(0) Obligation:

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

f(0, 1, X) → h(X, X)
h(0, X) → f(0, X, X)
g(X, Y) → X
g(X, Y) → Y

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(0, 1, z0) → h(z0, z0)
h(0, z0) → f(0, z0, z0)
g(z0, z1) → z0
g(z0, z1) → z1
Tuples:

F(0, 1, z0) → c(H(z0, z0))
H(0, z0) → c1(F(0, z0, z0))
S tuples:

F(0, 1, z0) → c(H(z0, z0))
H(0, z0) → c1(F(0, z0, z0))
K tuples:none
Defined Rule Symbols:

f, h, g

Defined Pair Symbols:

F, H

Compound Symbols:

c, c1

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

Use instantiation to replace F(0, 1, z0) → c(H(z0, z0)) by

F(0, 1, 1) → c(H(1, 1))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(0, 1, z0) → h(z0, z0)
h(0, z0) → f(0, z0, z0)
g(z0, z1) → z0
g(z0, z1) → z1
Tuples:

H(0, z0) → c1(F(0, z0, z0))
F(0, 1, 1) → c(H(1, 1))
S tuples:

H(0, z0) → c1(F(0, z0, z0))
F(0, 1, 1) → c(H(1, 1))
K tuples:none
Defined Rule Symbols:

f, h, g

Defined Pair Symbols:

H, F

Compound Symbols:

c1, c

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

Removed 2 trailing nodes:

H(0, z0) → c1(F(0, z0, z0))
F(0, 1, 1) → c(H(1, 1))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(0, 1, z0) → h(z0, z0)
h(0, z0) → f(0, z0, z0)
g(z0, z1) → z0
g(z0, z1) → z1
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

f, h, g

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))