(3) Strip Symbols Proof (SOUND transformation)
We were given the following TRS:
a(a(a(c(b(a(c(b(a(x))))))))) → c(b(a(c(b(a(c(b(a(a(a(a(x))))))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]:
a(a(a(c(b(a(c(b(x)))))))) → c(b(a(c(b(a(c(b(a(a(a(x)))))))))))
(5) 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:
a(a(a(c(b(a(c(b(x)))))))) → c(b(a(c(b(a(c(b(a(a(a(x)))))))))))
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177
Node 156 is start node and node 157 is final node.
Those nodes are connected through the following edges:
- 156 to 158 labelled c_1(0)
- 157 to 157 labelled #_1(0)
- 158 to 159 labelled b_1(0)
- 159 to 160 labelled a_1(0)
- 160 to 161 labelled c_1(0)
- 161 to 162 labelled b_1(0)
- 162 to 163 labelled a_1(0)
- 163 to 164 labelled c_1(0)
- 164 to 165 labelled b_1(0)
- 165 to 166 labelled a_1(0)
- 165 to 168 labelled c_1(1)
- 166 to 167 labelled a_1(0)
- 166 to 168 labelled c_1(1)
- 167 to 157 labelled a_1(0)
- 167 to 168 labelled c_1(1)
- 168 to 169 labelled b_1(1)
- 169 to 170 labelled a_1(1)
- 170 to 171 labelled c_1(1)
- 171 to 172 labelled b_1(1)
- 172 to 173 labelled a_1(1)
- 173 to 174 labelled c_1(1)
- 174 to 175 labelled b_1(1)
- 175 to 176 labelled a_1(1)
- 175 to 168 labelled c_1(1)
- 176 to 177 labelled a_1(1)
- 176 to 168 labelled c_1(1)
- 177 to 157 labelled a_1(1)
- 177 to 168 labelled c_1(1)