YES
Confluence Proof
Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
0(1(2(3(4(x))))) |
→ |
0(2(1(3(4(x))))) |
|
0(5(1(2(4(3(x)))))) |
→ |
0(5(2(1(4(3(x)))))) |
|
0(5(2(4(1(3(x)))))) |
→ |
0(1(5(2(4(3(x)))))) |
|
0(5(3(1(2(4(x)))))) |
→ |
0(1(5(3(2(4(x)))))) |
|
0(5(4(1(3(2(x)))))) |
→ |
0(5(4(3(1(2(x)))))) |
Proof
1 Compositional Parallel Critical Pair Systems
All parallel critical pairs of the TRS R are joinable by R.
This can be seen as follows:
The parallel critical pairs can be joined as follows. Here,
↔ is always chosen as an appropriate rewrite relation which
is automatically inferred by the certifier.
The TRS C is chosen as:
There are no rules.
Consequently, PCPS(R,C) is included in the following TRS P where
steps are used to show that certain pairs are C-convertible.
There are no rules.
Relative termination of P / R is proven as follows.
1.1 R is empty
There are no rules in the TRS R. Hence, R/S is relative terminating.
Confluence of C is proven as follows.
1.2 (Weakly) Orthogonal
Confluence is proven since the TRS is (weakly) orthogonal.
Tool configuration
Hakusan