(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
c(b(a(X))) → a(a(b(b(c(c(X))))))
a(X) → e
b(X) → e
c(X) → e
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1210941, 1210942, 1210946, 1210947, 1210943, 1210945, 1210944, 1210951, 1210952, 1210949, 1210950, 1210948
Node 1210941 is start node and node 1210942 is final node.
Those nodes are connect through the following edges:
- 1210941 to 1210942 labelled e(0)
- 1210941 to 1210943 labelled a_1(0), e(1)
- 1210942 to 1210942 labelled #_1(0)
- 1210946 to 1210947 labelled c_1(0), e(1)
- 1210947 to 1210942 labelled c_1(0), e(1)
- 1210947 to 1210948 labelled a_1(1), e(2)
- 1210943 to 1210944 labelled a_1(0), e(1)
- 1210945 to 1210946 labelled b_1(0), e(1)
- 1210944 to 1210945 labelled b_1(0), e(1)
- 1210951 to 1210952 labelled c_1(1), e(2)
- 1210952 to 1210942 labelled c_1(1), e(2)
- 1210952 to 1210948 labelled a_1(1), e(2)
- 1210949 to 1210950 labelled b_1(1), e(2)
- 1210950 to 1210951 labelled b_1(1), e(2)
- 1210948 to 1210949 labelled a_1(1), e(2)