(0) Obligation:

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

f(n__b, X, n__c) → f(X, c, X)
cb
bn__b
cn__c
activate(n__b) → b
activate(n__c) → c
activate(X) → X

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(n__b, z0, n__c) → f(z0, c, z0)
cb
cn__c
bn__b
activate(n__b) → b
activate(n__c) → c
activate(z0) → z0
Tuples:

F(n__b, z0, n__c) → c1(F(z0, c, z0), C)
Cc2(B)
ACTIVATE(n__b) → c5(B)
ACTIVATE(n__c) → c6(C)
S tuples:

F(n__b, z0, n__c) → c1(F(z0, c, z0), C)
Cc2(B)
ACTIVATE(n__b) → c5(B)
ACTIVATE(n__c) → c6(C)
K tuples:none
Defined Rule Symbols:

f, c, b, activate

Defined Pair Symbols:

F, C, ACTIVATE

Compound Symbols:

c1, c2, c5, c6

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

Removed 4 trailing nodes:

F(n__b, z0, n__c) → c1(F(z0, c, z0), C)
ACTIVATE(n__c) → c6(C)
ACTIVATE(n__b) → c5(B)
Cc2(B)

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f(n__b, z0, n__c) → f(z0, c, z0)
cb
cn__c
bn__b
activate(n__b) → b
activate(n__c) → c
activate(z0) → z0
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

f, c, b, activate

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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