(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x, f(y, a)) → f(f(f(f(a, x), y), a), h(a))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, f(z1, a)) → f(f(f(f(a, z0), z1), a), h(a))
Tuples:
F(z0, f(z1, a)) → c(F(f(f(f(a, z0), z1), a), h(a)), F(f(f(a, z0), z1), a), F(f(a, z0), z1), F(a, z0))
S tuples:
F(z0, f(z1, a)) → c(F(f(f(f(a, z0), z1), a), h(a)), F(f(f(a, z0), z1), a), F(f(a, z0), z1), F(a, 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(z0, f(z1, a)) → c(F(f(f(f(a, z0), z1), a), h(a)), F(f(f(a, z0), z1), a), F(f(a, z0), z1), F(a, z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, f(z1, a)) → f(f(f(f(a, z0), z1), a), h(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))