(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
b(x, y) → c(a(c(y), a(0, x)))
a(y, x) → y
a(y, c(b(a(0, x), 0))) → b(a(c(b(0, y)), x), 0)
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
B(x, y) → A(c(y), a(0, x))
B(x, y) → A(0, x)
A(y, c(b(a(0, x), 0))) → B(a(c(b(0, y)), x), 0)
A(y, c(b(a(0, x), 0))) → A(c(b(0, y)), x)
A(y, c(b(a(0, x), 0))) → B(0, y)
The TRS R consists of the following rules:
b(x, y) → c(a(c(y), a(0, x)))
a(y, x) → y
a(y, c(b(a(0, x), 0))) → b(a(c(b(0, y)), x), 0)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.