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proof of input_oSMhCZAtz0.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).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) ---------------------------------------- (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 ---------------------------------------- (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 ---------------------------------------- (2) BOUNDS(1, 1)