R
↳Dependency Pair Analysis
C(b(a(X))) -> A(a(b(b(c(c(X))))))
C(b(a(X))) -> A(b(b(c(c(X)))))
C(b(a(X))) -> B(b(c(c(X))))
C(b(a(X))) -> B(c(c(X)))
C(b(a(X))) -> C(c(X))
C(b(a(X))) -> C(X)
R
↳DPs
→DP Problem 1
↳Forward Instantiation Transformation
C(b(a(X))) -> C(X)
C(b(a(X))) -> C(c(X))
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e
no new Dependency Pairs are created.
C(b(a(X))) -> C(c(X))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳Argument Filtering and Ordering
C(b(a(X))) -> C(X)
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e
C(b(a(X))) -> C(X)
POL(C(x1)) = 1 + x1 POL(b(x1)) = 1 + x1 POL(a(x1)) = x1
C(x1) -> C(x1)
b(x1) -> b(x1)
a(x1) -> a(x1)
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳AFS
...
→DP Problem 3
↳Dependency Graph
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e