YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   b(a(a(b(a(x1))))) -> a(b(a(a(b(b(a(a(b(x1)))))))))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(b(a(x1)))))))))

Q is empty.

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(3) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(b(a(x1)))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220

Node 179 is start node and node 180 is final node.

Those nodes are connected through the following edges:

* 179 to 181 labelled b_1(0)* 180 to 180 labelled #_1(0)* 181 to 182 labelled a_1(0)* 182 to 183 labelled a_1(0)* 183 to 184 labelled b_1(0)* 184 to 185 labelled b_1(0)* 185 to 186 labelled a_1(0)* 185 to 197 labelled b_1(1)* 186 to 187 labelled a_1(0)* 186 to 189 labelled b_1(1)* 187 to 188 labelled b_1(0)* 188 to 180 labelled a_1(0)* 188 to 189 labelled b_1(1)* 189 to 190 labelled a_1(1)* 190 to 191 labelled a_1(1)* 191 to 192 labelled b_1(1)* 192 to 193 labelled b_1(1)* 193 to 194 labelled a_1(1)* 193 to 205 labelled b_1(2)* 194 to 195 labelled a_1(1)* 194 to 189 labelled b_1(1)* 195 to 196 labelled b_1(1)* 196 to 180 labelled a_1(1)* 196 to 189 labelled b_1(1)* 197 to 198 labelled a_1(1)* 198 to 199 labelled a_1(1)* 199 to 200 labelled b_1(1)* 200 to 201 labelled b_1(1)* 201 to 202 labelled a_1(1)* 202 to 203 labelled a_1(1)* 203 to 204 labelled b_1(1)* 204 to 192 labelled a_1(1)* 204 to 213 labelled b_1(2)* 205 to 206 labelled a_1(2)* 206 to 207 labelled a_1(2)* 207 to 208 labelled b_1(2)* 208 to 209 labelled b_1(2)* 209 to 210 labelled a_1(2)* 210 to 211 labelled a_1(2)* 211 to 212 labelled b_1(2)* 212 to 192 labelled a_1(2)* 212 to 213 labelled b_1(2)* 213 to 214 labelled a_1(2)* 214 to 215 labelled a_1(2)* 215 to 216 labelled b_1(2)* 216 to 217 labelled b_1(2)* 217 to 218 labelled a_1(2)* 217 to 205 labelled b_1(2)* 218 to 219 labelled a_1(2)* 218 to 189 labelled b_1(1)* 219 to 220 labelled b_1(2)* 220 to 196 labelled a_1(2)* 220 to 205 labelled b_1(2)


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(4)
YES