fib(0) -> 0

fib(s(0)) -> s(0)

fib(s(s(

+(

+(

R

↳Dependency Pair Analysis

FIB(s(s(x))) -> +'(fib(s(x)), fib(x))

FIB(s(s(x))) -> FIB(s(x))

FIB(s(s(x))) -> FIB(x)

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

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

fib(0) -> 0

fib(s(0)) -> s(0)

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

+(x, 0) ->x

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

innermost

The following dependency pair can be strictly oriented:

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+'(x)_{1}, x_{2})= x _{2}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Polo

fib(0) -> 0

fib(s(0)) -> s(0)

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

+(x, 0) ->x

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

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**FIB(s(s( x))) -> FIB(x)**

fib(0) -> 0

fib(s(0)) -> s(0)

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

+(x, 0) ->x

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

innermost

The following dependency pairs can be strictly oriented:

FIB(s(s(x))) -> FIB(x)

FIB(s(s(x))) -> FIB(s(x))

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(FIB(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Dependency Graph

fib(0) -> 0

fib(s(0)) -> s(0)

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

+(x, 0) ->x

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes