:(:(:(:(C,

R

↳Overlay and local confluence Check

The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost.

R

↳OC

→TRS2

↳Dependency Pair Analysis

:'(:(:(:(C,x),y),z),u) -> :'(:(x,z), :(:(:(x,y),z),u))

:'(:(:(:(C,x),y),z),u) -> :'(x,z)

:'(:(:(:(C,x),y),z),u) -> :'(:(:(x,y),z),u)

:'(:(:(:(C,x),y),z),u) -> :'(:(x,y),z)

:'(:(:(:(C,x),y),z),u) -> :'(x,y)

Furthermore,

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**:'(:(:(:(C, x), y), z), u) -> :'(x, y)**

:(:(:(:(C,x),y),z),u) -> :(:(x,z), :(:(:(x,y),z),u))

innermost

The following dependency pairs can be strictly oriented:

:'(:(:(:(C,x),y),z),u) -> :'(x,y)

:'(:(:(:(C,x),y),z),u) -> :'(:(x,y),z)

:'(:(:(:(C,x),y),z),u) -> :'(:(:(x,y),z),u)

:'(:(:(:(C,x),y),z),u) -> :'(x,z)

:'(:(:(:(C,x),y),z),u) -> :'(:(x,z), :(:(:(x,y),z),u))

The following usable rule w.r.t. the AFS can be oriented:

:(:(:(:(C,x),y),z),u) -> :(:(x,z), :(:(:(x,y),z),u))

Used ordering: Lexicographic Path Order with Precedence:

:' > :

resulting in one new DP problem.

Used Argument Filtering System:

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

:(x,_{1}x) -> :(_{2}x,_{1}x)_{2}

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳AFS

...

→DP Problem 2

↳Dependency Graph

:(:(:(:(C,x),y),z),u) -> :(:(x,z), :(:(:(x,y),z),u))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes