Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex9_Luc06_GM)
The rewrite relation of the following TRS is considered.
a__f(a,X,X) |
→ |
a__f(X,a__b,b) |
(1) |
a__b |
→ |
a |
(2) |
mark(f(X1,X2,X3)) |
→ |
a__f(X1,mark(X2),X3) |
(3) |
mark(b) |
→ |
a__b |
(4) |
mark(a) |
→ |
a |
(5) |
a__f(X1,X2,X3) |
→ |
f(X1,X2,X3) |
(6) |
a__b |
→ |
b |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by NaTT @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
mark#(f(X1,X2,X3)) |
→ |
mark#(X2) |
(8) |
mark#(b) |
→ |
a__b# |
(9) |
a__f#(a,X,X) |
→ |
a__f#(X,a__b,b) |
(10) |
mark#(f(X1,X2,X3)) |
→ |
a__f#(X1,mark(X2),X3) |
(11) |
a__f#(a,X,X) |
→ |
a__b# |
(12) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.