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


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NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1347 ms]
(2) NO


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

   +(X, 0) -> X
   +(X, s(Y)) -> s(+(X, Y))
   f(0, s(0), X) -> f(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:

   +(X, 0) -> X
   +(X, s(Y)) -> s(+(X, Y))
   f(0, s(0), X) -> f(X, +(X, X), X)
   g(X, Y) -> X
   g(X, Y) -> Y



Outermost Strategy.

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

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

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

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

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

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