Term Rewriting System R:
[y, x]
-(0, y) -> 0
-(x, 0) -> x
-(x, s(y)) -> if(greater(x, s(y)), s(-(x, p(s(y)))), 0)
p(0) -> 0
p(s(x)) -> x
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
-'(x, s(y)) -> -'(x, p(s(y)))
-'(x, s(y)) -> P(s(y))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
-'(x, s(y)) -> -'(x, p(s(y)))
Rules:
-(0, y) -> 0
-(x, 0) -> x
-(x, s(y)) -> if(greater(x, s(y)), s(-(x, p(s(y)))), 0)
p(0) -> 0
p(s(x)) -> x
Termination of R could not be shown.
Duration:
0:00 minutes