Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z112)
The rewrite relation of the following TRS is considered.
|
a(a(x1)) |
→ |
b(c(x1)) |
(1) |
|
b(b(x1)) |
→ |
c(d(x1)) |
(2) |
|
b(x1) |
→ |
a(x1) |
(3) |
|
c(c(x1)) |
→ |
d(f(x1)) |
(4) |
|
d(d(x1)) |
→ |
f(f(f(x1))) |
(5) |
|
d(x1) |
→ |
b(x1) |
(6) |
|
f(f(x1)) |
→ |
g(a(x1)) |
(7) |
|
g(g(x1)) |
→ |
a(x1) |
(8) |
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.
|
b#(b(x1)) |
→ |
d#(x1) |
(9) |
|
d#(d(x1)) |
→ |
f#(f(f(x1))) |
(10) |
|
c#(c(x1)) |
→ |
d#(f(x1)) |
(11) |
|
b#(x1) |
→ |
a#(x1) |
(12) |
|
a#(a(x1)) |
→ |
c#(x1) |
(13) |
|
g#(g(x1)) |
→ |
a#(x1) |
(14) |
|
c#(c(x1)) |
→ |
f#(x1) |
(15) |
|
d#(d(x1)) |
→ |
f#(f(x1)) |
(16) |
|
a#(a(x1)) |
→ |
b#(c(x1)) |
(17) |
|
f#(f(x1)) |
→ |
a#(x1) |
(18) |
|
d#(x1) |
→ |
b#(x1) |
(19) |
|
b#(b(x1)) |
→ |
c#(d(x1)) |
(20) |
|
d#(d(x1)) |
→ |
f#(x1) |
(21) |
|
f#(f(x1)) |
→ |
g#(a(x1)) |
(22) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.