

Proof

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = a(a(a(x1)))
1 a(b(c(x1)))
= t1

t0 = a(a(a(x1)))
ε b(c(a(x1)))
= t1

The two resulting terms cannot be joined for the following reason:

Tool configuration

Hakusan