3.20/1.69 YES 3.20/1.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.20/1.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.20/1.70 3.20/1.70 3.20/1.70 Termination w.r.t. Q of the given QTRS could be proven: 3.20/1.70 3.20/1.70 (0) QTRS 3.20/1.70 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.20/1.70 (2) YES 3.20/1.70 3.20/1.70 3.20/1.70 ---------------------------------------- 3.20/1.70 3.20/1.70 (0) 3.20/1.70 Obligation: 3.20/1.70 Q restricted rewrite system: 3.20/1.70 The TRS R consists of the following rules: 3.20/1.70 3.20/1.70 f(f(X)) -> c 3.20/1.70 c -> d 3.20/1.70 h(X) -> c 3.20/1.70 3.20/1.70 The set Q consists of the following terms: 3.20/1.70 3.20/1.70 f(f(x0)) 3.20/1.70 c 3.20/1.70 h(x0) 3.20/1.70 3.20/1.70 3.20/1.70 ---------------------------------------- 3.20/1.70 3.20/1.70 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.20/1.70 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 3.20/1.70 The following rules were used to construct the certificate: 3.20/1.70 3.20/1.70 f(f(X)) -> c 3.20/1.70 c -> d 3.20/1.70 h(X) -> c 3.20/1.70 3.20/1.70 The certificate found is represented by the following graph. 3.20/1.70 The certificate consists of the following enumerated nodes: 3.20/1.70 1, 2 3.20/1.70 3.20/1.70 Node 1 is start node and node 2 is final node. 3.20/1.70 3.20/1.70 Those nodes are connected through the following edges: 3.20/1.70 3.20/1.70 * 1 to 2 labelled c(0), d(0), d(1)* 2 to 2 labelled #_1(0) 3.20/1.70 3.20/1.70 3.20/1.70 ---------------------------------------- 3.20/1.70 3.20/1.70 (2) 3.20/1.70 YES 3.20/1.72 EOF