/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 56 ms]
(2) NO


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

   f(s(a), s(b), x) -> f(x, x, x)
   g(f(s(x), s(y), z)) -> g(f(x, y, z))
   cons(x, y) -> x
   cons(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(s(a), s(b), x) -> f(x, x, x)
   g(f(s(x), s(y), z)) -> g(f(x, y, z))
   cons(x, y) -> x
   cons(x, y) -> y



Outermost Strategy.

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

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

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

f(s(a), s(b), cons(s(a), s(b))) -> f(cons(s(a), s(b)), cons(s(a), s(b)), cons(s(a), s(b))) with rule f(s(a), s(b), x) -> f(x, x, x) at position [] and matcher [x / cons(s(a), s(b))]

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