by AProVE (version ba869e7b28377cd372aedcb96abeb62c4ad6aaa5 rene 20130719 unpublished dirty )
The rewrite relation of the following TRS is considered.
| Tgc(SRlbeta(x)) | → | SRlapp(W46(k,x)) |
| Tgc(SRlbeta(x)) | → | W52(k,x) |
| Tgc(SRcp(x)) | → | W74(k,x) |
| Tgc(SRllet(x)) | → | W89(k,x) |
| Tgc(SRlapp(x)) | → | SRlapp(W94(k,x)) |
| Tgc(SRlapp(x)) | → | W100(k,x) |
| Tgc(SRlcase(x)) | → | SRlcase(W122(k,x)) |
| Tgc(SRlcase(x)) | → | W128(k,x) |
| Tgc(SRlseq(x)) | → | SRlseq(W150(k,x)) |
| Tgc(SRlseq(x)) | → | W156(k,x) |
| Tgc(SRcase(x)) | → | SRlcase(W178(k,x)) |
| Tgc(SRcase(x)) | → | W184(k,x) |
| Tgc(SRseq(x)) | → | SRlseq(W211(k,x)) |
| Tgc(SRseq(x)) | → | W217(k,x) |
| Tgc(SRlbeta(x)) | → | SRlbeta(Tgc(x)) |
| Tgc(SRcp(x)) | → | SRcp(Tgc(x)) |
| Tgc(SRllet(x)) | → | SRllet(Tgc(x)) |
| Tgc(SRlapp(x)) | → | SRlapp(Tgc(x)) |
| Tgc(SRlcase(x)) | → | SRlcase(Tgc(x)) |
| Tgc(SRlseq(x)) | → | SRlseq(Tgc(x)) |
| Tgc(SRcase(x)) | → | SRcase(Tgc(x)) |
| Tgc(SRcase(x)) | → | SRcase(x) |
| Tgc(SRseq(x)) | → | SRseq(Tgc(x)) |
| Tgc(SRseq(x)) | → | SRseq(x) |
| Tgc(Answer) | → | Answer |
| W46(s(k),x) | → | SRlll(W46(k,x)) |
| W46(s(k),x) | → | SRlll(SRlbeta(Tgc(x))) |
| W52(s(k),x) | → | SRlll(W52(k,x)) |
| W52(s(k),x) | → | SRlll(SRlbeta(Tgc(x))) |
| Tgc(SRlbeta(x)) | → | SRlapp(SRlbeta(SRllet(Tgc(x)))) |
| Tgc(SRlbeta(x)) | → | SRlapp(SRllet(SRlbeta(Tgc(x)))) |
| Tgc(SRlbeta(x)) | → | SRllet(SRlbeta(Tgc(x))) |
| W74(s(k),x) | → | SRlll(W74(k,x)) |
| W74(s(k),x) | → | SRlll(SRcp(Tgc(x))) |
| Tgc(SRcp(x)) | → | SRllet(SRcp(Tgc(x))) |
| Tgc(SRllet(x)) | → | SRllet(SRllet(Tgc(x))) |
| W89(s(k),x) | → | SRlll(W89(k,x)) |
| W89(s(k),x) | → | SRlll(SRllet(Tgc(x))) |
| W94(s(k),x) | → | SRlll(W94(k,x)) |
| W94(s(k),x) | → | SRlll(SRlapp(Tgc(x))) |
| W100(s(k),x) | → | SRlll(W100(k,x)) |
| W100(s(k),x) | → | SRlll(SRlapp(Tgc(x))) |
| Tgc(SRlapp(x)) | → | SRlapp(SRlapp(SRllet(Tgc(x)))) |
| Tgc(SRlapp(x)) | → | SRlapp(SRllet(SRlapp(Tgc(x)))) |
| Tgc(SRlapp(x)) | → | SRllet(SRlapp(Tgc(x))) |
| W122(s(k),x) | → | SRlll(W122(k,x)) |
| W122(s(k),x) | → | SRlll(SRlcase(Tgc(x))) |
| W128(s(k),x) | → | SRlll(W128(k,x)) |
| W128(s(k),x) | → | SRlll(SRlcase(Tgc(x))) |
| Tgc(SRlcase(x)) | → | SRlcase(SRlcase(SRllet(Tgc(x)))) |
| Tgc(SRlcase(x)) | → | SRlcase(SRllet(SRlcase(Tgc(x)))) |
| Tgc(SRlcase(x)) | → | SRllet(SRlcase(Tgc(x))) |
| W150(s(k),x) | → | SRlll(W150(k,x)) |
| W150(s(k),x) | → | SRlll(SRlseq(Tgc(x))) |
| W156(s(k),x) | → | SRlll(W156(k,x)) |
| W156(s(k),x) | → | SRlll(SRlseq(Tgc(x))) |
| Tgc(SRlseq(x)) | → | SRlseq(SRlseq(SRllet(Tgc(x)))) |
| Tgc(SRlseq(x)) | → | SRlseq(SRllet(SRlseq(Tgc(x)))) |
| Tgc(SRlseq(x)) | → | SRllet(SRlseq(Tgc(x))) |
| W178(s(k),x) | → | SRlll(W178(k,x)) |
| W178(s(k),x) | → | SRlll(SRcase(Tgc(x))) |
| W184(s(k),x) | → | SRlll(W184(k,x)) |
| W184(s(k),x) | → | SRlll(SRcase(Tgc(x))) |
| Tgc(SRcase(x)) | → | SRlcase(SRcase(Tgc(x))) |
| Tgc(SRcase(x)) | → | SRlcase(SRcase(SRllet(Tgc(x)))) |
| Tgc(SRcase(x)) | → | SRlcase(SRllet(SRcase(Tgc(x)))) |
| Tgc(SRcase(x)) | → | SRllet(SRcase(Tgc(x))) |
| W211(s(k),x) | → | SRlll(W211(k,x)) |
| W211(s(k),x) | → | SRlll(SRseq(Tgc(x))) |
| W217(s(k),x) | → | SRlll(W217(k,x)) |
| W217(s(k),x) | → | SRlll(SRseq(Tgc(x))) |
| Tgc(SRseq(x)) | → | SRlseq(SRseq(Tgc(x))) |
| Tgc(SRseq(x)) | → | SRlseq(SRllet(SRseq(Tgc(x)))) |
| Tgc(SRseq(x)) | → | SRllet(SRseq(Tgc(x))) |
| Tgc(Answer) | → | SRllet(Answer) |
| SRlll(x) | → | SRlseq(x) |
| SRlll(x) | → | SRlapp(x) |
| SRlll(x) | → | SRllet(x) |
| SRlll(x) | → | SRlcase(x) |
There are no rules.
| Tgc#(SRlbeta(x)) | → | W46#(k,x) |
| Tgc#(SRlbeta(x)) | → | W52#(k,x) |
| Tgc#(SRcp(x)) | → | W74#(k,x) |
| Tgc#(SRllet(x)) | → | W89#(k,x) |
| Tgc#(SRlapp(x)) | → | W94#(k,x) |
| Tgc#(SRlapp(x)) | → | W100#(k,x) |
| Tgc#(SRlcase(x)) | → | W122#(k,x) |
| Tgc#(SRlcase(x)) | → | W128#(k,x) |
| Tgc#(SRlseq(x)) | → | W150#(k,x) |
| Tgc#(SRlseq(x)) | → | W156#(k,x) |
| Tgc#(SRcase(x)) | → | W178#(k,x) |
| Tgc#(SRcase(x)) | → | W184#(k,x) |
| Tgc#(SRseq(x)) | → | W211#(k,x) |
| Tgc#(SRseq(x)) | → | W217#(k,x) |
| Tgc#(SRlbeta(x)) | → | Tgc#(x) |
| Tgc#(SRcp(x)) | → | Tgc#(x) |
| Tgc#(SRllet(x)) | → | Tgc#(x) |
| Tgc#(SRlapp(x)) | → | Tgc#(x) |
| Tgc#(SRlcase(x)) | → | Tgc#(x) |
| Tgc#(SRlseq(x)) | → | Tgc#(x) |
| Tgc#(SRcase(x)) | → | Tgc#(x) |
| Tgc#(SRseq(x)) | → | Tgc#(x) |
| W46#(s(k),x) | → | SRlll#(W46(k,x)) |
| W46#(s(k),x) | → | W46#(k,x) |
| W46#(s(k),x) | → | SRlll#(SRlbeta(Tgc(x))) |
| W46#(s(k),x) | → | Tgc#(x) |
| W52#(s(k),x) | → | SRlll#(W52(k,x)) |
| W52#(s(k),x) | → | W52#(k,x) |
| W52#(s(k),x) | → | SRlll#(SRlbeta(Tgc(x))) |
| W52#(s(k),x) | → | Tgc#(x) |
| W74#(s(k),x) | → | SRlll#(W74(k,x)) |
| W74#(s(k),x) | → | W74#(k,x) |
| W74#(s(k),x) | → | SRlll#(SRcp(Tgc(x))) |
| W74#(s(k),x) | → | Tgc#(x) |
| W89#(s(k),x) | → | SRlll#(W89(k,x)) |
| W89#(s(k),x) | → | W89#(k,x) |
| W89#(s(k),x) | → | SRlll#(SRllet(Tgc(x))) |
| W89#(s(k),x) | → | Tgc#(x) |
| W94#(s(k),x) | → | SRlll#(W94(k,x)) |
| W94#(s(k),x) | → | W94#(k,x) |
| W94#(s(k),x) | → | SRlll#(SRlapp(Tgc(x))) |
| W94#(s(k),x) | → | Tgc#(x) |
| W100#(s(k),x) | → | SRlll#(W100(k,x)) |
| W100#(s(k),x) | → | W100#(k,x) |
| W100#(s(k),x) | → | SRlll#(SRlapp(Tgc(x))) |
| W100#(s(k),x) | → | Tgc#(x) |
| W122#(s(k),x) | → | SRlll#(W122(k,x)) |
| W122#(s(k),x) | → | W122#(k,x) |
| W122#(s(k),x) | → | SRlll#(SRlcase(Tgc(x))) |
| W122#(s(k),x) | → | Tgc#(x) |
| W128#(s(k),x) | → | SRlll#(W128(k,x)) |
| W128#(s(k),x) | → | W128#(k,x) |
| W128#(s(k),x) | → | SRlll#(SRlcase(Tgc(x))) |
| W128#(s(k),x) | → | Tgc#(x) |
| W150#(s(k),x) | → | SRlll#(W150(k,x)) |
| W150#(s(k),x) | → | W150#(k,x) |
| W150#(s(k),x) | → | SRlll#(SRlseq(Tgc(x))) |
| W150#(s(k),x) | → | Tgc#(x) |
| W156#(s(k),x) | → | SRlll#(W156(k,x)) |
| W156#(s(k),x) | → | W156#(k,x) |
| W156#(s(k),x) | → | SRlll#(SRlseq(Tgc(x))) |
| W156#(s(k),x) | → | Tgc#(x) |
| W178#(s(k),x) | → | SRlll#(W178(k,x)) |
| W178#(s(k),x) | → | W178#(k,x) |
| W178#(s(k),x) | → | SRlll#(SRcase(Tgc(x))) |
| W178#(s(k),x) | → | Tgc#(x) |
| W184#(s(k),x) | → | SRlll#(W184(k,x)) |
| W184#(s(k),x) | → | W184#(k,x) |
| W184#(s(k),x) | → | SRlll#(SRcase(Tgc(x))) |
| W184#(s(k),x) | → | Tgc#(x) |
| W211#(s(k),x) | → | SRlll#(W211(k,x)) |
| W211#(s(k),x) | → | W211#(k,x) |
| W211#(s(k),x) | → | SRlll#(SRseq(Tgc(x))) |
| W211#(s(k),x) | → | Tgc#(x) |
| W217#(s(k),x) | → | SRlll#(W217(k,x)) |
| W217#(s(k),x) | → | W217#(k,x) |
| W217#(s(k),x) | → | SRlll#(SRseq(Tgc(x))) |
| W217#(s(k),x) | → | Tgc#(x) |
The dependency pairs are split into 1 component.
| W46#(s(k),x) | → | W46#(k,x) |
| W46#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlbeta(x)) | → | W46#(k,x) |
| Tgc#(SRlbeta(x)) | → | W52#(k,x) |
| W52#(s(k),x) | → | W52#(k,x) |
| W52#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRcp(x)) | → | W74#(k,x) |
| W74#(s(k),x) | → | W74#(k,x) |
| W74#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRllet(x)) | → | W89#(k,x) |
| W89#(s(k),x) | → | W89#(k,x) |
| W89#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlapp(x)) | → | W94#(k,x) |
| W94#(s(k),x) | → | W94#(k,x) |
| W94#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlapp(x)) | → | W100#(k,x) |
| W100#(s(k),x) | → | W100#(k,x) |
| W100#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlcase(x)) | → | W122#(k,x) |
| W122#(s(k),x) | → | W122#(k,x) |
| W122#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlcase(x)) | → | W128#(k,x) |
| W128#(s(k),x) | → | W128#(k,x) |
| W128#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlseq(x)) | → | W150#(k,x) |
| W150#(s(k),x) | → | W150#(k,x) |
| W150#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlseq(x)) | → | W156#(k,x) |
| W156#(s(k),x) | → | W156#(k,x) |
| W156#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRcase(x)) | → | W178#(k,x) |
| W178#(s(k),x) | → | W178#(k,x) |
| W178#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRcase(x)) | → | W184#(k,x) |
| W184#(s(k),x) | → | W184#(k,x) |
| W184#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRseq(x)) | → | W211#(k,x) |
| W211#(s(k),x) | → | W211#(k,x) |
| W211#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRseq(x)) | → | W217#(k,x) |
| W217#(s(k),x) | → | W217#(k,x) |
| W217#(s(k),x) | → | Tgc#(x) |
| Tgc#(SRlbeta(x)) | → | Tgc#(x) |
| Tgc#(SRcp(x)) | → | Tgc#(x) |
| Tgc#(SRllet(x)) | → | Tgc#(x) |
| Tgc#(SRlapp(x)) | → | Tgc#(x) |
| Tgc#(SRlcase(x)) | → | Tgc#(x) |
| Tgc#(SRlseq(x)) | → | Tgc#(x) |
| Tgc#(SRcase(x)) | → | Tgc#(x) |
| Tgc#(SRseq(x)) | → | Tgc#(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.
| [W46#(x1, x2)] | = | 1 + 1 · x2 |
| [s(x1)] | = | 0 |
| [Tgc#(x1)] | = | 1 · x1 |
| [SRlbeta(x1)] | = | 1 + 1 · x1 |
| [W52#(x1, x2)] | = | 1 + 1 · x2 |
| [SRcp(x1)] | = | 1 + 1 · x1 |
| [W74#(x1, x2)] | = | 1 + 1 · x2 |
| [SRllet(x1)] | = | 1 + 1 · x1 |
| [W89#(x1, x2)] | = | 1 + 1 · x2 |
| [SRlapp(x1)] | = | 1 + 1 · x1 |
| [W94#(x1, x2)] | = | 1 + 1 · x2 |
| [W100#(x1, x2)] | = | 1 + 1 · x2 |
| [SRlcase(x1)] | = | 1 + 1 · x1 |
| [W122#(x1, x2)] | = | 1 + 1 · x2 |
| [W128#(x1, x2)] | = | 1 + 1 · x2 |
| [SRlseq(x1)] | = | 1 + 1 · x1 |
| [W150#(x1, x2)] | = | 1 + 1 · x2 |
| [W156#(x1, x2)] | = | 1 + 1 · x2 |
| [SRcase(x1)] | = | 1 + 1 · x1 |
| [W178#(x1, x2)] | = | 1 + 1 · x2 |
| [W184#(x1, x2)] | = | 1 + 1 · x2 |
| [SRseq(x1)] | = | 1 + 1 · x1 |
| [W211#(x1, x2)] | = | 1 + 1 · x2 |
| [W217#(x1, x2)] | = | 1 + 1 · x2 |
| W46#(s(k),x) | → | W46#(k,x) |
| Tgc#(SRlbeta(x)) | → | W46#(k,x) |
| Tgc#(SRlbeta(x)) | → | W52#(k,x) |
| W52#(s(k),x) | → | W52#(k,x) |
| Tgc#(SRcp(x)) | → | W74#(k,x) |
| W74#(s(k),x) | → | W74#(k,x) |
| Tgc#(SRllet(x)) | → | W89#(k,x) |
| W89#(s(k),x) | → | W89#(k,x) |
| Tgc#(SRlapp(x)) | → | W94#(k,x) |
| W94#(s(k),x) | → | W94#(k,x) |
| Tgc#(SRlapp(x)) | → | W100#(k,x) |
| W100#(s(k),x) | → | W100#(k,x) |
| Tgc#(SRlcase(x)) | → | W122#(k,x) |
| W122#(s(k),x) | → | W122#(k,x) |
| Tgc#(SRlcase(x)) | → | W128#(k,x) |
| W128#(s(k),x) | → | W128#(k,x) |
| Tgc#(SRlseq(x)) | → | W150#(k,x) |
| W150#(s(k),x) | → | W150#(k,x) |
| Tgc#(SRlseq(x)) | → | W156#(k,x) |
| W156#(s(k),x) | → | W156#(k,x) |
| Tgc#(SRcase(x)) | → | W178#(k,x) |
| W178#(s(k),x) | → | W178#(k,x) |
| Tgc#(SRcase(x)) | → | W184#(k,x) |
| W184#(s(k),x) | → | W184#(k,x) |
| Tgc#(SRseq(x)) | → | W211#(k,x) |
| W211#(s(k),x) | → | W211#(k,x) |
| Tgc#(SRseq(x)) | → | W217#(k,x) |
| W217#(s(k),x) | → | W217#(k,x) |
The dependency pairs are split into 14 components.
| W46#(s(k),x) | → | W46#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W46#(s(k),x) → W46#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W52#(s(k),x) | → | W52#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W52#(s(k),x) → W52#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W74#(s(k),x) | → | W74#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W74#(s(k),x) → W74#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W89#(s(k),x) | → | W89#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W89#(s(k),x) → W89#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W94#(s(k),x) | → | W94#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W94#(s(k),x) → W94#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W100#(s(k),x) | → | W100#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W100#(s(k),x) → W100#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W122#(s(k),x) | → | W122#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W122#(s(k),x) → W122#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W128#(s(k),x) | → | W128#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W128#(s(k),x) → W128#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W150#(s(k),x) | → | W150#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W150#(s(k),x) → W150#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W156#(s(k),x) | → | W156#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W156#(s(k),x) → W156#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W178#(s(k),x) | → | W178#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W178#(s(k),x) → W178#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W184#(s(k),x) | → | W184#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W184#(s(k),x) → W184#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W211#(s(k),x) | → | W211#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W211#(s(k),x) → W211#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.
| W217#(s(k),x) | → | W217#(k,x) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
W217#(s(k),x) → W217#(k,x):
1>1, 2>=2As there is no critical graph in the transitive closure, there are no infinite chains.