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/rtL-evo.trs
# AProVE Commit ID: 2b684c7cda508b1711f707cb42f127e64fe1df88 ffrohn 20140415 dirty
Termination of the given RelTRS could be disproven:
(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 629 ms]
(2) NO
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(0)
Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
top(U(x, y)) -> top(check(D(x, y)))
D(x, B) -> U(x, B)
F(x, U(O(y), z)) -> U(x, F(y, z))
F(x, U(N(y), z)) -> U(x, F(y, z))
D(O(x), F(y, z)) -> F(x, D(y, z))
D(N(x), F(y, z)) -> F(x, D(y, z))
F(x, U(E, y)) -> U(x, F(E, y))
D(E, F(x, y)) -> F(E, D(x, y))
The relative TRS consists of the following S rules:
E -> N(E)
check(O(x)) -> O(x)
check(U(x, y)) -> U(check(x), y)
check(U(x, y)) -> U(x, check(y))
check(D(x, y)) -> D(check(x), y)
check(D(x, y)) -> D(x, check(y))
check(F(x, y)) -> F(check(x), y)
check(F(x, y)) -> F(x, check(y))
check(O(x)) -> O(check(x))
check(N(x)) -> N(check(x))
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(1) RelTRSLoopFinderProof (COMPLETE)
The following loop was found:
---------- Loop: ----------
top(check(D(x, B))) -> top(D(check(x), B)) with rule check(D(x', y)) -> D(check(x'), y) at position [0] and matcher [x' / x, y / B]
top(D(check(x), B)) -> top(U(check(x), B)) with rule D(x', B) -> U(x', B) at position [0] and matcher [x' / check(x)]
top(U(check(x), B)) -> top(check(D(check(x), B))) with rule top(U(x', y)) -> top(check(D(x', y))) at position [] and matcher [x' / check(x), y / B]
Now an instance of the first term with Matcher [x / check(x)] occurs in the last term at position [].
Context: []
Therefore, the relative TRS problem does not terminate.
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(2)
NO