Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-522)

The rewrite relation of the following TRS is considered.

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

Prove or disprove termination.

No.

The following loop proves nontermination.

t₀	=	a(a(a(a(b(c(b(c(a(a(a(a(a(a(x1))))))))))))))
	→	a(a(a(c(c(a(a(a(c(b(c(a(a(a(a(a(a(x1)))))))))))))))))
	→	a(a(a(c(c(a(a(b(b(c(a(a(a(a(a(a(x1))))))))))))))))
	→	a(a(b(c(a(a(b(b(c(a(a(a(a(a(a(x1)))))))))))))))
	→	a(a(b(c(a(c(c(a(a(a(b(c(a(a(a(a(a(a(x1))))))))))))))))))
	→	a(a(b(c(b(c(a(a(a(b(c(a(a(a(a(a(a(x1)))))))))))))))))
	→	a(a(b(c(b(c(a(a(c(c(a(a(a(c(a(a(a(a(a(a(x1))))))))))))))))))))
	→	a(a(b(c(b(c(a(a(c(c(a(a(b(a(a(a(a(a(a(x1)))))))))))))))))))
	→	a(a(b(c(b(c(a(b(c(a(a(b(a(a(a(a(a(a(x1))))))))))))))))))
	→	a(a(b(c(b(c(a(b(c(a(c(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))
	→	a(a(b(c(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))
	→	a(c(c(a(a(a(c(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))
	→	a(c(c(a(a(b(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))
	→	b(c(a(a(b(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))
	→	b(c(a(c(c(a(a(a(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))
	→	b(c(b(c(a(a(a(b(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))
	→	b(c(b(c(a(a(c(c(a(a(a(c(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))))
	→	b(c(b(c(a(a(c(c(a(a(b(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))
	→	b(c(b(c(a(b(c(a(a(b(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))
	→	b(c(b(c(a(b(c(a(c(c(a(a(a(a(b(c(b(c(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))
	=	t₁₉

where t₁₉ = C[t₀σ] and σ = {x1/a(a(a(x1)))} and C = b(c(b(c(a(b(c(a(c(c(☐))))))))))