Tool CaT
stdout:
MAYBE
Problem:
t(N) -> cs(r(q(N)),nt(ns(N)))
q(0()) -> 0()
q(s(X)) -> s(p(q(X),d(X)))
d(0()) -> 0()
d(s(X)) -> s(s(d(X)))
p(0(),X) -> X
p(X,0()) -> X
p(s(X),s(Y)) -> s(s(p(X,Y)))
f(0(),X) -> nil()
f(s(X),cs(Y,Z)) -> cs(Y,nf(X,a(Z)))
t(X) -> nt(X)
s(X) -> ns(X)
f(X1,X2) -> nf(X1,X2)
a(nt(X)) -> t(a(X))
a(ns(X)) -> s(a(X))
a(nf(X1,X2)) -> f(a(X1),a(X2))
a(X) -> X
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ t(N) -> cs(r(q(N)), nt(ns(N)))
, q(0()) -> 0()
, q(s(X)) -> s(p(q(X), d(X)))
, d(0()) -> 0()
, d(s(X)) -> s(s(d(X)))
, p(0(), X) -> X
, p(X, 0()) -> X
, p(s(X), s(Y)) -> s(s(p(X, Y)))
, f(0(), X) -> nil()
, f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z)))
, t(X) -> nt(X)
, s(X) -> ns(X)
, f(X1, X2) -> nf(X1, X2)
, a(nt(X)) -> t(a(X))
, a(ns(X)) -> s(a(X))
, a(nf(X1, X2)) -> f(a(X1), a(X2))
, a(X) -> X}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ t(N) -> cs(r(q(N)), nt(ns(N)))
, q(0()) -> 0()
, q(s(X)) -> s(p(q(X), d(X)))
, d(0()) -> 0()
, d(s(X)) -> s(s(d(X)))
, p(0(), X) -> X
, p(X, 0()) -> X
, p(s(X), s(Y)) -> s(s(p(X, Y)))
, f(0(), X) -> nil()
, f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z)))
, t(X) -> nt(X)
, s(X) -> ns(X)
, f(X1, X2) -> nf(X1, X2)
, a(nt(X)) -> t(a(X))
, a(ns(X)) -> s(a(X))
, a(nf(X1, X2)) -> f(a(X1), a(X2))
, a(X) -> X}
Proof Output:
Computation stopped due to timeout after 60.0 seconds