/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 61 ms]
(2) NO


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

   f(h(x), y) -> h(f(y, f(x, h(f(a, a)))))



Outermost Strategy.

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

   f(h(x), y) -> h(f(y, f(x, h(f(a, a)))))



Outermost Strategy.

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

f(f(f(h(x), y''), h(x'')), f(f(h(x'), y'''), h(x'''))) -> f(f(h(f(y'', f(x, h(f(a, a))))), h(x'')), f(f(h(x'), y'''), h(x'''))) with rule f(h(x1), y'''') -> h(f(y'''', f(x1, h(f(a, a))))) at position [0,0] and matcher [x1 / x, y'''' / y'']

f(f(h(f(y'', f(x, h(f(a, a))))), h(x'')), f(f(h(x'), y'''), h(x'''))) -> f(h(f(h(x''), f(f(y'', f(x, h(f(a, a)))), h(f(a, a))))), f(f(h(x'), y'''), h(x'''))) with rule f(h(x'1), y') -> h(f(y', f(x'1, h(f(a, a))))) at position [0] and matcher [x'1 / f(y'', f(x, h(f(a, a)))), y' / h(x'')]

f(h(f(h(x''), f(f(y'', f(x, h(f(a, a)))), h(f(a, a))))), f(f(h(x'), y'''), h(x'''))) -> h(f(f(f(h(x'), y'''), h(x''')), f(f(h(x''), f(f(y'', f(x, h(f(a, a)))), h(f(a, a)))), h(f(a, a))))) with rule f(h(x1), y) -> h(f(y, f(x1, h(f(a, a))))) at position [] and matcher [x1 / f(h(x''), f(f(y'', f(x, h(f(a, a)))), h(f(a, a)))), y / f(f(h(x'), y'''), h(x'''))]

Now an instance of the first term with Matcher [y'' / y''', x / x', x' / x'', x'' / x''', y''' / f(f(y'', f(x, h(f(a, a)))), h(f(a, a))), x''' / f(a, a)] occurs in the last term at position [0].

Context: h([])

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