NO Non-Confluence Proof

Non-Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

a(a(x)) → b(x)
b(a(x)) → a(b(x))
b(b(c(x))) → c(a(x))
b(b(x)) → a(a(a(x)))
c(a(x)) → b(a(c(x)))

Proof

1 Non-Joinable Fork

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

t0 = c(a(a(x1013)))
→1 c(b(x1013))
= t1

t0 = c(a(a(x1013)))
→ε b(a(c(a(x1013))))
→ε a(b(c(a(x1013))))
→1.1 a(b(b(a(c(x1013)))))
→1.1 a(b(a(b(c(x1013)))))
→1 a(a(b(b(c(x1013)))))
→ε b(b(b(c(x1013))))
→1 b(c(a(x1013)))
→1 b(b(a(c(x1013))))
→1 b(a(b(c(x1013))))
→ε a(b(b(c(x1013))))
→1 a(c(a(x1013)))
→1 a(b(a(c(x1013))))
→1 a(a(b(c(x1013))))
→ε b(b(c(x1013)))
→ε c(a(x1013))
→ε b(a(c(x1013)))
→ε a(b(c(x1013)))
= t17

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

Tool configuration

csi