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:

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(b(x2), a(a(b(x1)))), p(x3, x0))

Rewrite Strategy: INNERMOST

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

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

p(p(b(a(z0)), z1), p(z2, z3)) → p(p(b(z2), a(a(b(z1)))), p(z3, z0))

Tuples:

P(p(b(a(z0)), z1), p(z2, z3)) → c(P(p(b(z2), a(a(b(z1)))), p(z3, z0)), P(b(z2), a(a(b(z1)))), P(z3, z0))

S tuples:

P(p(b(a(z0)), z1), p(z2, z3)) → c(P(p(b(z2), a(a(b(z1)))), p(z3, z0)), P(b(z2), a(a(b(z1)))), P(z3, z0))

K tuples:none
Defined Rule Symbols:

p

Defined Pair Symbols:

P

Compound Symbols:

c

(3) CdtUnreachableProof (EQUIVALENT transformation)

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

P(p(b(a(z0)), z1), p(z2, z3)) → c(P(p(b(z2), a(a(b(z1)))), p(z3, z0)), P(b(z2), a(a(b(z1)))), P(z3, z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

p(p(b(a(z0)), z1), p(z2, z3)) → p(p(b(z2), a(a(b(z1)))), p(z3, z0))

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

p

Defined Pair Symbols:none

Compound Symbols:none

(5) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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