Tool CaT
stdout:
MAYBE
Problem:
a(h(),h(),h(),x) -> s(x)
a(l,x,s(y),h()) -> a(l,x,y,s(h()))
a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
a(l,s(x),h(),z) -> a(l,x,z,z)
a(s(l),h(),h(),z) -> a(l,z,h(),z)
+(x,h()) -> x
+(h(),x) -> x
+(s(x),s(y)) -> s(s(+(x,y)))
+(+(x,y),z) -> +(x,+(y,z))
s(h()) -> 1()
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(),h()),l))
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:
{ a(h(), h(), h(), x) -> s(x)
, a(l, x, s(y), h()) -> a(l, x, y, s(h()))
, a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
, a(l, s(x), h(), z) -> a(l, x, z, z)
, a(s(l), h(), h(), z) -> a(l, z, h(), z)
, +(x, h()) -> x
, +(h(), x) -> x
, +(s(x), s(y)) -> s(s(+(x, y)))
, +(+(x, y), z) -> +(x, +(y, z))
, s(h()) -> 1()
, 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(), h()), l))}
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:
{ a(h(), h(), h(), x) -> s(x)
, a(l, x, s(y), h()) -> a(l, x, y, s(h()))
, a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
, a(l, s(x), h(), z) -> a(l, x, z, z)
, a(s(l), h(), h(), z) -> a(l, z, h(), z)
, +(x, h()) -> x
, +(h(), x) -> x
, +(s(x), s(y)) -> s(s(+(x, y)))
, +(+(x, y), z) -> +(x, +(y, z))
, s(h()) -> 1()
, 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(), h()), l))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds