(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
a(x1) → b(x1)
a(a(b(x1))) → a(b(a(a(c(x1)))))
c(b(x1)) → x1
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
a(z0) → b(z0)
a(a(b(z0))) → a(b(a(a(c(z0)))))
c(b(z0)) → z0
Tuples:
A(a(b(z0))) → c2(A(b(a(a(c(z0))))), A(a(c(z0))), A(c(z0)), C(z0))
S tuples:
A(a(b(z0))) → c2(A(b(a(a(c(z0))))), A(a(c(z0))), A(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:
a, c
Defined Pair Symbols:
A
Compound Symbols:
c2
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
A(a(b(z0))) → c2(A(b(a(a(c(z0))))), A(a(c(z0))), A(c(z0)), C(z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
a(z0) → b(z0)
a(a(b(z0))) → a(b(a(a(c(z0)))))
c(b(z0)) → z0
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
a, c
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(6) BOUNDS(O(1), O(1))