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