KILLED
proof of /export/starexec/sandbox/benchmark/theBenchmark.trs
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).

(0) CpxRelTRS


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(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   -'(z0, 0) -> c
   -'(s(z0), s(z1)) -> c1(-'(z0, z1))
   MIN(z0, 0) -> c2
   MIN(0, z0) -> c3
   MIN(s(z0), s(z1)) -> c4(MIN(z0, z1))
   TWICE(0) -> c5
   TWICE(s(z0)) -> c6(TWICE(z0))
   F(s(z0), s(z1)) -> c7(F(-(z1, min(z0, z1)), s(twice(min(z0, z1)))), -'(z1, min(z0, z1)), MIN(z0, z1))
   F(s(z0), s(z1)) -> c8(F(-(z1, min(z0, z1)), s(twice(min(z0, z1)))), TWICE(min(z0, z1)), MIN(z0, z1))
   F(s(z0), s(z1)) -> c9(F(-(z0, min(z0, z1)), s(twice(min(z0, z1)))), -'(z0, min(z0, z1)), MIN(z0, z1))
   F(s(z0), s(z1)) -> c10(F(-(z0, min(z0, z1)), s(twice(min(z0, z1)))), TWICE(min(z0, z1)), MIN(z0, z1))

The (relative) TRS S consists of the following rules:

   -(z0, 0) -> z0
   -(s(z0), s(z1)) -> -(z0, z1)
   min(z0, 0) -> 0
   min(0, z0) -> 0
   min(s(z0), s(z1)) -> s(min(z0, z1))
   twice(0) -> 0
   twice(s(z0)) -> s(s(twice(z0)))
   f(s(z0), s(z1)) -> f(-(z1, min(z0, z1)), s(twice(min(z0, z1))))
   f(s(z0), s(z1)) -> f(-(z0, min(z0, z1)), s(twice(min(z0, z1))))

Rewrite Strategy: INNERMOST