The rewrite relation of the following TRS is considered.
U11(tt,M,N) | → | U12(tt,activate(M),activate(N)) | (1) |
U12(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
U21(tt,M,N) | → | U22(tt,activate(M),activate(N)) | (3) |
U22(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
plus(N,0) | → | N | (5) |
plus(N,s(M)) | → | U11(tt,M,N) | (6) |
x(N,0) | → | 0 | (7) |
x(N,s(M)) | → | U21(tt,M,N) | (8) |
activate(X) | → | X | (9) |
U11#(tt,M,N) | → | activate#(N) | (10) |
U11#(tt,M,N) | → | activate#(M) | (11) |
U11#(tt,M,N) | → | U12#(tt,activate(M),activate(N)) | (12) |
U12#(tt,M,N) | → | activate#(M) | (13) |
U12#(tt,M,N) | → | activate#(N) | (14) |
U12#(tt,M,N) | → | plus#(activate(N),activate(M)) | (15) |
U21#(tt,M,N) | → | activate#(N) | (16) |
U21#(tt,M,N) | → | activate#(M) | (17) |
U21#(tt,M,N) | → | U22#(tt,activate(M),activate(N)) | (18) |
U22#(tt,M,N) | → | activate#(M) | (19) |
U22#(tt,M,N) | → | activate#(N) | (20) |
U22#(tt,M,N) | → | x#(activate(N),activate(M)) | (21) |
U22#(tt,M,N) | → | plus#(x(activate(N),activate(M)),activate(N)) | (22) |
plus#(N,s(M)) | → | U11#(tt,M,N) | (23) |
x#(N,s(M)) | → | U21#(tt,M,N) | (24) |
The dependency pairs are split into 2 components.
x#(N,s(M)) | → | U21#(tt,M,N) | (24) |
U21#(tt,M,N) | → | U22#(tt,activate(M),activate(N)) | (18) |
U22#(tt,M,N) | → | x#(activate(N),activate(M)) | (21) |
π(x#) | = | { 2 } |
π(U22#) | = | { 2 } |
π(U21#) | = | { 2 } |
π(activate) | = | { 1 } |
x#(N,s(M)) | → | U21#(tt,M,N) | (24) |
The dependency pairs are split into 0 components.
plus#(N,s(M)) | → | U11#(tt,M,N) | (23) |
U11#(tt,M,N) | → | U12#(tt,activate(M),activate(N)) | (12) |
U12#(tt,M,N) | → | plus#(activate(N),activate(M)) | (15) |
π(plus#) | = | { 2 } |
π(U12#) | = | { 2 } |
π(U11#) | = | { 2 } |
π(activate) | = | { 1 } |
plus#(N,s(M)) | → | U11#(tt,M,N) | (23) |
The dependency pairs are split into 0 components.