(0) Obligation:

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

f(h(x)) → f(i(x))
g(i(x)) → g(h(x))
h(a) → b
i(a) → b

Q is empty.

(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)

Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

f(h(x)) → f(i(x))
g(i(x)) → g(h(x))
h(a) → b
i(a) → b

The certificate found is represented by the following graph.

The certificate consists of the following enumerated nodes:

9113444, 9113445, 9113446, 9113447

Node 9113444 is start node and node 9113445 is final node.

Those nodes are connect through the following edges:

  • 9113444 to 9113446 labelled g_1(0)
  • 9113444 to 9113447 labelled f_1(0)
  • 9113444 to 9113445 labelled b(0)
  • 9113445 to 9113445 labelled #_1(0)
  • 9113446 to 9113445 labelled h_1(0), b(1)
  • 9113447 to 9113445 labelled i_1(0), b(1)

(2) TRUE