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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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__FIB(z0) -> c(A__SEL(mark(z0), a__fib1(s(0), s(0))), MARK(z0))
   A__FIB(z0) -> c1(A__SEL(mark(z0), a__fib1(s(0), s(0))), A__FIB1(s(0), s(0)))
   A__FIB(z0) -> c2
   A__FIB1(z0, z1) -> c3(MARK(z0))
   A__FIB1(z0, z1) -> c4
   A__ADD(0, z0) -> c5(MARK(z0))
   A__ADD(s(z0), z1) -> c6(A__ADD(mark(z0), mark(z1)), MARK(z0))
   A__ADD(s(z0), z1) -> c7(A__ADD(mark(z0), mark(z1)), MARK(z1))
   A__ADD(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(fib(z0)) -> c13(A__FIB(mark(z0)), MARK(z0))
   MARK(sel(z0, z1)) -> c14(A__SEL(mark(z0), mark(z1)), MARK(z0))
   MARK(sel(z0, z1)) -> c15(A__SEL(mark(z0), mark(z1)), MARK(z1))
   MARK(fib1(z0, z1)) -> c16(A__FIB1(mark(z0), mark(z1)), MARK(z0))
   MARK(fib1(z0, z1)) -> c17(A__FIB1(mark(z0), mark(z1)), MARK(z1))
   MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c20(MARK(z0))
   MARK(0) -> c21
   MARK(cons(z0, z1)) -> c22(MARK(z0))

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

   a__fib(z0) -> a__sel(mark(z0), a__fib1(s(0), s(0)))
   a__fib(z0) -> fib(z0)
   a__fib1(z0, z1) -> cons(mark(z0), fib1(z1, add(z0, z1)))
   a__fib1(z0, z1) -> fib1(z0, z1)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1)))
   a__add(z0, z1) -> add(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(fib(z0)) -> a__fib(mark(z0))
   mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1))
   mark(fib1(z0, z1)) -> a__fib1(mark(z0), mark(z1))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
   mark(cons(z0, z1)) -> cons(mark(z0), z1)

Rewrite Strategy: INNERMOST