(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Tuples:
F(g(f(a), h(a, f(a)))) → c(F(h(g(f(a), a), g(f(a), f(a)))), F(a), F(a), F(a))
S tuples:
F(g(f(a), h(a, f(a)))) → c(F(h(g(f(a), a), g(f(a), f(a)))), F(a), F(a), F(a))
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(g(f(a), h(a, f(a)))) → c(F(h(g(f(a), a), g(f(a), f(a)))), F(a), F(a), F(a))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
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))