KILLED
proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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:

   A__F(z0) -> c(MARK(z0))
   A__F(z0) -> c1
   A__G(0) -> c2
   A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0))
   A__G(z0) -> c4
   A__SEL(0, cons(z0, z1)) -> c5(MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2))
   A__SEL(z0, z1) -> c8
   MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0))
   MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0))
   MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0))
   MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c13(MARK(z0))
   MARK(0) -> c14
   MARK(s(z0)) -> c15(MARK(z0))

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

   a__f(z0) -> cons(mark(z0), f(g(z0)))
   a__f(z0) -> f(z0)
   a__g(0) -> s(0)
   a__g(s(z0)) -> s(s(a__g(mark(z0))))
   a__g(z0) -> g(z0)
   a__sel(0, cons(z0, z1)) -> mark(z0)
   a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2))
   a__sel(z0, z1) -> sel(z0, z1)
   mark(f(z0)) -> a__f(mark(z0))
   mark(g(z0)) -> a__g(mark(z0))
   mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))

Rewrite Strategy: INNERMOST