(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X, X) → f(a, n__b)
b → a
b → n__b
activate(n__b) → b
activate(X) → X
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(a) = 0
POL(activate(x1)) = 2 + x1
POL(b) = 1
POL(f(x1, x2)) = x1 + x2
POL(n__b) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
b → a
b → n__b
activate(n__b) → b
activate(X) → X
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X, X) → f(a, n__b)
Q is empty.
(3) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none
The TRS R 2 is
f(X, X) → f(a, n__b)
The signature Sigma is {
f}
(4) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X, X) → f(a, n__b)
The set Q consists of the following terms:
f(x0, x0)
(5) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(6) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(X, X) → F(a, n__b)
The TRS R consists of the following rules:
f(X, X) → f(a, n__b)
The set Q consists of the following terms:
f(x0, x0)
We have to consider all minimal (P,Q,R)-chains.
(7) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
(8) TRUE