WORST_CASE(?,O(1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).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: a__c -> a__f(g(c)) a__f(g(X)) -> g(X) mark(c) -> a__c mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) a__c -> c a__f(X) -> f(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: mark(g(x0)) ->^* g(x0) mark(f(x0)) ->^* f(x0) mark(f(g(x0))) ->^* g(x0) mark(c) ->^* c mark(c) ->^* f(g(c)) mark(c) ->^* g(c) a__f(x0) ->^* f(x0) a__f(g(x0)) ->^* g(x0) a__c ->^* c a__c ->^* f(g(c)) a__c ->^* g(c) ---------------------------------------- (2) BOUNDS(1, 1)