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 z:S) 0.00/0.01 (RULES 0.00/0.01 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 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 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 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 S(a) -> C 0.00/0.01 S(b) -> C 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 0.00/0.01 0.00/0.01 Conditional Termination Problem 2: 0.00/0.01 -> Pairs: 0.00/0.01 F(x:S) -> S(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 S(a) -> C 0.00/0.01 S(b) -> C 0.00/0.01 -> Rules: 0.00/0.01 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 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 S(a) -> C 0.00/0.01 S(b) -> C 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 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 F(x:S) -> S(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 S(a) -> C 0.00/0.01 S(b) -> C 0.00/0.01 -> Rules: 0.00/0.01 c -> t(k) 0.00/0.01 c -> t(l) 0.00/0.01 f(x:S) -> z:S | s(x:S) ->* z:S 0.00/0.01 g(x:S,x:S) -> h(x:S,x:S) 0.00/0.01 s(a) -> c 0.00/0.01 s(b) -> c 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