*** 1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(cons(x,y)) -> sent(y)
rest(nil()) -> sent(nil())
top(sent(x)) -> top(check(rest(x)))
Weak DP Rules:
Weak TRS Rules:
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1] x1 + [0]
p(cons) = [1] x1 + [1] x2 + [5]
p(nil) = [0]
p(rest) = [1] x1 + [0]
p(sent) = [1] x1 + [5]
p(top) = [1] x1 + [0]
Following rules are strictly oriented:
top(sent(x)) = [1] x + [5]
> [1] x + [0]
= top(check(rest(x)))
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1] x + [1] y + [5]
>= [1] x + [1] y + [5]
= cons(x,y)
check(cons(x,y)) = [1] x + [1] y + [5]
>= [1] x + [1] y + [5]
= cons(x,check(y))
check(cons(x,y)) = [1] x + [1] y + [5]
>= [1] x + [1] y + [5]
= cons(check(x),y)
check(rest(x)) = [1] x + [0]
>= [1] x + [0]
= rest(check(x))
check(sent(x)) = [1] x + [5]
>= [1] x + [5]
= sent(check(x))
rest(cons(x,y)) = [1] x + [1] y + [5]
>= [1] y + [5]
= sent(y)
rest(nil()) = [0]
>= [5]
= sent(nil())
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(cons(x,y)) -> sent(y)
rest(nil()) -> sent(nil())
Weak DP Rules:
Weak TRS Rules:
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1] x1 + [0]
p(cons) = [1] x1 + [1] x2 + [1]
p(nil) = [9]
p(rest) = [1] x1 + [0]
p(sent) = [1] x1 + [0]
p(top) = [1] x1 + [0]
Following rules are strictly oriented:
rest(cons(x,y)) = [1] x + [1] y + [1]
> [1] y + [0]
= sent(y)
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1] x + [1] y + [1]
>= [1] x + [1] y + [1]
= cons(x,y)
check(cons(x,y)) = [1] x + [1] y + [1]
>= [1] x + [1] y + [1]
= cons(x,check(y))
check(cons(x,y)) = [1] x + [1] y + [1]
>= [1] x + [1] y + [1]
= cons(check(x),y)
check(rest(x)) = [1] x + [0]
>= [1] x + [0]
= rest(check(x))
check(sent(x)) = [1] x + [0]
>= [1] x + [0]
= sent(check(x))
rest(nil()) = [9]
>= [9]
= sent(nil())
top(sent(x)) = [1] x + [0]
>= [1] x + [0]
= top(check(rest(x)))
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(nil()) -> sent(nil())
Weak DP Rules:
Weak TRS Rules:
rest(cons(x,y)) -> sent(y)
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1] x1 + [8]
p(cons) = [1] x1 + [1] x2 + [8]
p(nil) = [1]
p(rest) = [1] x1 + [0]
p(sent) = [1] x1 + [8]
p(top) = [1] x1 + [8]
Following rules are strictly oriented:
check(cons(x,y)) = [1] x + [1] y + [16]
> [1] x + [1] y + [8]
= cons(x,y)
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1] x + [1] y + [16]
>= [1] x + [1] y + [16]
= cons(x,check(y))
check(cons(x,y)) = [1] x + [1] y + [16]
>= [1] x + [1] y + [16]
= cons(check(x),y)
check(rest(x)) = [1] x + [8]
>= [1] x + [8]
= rest(check(x))
check(sent(x)) = [1] x + [16]
>= [1] x + [16]
= sent(check(x))
rest(cons(x,y)) = [1] x + [1] y + [8]
>= [1] y + [8]
= sent(y)
rest(nil()) = [1]
>= [9]
= sent(nil())
top(sent(x)) = [1] x + [16]
>= [1] x + [16]
= top(check(rest(x)))
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 1.1.1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(nil()) -> sent(nil())
Weak DP Rules:
Weak TRS Rules:
check(cons(x,y)) -> cons(x,y)
rest(cons(x,y)) -> sent(y)
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1 1] x1 + [0]
[0 1] [0]
p(cons) = [1 0] x1 + [1 4] x2 + [4]
[0 1] [0 1] [1]
p(nil) = [0]
[0]
p(rest) = [1 0] x1 + [0]
[0 2] [0]
p(sent) = [1 2] x1 + [0]
[0 1] [0]
p(top) = [4 0] x1 + [0]
[4 0] [2]
Following rules are strictly oriented:
check(cons(x,y)) = [1 1] x + [1 5] y + [5]
[0 1] [0 1] [1]
> [1 0] x + [1 5] y + [4]
[0 1] [0 1] [1]
= cons(x,check(y))
check(cons(x,y)) = [1 1] x + [1 5] y + [5]
[0 1] [0 1] [1]
> [1 1] x + [1 4] y + [4]
[0 1] [0 1] [1]
= cons(check(x),y)
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1 1] x + [1 5] y + [5]
[0 1] [0 1] [1]
>= [1 0] x + [1 4] y + [4]
[0 1] [0 1] [1]
= cons(x,y)
check(rest(x)) = [1 2] x + [0]
[0 2] [0]
>= [1 1] x + [0]
[0 2] [0]
= rest(check(x))
check(sent(x)) = [1 3] x + [0]
[0 1] [0]
>= [1 3] x + [0]
[0 1] [0]
= sent(check(x))
rest(cons(x,y)) = [1 0] x + [1 4] y + [4]
[0 2] [0 2] [2]
>= [1 2] y + [0]
[0 1] [0]
= sent(y)
rest(nil()) = [0]
[0]
>= [0]
[0]
= sent(nil())
top(sent(x)) = [4 8] x + [0]
[4 8] [2]
>= [4 8] x + [0]
[4 8] [2]
= top(check(rest(x)))
*** 1.1.1.1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(nil()) -> sent(nil())
Weak DP Rules:
Weak TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
rest(cons(x,y)) -> sent(y)
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
NaturalMI {miDimension = 4, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 3 non-zero interpretation-entries in the diagonal of the component-wise maxima):
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1 0 0 0] [0]
[0 0 1 0] x1 + [0]
[0 1 0 0] [0]
[0 0 0 0] [0]
p(cons) = [1 0 0 1] [1 1 1
0] [1]
[0 0 0 0] x1 + [0 0 0
1] x2 + [0]
[0 0 0 0] [0 0 0
1] [0]
[0 0 0 0] [0 0 0
0] [0]
p(nil) = [0]
[0]
[0]
[1]
p(rest) = [1 0 0 1] [0]
[0 1 0 1] x1 + [0]
[0 0 1 0] [0]
[0 0 0 0] [0]
p(sent) = [1 1 1 0] [0]
[0 0 0 1] x1 + [0]
[0 0 0 0] [0]
[0 0 0 0] [0]
p(top) = [1 1 0 0] [0]
[0 0 0 0] x1 + [0]
[0 0 0 0] [0]
[1 1 0 0] [0]
Following rules are strictly oriented:
rest(nil()) = [1]
[1]
[0]
[0]
> [0]
[1]
[0]
[0]
= sent(nil())
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,y)
check(cons(x,y)) = [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 0] y + [0]
[0 0 0 0] [0 0 0 0] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,check(y))
check(cons(x,y)) = [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 0 0] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(check(x),y)
check(rest(x)) = [1 0 0 1] [0]
[0 0 1 0] x + [0]
[0 1 0 1] [0]
[0 0 0 0] [0]
>= [1 0 0 0] [0]
[0 0 1 0] x + [0]
[0 1 0 0] [0]
[0 0 0 0] [0]
= rest(check(x))
check(sent(x)) = [1 1 1 0] [0]
[0 0 0 0] x + [0]
[0 0 0 1] [0]
[0 0 0 0] [0]
>= [1 1 1 0] [0]
[0 0 0 0] x + [0]
[0 0 0 0] [0]
[0 0 0 0] [0]
= sent(check(x))
rest(cons(x,y)) = [1 0 0 1] [1 1 1 0] [1]
[0 0 0 0] x + [0 0 0 1] y + [0]
[0 0 0 0] [0 0 0 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 1 1 0] [0]
[0 0 0 1] y + [0]
[0 0 0 0] [0]
[0 0 0 0] [0]
= sent(y)
top(sent(x)) = [1 1 1 1] [0]
[0 0 0 0] x + [0]
[0 0 0 0] [0]
[1 1 1 1] [0]
>= [1 0 1 1] [0]
[0 0 0 0] x + [0]
[0 0 0 0] [0]
[1 0 1 1] [0]
= top(check(rest(x)))
*** 1.1.1.1.1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
Weak DP Rules:
Weak TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
rest(cons(x,y)) -> sent(y)
rest(nil()) -> sent(nil())
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
NaturalMI {miDimension = 4, miDegree = 4, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1 0 1 0] [0]
[0 0 1 0] x1 + [0]
[0 0 1 0] [0]
[0 0 0 0] [0]
p(cons) = [1 0 1 0] [1 0 1
1] [0]
[0 0 0 0] x1 + [0 0 1
1] x2 + [1]
[0 0 1 0] [0 0 1
1] [1]
[0 0 0 0] [0 0 0
0] [0]
p(nil) = [1]
[1]
[0]
[1]
p(rest) = [1 0 0 0] [1]
[0 1 0 1] x1 + [0]
[0 0 1 1] [0]
[0 0 0 0] [0]
p(sent) = [1 0 1 1] [0]
[0 0 1 1] x1 + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
p(top) = [1 1 0 0] [1]
[0 0 0 0] x1 + [0]
[0 0 0 0] [0]
[1 1 0 0] [1]
Following rules are strictly oriented:
check(sent(x)) = [1 0 2 1] [1]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
> [1 0 2 0] [0]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
= sent(check(x))
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1 0 2 0] [1 0 2 2] [1]
[0 0 1 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 1 0] [1 0 1 1] [0]
[0 0 0 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,y)
check(cons(x,y)) = [1 0 2 0] [1 0 2 2] [1]
[0 0 1 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 1 0] [1 0 2 0] [0]
[0 0 0 0] x + [0 0 1 0] y + [1]
[0 0 1 0] [0 0 1 0] [1]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,check(y))
check(cons(x,y)) = [1 0 2 0] [1 0 2 2] [1]
[0 0 1 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 2 0] [1 0 1 1] [0]
[0 0 0 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
= cons(check(x),y)
check(rest(x)) = [1 0 1 1] [1]
[0 0 1 1] x + [0]
[0 0 1 1] [0]
[0 0 0 0] [0]
>= [1 0 1 0] [1]
[0 0 1 0] x + [0]
[0 0 1 0] [0]
[0 0 0 0] [0]
= rest(check(x))
rest(cons(x,y)) = [1 0 1 0] [1 0 1 1] [1]
[0 0 0 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 1 1] [0]
[0 0 1 1] y + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
= sent(y)
rest(nil()) = [2]
[2]
[1]
[0]
>= [2]
[2]
[1]
[0]
= sent(nil())
top(sent(x)) = [1 0 2 2] [2]
[0 0 0 0] x + [0]
[0 0 0 0] [0]
[1 0 2 2] [2]
>= [1 0 2 2] [2]
[0 0 0 0] x + [0]
[0 0 0 0] [0]
[1 0 2 2] [2]
= top(check(rest(x)))
*** 1.1.1.1.1.1.1 Progress [(O(1),O(n^2))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
check(rest(x)) -> rest(check(x))
Weak DP Rules:
Weak TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(sent(x)) -> sent(check(x))
rest(cons(x,y)) -> sent(y)
rest(nil()) -> sent(nil())
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
NaturalMI {miDimension = 4, miDegree = 4, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
Proof:
We apply a matrix interpretation of kind constructor based matrix interpretation:
Following symbols are considered usable:
{}
TcT has computed the following interpretation:
p(check) = [1 0 1 0] [0]
[0 0 1 0] x1 + [0]
[0 0 1 0] [0]
[0 0 0 0] [0]
p(cons) = [1 0 0 0] [1 0 1
0] [1]
[0 0 0 0] x1 + [0 0 1
1] x2 + [0]
[0 0 1 0] [0 0 1
1] [0]
[0 0 0 0] [0 0 0
0] [0]
p(nil) = [0]
[0]
[0]
[1]
p(rest) = [1 0 0 1] [0]
[0 1 0 1] x1 + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
p(sent) = [1 0 1 0] [1]
[0 0 1 1] x1 + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
p(top) = [1 1 0 0] [1]
[0 0 0 0] x1 + [1]
[0 0 1 0] [0]
[0 1 1 0] [1]
Following rules are strictly oriented:
check(rest(x)) = [1 0 1 1] [1]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
> [1 0 1 0] [0]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
= rest(check(x))
Following rules are (at-least) weakly oriented:
check(cons(x,y)) = [1 0 1 0] [1 0 2 1] [1]
[0 0 1 0] x + [0 0 1 1] y + [0]
[0 0 1 0] [0 0 1 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 0 0] [1 0 1 0] [1]
[0 0 0 0] x + [0 0 1 1] y + [0]
[0 0 1 0] [0 0 1 1] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,y)
check(cons(x,y)) = [1 0 1 0] [1 0 2 1] [1]
[0 0 1 0] x + [0 0 1 1] y + [0]
[0 0 1 0] [0 0 1 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 0 0] [1 0 2 0] [1]
[0 0 0 0] x + [0 0 1 0] y + [0]
[0 0 1 0] [0 0 1 0] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(x,check(y))
check(cons(x,y)) = [1 0 1 0] [1 0 2 1] [1]
[0 0 1 0] x + [0 0 1 1] y + [0]
[0 0 1 0] [0 0 1 1] [0]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 1 0] [1 0 1 0] [1]
[0 0 0 0] x + [0 0 1 1] y + [0]
[0 0 1 0] [0 0 1 1] [0]
[0 0 0 0] [0 0 0 0] [0]
= cons(check(x),y)
check(sent(x)) = [1 0 2 0] [2]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
>= [1 0 2 0] [1]
[0 0 1 0] x + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
= sent(check(x))
rest(cons(x,y)) = [1 0 0 0] [1 0 1 0] [1]
[0 0 0 0] x + [0 0 1 1] y + [1]
[0 0 1 0] [0 0 1 1] [1]
[0 0 0 0] [0 0 0 0] [0]
>= [1 0 1 0] [1]
[0 0 1 1] y + [1]
[0 0 1 0] [1]
[0 0 0 0] [0]
= sent(y)
rest(nil()) = [1]
[2]
[1]
[0]
>= [1]
[2]
[1]
[0]
= sent(nil())
top(sent(x)) = [1 0 2 1] [3]
[0 0 0 0] x + [1]
[0 0 1 0] [1]
[0 0 2 1] [3]
>= [1 0 2 1] [3]
[0 0 0 0] x + [1]
[0 0 1 0] [1]
[0 0 2 0] [3]
= top(check(rest(x)))
*** 1.1.1.1.1.1.1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
check(cons(x,y)) -> cons(x,y)
check(cons(x,y)) -> cons(x,check(y))
check(cons(x,y)) -> cons(check(x),y)
check(rest(x)) -> rest(check(x))
check(sent(x)) -> sent(check(x))
rest(cons(x,y)) -> sent(y)
rest(nil()) -> sent(nil())
top(sent(x)) -> top(check(rest(x)))
Signature:
{check/1,rest/1,top/1} / {cons/2,nil/0,sent/1}
Obligation:
Full
basic terms: {check,rest,top}/{cons,nil,sent}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).