Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-260)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(b(x1))	→	b(c(b(a(c(a(a(x1)))))))	(2)
c(c(x1))	→	x1	(3)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(a(b(x1))))
	→	a(a(b(c(b(a(c(a(a(x1)))))))))
	→	a(a(b(c(b(a(c(a(x1))))))))
	→	a(a(b(c(b(a(c(x1)))))))
	→	a(a(b(c(b(c(x1))))))
	→	a(b(c(b(a(c(a(a(c(b(c(x1)))))))))))
	→	a(b(c(b(a(c(a(c(b(c(x1))))))))))
	→	a(b(c(b(a(c(c(b(c(x1)))))))))
	→	a(b(c(b(a(b(c(x1)))))))
	→	a(b(c(b(b(c(b(a(c(a(a(c(x1))))))))))))
	→	a(b(c(b(b(c(b(a(c(a(c(x1)))))))))))
	→	a(b(c(b(b(c(b(a(c(c(x1))))))))))
	→	a(b(c(b(b(c(b(a(x1))))))))
	→	a(b(c(b(b(c(b(x1)))))))
	→	b(c(b(a(c(a(a(c(b(b(c(b(x1))))))))))))
	→	b(c(b(a(c(a(c(b(b(c(b(x1)))))))))))
	→	b(c(b(a(c(c(b(b(c(b(x1))))))))))
	→	b(c(b(a(b(b(c(b(x1))))))))
	→	b(c(b(b(c(b(a(c(a(a(b(c(b(x1)))))))))))))
	→	b(c(b(b(c(b(c(a(a(b(c(b(x1))))))))))))
	→	b(c(b(b(c(b(c(a(b(c(b(a(c(a(a(c(b(x1)))))))))))))))))
	→	b(c(b(b(c(b(c(a(b(c(b(a(c(a(c(b(x1))))))))))))))))
	→	b(c(b(b(c(b(c(a(b(c(b(a(c(c(b(x1)))))))))))))))
	→	b(c(b(b(c(b(c(a(b(c(b(a(b(x1)))))))))))))
	→	b(c(b(b(c(b(c(b(c(b(a(c(a(a(c(b(a(b(x1))))))))))))))))))
	→	b(c(b(b(c(b(c(b(c(b(a(c(a(c(b(a(b(x1)))))))))))))))))
	→	b(c(b(b(c(b(c(b(c(b(a(c(c(b(a(b(x1))))))))))))))))
	→	b(c(b(b(c(b(c(b(c(b(a(b(a(b(x1))))))))))))))
	→	b(c(b(b(c(b(c(b(c(b(b(c(b(a(c(a(a(a(b(x1)))))))))))))))))))
	=	t₂₈

where t₂₈ = C[t₀σ] and σ = {x1/x1} and C = b(c(b(b(c(b(c(b(c(b(b(c(b(a(c(☐)))))))))))))))