Tool CaT
stdout:
YES(?,O(n^1))
Problem:
i(x,x) -> i(a(),b())
g(x,x) -> g(a(),b())
h(s(f(x))) -> h(f(x))
f(s(x)) -> s(s(f(h(s(x)))))
f(g(s(x),y)) -> f(g(x,s(y)))
h(g(x,s(y))) -> h(g(s(x),y))
h(i(x,y)) -> i(i(c(),h(h(y))),x)
g(a(),g(x,g(b(),g(a(),g(x,y))))) -> g(a(),g(a(),g(a(),g(x,g(b(),g(b(),y))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {20,8,7,6,5}
transitions:
i0(17,18) -> 5*
i0(18,1) -> 5*
i0(2,18) -> 5*
i0(18,3) -> 5*
i0(3,1) -> 5*
i0(3,3) -> 5*
i0(18,17) -> 5*
i0(18,19) -> 5*
i0(3,17) -> 5*
i0(19,2) -> 5*
i0(3,19) -> 5*
i0(19,4) -> 5*
i0(4,2) -> 5*
i0(4,4) -> 5*
i0(19,18) -> 5*
i0(4,18) -> 5*
i0(1,2) -> 5*
i0(1,4) -> 5*
i0(17,1) -> 5*
i0(1,18) -> 5*
i0(17,3) -> 5*
i0(2,1) -> 5*
i0(2,3) -> 5*
i0(17,17) -> 5*
i0(17,19) -> 5*
i0(2,17) -> 5*
i0(18,2) -> 5*
i0(2,19) -> 5*
i0(18,4) -> 5*
i0(3,2) -> 5*
i0(3,4) -> 5*
i0(18,18) -> 5*
i0(19,1) -> 5*
i0(3,18) -> 5*
i0(19,3) -> 5*
i0(4,1) -> 5*
i0(4,3) -> 5*
i0(19,17) -> 5*
i0(19,19) -> 5*
i0(4,17) -> 5*
i0(4,19) -> 5*
i0(1,1) -> 5*
i0(1,3) -> 5*
i0(1,17) -> 5*
i0(17,2) -> 5*
i0(1,19) -> 5*
i0(17,4) -> 5*
i0(2,2) -> 5*
i0(2,4) -> 5*
g0(17,18) -> 6*
g0(18,1) -> 6*
g0(2,18) -> 6*
g0(18,3) -> 6*
g0(3,1) -> 6*
g0(3,3) -> 6*
g0(18,17) -> 6*
g0(18,19) -> 6*
g0(3,17) -> 6*
g0(19,2) -> 6*
g0(3,19) -> 6*
g0(19,4) -> 6*
g0(4,2) -> 6*
g0(4,4) -> 6*
g0(19,18) -> 6*
g0(4,18) -> 6*
g0(1,2) -> 6*
g0(1,4) -> 6*
g0(17,1) -> 6*
g0(1,18) -> 6*
g0(17,3) -> 6*
g0(2,1) -> 6*
g0(2,3) -> 6*
g0(17,17) -> 6*
g0(17,19) -> 6*
g0(2,17) -> 6*
g0(18,2) -> 6*
g0(2,19) -> 6*
g0(18,4) -> 6*
g0(3,2) -> 6*
g0(3,4) -> 6*
g0(18,18) -> 6*
g0(19,1) -> 6*
g0(3,18) -> 6*
g0(19,3) -> 6*
g0(4,1) -> 6*
g0(4,3) -> 6*
g0(19,17) -> 6*
g0(19,19) -> 6*
g0(4,17) -> 6*
g0(4,19) -> 6*
g0(1,1) -> 6*
g0(1,3) -> 6*
g0(1,17) -> 6*
g0(17,2) -> 6*
g0(1,19) -> 6*
g0(17,4) -> 6*
g0(2,2) -> 6*
g0(2,4) -> 6*
h0(17) -> 7*
h0(2) -> 7*
h0(19) -> 7*
h0(4) -> 7*
h0(1) -> 7*
h0(18) -> 7*
h0(3) -> 7*
f0(17) -> 8*
f0(2) -> 8*
f0(19) -> 8*
f0(4) -> 8*
f0(1) -> 8*
f0(18) -> 8*
f0(3) -> 8*
c0() -> 4*
s1(15) -> 16*
s1(17) -> 17*
s1(2) -> 17*,3,13
s1(19) -> 17*
s1(4) -> 17*,3,13
s1(16) -> 8*
s1(1) -> 17*,3,13
s1(18) -> 17*
s1(3) -> 17*,3,13
f1(20) -> 15*
f1(14) -> 15*
h1(17) -> 20*,7,14
h1(13) -> 14*
g1(18,9) -> 6*
g1(18,19) -> 6*
g1(10,9) -> 6*
g1(10,19) -> 6*
a1() -> 18*,1,10
b1() -> 19*,2,9
i1(18,9) -> 5*
i1(18,19) -> 5*
i1(10,9) -> 5*
i1(10,19) -> 5*
problem:
QedTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ i(x, x) -> i(a(), b())
, g(x, x) -> g(a(), b())
, h(s(f(x))) -> h(f(x))
, f(s(x)) -> s(s(f(h(s(x)))))
, f(g(s(x), y)) -> f(g(x, s(y)))
, h(g(x, s(y))) -> h(g(s(x), y))
, h(i(x, y)) -> i(i(c(), h(h(y))), x)
, g(a(), g(x, g(b(), g(a(), g(x, y))))) ->
g(a(), g(a(), g(a(), g(x, g(b(), g(b(), y))))))}
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:
{ i(x, x) -> i(a(), b())
, g(x, x) -> g(a(), b())
, h(s(f(x))) -> h(f(x))
, f(s(x)) -> s(s(f(h(s(x)))))
, f(g(s(x), y)) -> f(g(x, s(y)))
, h(g(x, s(y))) -> h(g(s(x), y))
, h(i(x, y)) -> i(i(c(), h(h(y))), x)
, g(a(), g(x, g(b(), g(a(), g(x, y))))) ->
g(a(), g(a(), g(a(), g(x, g(b(), g(b(), y))))))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds