Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-101)

The rewrite relation of the following TRS is considered.

a(x1)	→	x1	(1)
a(a(a(x1)))	→	b(x1)	(2)
b(c(x1))	→	c(c(a(b(x1))))	(3)
c(x1)	→	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(b(b(c(c(x1))))))
	→	a(a(b(c(c(a(b(c(x1))))))))
	→	a(a(b(c(c(b(c(x1)))))))
	→	a(a(c(c(a(b(c(b(c(x1)))))))))
	→	a(a(c(a(b(c(b(c(x1))))))))
	→	a(a(a(b(c(b(c(x1)))))))
	→	b(b(c(b(c(x1)))))
	→	b(c(c(a(b(b(c(x1)))))))
	→	b(c(c(b(b(c(x1))))))
	→	c(c(a(b(c(b(b(c(x1))))))))
	→	c(a(b(c(b(b(c(x1)))))))
	→	a(b(c(b(b(c(x1))))))
	→	a(c(c(a(b(b(b(c(x1))))))))
	→	a(c(a(b(b(b(c(x1)))))))
	→	a(a(b(b(b(c(x1))))))
	→	a(a(b(b(c(c(a(b(x1))))))))
	=	t₁₅

where t₁₅ = t₀σ and σ = {x1/a(b(x1))}