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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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:

   A__DBL(0) -> c
   A__DBL(s(z0)) -> c1
   A__DBL(z0) -> c2
   A__DBLS(nil) -> c3
   A__DBLS(cons(z0, z1)) -> c4
   A__DBLS(z0) -> c5
   A__SEL(0, cons(z0, z1)) -> c6(MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c8(A__SEL(mark(z0), mark(z2)), MARK(z2))
   A__SEL(z0, z1) -> c9
   A__INDX(nil, z0) -> c10
   A__INDX(cons(z0, z1), z2) -> c11
   A__INDX(z0, z1) -> c12
   A__FROM(z0) -> c13
   A__FROM(z0) -> c14
   A__DBL1(0) -> c15
   A__DBL1(s(z0)) -> c16(A__DBL1(mark(z0)), MARK(z0))
   A__DBL1(z0) -> c17
   A__SEL1(0, cons(z0, z1)) -> c18(MARK(z0))
   A__SEL1(s(z0), cons(z1, z2)) -> c19(A__SEL1(mark(z0), mark(z2)), MARK(z0))
   A__SEL1(s(z0), cons(z1, z2)) -> c20(A__SEL1(mark(z0), mark(z2)), MARK(z2))
   A__SEL1(z0, z1) -> c21
   A__QUOTE(0) -> c22
   A__QUOTE(s(z0)) -> c23(A__QUOTE(mark(z0)), MARK(z0))
   A__QUOTE(dbl(z0)) -> c24(A__DBL1(mark(z0)), MARK(z0))
   A__QUOTE(sel(z0, z1)) -> c25(A__SEL1(mark(z0), mark(z1)), MARK(z0))
   A__QUOTE(sel(z0, z1)) -> c26(A__SEL1(mark(z0), mark(z1)), MARK(z1))
   A__QUOTE(z0) -> c27
   MARK(dbl(z0)) -> c28(A__DBL(mark(z0)), MARK(z0))
   MARK(dbls(z0)) -> c29(A__DBLS(mark(z0)), MARK(z0))
   MARK(sel(z0, z1)) -> c30(A__SEL(mark(z0), mark(z1)), MARK(z0))
   MARK(sel(z0, z1)) -> c31(A__SEL(mark(z0), mark(z1)), MARK(z1))
   MARK(indx(z0, z1)) -> c32(A__INDX(mark(z0), z1), MARK(z0))
   MARK(from(z0)) -> c33(A__FROM(z0))
   MARK(dbl1(z0)) -> c34(A__DBL1(mark(z0)), MARK(z0))
   MARK(sel1(z0, z1)) -> c35(A__SEL1(mark(z0), mark(z1)), MARK(z0))
   MARK(sel1(z0, z1)) -> c36(A__SEL1(mark(z0), mark(z1)), MARK(z1))
   MARK(quote(z0)) -> c37(A__QUOTE(mark(z0)), MARK(z0))
   MARK(0) -> c38
   MARK(s(z0)) -> c39
   MARK(nil) -> c40
   MARK(cons(z0, z1)) -> c41
   MARK(01) -> c42
   MARK(s1(z0)) -> c43(MARK(z0))

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

   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__dbls(nil) -> nil
   a__dbls(cons(z0, z1)) -> cons(dbl(z0), dbls(z1))
   a__dbls(z0) -> dbls(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)
   a__indx(nil, z0) -> nil
   a__indx(cons(z0, z1), z2) -> cons(sel(z0, z2), indx(z1, z2))
   a__indx(z0, z1) -> indx(z0, z1)
   a__from(z0) -> cons(z0, from(s(z0)))
   a__from(z0) -> from(z0)
   a__dbl1(0) -> 01
   a__dbl1(s(z0)) -> s1(s1(a__dbl1(mark(z0))))
   a__dbl1(z0) -> dbl1(z0)
   a__sel1(0, cons(z0, z1)) -> mark(z0)
   a__sel1(s(z0), cons(z1, z2)) -> a__sel1(mark(z0), mark(z2))
   a__sel1(z0, z1) -> sel1(z0, z1)
   a__quote(0) -> 01
   a__quote(s(z0)) -> s1(a__quote(mark(z0)))
   a__quote(dbl(z0)) -> a__dbl1(mark(z0))
   a__quote(sel(z0, z1)) -> a__sel1(mark(z0), mark(z1))
   a__quote(z0) -> quote(z0)
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(dbls(z0)) -> a__dbls(mark(z0))
   mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1))
   mark(indx(z0, z1)) -> a__indx(mark(z0), z1)
   mark(from(z0)) -> a__from(z0)
   mark(dbl1(z0)) -> a__dbl1(mark(z0))
   mark(sel1(z0, z1)) -> a__sel1(mark(z0), mark(z1))
   mark(quote(z0)) -> a__quote(mark(z0))
   mark(0) -> 0
   mark(s(z0)) -> s(z0)
   mark(nil) -> nil
   mark(cons(z0, z1)) -> cons(z0, z1)
   mark(01) -> 01
   mark(s1(z0)) -> s1(mark(z0))

Rewrite Strategy: INNERMOST