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


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 48 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

   f(a) -> b
   f(c) -> d
   f(g(x, y)) -> g(f(x), f(y))
   f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
   g(x, x) -> h(e, x)

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Quasi precedence:
f_1 > b > h_2
f_1 > g_2 > e > h_2
a > b > h_2
c > d > h_2


Status:
f_1: multiset status
a: multiset status
b: multiset status
c: multiset status
d: multiset status
g_2: multiset status
h_2: multiset status
e: multiset status

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   f(a) -> b
   f(c) -> d
   f(g(x, y)) -> g(f(x), f(y))
   f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
   g(x, x) -> h(e, x)




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(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES