NO Non-Confluence Proof

Non-Confluence Proof

by ACP

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 = c(b(b(c_1)))
1 c(c(d(c_1)))
ε d(d(d(d(c_1))))
ε a(c(d(c_1)))
= t3

t0 = c(b(b(c_1)))
1 c(c(d(c_1)))
ε d(d(d(d(c_1))))
1 d(a(c(c_1)))
= t3

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

Tool configuration

ACP