(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(f(a)) → c(n__f(g(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 CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(a)) → c(n__f(g(f(a))))
f(z0) → n__f(z0)
activate(n__f(z0)) → f(z0)
activate(z0) → z0
Tuples:
F(f(a)) → c1(F(a))
ACTIVATE(n__f(z0)) → c3(F(z0))
S tuples:
F(f(a)) → c1(F(a))
ACTIVATE(n__f(z0)) → c3(F(z0))
K tuples:none
Defined Rule Symbols:
f, activate
Defined Pair Symbols:
F, ACTIVATE
Compound Symbols:
c1, c3
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
F(f(a)) → c1(F(a))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(a)) → c(n__f(g(f(a))))
f(z0) → n__f(z0)
activate(n__f(z0)) → f(z0)
activate(z0) → z0
Tuples:
ACTIVATE(n__f(z0)) → c3(F(z0))
S tuples:
ACTIVATE(n__f(z0)) → c3(F(z0))
K tuples:none
Defined Rule Symbols:
f, activate
Defined Pair Symbols:
ACTIVATE
Compound Symbols:
c3
(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
ACTIVATE(n__f(z0)) → c3(F(z0))
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(a)) → c(n__f(g(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
(7) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(8) BOUNDS(O(1), O(1))