/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 202 ms]
(2) NO


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

   zeros -> cons(0, n__zeros)
   U11(tt, L) -> U12(tt, activate(L))
   U12(tt, L) -> s(length(activate(L)))
   length(nil) -> 0
   length(cons(N, L)) -> U11(tt, activate(L))
   zeros -> n__zeros
   activate(n__zeros) -> zeros
   activate(X) -> X



Outermost Strategy.

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

   zeros -> cons(0, n__zeros)
   U11(tt, L) -> U12(tt, activate(L))
   U12(tt, L) -> s(length(activate(L)))
   length(nil) -> 0
   length(cons(N, L)) -> U11(tt, activate(L))
   zeros -> n__zeros
   activate(n__zeros) -> zeros
   activate(X) -> X



Outermost Strategy.

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

U12(tt, activate(activate(n__zeros))) -> s(length(activate(activate(activate(n__zeros))))) with rule U12(tt, L) -> s(length(activate(L))) at position [] and matcher [L / activate(activate(n__zeros))]

s(length(activate(activate(activate(n__zeros))))) -> s(length(activate(activate(n__zeros)))) with rule activate(X) -> X at position [0,0] and matcher [X / activate(activate(n__zeros))]

s(length(activate(activate(n__zeros)))) -> s(length(activate(n__zeros))) with rule activate(X) -> X at position [0,0] and matcher [X / activate(n__zeros)]

s(length(activate(n__zeros))) -> s(length(zeros)) with rule activate(n__zeros) -> zeros at position [0,0] and matcher [ ]

s(length(zeros)) -> s(length(cons(0, n__zeros))) with rule zeros -> cons(0, n__zeros) at position [0,0] and matcher [ ]

s(length(cons(0, n__zeros))) -> s(U11(tt, activate(n__zeros))) with rule length(cons(N, L)) -> U11(tt, activate(L)) at position [0] and matcher [N / 0, L / n__zeros]

s(U11(tt, activate(n__zeros))) -> s(U12(tt, activate(activate(n__zeros)))) with rule U11(tt, L) -> U12(tt, activate(L)) at position [0] and matcher [L / activate(n__zeros)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].

Context: s([])

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