Tool CaT
stdout:
YES(?,O(n^1))
Problem:
f(s(X)) -> f(X)
g(cons(0(),Y)) -> g(Y)
g(cons(s(X),Y)) -> s(X)
h(cons(X,Y)) -> h(g(cons(X,Y)))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5,4}
transitions:
h1(8) -> 6*
g1(7) -> 8*
g1(2) -> 8,5
g1(1) -> 8,5
g1(3) -> 8,5
cons1(3,1) -> 7*
cons1(3,3) -> 7*
cons1(1,2) -> 7*
cons1(2,1) -> 7*
cons1(2,3) -> 7*
cons1(3,2) -> 7*
cons1(1,1) -> 7*
cons1(1,3) -> 7*
cons1(2,2) -> 7*
s1(2) -> 8,5
s1(1) -> 8,5
s1(3) -> 8,5
f1(2) -> 4*
f1(1) -> 4*
f1(3) -> 4*
f0(2) -> 4*
f0(1) -> 4*
f0(3) -> 4*
s0(2) -> 1*
s0(1) -> 1*
s0(3) -> 1*
g0(2) -> 5*
g0(1) -> 5*
g0(3) -> 5*
cons0(3,1) -> 2*
cons0(3,3) -> 2*
cons0(1,2) -> 2*
cons0(2,1) -> 2*
cons0(2,3) -> 2*
cons0(3,2) -> 2*
cons0(1,1) -> 2*
cons0(1,3) -> 2*
cons0(2,2) -> 2*
00() -> 3*
h0(2) -> 6*
h0(1) -> 6*
h0(3) -> 6*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
Tool IRC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y)))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y)))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 1
, s_0(2) -> 2
, s_1(2) -> 1
, s_1(2) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(2) -> 3
, g_1(4) -> 3
, cons_0(2, 2) -> 2
, cons_1(2, 2) -> 4
, 0_0() -> 2
, h_0(2) -> 1
, h_1(3) -> 1}Tool RC1
stdout:
YES(?,O(n^1))
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y)))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(s(X)) -> f(X)
, g(cons(0(), Y)) -> g(Y)
, g(cons(s(X), Y)) -> s(X)
, h(cons(X, Y)) -> h(g(cons(X, Y)))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 1
, s_0(2) -> 2
, s_1(2) -> 1
, s_1(2) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(2) -> 3
, g_1(4) -> 3
, cons_0(2, 2) -> 2
, cons_1(2, 2) -> 4
, 0_0() -> 2
, h_0(2) -> 1
, h_1(3) -> 1}