Term Rewriting System R:
[X, Y, Z, X1, X2]
a2nd(cons1(X, cons(Y, Z))) -> mark(Y)
a2nd(cons(X, X1)) -> a2nd(cons1(mark(X), mark(X1)))
a2nd(X) -> 2nd(X)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(2nd(X)) -> a2nd(mark(X))
mark(from(X)) -> afrom(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
mark(s(X)) -> s(mark(X))
mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2))

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

A2ND(cons1(X, cons(Y, Z))) -> MARK(Y)
A2ND(cons(X, X1)) -> A2ND(cons1(mark(X), mark(X1)))
A2ND(cons(X, X1)) -> MARK(X)
A2ND(cons(X, X1)) -> MARK(X1)
AFROM(X) -> MARK(X)
MARK(2nd(X)) -> A2ND(mark(X))
MARK(2nd(X)) -> MARK(X)
MARK(from(X)) -> AFROM(mark(X))
MARK(from(X)) -> MARK(X)
MARK(cons(X1, X2)) -> MARK(X1)
MARK(s(X)) -> MARK(X)
MARK(cons1(X1, X2)) -> MARK(X1)
MARK(cons1(X1, X2)) -> MARK(X2)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

A2ND(cons(X, X1)) -> MARK(X1)
MARK(cons1(X1, X2)) -> MARK(X2)
MARK(cons1(X1, X2)) -> MARK(X1)
MARK(s(X)) -> MARK(X)
MARK(cons(X1, X2)) -> MARK(X1)
MARK(from(X)) -> MARK(X)
AFROM(X) -> MARK(X)
MARK(from(X)) -> AFROM(mark(X))
MARK(2nd(X)) -> MARK(X)
A2ND(cons(X, X1)) -> MARK(X)
A2ND(cons(X, X1)) -> A2ND(cons1(mark(X), mark(X1)))
MARK(2nd(X)) -> A2ND(mark(X))
A2ND(cons1(X, cons(Y, Z))) -> MARK(Y)


Rules:


a2nd(cons1(X, cons(Y, Z))) -> mark(Y)
a2nd(cons(X, X1)) -> a2nd(cons1(mark(X), mark(X1)))
a2nd(X) -> 2nd(X)
afrom(X) -> cons(mark(X), from(s(X)))
afrom(X) -> from(X)
mark(2nd(X)) -> a2nd(mark(X))
mark(from(X)) -> afrom(mark(X))
mark(cons(X1, X2)) -> cons(mark(X1), X2)
mark(s(X)) -> s(mark(X))
mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2))


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:01 minutes