0.00/0.29 YES 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 (VAR v_NonEmpty:S L:S X:S X1:S X2:S XS:S Y:S YS:S) 0.00/0.29 (RULES 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ) 0.00/0.29 (STRATEGY INNERMOST) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Dependency Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S) 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> A__PREFIX(mark(X:S)) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S) 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> A__PREFIX(mark(X:S)) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S) 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S) 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 -> Usable rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [a__app](X1,X2) = X1 + 2.X2 + 2 0.00/0.29 [a__from](X) = X + 2 0.00/0.29 [a__prefix](X) = 2.X + 2 0.00/0.29 [a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [app](X1,X2) = X1 + 2.X2 + 2 0.00/0.29 [cons](X1,X2) = X1 + 2 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [from](X) = X + 2 0.00/0.29 [nil] = 0 0.00/0.29 [prefix](X) = 2.X + 2 0.00/0.29 [s](X) = 2.X + 2 0.00/0.29 [zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [A__APP](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [A__FROM](X) = 2.X + 2 0.00/0.29 [A__PREFIX](X) = 0 0.00/0.29 [A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 1 0.00/0.29 [MARK](X) = 2.X + 1 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__APP(nil,YS:S) -> MARK(YS:S) 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 -> Usable rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [a__app](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [a__from](X) = 2.X + 2 0.00/0.29 [a__prefix](X) = 2.X + 2 0.00/0.29 [a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [app](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [cons](X1,X2) = X1 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [from](X) = 2.X + 2 0.00/0.29 [nil] = 2 0.00/0.29 [prefix](X) = 2.X + 2 0.00/0.29 [s](X) = X + 2 0.00/0.29 [zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [A__APP](X1,X2) = X1 + 2.X2 + 1 0.00/0.29 [A__FROM](X) = 2.X + 2 0.00/0.29 [A__PREFIX](X) = 0 0.00/0.29 [A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [MARK](X) = 2.X + 2 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil)) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__FROM(X:S) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 -> Usable rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [a__app](X1,X2) = 2.X1 + X2 + 1 0.00/0.29 [a__from](X) = 2.X + 2 0.00/0.29 [a__prefix](X) = X + 2 0.00/0.29 [a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [app](X1,X2) = 2.X1 + X2 + 1 0.00/0.29 [cons](X1,X2) = 2.X1 + 2 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [from](X) = 2.X + 2 0.00/0.29 [nil] = 0 0.00/0.29 [prefix](X) = X + 2 0.00/0.29 [s](X) = 2.X + 2 0.00/0.29 [zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [A__APP](X1,X2) = 0 0.00/0.29 [A__FROM](X) = 2.X + 2 0.00/0.29 [A__PREFIX](X) = 0 0.00/0.29 [A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [MARK](X) = 2.X + 1 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S) 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 -> Usable rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [a__app](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [a__from](X) = 2.X + 2 0.00/0.29 [a__prefix](X) = 2.X + 2 0.00/0.29 [a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [mark](X) = X 0.00/0.29 [app](X1,X2) = 2.X1 + X2 + 2 0.00/0.29 [cons](X1,X2) = 2.X1 + 2 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [from](X) = 2.X + 2 0.00/0.29 [nil] = 0 0.00/0.29 [prefix](X) = 2.X + 2 0.00/0.29 [s](X) = 2.X + 1 0.00/0.29 [zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [A__APP](X1,X2) = 0 0.00/0.29 [A__FROM](X) = 0 0.00/0.29 [A__PREFIX](X) = 0 0.00/0.29 [A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.29 [MARK](X) = 2.X + 1 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Reduction Pairs Processor: 0.00/0.29 -> Pairs: 0.00/0.29 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 -> Usable rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Interpretation type: 0.00/0.29 Linear 0.00/0.29 ->Coefficients: 0.00/0.29 Natural Numbers 0.00/0.29 ->Dimension: 0.00/0.29 1 0.00/0.29 ->Bound: 0.00/0.29 2 0.00/0.29 ->Interpretation: 0.00/0.29 0.00/0.29 [a__app](X1,X2) = X1 + 2.X2 + 2 0.00/0.29 [a__from](X) = 2.X + 2 0.00/0.29 [a__prefix](X) = 2.X + 2 0.00/0.29 [a__zWadr](X1,X2) = 2.X1 + 2.X2 + 1 0.00/0.29 [mark](X) = X 0.00/0.29 [app](X1,X2) = X1 + 2.X2 + 2 0.00/0.29 [cons](X1,X2) = X1 + 2 0.00/0.29 [fSNonEmpty] = 0 0.00/0.29 [from](X) = 2.X + 2 0.00/0.29 [nil] = 0 0.00/0.29 [prefix](X) = 2.X + 2 0.00/0.29 [s](X) = 2.X + 2 0.00/0.29 [zWadr](X1,X2) = 2.X1 + 2.X2 + 1 0.00/0.29 [A__APP](X1,X2) = 0 0.00/0.29 [A__FROM](X) = 0 0.00/0.29 [A__PREFIX](X) = 0 0.00/0.29 [A__ZWADR](X1,X2) = 2.X2 + 2 0.00/0.29 [MARK](X) = 2.X + 2 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S)) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 ->->Cycle: 0.00/0.29 ->->-> Pairs: 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 ->->-> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 Subterm Processor: 0.00/0.29 -> Pairs: 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(app(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(from(X:S)) -> MARK(X:S) 0.00/0.29 MARK(prefix(X:S)) -> MARK(X:S) 0.00/0.29 MARK(s(X:S)) -> MARK(X:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.29 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Projection: 0.00/0.29 pi(MARK) = 1 0.00/0.29 0.00/0.29 Problem 1: 0.00/0.29 0.00/0.29 SCC Processor: 0.00/0.29 -> Pairs: 0.00/0.29 Empty 0.00/0.29 -> Rules: 0.00/0.29 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S)) 0.00/0.29 a__app(nil,YS:S) -> mark(YS:S) 0.00/0.29 a__app(X1:S,X2:S) -> app(X1:S,X2:S) 0.00/0.29 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.29 a__from(X:S) -> from(X:S) 0.00/0.29 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S))) 0.00/0.29 a__prefix(X:S) -> prefix(X:S) 0.00/0.29 a__zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(a__app(mark(Y:S),cons(mark(X:S),nil)),zWadr(XS:S,YS:S)) 0.00/0.29 a__zWadr(nil,YS:S) -> nil 0.00/0.29 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S) 0.00/0.29 a__zWadr(XS:S,nil) -> nil 0.00/0.29 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S)) 0.00/0.29 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.29 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.29 mark(nil) -> nil 0.00/0.29 mark(prefix(X:S)) -> a__prefix(mark(X:S)) 0.00/0.29 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.29 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S)) 0.00/0.29 ->Strongly Connected Components: 0.00/0.29 There is no strongly connected component 0.00/0.29 0.00/0.29 The problem is finite. 0.00/0.29 EOF