WORST_CASE(?,O(1))
proof of input_oSMhCZAtz0.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

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


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


The TRS R consists of the following rules:

   fst(0, Z) -> nil
   fst(s, cons(Y)) -> cons(Y)
   from(X) -> cons(X)
   add(0, X) -> X
   add(s, Y) -> s
   len(nil) -> 0
   len(cons(X)) -> s

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
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(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:

len(cons(x0)) ->^* s

len(nil) ->^* 0

add(s, x0) ->^* s

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

fst(s, cons(x0)) ->^* cons(x0)

fst(0, x0) ->^* nil




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(2)
BOUNDS(1, 1)