(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x1) → b(x1)
a(c(b(x1))) → c(a(b(a(c(x1)))))
b(c(x1)) → x1
Q is empty.
(1) QTRS Reverse (EQUIVALENT transformation)
We applied the QTRS Reverse Processor [REVERSE].
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x) → b(x)
b(c(a(x))) → c(a(b(a(c(x)))))
c(b(x)) → x
Q is empty.
(3) NonTerminationProof (EQUIVALENT transformation)
We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
Found the self-embedding DerivationStructure:
b c a a a a → c b b c a a a a a c
b c a a a a →
c b b c a a a a a cby OverlapClosure OC 2
b c a → c b b b c
by OverlapClosure OC 3b c a → c b b a c
by OverlapClosure OC 3b c a → c a b a c
by original rule (OC 1)
a → b
by original rule (OC 1)
a → b
by original rule (OC 1)
b c a a a → c a a a a a c
by OverlapClosure OC 3b c a a a → c a c b a a a a c
by OverlapClosure OC 3b c a a a → c a c a c a b a a a c
by OverlapClosure OC 3b c a a a → c a c a b c a b a a c
by OverlapClosure OC 3b c a a a → c a c a b a c a b a c
by OverlapClosure OC 2b c a a → c a c a b a a c
by OverlapClosure OC 3b c a a → c a c a b a c b a c
by OverlapClosure OC 3b c a a → c a b c a b a c
by OverlapClosure OC 2b c a → c a b b c
by OverlapClosure OC 3b c a → c a b a c
by original rule (OC 1)
a → b
by original rule (OC 1)
b c a → c a b a c
by original rule (OC 1)
b c a → c a b a c
by original rule (OC 1)
c b →
by original rule (OC 1)
a c a → c a b a c
by OverlapClosure OC 2a → b
by original rule (OC 1)
b c a → c a b a c
by original rule (OC 1)
a c a b → c a b a
by OverlapClosure OC 2a → b
by original rule (OC 1)
b c a b → c a b a
by OverlapClosure OC 2b c a → c a b a c
by original rule (OC 1)
c b →
by original rule (OC 1)
b c a b → c a b a
by OverlapClosure OC 2b c a → c a b a c
by original rule (OC 1)
c b →
by original rule (OC 1)
a c a b → b a
by OverlapClosure OC 3a c a b → c b b a
by OverlapClosure OC 2a → b
by original rule (OC 1)
b c a b → c b b a
by OverlapClosure OC 2b c a → c b b a c
by OverlapClosure OC 3b c a → c a b a c
by original rule (OC 1)
a → b
by original rule (OC 1)
c b →
by original rule (OC 1)
c b →
by original rule (OC 1)
c b →
by original rule (OC 1)
(4) NO