(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
0(x1) → 1(x1)
4(5(4(5(x1)))) → 4(4(5(5(x1))))
5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) → 2(x1)
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
0(z0) → 1(z0)
4(5(4(5(z0)))) → 4(4(5(5(z0))))
5(5(5(5(5(5(4(4(4(4(4(4(z0)))))))))))) → 2(z0)
Tuples:
4'(5(4(5(z0)))) → c1(4'(4(5(5(z0)))), 4'(5(5(z0))), 5'(5(z0)), 5'(z0))
S tuples:
4'(5(4(5(z0)))) → c1(4'(4(5(5(z0)))), 4'(5(5(z0))), 5'(5(z0)), 5'(z0))
K tuples:none
Defined Rule Symbols:
0, 4, 5
Defined Pair Symbols:
4'
Compound Symbols:
c1
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
4'(5(4(5(z0)))) → c1(4'(4(5(5(z0)))), 4'(5(5(z0))), 5'(5(z0)), 5'(z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
0(z0) → 1(z0)
4(5(4(5(z0)))) → 4(4(5(5(z0))))
5(5(5(5(5(5(4(4(4(4(4(4(z0)))))))))))) → 2(z0)
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
0, 4, 5
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(6) BOUNDS(O(1), O(1))