YES(?,O(1)) 0.00/0.20 YES(?,O(1)) 0.00/0.20 0.00/0.20 We are left with following problem, upon which TcT provides the 0.00/0.20 certificate YES(?,O(1)). 0.00/0.20 0.00/0.20 Strict Trs: 0.00/0.20 { app(nil(), YS) -> YS 0.00/0.20 , app(cons(X), YS) -> cons(X) 0.00/0.20 , from(X) -> cons(X) 0.00/0.20 , zWadr(XS, nil()) -> nil() 0.00/0.20 , zWadr(nil(), YS) -> nil() 0.00/0.20 , zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) 0.00/0.20 , prefix(L) -> cons(nil()) } 0.00/0.20 Obligation: 0.00/0.20 innermost runtime complexity 0.00/0.20 Answer: 0.00/0.20 YES(?,O(1)) 0.00/0.20 0.00/0.20 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.20 Order (PS,0-bounded)' as induced by the safe mapping 0.00/0.20 0.00/0.20 safe(app) = {1, 2}, safe(nil) = {}, safe(cons) = {1}, 0.00/0.20 safe(from) = {}, safe(zWadr) = {}, safe(prefix) = {1} 0.00/0.20 0.00/0.20 and precedence 0.00/0.20 0.00/0.20 app > from, zWadr > app, zWadr > from, zWadr > prefix, 0.00/0.20 prefix > from, app ~ prefix . 0.00/0.20 0.00/0.20 Following symbols are considered recursive: 0.00/0.20 0.00/0.20 {} 0.00/0.20 0.00/0.20 The recursion depth is 0. 0.00/0.20 0.00/0.20 For your convenience, here are the satisfied ordering constraints: 0.00/0.20 0.00/0.20 app(; nil(), YS) > YS 0.00/0.20 0.00/0.20 app(; cons(; X), YS) > cons(; X) 0.00/0.20 0.00/0.20 from(X;) > cons(; X) 0.00/0.20 0.00/0.20 zWadr(XS, nil();) > nil() 0.00/0.20 0.00/0.20 zWadr(nil(), YS;) > nil() 0.00/0.20 0.00/0.20 zWadr(cons(; X), cons(; Y);) > cons(; app(; Y, cons(; X))) 0.00/0.20 0.00/0.20 prefix(; L) > cons(; nil()) 0.00/0.20 0.00/0.20 0.00/0.20 Hurray, we answered YES(?,O(1)) 0.00/0.21 EOF