Tool CaT
stdout:
MAYBE
Problem:
app(nil(),xs) -> nil()
app(cons(x,xs),ys) -> cons(x,app(xs,ys))
rev(nil()) -> nil()
rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
Proof:
Complexity Transformation Processor:
strict:
app(nil(),xs) -> nil()
app(cons(x,xs),ys) -> cons(x,app(xs,ys))
rev(nil()) -> nil()
rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
weak:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4}
transitions:
nil1() -> 7*
cons1(3,7) -> 14*
cons1(2,7) -> 14*
cons1(1,7) -> 21*
append1(7,22) -> 22*
append1(2,22) -> 5*
append1(3,15) -> 5*
append1(1,22) -> 5*
append1(7,15) -> 15*
append1(2,15) -> 5*
append1(3,22) -> 5*
append1(1,15) -> 5*
rev1(14) -> 15*
rev1(21) -> 22*
app0(3,1) -> 4*
app0(3,3) -> 4*
app0(1,2) -> 4*
app0(2,1) -> 4*
app0(2,3) -> 4*
app0(3,2) -> 4*
app0(1,1) -> 4*
app0(1,3) -> 4*
app0(2,2) -> 4*
nil0() -> 4,1
cons0(3,1) -> 2*
cons0(3,3) -> 2*
cons0(1,2) -> 2*
cons0(1,4) -> 4*
cons0(2,1) -> 2*
cons0(2,3) -> 2*
cons0(3,2) -> 2*
cons0(3,4) -> 4*
cons0(1,1) -> 2*
cons0(1,3) -> 2*
cons0(2,2) -> 2*
cons0(2,4) -> 4*
rev0(2) -> 5*
rev0(1) -> 5*
rev0(3) -> 5*
append0(3,1) -> 3*
append0(3,3) -> 3*
append0(1,2) -> 3*
append0(2,1) -> 3*
append0(2,3) -> 3*
append0(3,2) -> 3*
append0(1,1) -> 3*
append0(1,3) -> 3*
append0(2,2) -> 3*
7 -> 5*
problem:
strict:
app(nil(),xs) -> nil()
app(cons(x,xs),ys) -> cons(x,app(xs,ys))
rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
weak:
rev(nil()) -> nil()
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4}
transitions:
nil1() -> 4*
cons1(1,4) -> 15*
cons1(3,4) -> 13*
cons1(2,4) -> 13*
append1(2,14) -> 5*
append1(2,16) -> 5*
append1(4,14) -> 14*
append1(4,16) -> 16*
append1(1,14) -> 5*
append1(1,16) -> 5*
append1(3,14) -> 5*
append1(3,16) -> 5*
rev1(15) -> 16*
rev1(13) -> 14*
app0(3,1) -> 4*
app0(3,3) -> 4*
app0(1,2) -> 4*
app0(2,1) -> 4*
app0(2,3) -> 4*
app0(3,2) -> 4*
app0(1,1) -> 4*
app0(1,3) -> 4*
app0(2,2) -> 4*
nil0() -> 5,1
cons0(3,1) -> 2*
cons0(3,3) -> 2*
cons0(1,2) -> 2*
cons0(1,4) -> 4*
cons0(2,1) -> 2*
cons0(2,3) -> 2*
cons0(3,2) -> 2*
cons0(3,4) -> 4*
cons0(1,1) -> 2*
cons0(1,3) -> 2*
cons0(2,2) -> 2*
cons0(2,4) -> 4*
rev0(2) -> 5*
rev0(1) -> 5*
rev0(3) -> 5*
append0(3,1) -> 3*
append0(3,3) -> 3*
append0(1,2) -> 3*
append0(2,1) -> 3*
append0(2,3) -> 3*
append0(3,2) -> 3*
append0(1,1) -> 3*
append0(1,3) -> 3*
append0(2,2) -> 3*
problem:
strict:
app(cons(x,xs),ys) -> cons(x,app(xs,ys))
rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
weak:
app(nil(),xs) -> nil()
rev(nil()) -> nil()
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4}
transitions:
nil1() -> 6,36
cons1(2,36) -> 37*
cons1(1,6) -> 6,4
cons1(1,10) -> 6,4
cons1(1,36) -> 41*
cons1(3,6) -> 6,4
cons1(3,10) -> 6,4
cons1(3,36) -> 37*
cons1(2,6) -> 6,4
cons1(2,10) -> 6,4
app1(3,1) -> 6*
app1(3,3) -> 6*
app1(1,2) -> 6*
app1(2,1) -> 6*
app1(2,3) -> 10*
app1(3,2) -> 6*
app1(1,1) -> 6*
app1(1,3) -> 6*
app1(2,2) -> 6*
append1(2,38) -> 5*
append1(2,42) -> 5*
append1(36,38) -> 38*
append1(36,42) -> 42*
append1(1,38) -> 5*
append1(1,42) -> 5*
append1(3,38) -> 5*
append1(3,42) -> 5*
rev1(37) -> 38*
rev1(41) -> 42*
app0(3,1) -> 4*
app0(3,3) -> 4*
app0(1,2) -> 4*
app0(2,1) -> 4*
app0(2,3) -> 4*
app0(3,2) -> 4*
app0(1,1) -> 4*
app0(1,3) -> 4*
app0(2,2) -> 4*
nil0() -> 5,4,3
cons0(3,1) -> 1*
cons0(3,3) -> 1*
cons0(1,2) -> 1*
cons0(2,1) -> 1*
cons0(2,3) -> 1*
cons0(3,2) -> 1*
cons0(1,1) -> 1*
cons0(1,3) -> 1*
cons0(2,2) -> 1*
rev0(2) -> 5*
rev0(1) -> 5*
rev0(3) -> 5*
append0(3,1) -> 2*
append0(3,3) -> 2*
append0(1,2) -> 2*
append0(2,1) -> 2*
append0(2,3) -> 2*
append0(3,2) -> 2*
append0(1,1) -> 2*
append0(1,3) -> 2*
append0(2,2) -> 2*
problem:
strict:
rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
weak:
app(cons(x,xs),ys) -> cons(x,app(xs,ys))
app(nil(),xs) -> nil()
rev(nil()) -> nil()
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(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
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(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool pair1rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool tup3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))
, rev(nil()) -> nil()
, rev(cons(x, xs)) -> append(xs, rev(cons(x, nil())))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..