Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-564)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	c(c(b(a(a(a(c(c(x1))))))))
	→	c(c(b(a(a(c(c(b(b(c(x1))))))))))
	→	c(c(b(a(c(c(b(b(c(b(b(c(x1))))))))))))
	→	c(c(b(a(c(c(b(a(a(b(b(c(x1))))))))))))
	→	c(c(b(a(c(c(b(a(b(c(x1))))))))))
	→	c(c(b(a(c(c(b(c(x1))))))))
	→	c(c(b(c(c(b(b(c(b(c(x1))))))))))
	→	c(c(b(c(c(b(a(a(b(c(x1))))))))))
	→	c(c(b(c(c(b(a(c(x1))))))))
	→	c(c(a(a(c(b(a(c(x1))))))))
	→	c(c(a(a(c(b(c(c(b(b(x1))))))))))
	→	c(c(a(a(c(a(a(c(b(b(x1))))))))))
	→	c(c(a(a(c(a(c(c(b(b(b(b(x1))))))))))))
	→	c(c(a(a(c(c(c(b(b(c(b(b(b(b(x1))))))))))))))
	→	c(c(a(a(c(c(c(b(a(a(b(b(b(b(x1))))))))))))))
	→	c(c(a(a(c(c(c(b(a(b(b(b(x1))))))))))))
	→	c(c(a(a(c(c(c(b(b(b(x1))))))))))
	→	c(c(a(c(c(b(b(c(c(b(b(b(x1))))))))))))
	→	c(c(a(c(c(b(a(a(c(b(b(b(x1))))))))))))
	→	c(c(a(c(c(b(a(c(c(b(b(b(b(b(x1))))))))))))))
	→	c(c(a(c(c(b(c(c(b(b(c(b(b(b(b(b(x1))))))))))))))))
	→	c(c(a(c(c(b(c(c(b(a(a(b(b(b(b(b(x1))))))))))))))))
	→	c(c(a(c(c(b(c(c(b(a(b(b(b(b(x1))))))))))))))
	→	c(c(a(c(c(b(c(c(b(b(b(b(x1))))))))))))
	→	c(c(a(c(c(a(a(c(b(b(b(b(x1))))))))))))
	→	c(c(c(c(b(b(c(a(a(c(b(b(b(b(x1))))))))))))))
	→	c(c(c(c(b(a(a(a(a(c(b(b(b(b(x1))))))))))))))
	→	c(c(c(c(b(a(a(a(c(c(b(b(b(b(b(b(x1))))))))))))))))
	=	t₂₇

where t₂₇ = C[t₀σ] and σ = {x1/b(b(b(b(b(b(x1))))))} and C = c(c(☐))