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