(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

a(b(x)) → a(c(b(x)))

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

a(b(x)) → a(c(b(x)))

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

725881, 725882, 725884, 725883

Node 725881 is start node and node 725882 is final node.

Those nodes are connect through the following edges:

  • 725881 to 725883 labelled a_1(0)
  • 725882 to 725882 labelled #_1(0)
  • 725884 to 725882 labelled b_1(0)
  • 725883 to 725884 labelled c_1(0)

(2) TRUE