YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 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(b(a(X))) -> a(a(b(b(c(c(X))))))
   a(X) -> e
   b(X) -> e
   c(X) -> e

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(c(X))) -> c(c(b(b(a(a(X))))))
   a(X) -> e'(X)
   b(X) -> e'(X)
   c(X) -> e'(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(b(c(X))) -> c(c(b(b(a(a(X))))))
   a(X) -> e'(X)
   b(X) -> e'(X)
   c(X) -> e'(X)

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Node 13 is start node and node 14 is final node.

Those nodes are connected through the following edges:

* 13 to 15 labelled c_1(0), e'_1(1)* 13 to 14 labelled e'_1(0)* 14 to 14 labelled #_1(0)* 15 to 16 labelled c_1(0), e'_1(1)* 16 to 17 labelled b_1(0), e'_1(1)* 17 to 18 labelled b_1(0), e'_1(1)* 18 to 19 labelled a_1(0), e'_1(1)* 19 to 14 labelled a_1(0), e'_1(1)* 19 to 20 labelled c_1(1), e'_1(2)* 20 to 21 labelled c_1(1), e'_1(2)* 21 to 22 labelled b_1(1), e'_1(2)* 22 to 23 labelled b_1(1), e'_1(2)* 23 to 24 labelled a_1(1), e'_1(2)* 24 to 14 labelled a_1(1), e'_1(2)* 24 to 20 labelled c_1(1), e'_1(2)


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(4)
YES