The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

-(-(neg(x), neg(x)), -(neg(y), neg(y))) → -(-(x, y), -(x, y))

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

-(-(neg(z0), neg(z0)), -(neg(z1), neg(z1))) → -(-(z0, z1), -(z0, z1))

Tuples:

-'(-(neg(z0), neg(z0)), -(neg(z1), neg(z1))) → c(-'(-(z0, z1), -(z0, z1)), -'(z0, z1), -'(z0, z1))

S tuples:

-'(-(neg(z0), neg(z0)), -(neg(z1), neg(z1))) → c(-'(-(z0, z1), -(z0, z1)), -'(z0, z1), -'(z0, z1))

K tuples:none
Defined Rule Symbols:

-

Defined Pair Symbols:

-'

Compound Symbols:

c

(3) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

-'(-(neg(z0), neg(z0)), -(neg(z1), neg(z1))) → c(-'(-(z0, z1), -(z0, z1)), -'(z0, z1), -'(z0, z1))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

-(-(neg(z0), neg(z0)), -(neg(z1), neg(z1))) → -(-(z0, z1), -(z0, z1))

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

-

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(6) BOUNDS(O(1), O(1))