(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
a(f, a(f, a(g, a(g, x)))) → a(g, a(g, a(g, a(f, a(f, a(f, x))))))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
a(f, a(f, a(g, a(g, z0)))) → a(g, a(g, a(g, a(f, a(f, a(f, z0))))))
Tuples:
A(f, a(f, a(g, a(g, z0)))) → c(A(g, a(g, a(g, a(f, a(f, a(f, z0)))))), A(g, a(g, a(f, a(f, a(f, z0))))), A(g, a(f, a(f, a(f, z0)))), A(f, a(f, a(f, z0))), A(f, a(f, z0)), A(f, z0))
S tuples:
A(f, a(f, a(g, a(g, z0)))) → c(A(g, a(g, a(g, a(f, a(f, a(f, z0)))))), A(g, a(g, a(f, a(f, a(f, z0))))), A(g, a(f, a(f, a(f, z0)))), A(f, a(f, a(f, z0))), A(f, a(f, z0)), A(f, z0))
K tuples:none
Defined Rule Symbols:
a
Defined Pair Symbols:
A
Compound Symbols:
c
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
A(f, a(f, a(g, a(g, z0)))) → c(A(g, a(g, a(g, a(f, a(f, a(f, z0)))))), A(g, a(g, a(f, a(f, a(f, z0))))), A(g, a(f, a(f, a(f, z0)))), A(f, a(f, a(f, z0))), A(f, a(f, z0)), A(f, z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
a(f, a(f, a(g, a(g, z0)))) → a(g, a(g, a(g, a(f, a(f, a(f, z0))))))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
a
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(6) BOUNDS(O(1), O(1))