LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,PRIMREC)
Proof:
The input was oriented with the instance of
'multiset path orders' as induced by the precedence
terms > cons, terms > recip, terms > sqr, terms > n__terms,
terms > s, sqr > s, sqr > add, add > s, dbl > s, first > cons,
first > n__first, activate > terms, sqr ~ dbl, 0 ~ nil,
first ~ activate .
Hurray, we answered YES(?,PRIMREC)
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
, sqr(0()) -> 0()
, sqr(s(X)) -> s(add(sqr(X), dbl(X)))
, dbl(0()) -> 0()
, dbl(s(X)) -> s(s(dbl(X)))
, add(0(), X) -> X
, add(s(X), Y) -> s(add(X, Y))
, first(0(), X) -> nil()
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, terms(X) -> n__terms(X)
, first(X1, X2) -> n__first(X1, X2)
, activate(n__terms(X)) -> terms(X)
, activate(n__first(X1, X2)) -> first(X1, X2)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..