(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(f(X)) → c
c → d
h(X) → c
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(z0)) → c
c → d
h(z0) → c
Tuples:
F(f(z0)) → c1(C)
H(z0) → c3(C)
S tuples:
F(f(z0)) → c1(C)
H(z0) → c3(C)
K tuples:none
Defined Rule Symbols:
f, c, h
Defined Pair Symbols:
F, H
Compound Symbols:
c1, c3
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
F(f(z0)) → c1(C)
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(z0)) → c
c → d
h(z0) → c
Tuples:
H(z0) → c3(C)
S tuples:
H(z0) → c3(C)
K tuples:none
Defined Rule Symbols:
f, c, h
Defined Pair Symbols:
H
Compound Symbols:
c3
(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
H(z0) → c3(C)
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(f(z0)) → c
c → d
h(z0) → c
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
f, c, h
Defined Pair Symbols:none
Compound Symbols:none
(7) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(8) BOUNDS(O(1), O(1))