(0) Obligation:

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

a(c(d(x))) → c(x)
u(b(d(d(x)))) → b(x)
v(a(a(x))) → u(v(x))
v(a(c(x))) → u(b(d(x)))
v(c(x)) → b(x)
w(a(a(x))) → u(w(x))
w(a(c(x))) → u(b(d(x)))
w(c(x)) → b(x)

Rewrite Strategy: INNERMOST

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

Converted Cpx (relative) TRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

a(c(d(z0))) → c(z0)
u(b(d(d(z0)))) → b(z0)
v(a(a(z0))) → u(v(z0))
v(a(c(z0))) → u(b(d(z0)))
v(c(z0)) → b(z0)
w(a(a(z0))) → u(w(z0))
w(a(c(z0))) → u(b(d(z0)))
w(c(z0)) → b(z0)
Tuples:

A(c(d(z0))) → c1
U(b(d(d(z0)))) → c2
V(a(a(z0))) → c3(U(v(z0)), V(z0))
V(a(c(z0))) → c4(U(b(d(z0))))
V(c(z0)) → c5
W(a(a(z0))) → c6(U(w(z0)), W(z0))
W(a(c(z0))) → c7(U(b(d(z0))))
W(c(z0)) → c8
S tuples:

A(c(d(z0))) → c1
U(b(d(d(z0)))) → c2
V(a(a(z0))) → c3(U(v(z0)), V(z0))
V(a(c(z0))) → c4(U(b(d(z0))))
V(c(z0)) → c5
W(a(a(z0))) → c6(U(w(z0)), W(z0))
W(a(c(z0))) → c7(U(b(d(z0))))
W(c(z0)) → c8
K tuples:none
Defined Rule Symbols:

a, u, v, w

Defined Pair Symbols:

A, U, V, W

Compound Symbols:

c1, c2, c3, c4, c5, c6, c7, c8

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing nodes:

U(b(d(d(z0)))) → c2
W(a(c(z0))) → c7(U(b(d(z0))))
W(c(z0)) → c8
V(a(c(z0))) → c4(U(b(d(z0))))
A(c(d(z0))) → c1
V(c(z0)) → c5

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

a(c(d(z0))) → c(z0)
u(b(d(d(z0)))) → b(z0)
v(a(a(z0))) → u(v(z0))
v(a(c(z0))) → u(b(d(z0)))
v(c(z0)) → b(z0)
w(a(a(z0))) → u(w(z0))
w(a(c(z0))) → u(b(d(z0)))
w(c(z0)) → b(z0)
Tuples:

V(a(a(z0))) → c3(U(v(z0)), V(z0))
W(a(a(z0))) → c6(U(w(z0)), W(z0))
S tuples:

V(a(a(z0))) → c3(U(v(z0)), V(z0))
W(a(a(z0))) → c6(U(w(z0)), W(z0))
K tuples:none
Defined Rule Symbols:

a, u, v, w

Defined Pair Symbols:

V, W

Compound Symbols:

c3, c6

(5) CdtUnreachableProof (EQUIVALENT transformation)

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

V(a(a(z0))) → c3(U(v(z0)), V(z0))
W(a(a(z0))) → c6(U(w(z0)), W(z0))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

a(c(d(z0))) → c(z0)
u(b(d(d(z0)))) → b(z0)
v(a(a(z0))) → u(v(z0))
v(a(c(z0))) → u(b(d(z0)))
v(c(z0)) → b(z0)
w(a(a(z0))) → u(w(z0))
w(a(c(z0))) → u(b(d(z0)))
w(c(z0)) → b(z0)
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

a, u, v, w

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)

The set S is empty

(8) BOUNDS(1, 1)