/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 34 ms]
(2) NO


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

   g(X) -> u(h(X), h(X), X)
   u(d, c(Y), X) -> k(Y)
   h(d) -> c(a)
   h(d) -> c(b)
   f(k(a), k(b), X) -> f(X, X, X)



Outermost Strategy.

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

   g(X) -> u(h(X), h(X), X)
   u(d, c(Y), X) -> k(Y)
   h(d) -> c(a)
   h(d) -> c(b)
   f(k(a), k(b), X) -> f(X, X, X)



Outermost Strategy.

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

f(u(d, h(d), X'), u(d, h(d), X'), u(d, h(d), X')) -> f(u(d, h(d), X'), u(d, c(b), X'), u(d, h(d), X')) with rule h(d) -> c(b) at position [1,1] and matcher [ ]

f(u(d, h(d), X'), u(d, c(b), X'), u(d, h(d), X')) -> f(u(d, h(d), X'), k(b), u(d, h(d), X')) with rule u(d, c(Y), X'') -> k(Y) at position [1] and matcher [Y / b, X'' / X']

f(u(d, h(d), X'), k(b), u(d, h(d), X')) -> f(u(d, c(a), X'), k(b), u(d, h(d), X')) with rule h(d) -> c(a) at position [0,1] and matcher [ ]

f(u(d, c(a), X'), k(b), u(d, h(d), X')) -> f(k(a), k(b), u(d, h(d), X')) with rule u(d, c(Y), X'') -> k(Y) at position [0] and matcher [Y / a, X'' / X']

f(k(a), k(b), u(d, h(d), X')) -> f(u(d, h(d), X'), u(d, h(d), X'), u(d, h(d), X')) with rule f(k(a), k(b), X) -> f(X, X, X) at position [] and matcher [X / u(d, h(d), X')]

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