/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) Strip Symbols Proof [SOUND, 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:

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

Q is empty.

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(1) Strip Symbols Proof (SOUND)
We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))

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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))

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 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
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

Node 185 is start node and node 186 is final node.

Those nodes are connected through the following edges:

* 185 to 187 labelled a_1(0)* 186 to 186 labelled #_1(0)* 187 to 188 labelled a_1(0)* 188 to 189 labelled b_1(0)* 189 to 190 labelled c_1(0)* 190 to 191 labelled c_1(0)* 191 to 192 labelled a_1(0)* 192 to 193 labelled a_1(0)* 193 to 194 labelled b_1(0)* 194 to 195 labelled c_1(0)* 194 to 199 labelled a_1(1)* 195 to 196 labelled a_1(0)* 196 to 197 labelled a_1(0)* 197 to 198 labelled b_1(0)* 198 to 186 labelled c_1(0)* 198 to 199 labelled a_1(1)* 199 to 200 labelled a_1(1)* 200 to 201 labelled b_1(1)* 201 to 202 labelled c_1(1)* 202 to 203 labelled c_1(1)* 203 to 204 labelled a_1(1)* 204 to 205 labelled a_1(1)* 205 to 206 labelled b_1(1)* 206 to 207 labelled c_1(1)* 206 to 199 labelled a_1(1)* 207 to 208 labelled a_1(1)* 208 to 209 labelled a_1(1)* 209 to 210 labelled b_1(1)* 210 to 186 labelled c_1(1)* 210 to 199 labelled a_1(1)


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(4)
YES