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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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:
187, 188, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251

Node 187 is start node and node 188 is final node.

Those nodes are connected through the following edges:

* 187 to 215 labelled a_1(0)* 188 to 188 labelled #_1(0)* 215 to 216 labelled a_1(0)* 216 to 217 labelled b_1(0)* 217 to 218 labelled c_1(0)* 218 to 219 labelled c_1(0)* 219 to 220 labelled a_1(0)* 220 to 221 labelled a_1(0)* 221 to 222 labelled b_1(0)* 222 to 223 labelled c_1(0)* 222 to 240 labelled a_1(1)* 223 to 224 labelled a_1(0)* 224 to 225 labelled a_1(0)* 225 to 226 labelled b_1(0)* 226 to 188 labelled c_1(0)* 226 to 240 labelled a_1(1)* 240 to 241 labelled a_1(1)* 241 to 242 labelled b_1(1)* 242 to 243 labelled c_1(1)* 243 to 244 labelled c_1(1)* 244 to 245 labelled a_1(1)* 245 to 246 labelled a_1(1)* 246 to 247 labelled b_1(1)* 247 to 248 labelled c_1(1)* 247 to 240 labelled a_1(1)* 248 to 249 labelled a_1(1)* 249 to 250 labelled a_1(1)* 250 to 251 labelled b_1(1)* 251 to 188 labelled c_1(1)* 251 to 240 labelled a_1(1)


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(4)
YES