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


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
(6) YES


----------------------------------------

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

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

Q is empty.

----------------------------------------

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

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

Q is empty.

----------------------------------------

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

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

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

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

----------------------------------------

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

----------------------------------------

(5) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186

Node 163 is start node and node 164 is final node.

Those nodes are connected through the following edges:

* 163 to 165 labelled c_1(0)* 164 to 164 labelled #_1(0)* 165 to 166 labelled c_1(0)* 166 to 167 labelled b_1(0)* 167 to 168 labelled a_1(0)* 168 to 169 labelled c_1(0)* 169 to 170 labelled c_1(0)* 170 to 171 labelled b_1(0)* 171 to 172 labelled a_1(0)* 171 to 176 labelled c_1(1)* 172 to 173 labelled a_1(0)* 172 to 176 labelled c_1(1)* 173 to 174 labelled a_1(0)* 173 to 176 labelled c_1(1)* 174 to 175 labelled a_1(0)* 174 to 176 labelled c_1(1)* 175 to 164 labelled a_1(0)* 175 to 176 labelled c_1(1)* 176 to 177 labelled c_1(1)* 177 to 178 labelled b_1(1)* 178 to 179 labelled a_1(1)* 179 to 180 labelled c_1(1)* 180 to 181 labelled c_1(1)* 181 to 182 labelled b_1(1)* 182 to 183 labelled a_1(1)* 182 to 176 labelled c_1(1)* 183 to 184 labelled a_1(1)* 183 to 176 labelled c_1(1)* 184 to 185 labelled a_1(1)* 184 to 176 labelled c_1(1)* 185 to 186 labelled a_1(1)* 185 to 176 labelled c_1(1)* 186 to 164 labelled a_1(1)* 186 to 176 labelled c_1(1)


----------------------------------------

(6)
YES