Term Rewriting System R:
[X, Y]
f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c
Innermost Termination of R to be shown.
R
↳Removing Redundant Rules for Innermost Termination
Removing the following rules from R which left hand sides contain non normal subterms
g(b) -> c
R
↳RRRI
→TRS2
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(X, g(X), Y) -> F(Y, Y, Y)
Furthermore, R contains one SCC.
R
↳RRRI
→TRS2
↳DPs
→DP Problem 1
↳Non-Overlappingness Check
Dependency Pair:
F(X, g(X), Y) -> F(Y, Y, Y)
Rules:
f(X, g(X), Y) -> f(Y, Y, Y)
b -> c
R does not overlap into P. Moreover, R is locally confluent (all critical pairs are trivially joinable).Hence we can switch to innermost.
The transformation is resulting in one subcycle:
R
↳RRRI
→TRS2
↳DPs
→DP Problem 1
↳NOC
...
→DP Problem 2
↳Dependency Graph
Dependency Pair:
F(X, g(X), Y) -> F(Y, Y, Y)
Rules:
f(X, g(X), Y) -> f(Y, Y, Y)
b -> c
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes