/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 117 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) -> h(X, X)
   h(0, X) -> f(0, 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) -> h(X, X)
   h(0, X) -> f(0, X, X)
   g(X, Y) -> X
   g(X, Y) -> Y



Outermost Strategy.

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

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

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

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

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

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