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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) RFCMatchBoundsTRSProof [EQUIVALENT, 10 ms]
(2) YES


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

   d(x) -> e(u(x))
   d(u(x)) -> c(x)
   c(u(x)) -> b(x)
   v(e(x)) -> x
   b(u(x)) -> a(e(x))

Q is empty.

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(1) 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:

   d(x) -> e(u(x))
   d(u(x)) -> c(x)
   c(u(x)) -> b(x)
   v(e(x)) -> x
   b(u(x)) -> a(e(x))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 8, 11, 12, 13

Node 1 is start node and node 3 is final node.

Those nodes are connected through the following edges:

* 1 to 8 labelled e_1(0)* 1 to 3 labelled c_1(0), b_1(0), d_1(0), e_1(0), u_1(0), v_1(0), a_1(0), b_1(1), c_1(1), d_1(1), e_1(1), u_1(1), v_1(1), a_1(1)* 1 to 1 labelled a_1(0), a_1(1)* 1 to 11 labelled e_1(1)* 1 to 12 labelled a_1(1)* 1 to 13 labelled e_1(2)* 3 to 3 labelled #_1(0)* 8 to 3 labelled u_1(0)* 11 to 3 labelled u_1(1)* 12 to 3 labelled e_1(1)* 13 to 3 labelled u_1(2)


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(2)
YES