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