Certification Problem
Input (TPDB TRS_Standard/SK90/2.31)
The rewrite relation of the following TRS is considered.
|
not(true) |
→ |
false |
(1) |
|
not(false) |
→ |
true |
(2) |
|
odd(0) |
→ |
false |
(3) |
|
odd(s(x)) |
→ |
not(odd(x)) |
(4) |
|
+(x,0) |
→ |
x |
(5) |
|
+(x,s(y)) |
→ |
s(+(x,y)) |
(6) |
|
+(s(x),y) |
→ |
s(+(x,y)) |
(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.
|
+#(s(x),y) |
→ |
+#(x,y) |
(8) |
|
odd#(s(x)) |
→ |
not#(odd(x)) |
(9) |
|
+#(x,s(y)) |
→ |
+#(x,y) |
(10) |
|
odd#(s(x)) |
→ |
odd#(x) |
(11) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.