WORST_CASE(?,O(1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.trs
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).

(0) CpxTRS
(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
(2) BOUNDS(1, 1)


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

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   first(0, X) -> nil
   first(s(X), cons(Y)) -> cons(Y)
   from(X) -> cons(X)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
Constant runtime complexity proven by termination of constructor-based narrowing.

The maximal most general narrowing sequences give rise to the following rewrite sequences:

from(x0) ->^* cons(x0)

first(s(x0), cons(x1)) ->^* cons(x1)

first(0, x0) ->^* nil




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

(2)
BOUNDS(1, 1)