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:

f(f(X)) → c
c → d
h(X) → c

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(f(z0)) → c
c → d
h(z0) → c

Tuples:

F(f(z0)) → c1(C)
H(z0) → c3(C)

S tuples:

F(f(z0)) → c1(C)
H(z0) → c3(C)

K tuples:none
Defined Rule Symbols:

f, c, h

Defined Pair Symbols:

F, H

Compound Symbols:

c1, c3

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

Removed 2 trailing nodes:

F(f(z0)) → c1(C)
H(z0) → c3(C)

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(f(z0)) → c
c → d
h(z0) → c

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

f, c, h

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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