Platform claims not to support CPU time, falling back to wall time.
Cannot find out cpu time on external processes, falling back to wall time!
proof of /home/fs5/ayamada/tpdb/relative/Relative_05/rt3-8.trs
# AProVE Commit ID: 2b684c7cda508b1711f707cb42f127e64fe1df88 ffrohn 20140415 dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 93 ms]
(2) NO


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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:

   f(s(x), y) -> f(-(s(x), y), y)

The relative TRS consists of the following S rules:

   +(0, y) -> y
   +(s(x), y) -> s(+(x, y))
   -(x, 0) -> x
   -(0, y) -> 0
   -(s(x), s(y)) -> -(x, y)
   f(x, y) -> f(x, +(x, y))


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(1) RelTRSLoopFinderProof (COMPLETE)
The following loop was found:

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

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

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

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

Context: []

Therefore, the relative TRS problem does not terminate.
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(2)
NO