Certification Problem

Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-2)

The rewrite relation of the following TRS is considered.

a(a(a(a(x1))))	→	a(c(a(c(c(x1)))))	(1)
c(c(c(x1)))	→	a(a(a(x1)))	(2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(a(a(c(a(a(a(c(a(a(c(a(x7666)))))))))))))
	→	a(c(a(c(c(c(a(a(a(c(a(a(c(a(x7666))))))))))))))
	→	a(c(a(a(a(a(a(a(a(c(a(a(c(a(x7666))))))))))))))
	→	a(c(a(a(a(a(c(a(c(c(c(a(a(c(a(x7666)))))))))))))))
	→	a(c(a(a(a(a(c(a(a(a(a(a(a(c(a(x7666)))))))))))))))
	→	a(c(a(a(a(a(c(a(a(a(c(a(c(c(c(a(x7666))))))))))))))))
	→	a(c(a(a(a(a(c(a(a(a(c(a(a(a(a(a(x7666))))))))))))))))
	→	a(c(a(a(a(a(c(a(a(a(c(a(a(c(a(c(c(x7666)))))))))))))))))
	=	t₇

where t₇ = C[t₀σ] and σ = {x7666/c(c(x7666))} and C = a(c(☐))