Tool CaT
stdout:
MAYBE
Problem:
eq(0(),0()) -> true()
eq(0(),s(X)) -> false()
eq(s(X),0()) -> false()
eq(s(X),s(Y)) -> eq(X,Y)
rm(N,nil()) -> nil()
rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X))
ifrm(true(),N,add(M,X)) -> rm(N,X)
ifrm(false(),N,add(M,X)) -> add(M,rm(N,X))
purge(nil()) -> nil()
purge(add(N,X)) -> add(N,purge(rm(N,X)))
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(X)) -> false()
, eq(s(X), 0()) -> false()
, eq(s(X), s(Y)) -> eq(X, Y)
, rm(N, nil()) -> nil()
, rm(N, add(M, X)) -> ifrm(eq(N, M), N, add(M, X))
, ifrm(true(), N, add(M, X)) -> rm(N, X)
, ifrm(false(), N, add(M, X)) -> add(M, rm(N, X))
, purge(nil()) -> nil()
, purge(add(N, X)) -> add(N, purge(rm(N, X)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(X)) -> false()
, eq(s(X), 0()) -> false()
, eq(s(X), s(Y)) -> eq(X, Y)
, rm(N, nil()) -> nil()
, rm(N, add(M, X)) -> ifrm(eq(N, M), N, add(M, X))
, ifrm(true(), N, add(M, X)) -> rm(N, X)
, ifrm(false(), N, add(M, X)) -> add(M, rm(N, X))
, purge(nil()) -> nil()
, purge(add(N, X)) -> add(N, purge(rm(N, X)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds