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


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 52 ms]
(2) NO


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

   f(0, 1, X) -> f(g(X, X), X, X)
   g(X, Y) -> X
   g(X, Y) -> Y



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   f(0, 1, X) -> f(g(X, X), X, X)
   g(X, Y) -> X
   g(X, Y) -> Y



Outermost Strategy.

---------- Loop: ----------

f(g(g(0, 1), g(0, 1)), g(0, 1), g(0, 1)) -> f(g(g(0, 1), g(0, 1)), 1, g(0, 1)) with rule g(X', Y'') -> Y'' at position [1] and matcher [X' / 0, Y'' / 1]

f(g(g(0, 1), g(0, 1)), 1, g(0, 1)) -> f(g(0, 1), 1, g(0, 1)) with rule g(X', Y') -> X' at position [0] and matcher [X' / g(0, 1), Y' / g(0, 1)]

f(g(0, 1), 1, g(0, 1)) -> f(0, 1, g(0, 1)) with rule g(X', Y) -> X' at position [0] and matcher [X' / 0, Y / 1]

f(0, 1, g(0, 1)) -> f(g(g(0, 1), g(0, 1)), g(0, 1), g(0, 1)) with rule f(0, 1, X) -> f(g(X, X), X, X) at position [] and matcher [X / g(0, 1)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [].

Context: []

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO