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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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


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

(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__FROM(z0) -> c(MARK(z0))
   A__FROM(z0) -> c1
   A__HEAD(cons(z0, z1)) -> c2(MARK(z0))
   A__HEAD(z0) -> c3
   A__2ND(cons(z0, z1)) -> c4(A__HEAD(mark(z1)), MARK(z1))
   A__2ND(z0) -> c5
   A__TAKE(0, z0) -> c6
   A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1))
   A__TAKE(z0, z1) -> c8
   A__SEL(0, cons(z0, z1)) -> c9(MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c10(A__SEL(mark(z0), mark(z2)), MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c11(A__SEL(mark(z0), mark(z2)), MARK(z2))
   A__SEL(z0, z1) -> c12
   MARK(from(z0)) -> c13(A__FROM(mark(z0)), MARK(z0))
   MARK(head(z0)) -> c14(A__HEAD(mark(z0)), MARK(z0))
   MARK(2nd(z0)) -> c15(A__2ND(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c16(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c17(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(sel(z0, z1)) -> c18(A__SEL(mark(z0), mark(z1)), MARK(z0))
   MARK(sel(z0, z1)) -> c19(A__SEL(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c20(MARK(z0))
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(0) -> c22
   MARK(nil) -> c23

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

   a__from(z0) -> cons(mark(z0), from(s(z0)))
   a__from(z0) -> from(z0)
   a__head(cons(z0, z1)) -> mark(z0)
   a__head(z0) -> head(z0)
   a__2nd(cons(z0, z1)) -> a__head(mark(z1))
   a__2nd(z0) -> 2nd(z0)
   a__take(0, z0) -> nil
   a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2))
   a__take(z0, z1) -> take(z0, z1)
   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(from(z0)) -> a__from(mark(z0))
   mark(head(z0)) -> a__head(mark(z0))
   mark(2nd(z0)) -> a__2nd(mark(z0))
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
   mark(nil) -> nil

Rewrite Strategy: INNERMOST