not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(

+(

+(

+(s(

R

↳Dependency Pair Analysis

ODD(s(x)) -> NOT(odd(x))

ODD(s(x)) -> ODD(x)

+'(x, s(y)) -> +'(x,y)

+'(s(x),y) -> +'(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

**ODD(s( x)) -> ODD(x)**

not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(x)) -> not(odd(x))

+(x, 0) ->x

+(x, s(y)) -> s(+(x,y))

+(s(x),y) -> s(+(x,y))

The following dependency pair can be strictly oriented:

ODD(s(x)) -> ODD(x)

There are no usable rules w.r.t. to the AFS that need to be oriented.

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

ODD(x) -> ODD(_{1}x)_{1}

s(x) -> s(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(x)) -> not(odd(x))

+(x, 0) ->x

+(x, s(y)) -> s(+(x,y))

+(s(x),y) -> s(+(x,y))

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

**+'(s( x), y) -> +'(x, y)**

not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(x)) -> not(odd(x))

+(x, 0) ->x

+(x, s(y)) -> s(+(x,y))

+(s(x),y) -> s(+(x,y))

The following dependency pairs can be strictly oriented:

+'(s(x),y) -> +'(x,y)

+'(x, s(y)) -> +'(x,y)

There are no usable rules w.r.t. to the AFS that need to be oriented.

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

+'(x,_{1}x) -> +'(_{2}x,_{1}x)_{2}

s(x) -> s(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

not(true) -> false

not(false) -> true

odd(0) -> false

odd(s(x)) -> not(odd(x))

+(x, 0) ->x

+(x, s(y)) -> s(+(x,y))

+(s(x),y) -> s(+(x,y))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes