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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

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


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

(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.

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

(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, 2, 3, 4, 7, 8

Node 1 is start node and node 2 is final node.

Those nodes are connected through the following edges:

* 1 to 3 labelled e_1(0)* 1 to 2 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 4 labelled e_1(1)* 1 to 7 labelled a_1(1)* 1 to 8 labelled e_1(2)* 2 to 2 labelled #_1(0)* 3 to 2 labelled u_1(0)* 4 to 2 labelled u_1(1)* 7 to 2 labelled e_1(1)* 8 to 2 labelled u_1(2)


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

(2)
YES