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(s(X), Y) → h(s(f(h(Y), X)))

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(s(z0), z1) → h(s(f(h(z1), z0)))

Tuples:

F(s(z0), z1) → c(F(h(z1), z0))

S tuples:

F(s(z0), z1) → c(F(h(z1), z0))

K tuples:none
Defined Rule Symbols:

f

Defined Pair Symbols:

F

Compound Symbols:

c

(3) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 1 of 1 dangling nodes:

F(s(z0), z1) → c(F(h(z1), z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(s(z0), z1) → h(s(f(h(z1), z0)))

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

f

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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