(0) Obligation:
The Runtime Complexity (full) of the given
CpxTRS could be proven to be
BOUNDS(1, n^1).
The TRS R consists of the following rules:
a(b(x)) → b(b(a(x)))
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, n^1).
The TRS R consists of the following rules:
a(b(x)) → b(b(a(x)))
Rewrite Strategy: INNERMOST
(3) CpxTrsMatchBoundsProof (EQUIVALENT transformation)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1.
The certificate found is represented by the following graph.
Start state: 2
Accept states: [3]
Transitions:
2→3[a_1|0]
2→4[b_1|1]
3→3[b_1|0]
4→5[b_1|1]
5→3[a_1|1]
5→4[b_1|1]
(4) BOUNDS(1, n^1)