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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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__SEL(s(z0), cons(z1, z2)) -> c(A__SEL(mark(z0), mark(z2)), MARK(z0))
   A__SEL(s(z0), cons(z1, z2)) -> c1(A__SEL(mark(z0), mark(z2)), MARK(z2))
   A__SEL(0, cons(z0, z1)) -> c2(MARK(z0))
   A__SEL(z0, z1) -> c3
   A__FIRST(0, z0) -> c4
   A__FIRST(s(z0), cons(z1, z2)) -> c5(MARK(z1))
   A__FIRST(z0, z1) -> c6
   A__FROM(z0) -> c7(MARK(z0))
   A__FROM(z0) -> c8
   A__SEL1(s(z0), cons(z1, z2)) -> c9(A__SEL1(mark(z0), mark(z2)), MARK(z0))
   A__SEL1(s(z0), cons(z1, z2)) -> c10(A__SEL1(mark(z0), mark(z2)), MARK(z2))
   A__SEL1(0, cons(z0, z1)) -> c11(A__QUOTE(z0))
   A__SEL1(z0, z1) -> c12
   A__FIRST1(0, z0) -> c13
   A__FIRST1(s(z0), cons(z1, z2)) -> c14(A__QUOTE(z1))
   A__FIRST1(s(z0), cons(z1, z2)) -> c15(A__FIRST1(mark(z0), mark(z2)), MARK(z0))
   A__FIRST1(s(z0), cons(z1, z2)) -> c16(A__FIRST1(mark(z0), mark(z2)), MARK(z2))
   A__FIRST1(z0, z1) -> c17
   A__QUOTE(0) -> c18
   A__QUOTE(s(z0)) -> c19(A__QUOTE(z0))
   A__QUOTE(sel(z0, z1)) -> c20(A__SEL1(mark(z0), mark(z1)), MARK(z0))
   A__QUOTE(sel(z0, z1)) -> c21(A__SEL1(mark(z0), mark(z1)), MARK(z1))
   A__QUOTE(z0) -> c22
   A__QUOTE1(cons(z0, z1)) -> c23(A__QUOTE(z0))
   A__QUOTE1(cons(z0, z1)) -> c24(A__QUOTE1(z1))
   A__QUOTE1(nil) -> c25
   A__QUOTE1(first(z0, z1)) -> c26(A__FIRST1(mark(z0), mark(z1)), MARK(z0))
   A__QUOTE1(first(z0, z1)) -> c27(A__FIRST1(mark(z0), mark(z1)), MARK(z1))
   A__QUOTE1(z0) -> c28
   A__UNQUOTE(01) -> c29
   A__UNQUOTE(s1(z0)) -> c30(A__UNQUOTE(mark(z0)), MARK(z0))
   A__UNQUOTE(z0) -> c31
   A__UNQUOTE1(nil1) -> c32
   A__UNQUOTE1(cons1(z0, z1)) -> c33(A__FCONS(a__unquote(mark(z0)), a__unquote1(mark(z1))), A__UNQUOTE(mark(z0)), MARK(z0))
   A__UNQUOTE1(cons1(z0, z1)) -> c34(A__FCONS(a__unquote(mark(z0)), a__unquote1(mark(z1))), A__UNQUOTE1(mark(z1)), MARK(z1))
   A__UNQUOTE1(z0) -> c35
   A__FCONS(z0, z1) -> c36(MARK(z0))
   A__FCONS(z0, z1) -> c37
   MARK(sel(z0, z1)) -> c38(A__SEL(mark(z0), mark(z1)), MARK(z0))
   MARK(sel(z0, z1)) -> c39(A__SEL(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c40(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c41(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(from(z0)) -> c42(A__FROM(mark(z0)), MARK(z0))
   MARK(sel1(z0, z1)) -> c43(A__SEL1(mark(z0), mark(z1)), MARK(z0))
   MARK(sel1(z0, z1)) -> c44(A__SEL1(mark(z0), mark(z1)), MARK(z1))
   MARK(quote(z0)) -> c45(A__QUOTE(z0))
   MARK(first1(z0, z1)) -> c46(A__FIRST1(mark(z0), mark(z1)), MARK(z0))
   MARK(first1(z0, z1)) -> c47(A__FIRST1(mark(z0), mark(z1)), MARK(z1))
   MARK(quote1(z0)) -> c48(A__QUOTE1(z0))
   MARK(unquote(z0)) -> c49(A__UNQUOTE(mark(z0)), MARK(z0))
   MARK(unquote1(z0)) -> c50(A__UNQUOTE1(mark(z0)), MARK(z0))
   MARK(fcons(z0, z1)) -> c51(A__FCONS(mark(z0), mark(z1)), MARK(z0))
   MARK(fcons(z0, z1)) -> c52(A__FCONS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c53(MARK(z0))
   MARK(cons(z0, z1)) -> c54(MARK(z0))
   MARK(0) -> c55
   MARK(nil) -> c56
   MARK(nil1) -> c57
   MARK(cons1(z0, z1)) -> c58(MARK(z0))
   MARK(cons1(z0, z1)) -> c59(MARK(z1))
   MARK(01) -> c60
   MARK(s1(z0)) -> c61(MARK(z0))

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

   a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2))
   a__sel(0, cons(z0, z1)) -> mark(z0)
   a__sel(z0, z1) -> sel(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   a__from(z0) -> cons(mark(z0), from(s(z0)))
   a__from(z0) -> from(z0)
   a__sel1(s(z0), cons(z1, z2)) -> a__sel1(mark(z0), mark(z2))
   a__sel1(0, cons(z0, z1)) -> a__quote(z0)
   a__sel1(z0, z1) -> sel1(z0, z1)
   a__first1(0, z0) -> nil1
   a__first1(s(z0), cons(z1, z2)) -> cons1(a__quote(z1), a__first1(mark(z0), mark(z2)))
   a__first1(z0, z1) -> first1(z0, z1)
   a__quote(0) -> 01
   a__quote(s(z0)) -> s1(a__quote(z0))
   a__quote(sel(z0, z1)) -> a__sel1(mark(z0), mark(z1))
   a__quote(z0) -> quote(z0)
   a__quote1(cons(z0, z1)) -> cons1(a__quote(z0), a__quote1(z1))
   a__quote1(nil) -> nil1
   a__quote1(first(z0, z1)) -> a__first1(mark(z0), mark(z1))
   a__quote1(z0) -> quote1(z0)
   a__unquote(01) -> 0
   a__unquote(s1(z0)) -> s(a__unquote(mark(z0)))
   a__unquote(z0) -> unquote(z0)
   a__unquote1(nil1) -> nil
   a__unquote1(cons1(z0, z1)) -> a__fcons(a__unquote(mark(z0)), a__unquote1(mark(z1)))
   a__unquote1(z0) -> unquote1(z0)
   a__fcons(z0, z1) -> cons(mark(z0), z1)
   a__fcons(z0, z1) -> fcons(z0, z1)
   mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(from(z0)) -> a__from(mark(z0))
   mark(sel1(z0, z1)) -> a__sel1(mark(z0), mark(z1))
   mark(quote(z0)) -> a__quote(z0)
   mark(first1(z0, z1)) -> a__first1(mark(z0), mark(z1))
   mark(quote1(z0)) -> a__quote1(z0)
   mark(unquote(z0)) -> a__unquote(mark(z0))
   mark(unquote1(z0)) -> a__unquote1(mark(z0))
   mark(fcons(z0, z1)) -> a__fcons(mark(z0), mark(z1))
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(nil) -> nil
   mark(nil1) -> nil1
   mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1))
   mark(01) -> 01
   mark(s1(z0)) -> s1(mark(z0))

Rewrite Strategy: INNERMOST