(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(f(a)) → f(g(n__f(a)))
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted Cpx (relative) TRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(a)) → f(g(n__f(a)))
f(z0) → n__f(z0)
activate(n__f(z0)) → f(z0)
activate(z0) → z0
Tuples:
F(f(a)) → c(F(g(n__f(a))))
F(z0) → c1
ACTIVATE(n__f(z0)) → c2(F(z0))
ACTIVATE(z0) → c3
S tuples:
F(f(a)) → c(F(g(n__f(a))))
F(z0) → c1
ACTIVATE(n__f(z0)) → c2(F(z0))
ACTIVATE(z0) → c3
K tuples:none
Defined Rule Symbols:
f, activate
Defined Pair Symbols:
F, ACTIVATE
Compound Symbols:
c, c1, c2, c3
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing nodes:
F(z0) → c1
ACTIVATE(n__f(z0)) → c2(F(z0))
F(f(a)) → c(F(g(n__f(a))))
ACTIVATE(z0) → c3
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(a)) → f(g(n__f(a)))
f(z0) → n__f(z0)
activate(n__f(z0)) → f(z0)
activate(z0) → z0
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
f, activate
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
(6) BOUNDS(1, 1)