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) 0.00/0.01 (RULES 0.00/0.01 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 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 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 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 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 0.00/0.01 0.00/0.01 Conditional Termination Problem 2: 0.00/0.01 -> Pairs: 0.00/0.01 POS(p(x:S)) -> POS(x:S) 0.00/0.01 POS(s(x:S)) -> POS(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 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 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 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 POS(p(x:S)) -> POS(x:S) 0.00/0.01 POS(s(x:S)) -> POS(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 ->->Cycle: 0.00/0.01 ->->-> Pairs: 0.00/0.01 POS(p(x:S)) -> POS(x:S) 0.00/0.01 POS(s(x:S)) -> POS(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 ->->-> Rules: 0.00/0.01 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 0.00/0.01 0.00/0.01 Problem 1.2: 0.00/0.01 0.00/0.01 Conditional Subterm Processor: 0.00/0.01 -> Pairs: 0.00/0.01 POS(p(x:S)) -> POS(x:S) 0.00/0.01 POS(s(x:S)) -> POS(x:S) 0.00/0.01 -> QPairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 0.00/0.01 ->Projection: 0.00/0.01 pi(POS) = 1 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 pos(0) -> ffalse 0.00/0.01 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse 0.00/0.01 pos(s(0)) -> ttrue 0.00/0.01 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue 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