0.00/0.01 YES 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 (VAR v_NonEmpty:S x:S x':S x'':S y:S y':S y'':S) 0.00/0.01 (RULES 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 ) 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 Valid CTRS Processor: 0.00/0.01 -> Rules: 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 -> The system is a deterministic 3-CTRS. 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 Dependency Pairs Processor: 0.00/0.01 0.00/0.01 Conditional Termination Problem 1: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 0.00/0.01 Conditional Termination Problem 2: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 0.00/0.01 0.00/0.01 The problem is decomposed in 2 subproblems. 0.00/0.01 0.00/0.01 Problem 1.1: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 There is no strongly connected component 0.00/0.01 0.00/0.01 The problem is finite. 0.00/0.01 0.00/0.01 Problem 1.2: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 f(x':S,x'':S) -> g(x:S) | x':S ->* x:S, x'':S ->* x:S 0.00/0.01 f(y':S,h(y'':S)) -> g(y:S) | y':S ->* y:S, y'':S ->* y:S 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 There is no strongly connected component 0.00/0.01 0.00/0.01 The problem is finite. 0.00/0.01 EOF