by AProVE (version ba869e7b28377cd372aedcb96abeb62c4ad6aaa5 rene 20130719 unpublished dirty )
The rewrite relation of the following TRS is considered.
| Tllet(SRlbeta(x)) | → | SRlbeta(Tllet(x)) |
| Tllet(SRlbeta(x)) | → | SRllet(SRlbeta(x)) |
| Tllet(SRcp(x)) | → | SRcp(Tllet(x)) |
| Tllet(SRcp(x)) | → | SRllet(SRcp(x)) |
| Tllet(SRllet(x)) | → | SRllet(Tllet(x)) |
| Tllet(SRllet(x)) | → | SRllet(SRllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tlapp(Tllet(x))) |
| Tllet(SRlapp(x)) | → | SRlapp(SRlapp(SRllet(x))) |
| Tllet(SRlapp(x)) | → | SRllet(SRlapp(x)) |
| Tllet(Answer) | → | Answer |
| Tllet(Answer) | → | SRllet(Answer) |
| SRlll(x) | → | SRlapp(x) |
| SRlll(x) | → | SRllet(x) |
| Tlapp(SRlbeta(x)) | → | SRlbeta(Tlapp(x)) |
| Tlapp(SRlbeta(x)) | → | SRlapp(SRlbeta(x)) |
| Tlapp(SRcp(x)) | → | SRcp(Tlapp(x)) |
| Tlapp(SRcp(x)) | → | SRlapp(SRcp(x)) |
| Tlapp(SRllet(x)) | → | SRllet(Tlapp(x)) |
| Tlapp(SRllet(x)) | → | SRlapp(SRllet(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(Tlapp(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(SRlapp(x)) |
| Tlapp(Answer) | → | Answer |
| [Tllet(x1)] | = | 1 · x1 + 1 |
| [SRlbeta(x1)] | = | 1 · x1 |
| [SRllet(x1)] | = | 1 · x1 + 1 |
| [SRcp(x1)] | = | 1 · x1 |
| [SRlapp(x1)] | = | 1 · x1 |
| [Tlapp(x1)] | = | 1 · x1 |
| [Answer] | = | 0 |
| [SRlll(x1)] | = | 1 · x1 + 2 |
| Tllet(SRlbeta(x)) | → | SRlbeta(Tllet(x)) |
| Tllet(SRlbeta(x)) | → | SRllet(SRlbeta(x)) |
| Tllet(SRcp(x)) | → | SRcp(Tllet(x)) |
| Tllet(SRcp(x)) | → | SRllet(SRcp(x)) |
| Tllet(SRllet(x)) | → | SRllet(Tllet(x)) |
| Tllet(SRllet(x)) | → | SRllet(SRllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tlapp(Tllet(x))) |
| Tllet(SRlapp(x)) | → | SRlapp(SRlapp(SRllet(x))) |
| Tllet(SRlapp(x)) | → | SRllet(SRlapp(x)) |
| Tllet(Answer) | → | SRllet(Answer) |
| Tlapp(SRlbeta(x)) | → | SRlbeta(Tlapp(x)) |
| Tlapp(SRlbeta(x)) | → | SRlapp(SRlbeta(x)) |
| Tlapp(SRcp(x)) | → | SRcp(Tlapp(x)) |
| Tlapp(SRcp(x)) | → | SRlapp(SRcp(x)) |
| Tlapp(SRllet(x)) | → | SRllet(Tlapp(x)) |
| Tlapp(SRllet(x)) | → | SRlapp(SRllet(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(Tlapp(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(SRlapp(x)) |
| Tlapp(Answer) | → | Answer |
| [Tllet(x1)] | = | 1 · x1 + 1 |
| [SRlbeta(x1)] | = | 1 · x1 |
| [SRllet(x1)] | = | 1 · x1 |
| [SRcp(x1)] | = | 1 · x1 |
| [SRlapp(x1)] | = | 1 · x1 |
| [Tlapp(x1)] | = | 1 · x1 |
| [Answer] | = | 0 |
| Tllet(SRlbeta(x)) | → | SRlbeta(Tllet(x)) |
| Tllet(SRcp(x)) | → | SRcp(Tllet(x)) |
| Tllet(SRllet(x)) | → | SRllet(Tllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tllet(x)) |
| Tllet(SRlapp(x)) | → | SRlapp(Tlapp(Tllet(x))) |
| Tlapp(SRlbeta(x)) | → | SRlbeta(Tlapp(x)) |
| Tlapp(SRlbeta(x)) | → | SRlapp(SRlbeta(x)) |
| Tlapp(SRcp(x)) | → | SRcp(Tlapp(x)) |
| Tlapp(SRcp(x)) | → | SRlapp(SRcp(x)) |
| Tlapp(SRllet(x)) | → | SRllet(Tlapp(x)) |
| Tlapp(SRllet(x)) | → | SRlapp(SRllet(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(Tlapp(x)) |
| Tlapp(SRlapp(x)) | → | SRlapp(SRlapp(x)) |
| Tlapp(Answer) | → | Answer |
| Tllet#(SRlbeta(x)) | → | Tllet#(x) |
| Tllet#(SRcp(x)) | → | Tllet#(x) |
| Tllet#(SRllet(x)) | → | Tllet#(x) |
| Tllet#(SRlapp(x)) | → | Tllet#(x) |
| Tllet#(SRlapp(x)) | → | Tlapp#(Tllet(x)) |
| Tlapp#(SRlbeta(x)) | → | Tlapp#(x) |
| Tlapp#(SRcp(x)) | → | Tlapp#(x) |
| Tlapp#(SRllet(x)) | → | Tlapp#(x) |
| Tlapp#(SRlapp(x)) | → | Tlapp#(x) |
The dependency pairs are split into 2 components.
| Tllet#(SRcp(x)) | → | Tllet#(x) |
| Tllet#(SRlbeta(x)) | → | Tllet#(x) |
| Tllet#(SRllet(x)) | → | Tllet#(x) |
| Tllet#(SRlapp(x)) | → | Tllet#(x) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
There are no lhss.
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
Tllet#(SRcp(x)) → Tllet#(x):
1>1Tllet#(SRlbeta(x)) → Tllet#(x):
1>1Tllet#(SRllet(x)) → Tllet#(x):
1>1Tllet#(SRlapp(x)) → Tllet#(x):
1>1As there is no critical graph in the transitive closure, there are no infinite chains.
| Tlapp#(SRcp(x)) | → | Tlapp#(x) |
| Tlapp#(SRlbeta(x)) | → | Tlapp#(x) |
| Tlapp#(SRllet(x)) | → | Tlapp#(x) |
| Tlapp#(SRlapp(x)) | → | Tlapp#(x) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
There are no lhss.
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
Tlapp#(SRcp(x)) → Tlapp#(x):
1>1Tlapp#(SRlbeta(x)) → Tlapp#(x):
1>1Tlapp#(SRllet(x)) → Tlapp#(x):
1>1Tlapp#(SRlapp(x)) → Tlapp#(x):
1>1As there is no critical graph in the transitive closure, there are no infinite chains.