Tool Bounds
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ add() -> app(curry(), plus())
, app(app(app(curry(), f), x), y) -> app(app(f, x), y)
, app(app(plus(), app(s(), x)), y) ->
app(s(), app(app(plus(), x), y))
, app(app(plus(), 0()), y) -> y}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 2695
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ add() -> app(curry(), plus())
, app(app(app(curry(), f), x), y) -> app(app(f, x), y)
, app(app(plus(), app(s(), x)), y) ->
app(s(), app(app(plus(), x), y))
, app(app(plus(), 0()), y) -> y}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
plus() = [0]
[0]
0() = [0]
[0]
app(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
[0 1] [0 1] [2]
s() = [0]
[0]
curry() = [0]
[0]
add() = [3]
[3]
Hurray, we answered YES(?,O(n^2))Tool IDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ add() -> app(curry(), plus())
, app(app(app(curry(), f), x), y) -> app(app(f, x), y)
, app(app(plus(), app(s(), x)), y) ->
app(s(), app(app(plus(), x), y))
, app(app(plus(), 0()), y) -> y}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
Interpretation Functions:
plus() = [0]
[0]
0() = [0]
[2]
app(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
[0 1] [0 1] [2]
s() = [0]
[0]
curry() = [0]
[0]
add() = [3]
[3]
Hurray, we answered YES(?,O(n^2))Tool TRI
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ add() -> app(curry(), plus())
, app(app(app(curry(), f), x), y) -> app(app(f, x), y)
, app(app(plus(), app(s(), x)), y) ->
app(s(), app(app(plus(), x), y))
, app(app(plus(), 0()), y) -> y}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
plus() = [0]
[0]
0() = [3]
[0]
app(x1, x2) = [1 2] x1 + [1 0] x2 + [1]
[0 1] [0 1] [1]
s() = [0]
[0]
curry() = [0]
[0]
add() = [3]
[3]
Hurray, we answered YES(?,O(n^2))Tool TRI2
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ add() -> app(curry(), plus())
, app(app(app(curry(), f), x), y) -> app(app(f, x), y)
, app(app(plus(), app(s(), x)), y) ->
app(s(), app(app(plus(), x), y))
, app(app(plus(), 0()), y) -> y}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
plus() = [0]
[0]
0() = [0]
[0]
app(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
[0 1] [0 1] [2]
s() = [0]
[2]
curry() = [0]
[0]
add() = [3]
[3]
Hurray, we answered YES(?,O(n^2))