/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__FROM(X) -> MARK(X)
 A__ZWADR(cons(X,XS),cons(Y,YS)) -> MARK(X)
 A__ZWADR(cons(X,XS),cons(Y,YS)) -> MARK(Y)
 MARK(app(X1,X2)) -> MARK(X1)
 MARK(app(X1,X2)) -> MARK(X2)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(prefix(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(zWadr(X1,X2)) -> A__ZWADR(mark(X1),mark(X2))
 MARK(zWadr(X1,X2)) -> MARK(X1)
 MARK(zWadr(X1,X2)) -> MARK(X2)
-> Rules:
 a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS))
 a__app(nil,YS) -> mark(YS)
 a__app(X1,X2) -> app(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 a__prefix(L) -> cons(nil,zWadr(L,prefix(L)))
 a__prefix(X) -> prefix(X)
 a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil)),zWadr(XS,YS))
 a__zWadr(nil,YS) -> nil
 a__zWadr(X1,X2) -> zWadr(X1,X2)
 a__zWadr(XS,nil) -> nil
 mark(app(X1,X2)) -> a__app(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(prefix(X)) -> a__prefix(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2))
-> Usable rules:
 a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS))
 a__app(nil,YS) -> mark(YS)
 a__app(X1,X2) -> app(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 a__prefix(L) -> cons(nil,zWadr(L,prefix(L)))
 a__prefix(X) -> prefix(X)
 a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil)),zWadr(XS,YS))
 a__zWadr(nil,YS) -> nil
 a__zWadr(X1,X2) -> zWadr(X1,X2)
 a__zWadr(XS,nil) -> nil
 mark(app(X1,X2)) -> a__app(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(prefix(X)) -> a__prefix(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2))
->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) = 2.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
[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__FROM](X) = 2.X + 2
[A__ZWADR](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.