(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:
p(f(f(x))) → q(f(g(x)))
p(g(g(x))) → q(g(f(x)))
q(f(f(x))) → p(f(g(x)))
q(g(g(x))) → p(g(f(x)))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7540259, 7540260, 7540262, 7540261, 7540263, 7540264
Node 7540259 is start node and node 7540260 is final node.
Those nodes are connect through the following edges:
- 7540259 to 7540261 labelled p_1(0), q_1(0)
- 7540259 to 7540263 labelled p_1(0), q_1(0)
- 7540260 to 7540260 labelled #_1(0)
- 7540262 to 7540260 labelled f_1(0)
- 7540261 to 7540262 labelled g_1(0)
- 7540263 to 7540264 labelled f_1(0)
- 7540264 to 7540260 labelled g_1(0)