YES

Problem 1: 

(VAR v_NonEmpty:S L:S X:S X1:S X2:S XS:S Y:S YS:S)
(RULES
a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
a__app(nil,YS:S) -> mark(YS:S)
a__app(X1:S,X2:S) -> app(X1:S,X2:S)
a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
a__from(X:S) -> from(X:S)
a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
a__prefix(X:S) -> prefix(X:S)
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))
a__zWadr(nil,YS:S) -> nil
a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
a__zWadr(XS:S,nil) -> nil
mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
mark(from(X:S)) -> a__from(mark(X:S))
mark(nil) -> nil
mark(prefix(X:S)) -> a__prefix(mark(X:S))
mark(s(X:S)) -> s(mark(X:S))
mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S)
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> A__PREFIX(mark(X:S))
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

SCC Processor:
-> Pairs:
 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S)
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> A__PREFIX(mark(X:S))
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S)
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__APP(cons(X:S,XS:S),YS:S) -> MARK(X:S)
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__app](X1,X2) = X1 + 2.X2 + 2
[a__from](X) = X + 2
[a__prefix](X) = 2.X + 2
[a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[app](X1,X2) = X1 + 2.X2 + 2
[cons](X1,X2) = X1 + 2
[fSNonEmpty] = 0
[from](X) = X + 2
[nil] = 0
[prefix](X) = 2.X + 2
[s](X) = 2.X + 2
[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[A__APP](X1,X2) = 2.X1 + 2.X2 + 2
[A__FROM](X) = 2.X + 2
[A__PREFIX](X) = 0
[A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 1
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__APP(nil,YS:S) -> MARK(YS:S)
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__app](X1,X2) = 2.X1 + X2 + 2
[a__from](X) = 2.X + 2
[a__prefix](X) = 2.X + 2
[a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[app](X1,X2) = 2.X1 + X2 + 2
[cons](X1,X2) = X1
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[nil] = 2
[prefix](X) = 2.X + 2
[s](X) = X + 2
[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[A__APP](X1,X2) = X1 + 2.X2 + 1
[A__FROM](X) = 2.X + 2
[A__PREFIX](X) = 0
[A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> A__APP(mark(Y:S),cons(mark(X:S),nil))
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> A__APP(mark(X1:S),mark(X2:S))
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__app](X1,X2) = 2.X1 + X2 + 1
[a__from](X) = 2.X + 2
[a__prefix](X) = X + 2
[a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[app](X1,X2) = 2.X1 + X2 + 1
[cons](X1,X2) = 2.X1 + 2
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[nil] = 0
[prefix](X) = X + 2
[s](X) = 2.X + 2
[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[A__APP](X1,X2) = 0
[A__FROM](X) = 2.X + 2
[A__PREFIX](X) = 0
[A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__app](X1,X2) = 2.X1 + X2 + 2
[a__from](X) = 2.X + 2
[a__prefix](X) = 2.X + 2
[a__zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[app](X1,X2) = 2.X1 + X2 + 2
[cons](X1,X2) = 2.X1 + 2
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[nil] = 0
[prefix](X) = 2.X + 2
[s](X) = 2.X + 1
[zWadr](X1,X2) = 2.X1 + 2.X2 + 2
[A__APP](X1,X2) = 0
[A__FROM](X) = 0
[A__PREFIX](X) = 0
[A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__app](X1,X2) = X1 + 2.X2 + 2
[a__from](X) = 2.X + 2
[a__prefix](X) = 2.X + 2
[a__zWadr](X1,X2) = 2.X1 + 2.X2 + 1
[mark](X) = X
[app](X1,X2) = X1 + 2.X2 + 2
[cons](X1,X2) = X1 + 2
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[nil] = 0
[prefix](X) = 2.X + 2
[s](X) = 2.X + 2
[zWadr](X1,X2) = 2.X1 + 2.X2 + 1
[A__APP](X1,X2) = 0
[A__FROM](X) = 0
[A__PREFIX](X) = 0
[A__ZWADR](X1,X2) = 2.X2 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> A__ZWADR(mark(X1:S),mark(X2:S))
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(app(X1:S,X2:S)) -> MARK(X1:S)
 MARK(app(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(prefix(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zWadr(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__app(cons(X:S,XS:S),YS:S) -> cons(mark(X:S),app(XS:S,YS:S))
 a__app(nil,YS:S) -> mark(YS:S)
 a__app(X1:S,X2:S) -> app(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__prefix(L:S) -> cons(nil,zWadr(L:S,prefix(L:S)))
 a__prefix(X:S) -> prefix(X:S)
 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))
 a__zWadr(nil,YS:S) -> nil
 a__zWadr(X1:S,X2:S) -> zWadr(X1:S,X2:S)
 a__zWadr(XS:S,nil) -> nil
 mark(app(X1:S,X2:S)) -> a__app(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(nil) -> nil
 mark(prefix(X:S)) -> a__prefix(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(zWadr(X1:S,X2:S)) -> a__zWadr(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.