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
↳Forward Instantiation Transformation
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
one new Dependency Pair is created:
C(b(a(X))) -> C(X)
C(b(a(b(x'')))) -> C(b(x''))
R
↳DPs
→DP Problem 1
↳FwdInst
→DP Problem 2
↳FwdInst
...
→DP Problem 3
↳Remaining Obligation(s)
C(b(a(b(x'')))) -> C(b(x''))
c(b(a(X))) -> a(a(b(b(c(c(X))))))
c(X) -> e
a(X) -> e
b(X) -> e