Tool CaT
stdout:
MAYBE
Problem:
app(nil(),k) -> k
app(l,nil()) -> l
app(cons(x,l),k) -> cons(x,app(l,k))
sum(cons(x,nil())) -> cons(x,nil())
sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
a(h(),h(),x) -> s(x)
a(x,s(y),h()) -> a(x,y,s(h()))
a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
a(s(x),h(),z) -> a(x,z,z)
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:
{ app(nil(), k) -> k
, app(l, nil()) -> l
, app(cons(x, l), k) -> cons(x, app(l, k))
, sum(cons(x, nil())) -> cons(x, nil())
, sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h()), l))
, a(h(), h(), x) -> s(x)
, a(x, s(y), h()) -> a(x, y, s(h()))
, a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z))
, a(s(x), h(), z) -> a(x, z, z)}
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:
{ app(nil(), k) -> k
, app(l, nil()) -> l
, app(cons(x, l), k) -> cons(x, app(l, k))
, sum(cons(x, nil())) -> cons(x, nil())
, sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h()), l))
, a(h(), h(), x) -> s(x)
, a(x, s(y), h()) -> a(x, y, s(h()))
, a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z))
, a(s(x), h(), z) -> a(x, z, z)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds