NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given RelTRS could be disproven:

(0) RelTRS
(1) RelTRSLoopFinderProof [COMPLETE, 34 ms]
(2) NO


----------------------------------------

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

   min(x, 0) -> 0
   min(0, y) -> 0
   min(s(x), s(y)) -> s(min(x, y))
   max(x, 0) -> x
   max(0, y) -> y
   max(s(x), s(y)) -> s(max(x, y))
   -(x, 0) -> x
   -(s(x), s(y)) -> -(x, y)
   gcd(nil) -> 0
   gcd(cons(x, nil)) -> x
   gcd(cons(0, y)) -> gcd(y)
   gcd(cons(x, cons(y, z))) -> gcd(cons(-(x, y), cons(y, z)))

The relative TRS consists of the following S rules:

   gcd(cons(x, cons(y, z))) -> gcd(cons(max(x, y), cons(min(x, y), z)))


----------------------------------------

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

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

gcd(cons(x, cons(y, z))) -> gcd(cons(-(x, y), cons(y, z))) with rule gcd(cons(x', cons(y', z'))) -> gcd(cons(-(x', y'), cons(y', z'))) at position [] and matcher [x' / x, y' / y, z' / z]

Now an instance of the first term with Matcher [x / -(x, y)] occurs in the last term at position [].

Context: []

Therefore, the relative TRS problem does not terminate.
----------------------------------------

(2)
NO