### (0) Obligation:

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

The TRS R consists of the following rules:

app(nil, YS) → YS
app(cons(X), YS) → cons(X)
from(X) → cons(X)
prefix(L) → cons(nil)

Rewrite Strategy: FULL

### (1) RcToIrcProof (BOTH BOUNDS(ID, ID) transformation)

Converted rc-obligation to irc-obligation.

As the TRS does not nest defined symbols, we have rc = irc.

### (2) Obligation:

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

The TRS R consists of the following rules:

app(nil, YS) → YS
app(cons(X), YS) → cons(X)
from(X) → cons(X)
prefix(L) → cons(nil)

Rewrite Strategy: INNERMOST

### (3) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted Cpx (relative) TRS to CDT

### (4) Obligation:

Complexity Dependency Tuples Problem
Rules:

app(nil, z0) → z0
app(cons(z0), z1) → cons(z0)
from(z0) → cons(z0)
prefix(z0) → cons(nil)
Tuples:

APP(nil, z0) → c
APP(cons(z0), z1) → c1
FROM(z0) → c2
PREFIX(z0) → c6
S tuples:

APP(nil, z0) → c
APP(cons(z0), z1) → c1
FROM(z0) → c2
PREFIX(z0) → c6
K tuples:none
Defined Rule Symbols:

Defined Pair Symbols:

Compound Symbols:

c, c1, c2, c3, c4, c5, c6

### (5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 7 trailing nodes:

FROM(z0) → c2
PREFIX(z0) → c6
APP(nil, z0) → c
APP(cons(z0), z1) → c1

### (6) Obligation:

Complexity Dependency Tuples Problem
Rules:

app(nil, z0) → z0
app(cons(z0), z1) → cons(z0)
from(z0) → cons(z0)
prefix(z0) → cons(nil)
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols: