Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-220)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(b(x1))	→	b(b(c(a(x1))))	(2)
b(x1)	→	x1	(3)
c(c(c(x1)))	→	a(x1)	(4)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	a(a(c(c(a(a(b(b(x1))))))))
	→	a(a(c(c(a(b(b(c(a(b(x1))))))))))
	→	a(a(c(c(b(b(c(a(b(c(a(b(x1))))))))))))
	→	a(a(c(c(b(c(a(b(c(a(b(x1)))))))))))
	→	a(a(c(c(c(a(b(c(a(b(x1))))))))))
	→	a(a(a(a(b(c(a(b(x1))))))))
	→	a(a(a(b(b(c(a(c(a(b(x1))))))))))
	→	a(a(a(b(b(c(c(a(b(x1)))))))))
	→	a(a(b(b(c(a(b(c(c(a(b(x1)))))))))))
	→	a(a(b(b(c(b(b(c(a(c(c(a(b(x1)))))))))))))
	→	a(a(b(b(c(b(b(c(c(c(a(b(x1))))))))))))
	→	a(a(b(b(c(b(b(a(a(b(x1))))))))))
	→	a(b(b(c(a(b(c(b(b(a(a(b(x1))))))))))))
	→	a(b(c(a(b(c(b(b(a(a(b(x1)))))))))))
	→	a(b(c(b(b(c(a(c(b(b(a(a(b(x1)))))))))))))
	→	a(b(c(b(b(c(c(b(b(a(a(b(x1))))))))))))
	→	a(b(c(b(c(c(b(b(a(a(b(x1)))))))))))
	→	a(b(c(c(c(b(b(a(a(b(x1))))))))))
	→	a(b(a(b(b(a(a(b(x1))))))))
	→	b(b(c(a(a(b(b(a(a(b(x1))))))))))
	→	b(c(a(a(b(b(a(a(b(x1)))))))))
	→	c(a(a(b(b(a(a(b(x1))))))))
	→	c(a(b(b(c(a(b(a(a(b(x1))))))))))
	→	c(b(b(c(a(b(c(a(b(a(a(b(x1))))))))))))
	→	c(b(c(a(b(c(a(b(a(a(b(x1)))))))))))
	→	c(c(a(b(c(a(b(a(a(b(x1))))))))))
	→	c(c(a(b(c(b(b(c(a(a(a(b(x1))))))))))))
	→	c(c(a(b(c(b(c(a(a(a(b(x1)))))))))))
	→	c(c(a(b(c(c(a(a(a(b(x1))))))))))
	→	c(c(b(b(c(a(c(c(a(a(a(b(x1))))))))))))
	→	c(c(b(c(a(c(c(a(a(a(b(x1)))))))))))
	→	c(c(c(a(c(c(a(a(a(b(x1))))))))))
	→	a(a(c(c(a(a(a(b(x1))))))))
	→	a(a(c(c(a(a(b(b(c(a(x1))))))))))
	=	t₃₃

where t₃₃ = t₀σ and σ = {x1/c(a(x1))}