100.81/100.98 NO 100.81/100.98 100.81/100.98 Problem 1: 100.81/100.98 100.81/100.98 (VAR v_NonEmpty:S x:S) 100.81/100.98 (RULES 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 ) 100.81/100.98 100.81/100.98 Problem 1: 100.81/100.98 Valid CTRS Processor: 100.81/100.98 -> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 -> The system is a deterministic 3-CTRS. 100.81/100.98 100.81/100.98 Problem 1: 100.81/100.98 100.81/100.98 Dependency Pairs Processor: 100.81/100.98 100.81/100.98 Conditional Termination Problem 1: 100.81/100.98 -> Pairs: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 -> QPairs: 100.81/100.98 Empty 100.81/100.98 -> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 100.81/100.98 Conditional Termination Problem 2: 100.81/100.98 -> Pairs: 100.81/100.98 EVEN(s(x:S)) -> EQ(odd(x:S),ffalse) 100.81/100.98 EVEN(s(x:S)) -> EQ(odd(x:S),ttrue) 100.81/100.98 EVEN(s(x:S)) -> ODD(x:S) 100.81/100.98 ODD(s(x:S)) -> EQ(even(x:S),ffalse) 100.81/100.98 ODD(s(x:S)) -> EQ(even(x:S),ttrue) 100.81/100.98 ODD(s(x:S)) -> EVEN(x:S) 100.81/100.98 -> QPairs: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 -> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 100.81/100.98 Problem 1: 100.81/100.98 100.81/100.98 SCC Processor: 100.81/100.98 -> Pairs: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 -> QPairs: 100.81/100.98 Empty 100.81/100.98 -> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 ->Strongly Connected Components: 100.81/100.98 ->->Cycle: 100.81/100.98 ->->-> Pairs: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 -> QPairs: 100.81/100.98 Empty 100.81/100.98 ->->-> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 100.81/100.98 Problem 1: 100.81/100.98 100.81/100.98 Infinite Processor: 100.81/100.98 -> Pairs: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 -> QPairs: 100.81/100.98 Empty 100.81/100.98 -> Rules: 100.81/100.98 eq(x:S,x:S) -> eq(T,T) 100.81/100.98 even(0) -> ttrue 100.81/100.98 even(s(x:S)) -> ffalse | eq(odd(x:S),ffalse) ->* eq(T,T) 100.81/100.98 even(s(x:S)) -> ttrue | eq(odd(x:S),ttrue) ->* eq(T,T) 100.81/100.98 odd(0) -> ffalse 100.81/100.98 odd(s(x:S)) -> ffalse | eq(even(x:S),ffalse) ->* eq(T,T) 100.81/100.98 odd(s(x:S)) -> ttrue | eq(even(x:S),ttrue) ->* eq(T,T) 100.81/100.98 -> Pairs in cycle: 100.81/100.98 EQ(x:S,x:S) -> EQ(T,T) 100.81/100.98 100.81/100.98 The problem is infinite. 100.81/100.98 EOF