WORST_CASE(?,O(1))
proof of input_5fuXKUroiT.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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:

   app(nil, YS) -> YS
   app(cons(X), YS) -> cons(X)
   from(X) -> cons(X)
   zWadr(nil, YS) -> nil
   zWadr(XS, nil) -> nil
   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
   prefix(L) -> cons(nil)

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:

prefix(x0) ->^* cons(nil)

zWadr(cons(x0), cons(cons(x1))) ->^* cons(cons(x1))

zWadr(cons(x0), cons(nil)) ->^* cons(cons(x0))

zWadr(x0, nil) ->^* nil

zWadr(nil, x0) ->^* nil

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

app(cons(x0), x1) ->^* cons(x0)




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(2)
BOUNDS(1, 1)