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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).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: 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: 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: 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) ---------------------------------------- (2) BOUNDS(1, 1)