/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 31 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:

   s(a) -> a
   s(s(x)) -> x
   s(f(x, y)) -> f(s(y), s(x))
   s(g(x, y)) -> g(s(x), s(y))
   f(x, a) -> x
   f(a, y) -> y
   f(g(x, y), g(u, v)) -> g(f(x, u), f(y, v))
   g(a, a) -> a

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:s_1 > f_2 > g_2 > a

and weight map:

   a=1
   s_1=0
   f_2=0
   g_2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   s(a) -> a
   s(s(x)) -> x
   s(f(x, y)) -> f(s(y), s(x))
   s(g(x, y)) -> g(s(x), s(y))
   f(x, a) -> x
   f(a, y) -> y
   f(g(x, y), g(u, v)) -> g(f(x, u), f(y, v))
   g(a, a) -> a




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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