/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 v_NonEmpty:S X:S X1:S X2:S Y:S Z:S)
(RULES
activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
activate(n__from(X:S)) -> from(activate(X:S))
activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
activate(n__len(X:S)) -> len(activate(X:S))
activate(n__s(X:S)) -> s(X:S)
activate(X:S) -> X:S
add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
add(0,X:S) -> X:S
add(X1:S,X2:S) -> n__add(X1:S,X2:S)
from(X:S) -> cons(X:S,n__from(n__s(X:S)))
from(X:S) -> n__from(X:S)
fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
fst(0,Z:S) -> nil
fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
len(nil) -> 0
len(X:S) -> n__len(X:S)
s(X:S) -> n__s(X:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ACTIVATE(n__s(X:S)) -> S(X:S)
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 ADD(s(X:S),Y:S) -> S(n__add(activate(X:S),Y:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> S(n__len(activate(Z:S)))
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ACTIVATE(n__s(X:S)) -> S(X:S)
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 ADD(s(X:S),Y:S) -> S(n__add(activate(X:S),Y:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> S(n__len(activate(Z:S)))
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X1 + 2.X2 + 2
[from](X) = X + 2
[fst](X1,X2) = 2.X1 + 2.X2 + 1
[len](X) = 2.X
[s](X) = X
[0] = 2
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X1 + 2.X2 + 2
[n__from](X) = X + 2
[n__fst](X1,X2) = 2.X1 + 2.X2 + 1
[n__len](X) = 2.X
[n__s](X) = X
[nil] = 2
[ACTIVATE](X) = 2.X
[ADD](X1,X2) = 2.X1 + 2.X2 + 2
[FST](X1,X2) = 2.X1 + 2.X2
[LEN](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X1 + 2.X2 + 2
[from](X) = 2.X + 2
[fst](X1,X2) = 2.X1 + 2.X2
[len](X) = 2.X + 2
[s](X) = X
[0] = 2
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X1 + 2.X2 + 2
[n__from](X) = 2.X + 2
[n__fst](X1,X2) = 2.X1 + 2.X2
[n__len](X) = 2.X + 2
[n__s](X) = X
[nil] = 0
[ACTIVATE](X) = 2.X + 2
[ADD](X1,X2) = 2.X1 + 2.X2 + 2
[FST](X1,X2) = 2.X1 + 2.X2 + 2
[LEN](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__add(X1:S,X2:S)) -> ADD(activate(X1:S),activate(X2:S))
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = X1 + 2.X2 + 2
[from](X) = X
[fst](X1,X2) = 2.X1 + 2.X2 + 2
[len](X) = 2.X + 1
[s](X) = X
[0] = 1
[cons](X1,X2) = X2
[n__add](X1,X2) = X1 + 2.X2 + 2
[n__from](X) = X
[n__fst](X1,X2) = 2.X1 + 2.X2 + 2
[n__len](X) = 2.X + 1
[n__s](X) = X
[nil] = 1
[ACTIVATE](X) = 2.X
[ADD](X1,X2) = 2.X1 + 2.X2 + 2
[FST](X1,X2) = 2.X1 + 2.X2
[LEN](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 ADD(s(X:S),Y:S) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X1 + 2.X2 + 2
[from](X) = 2.X + 1
[fst](X1,X2) = X1 + 2.X2 + 2
[len](X) = 2.X + 1
[s](X) = X
[0] = 0
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X1 + 2.X2 + 2
[n__from](X) = 2.X + 1
[n__fst](X1,X2) = X1 + 2.X2 + 2
[n__len](X) = 2.X + 1
[n__s](X) = X
[nil] = 2
[ACTIVATE](X) = 2.X
[FST](X1,X2) = 2.X1 + 2.X2
[LEN](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X1 + 2.X2
[from](X) = 2.X + 1
[fst](X1,X2) = 2.X1 + 2.X2 + 2
[len](X) = 2.X + 1
[s](X) = X
[0] = 1
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X1 + 2.X2
[n__from](X) = 2.X + 1
[n__fst](X1,X2) = 2.X1 + 2.X2 + 2
[n__len](X) = 2.X + 1
[n__s](X) = X
[nil] = 2
[ACTIVATE](X) = 2.X + 2
[FST](X1,X2) = 2.X1 + 2.X2 + 2
[LEN](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> ACTIVATE(X2:S)
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X1 + X2 + 2
[from](X) = 2.X + 2
[fst](X1,X2) = 2.X1 + X2 + 2
[len](X) = 2.X
[s](X) = X
[0] = 2
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X1 + X2 + 2
[n__from](X) = 2.X + 2
[n__fst](X1,X2) = 2.X1 + X2 + 2
[n__len](X) = 2.X
[n__s](X) = X
[nil] = 1
[ACTIVATE](X) = 2.X
[FST](X1,X2) = 2.X1 + 2.X2
[LEN](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__fst(X1:S,X2:S)) -> FST(activate(X1:S),activate(X2:S))
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X
[add](X1,X2) = 2.X2 + 2
[from](X) = 2.X + 1
[fst](X1,X2) = 2.X1 + 2.X2 + 2
[len](X) = 2.X + 2
[s](X) = X
[0] = 2
[cons](X1,X2) = X2
[n__add](X1,X2) = 2.X2 + 2
[n__from](X) = 2.X + 1
[n__fst](X1,X2) = 2.X1 + 2.X2 + 2
[n__len](X) = 2.X + 2
[n__s](X) = X
[nil] = 2
[ACTIVATE](X) = 2.X + 2
[FST](X1,X2) = 2.X1 + 2.X2 + 2
[LEN](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(X:S)
 FST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__len(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = 2.X + 1
[add](X1,X2) = X1 + X2 + 1
[from](X) = 2
[fst](X1,X2) = 2
[len](X) = 2.X + 2
[s](X) = 2
[0] = 2
[cons](X1,X2) = X2 + 1
[n__add](X1,X2) = X1 + X2 + 1
[n__from](X) = 1
[n__fst](X1,X2) = 1
[n__len](X) = 2.X + 2
[n__s](X) = 2
[nil] = 1
[ACTIVATE](X) = 2.X + 2
[LEN](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__len(X:S)) -> LEN(activate(X:S))
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
-> Usable rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = 2.X + 1
[add](X1,X2) = X1 + 2.X2 + 2
[from](X) = X
[fst](X1,X2) = 2
[len](X) = 2.X + 2
[s](X) = 1
[0] = 1
[cons](X1,X2) = 2.X2
[n__add](X1,X2) = X1 + 2.X2 + 2
[n__from](X) = X
[n__fst](X1,X2) = 1
[n__len](X) = 2.X + 2
[n__s](X) = 0
[nil] = 2
[ACTIVATE](X) = 2.X
[LEN](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 LEN(cons(X:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__add(X1:S,X2:S)) -> add(activate(X1:S),activate(X2:S))
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__fst(X1:S,X2:S)) -> fst(activate(X1:S),activate(X2:S))
 activate(n__len(X:S)) -> len(activate(X:S))
 activate(n__s(X:S)) -> s(X:S)
 activate(X:S) -> X:S
 add(s(X:S),Y:S) -> s(n__add(activate(X:S),Y:S))
 add(0,X:S) -> X:S
 add(X1:S,X2:S) -> n__add(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 fst(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__fst(activate(X:S),activate(Z:S)))
 fst(0,Z:S) -> nil
 fst(X1:S,X2:S) -> n__fst(X1:S,X2:S)
 len(cons(X:S,Z:S)) -> s(n__len(activate(Z:S)))
 len(nil) -> 0
 len(X:S) -> n__len(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.