3.28/1.60 WORST_CASE(?, O(1)) 3.28/1.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.28/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.28/1.60 3.28/1.60 3.28/1.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.28/1.60 3.28/1.60 (0) CpxTRS 3.28/1.60 (1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] 3.28/1.60 (2) BOUNDS(1, 1) 3.28/1.60 3.28/1.60 3.28/1.60 ---------------------------------------- 3.28/1.60 3.28/1.60 (0) 3.28/1.60 Obligation: 3.28/1.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.28/1.60 3.28/1.60 3.28/1.60 The TRS R consists of the following rules: 3.28/1.60 3.28/1.60 a(b(x)) -> a(c(b(x))) 3.28/1.60 3.28/1.60 S is empty. 3.28/1.60 Rewrite Strategy: INNERMOST 3.28/1.60 ---------------------------------------- 3.28/1.60 3.28/1.60 (1) NarrowingOnBasicTermsTerminatesProof (FINISHED) 3.28/1.60 Constant runtime complexity proven by termination of constructor-based narrowing. 3.28/1.60 3.28/1.60 The maximal most general narrowing sequences give rise to the following rewrite sequences: 3.28/1.60 3.28/1.60 a(b(x0)) ->^* a(c(b(x0))) 3.28/1.60 3.28/1.60 3.28/1.60 3.28/1.60 3.28/1.60 ---------------------------------------- 3.28/1.60 3.28/1.60 (2) 3.28/1.60 BOUNDS(1, 1) 3.28/1.64 EOF