The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

g(x, a, b) → g(b, b, a)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

g(z0, a, b) → g(b, b, a)

Tuples:

G(z0, a, b) → c(G(b, b, a))

S tuples:

G(z0, a, b) → c(G(b, b, a))

K tuples:none
Defined Rule Symbols:

g

Defined Pair Symbols:

G

Compound Symbols:

c

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing nodes:

G(z0, a, b) → c(G(b, b, a))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

g(z0, a, b) → g(b, b, a)

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

g

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(6) BOUNDS(O(1), O(1))