The rewrite relation of the following TRS is considered.
a__U11(tt,M,N) | → | a__U12(tt,M,N) | (1) |
a__U12(tt,M,N) | → | s(a__plus(mark(N),mark(M))) | (2) |
a__U21(tt,M,N) | → | a__U22(tt,M,N) | (3) |
a__U22(tt,M,N) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (4) |
a__plus(N,0) | → | mark(N) | (5) |
a__plus(N,s(M)) | → | a__U11(tt,M,N) | (6) |
a__x(N,0) | → | 0 | (7) |
a__x(N,s(M)) | → | a__U21(tt,M,N) | (8) |
mark(U11(X1,X2,X3)) | → | a__U11(mark(X1),X2,X3) | (9) |
mark(U12(X1,X2,X3)) | → | a__U12(mark(X1),X2,X3) | (10) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (11) |
mark(U21(X1,X2,X3)) | → | a__U21(mark(X1),X2,X3) | (12) |
mark(U22(X1,X2,X3)) | → | a__U22(mark(X1),X2,X3) | (13) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (14) |
mark(tt) | → | tt | (15) |
mark(s(X)) | → | s(mark(X)) | (16) |
mark(0) | → | 0 | (17) |
a__U11(X1,X2,X3) | → | U11(X1,X2,X3) | (18) |
a__U12(X1,X2,X3) | → | U12(X1,X2,X3) | (19) |
a__plus(X1,X2) | → | plus(X1,X2) | (20) |
a__U21(X1,X2,X3) | → | U21(X1,X2,X3) | (21) |
a__U22(X1,X2,X3) | → | U22(X1,X2,X3) | (22) |
a__x(X1,X2) | → | x(X1,X2) | (23) |
a__U12#(tt,M,N) | → | mark#(N) | (24) |
mark#(U22(X1,X2,X3)) | → | mark#(X1) | (25) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (26) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (27) |
mark#(plus(X1,X2)) | → | mark#(X2) | (28) |
a__U22#(tt,M,N) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
a__x#(N,s(M)) | → | a__U21#(tt,M,N) | (30) |
mark#(U21(X1,X2,X3)) | → | a__U21#(mark(X1),X2,X3) | (31) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (32) |
a__U22#(tt,M,N) | → | a__x#(mark(N),mark(M)) | (33) |
mark#(s(X)) | → | mark#(X) | (34) |
mark#(U11(X1,X2,X3)) | → | a__U11#(mark(X1),X2,X3) | (35) |
mark#(plus(X1,X2)) | → | mark#(X1) | (36) |
mark#(U22(X1,X2,X3)) | → | a__U22#(mark(X1),X2,X3) | (37) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
a__U11#(tt,M,N) | → | a__U12#(tt,M,N) | (39) |
a__U22#(tt,M,N) | → | mark#(M) | (40) |
mark#(U12(X1,X2,X3)) | → | a__U12#(mark(X1),X2,X3) | (41) |
a__plus#(N,0) | → | mark#(N) | (42) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
a__U21#(tt,M,N) | → | a__U22#(tt,M,N) | (43) |
mark#(x(X1,X2)) | → | mark#(X2) | (44) |
a__U12#(tt,M,N) | → | mark#(M) | (45) |
a__U12#(tt,M,N) | → | a__plus#(mark(N),mark(M)) | (46) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (47) |
mark#(x(X1,X2)) | → | mark#(X1) | (48) |
a__plus#(N,s(M)) | → | a__U11#(tt,M,N) | (49) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (50) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (50) |
a__U22#(tt,M,N) | → | a__x#(mark(N),mark(M)) | (33) |
a__plus#(N,s(M)) | → | a__U11#(tt,M,N) | (49) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (32) |
mark#(x(X1,X2)) | → | mark#(X1) | (48) |
mark#(U21(X1,X2,X3)) | → | a__U21#(mark(X1),X2,X3) | (31) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (47) |
a__U12#(tt,M,N) | → | a__plus#(mark(N),mark(M)) | (46) |
a__x#(N,s(M)) | → | a__U21#(tt,M,N) | (30) |
a__U12#(tt,M,N) | → | mark#(M) | (45) |
a__U22#(tt,M,N) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
mark#(x(X1,X2)) | → | mark#(X2) | (44) |
a__U21#(tt,M,N) | → | a__U22#(tt,M,N) | (43) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
mark#(plus(X1,X2)) | → | mark#(X2) | (28) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (27) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (26) |
a__plus#(N,0) | → | mark#(N) | (42) |
mark#(U12(X1,X2,X3)) | → | a__U12#(mark(X1),X2,X3) | (41) |
mark#(U22(X1,X2,X3)) | → | mark#(X1) | (25) |
a__U22#(tt,M,N) | → | mark#(M) | (40) |
a__U11#(tt,M,N) | → | a__U12#(tt,M,N) | (39) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
mark#(U22(X1,X2,X3)) | → | a__U22#(mark(X1),X2,X3) | (37) |
mark#(plus(X1,X2)) | → | mark#(X1) | (36) |
mark#(U11(X1,X2,X3)) | → | a__U11#(mark(X1),X2,X3) | (35) |
a__U12#(tt,M,N) | → | mark#(N) | (24) |
mark#(s(X)) | → | mark#(X) | (34) |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 18815, 0) |
[U21(x1, x2, x3)] | = | max(x1 + 13215, x2 + 1, x3 + 18815, 0) |
[U11(x1, x2, x3)] | = | max(x1 + 18814, x2 + 18815, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[a__x#(x1, x2)] | = | max(x1 + 75553, x2 + 56739, 0) |
[a__U22(x1, x2, x3)] | = | max(x1 + 18814, x2 + 1, x3 + 18815, 0) |
[a__U11#(x1, x2, x3)] | = | max(x1 + 75552, x2 + 75553, x3 + 56738, 0) |
[a__x(x1, x2)] | = | max(x1 + 18815, x2 + 1, 0) |
[U12(x1, x2, x3)] | = | max(x1 + 18814, x2 + 18815, x3 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 18815, x2 + 1, 0) |
[a__U12#(x1, x2, x3)] | = | max(x1 + 75551, x2 + 75553, x3 + 56738, 0) |
[a__U21#(x1, x2, x3)] | = | max(x2 + 56739, x3 + 75553, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 56738, x2 + 75553, 0) |
[mark#(x1)] | = | x1 + 56738 |
[0] | = | 4684 |
[a__U21(x1, x2, x3)] | = | max(x1 + 13215, x2 + 1, x3 + 18815, 0) |
[mark(x1)] | = | x1 + 0 |
[a__U11(x1, x2, x3)] | = | max(x1 + 18814, x2 + 18815, x3 + 0, 0) |
[a__U12(x1, x2, x3)] | = | max(x1 + 18814, x2 + 18815, x3 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 18815, 0) |
[a__U22#(x1, x2, x3)] | = | max(x1 + 31964, x2 + 56739, x3 + 75553, 0) |
[tt] | = | 1 |
[U22(x1, x2, x3)] | = | max(x1 + 18814, x2 + 1, x3 + 18815, 0) |
a__U11(X1,X2,X3) | → | U11(X1,X2,X3) | (18) |
a__U22(tt,M,N) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (4) |
mark(tt) | → | tt | (15) |
a__x(N,s(M)) | → | a__U21(tt,M,N) | (8) |
a__U11(tt,M,N) | → | a__U12(tt,M,N) | (1) |
a__U21(tt,M,N) | → | a__U22(tt,M,N) | (3) |
mark(s(X)) | → | s(mark(X)) | (16) |
a__U21(X1,X2,X3) | → | U21(X1,X2,X3) | (21) |
a__U12(X1,X2,X3) | → | U12(X1,X2,X3) | (19) |
mark(0) | → | 0 | (17) |
a__U22(X1,X2,X3) | → | U22(X1,X2,X3) | (22) |
a__plus(N,0) | → | mark(N) | (5) |
mark(U12(X1,X2,X3)) | → | a__U12(mark(X1),X2,X3) | (10) |
a__x(N,0) | → | 0 | (7) |
a__plus(X1,X2) | → | plus(X1,X2) | (20) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (14) |
mark(U21(X1,X2,X3)) | → | a__U21(mark(X1),X2,X3) | (12) |
a__x(X1,X2) | → | x(X1,X2) | (23) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (11) |
mark(U11(X1,X2,X3)) | → | a__U11(mark(X1),X2,X3) | (9) |
mark(U22(X1,X2,X3)) | → | a__U22(mark(X1),X2,X3) | (13) |
a__plus(N,s(M)) | → | a__U11(tt,M,N) | (6) |
a__U12(tt,M,N) | → | s(a__plus(mark(N),mark(M))) | (2) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (50) |
mark#(x(X1,X2)) | → | mark#(X1) | (48) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (47) |
a__U12#(tt,M,N) | → | mark#(M) | (45) |
mark#(x(X1,X2)) | → | mark#(X2) | (44) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
mark#(plus(X1,X2)) | → | mark#(X2) | (28) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (26) |
mark#(U22(X1,X2,X3)) | → | mark#(X1) | (25) |
a__U22#(tt,M,N) | → | mark#(M) | (40) |
a__U22#(tt,M,N) | → | mark#(N) | (38) |
The dependency pairs are split into 1 component.
a__U22#(tt,M,N) | → | a__x#(mark(N),mark(M)) | (33) |
a__U22#(tt,M,N) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
a__x#(N,s(M)) | → | a__U21#(tt,M,N) | (30) |
a__U11#(tt,M,N) | → | a__U12#(tt,M,N) | (39) |
a__U21#(tt,M,N) | → | a__U22#(tt,M,N) | (43) |
mark#(s(X)) | → | mark#(X) | (34) |
a__plus#(N,0) | → | mark#(N) | (42) |
mark#(U12(X1,X2,X3)) | → | a__U12#(mark(X1),X2,X3) | (41) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (32) |
mark#(U21(X1,X2,X3)) | → | a__U21#(mark(X1),X2,X3) | (31) |
mark#(plus(X1,X2)) | → | mark#(X1) | (36) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (27) |
mark#(U11(X1,X2,X3)) | → | a__U11#(mark(X1),X2,X3) | (35) |
mark#(U22(X1,X2,X3)) | → | a__U22#(mark(X1),X2,X3) | (37) |
a__plus#(N,s(M)) | → | a__U11#(tt,M,N) | (49) |
a__U12#(tt,M,N) | → | mark#(N) | (24) |
a__U12#(tt,M,N) | → | a__plus#(mark(N),mark(M)) | (46) |
π(a__U11#) | = | 3 |
π(a__U12#) | = | 3 |
π(a__plus#) | = | 1 |
π(mark#) | = | 1 |
π(mark) | = | 1 |
prec(a__plus) | = | 3 | status(a__plus) | = | [1, 2] | list-extension(a__plus) | = | Lex | ||
prec(U21) | = | 4 | status(U21) | = | [3, 2, 1] | list-extension(U21) | = | Lex | ||
prec(U11) | = | 3 | status(U11) | = | [3, 2, 1] | list-extension(U11) | = | Lex | ||
prec(s) | = | 0 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__x#) | = | 4 | status(a__x#) | = | [1, 2] | list-extension(a__x#) | = | Lex | ||
prec(a__U22) | = | 4 | status(a__U22) | = | [3, 2, 1] | list-extension(a__U22) | = | Lex | ||
prec(a__x) | = | 4 | status(a__x) | = | [1, 2] | list-extension(a__x) | = | Lex | ||
prec(U12) | = | 3 | status(U12) | = | [3, 2, 1] | list-extension(U12) | = | Lex | ||
prec(x) | = | 4 | status(x) | = | [1, 2] | list-extension(x) | = | Lex | ||
prec(a__U21#) | = | 4 | status(a__U21#) | = | [3, 2, 1] | list-extension(a__U21#) | = | Lex | ||
prec(0) | = | 2 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__U21) | = | 4 | status(a__U21) | = | [3, 2, 1] | list-extension(a__U21) | = | Lex | ||
prec(a__U11) | = | 3 | status(a__U11) | = | [3, 2, 1] | list-extension(a__U11) | = | Lex | ||
prec(a__U12) | = | 3 | status(a__U12) | = | [3, 2, 1] | list-extension(a__U12) | = | Lex | ||
prec(plus) | = | 3 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(a__U22#) | = | 4 | status(a__U22#) | = | [3, 2] | list-extension(a__U22#) | = | Lex | ||
prec(tt) | = | 2 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U22) | = | 4 | status(U22) | = | [3, 2, 1] | list-extension(U22) | = | Lex |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U11(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[a__x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U22(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U12(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U21#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[0] | = | 0 |
[a__U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__U11(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__U12(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U22#(x1, x2, x3)] | = | max(x2 + 0, x3 + 0, 0) |
[tt] | = | 0 |
[U22(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
a__U11(X1,X2,X3) | → | U11(X1,X2,X3) | (18) |
a__U22(tt,M,N) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (4) |
mark(tt) | → | tt | (15) |
a__x(N,s(M)) | → | a__U21(tt,M,N) | (8) |
a__U11(tt,M,N) | → | a__U12(tt,M,N) | (1) |
a__U21(tt,M,N) | → | a__U22(tt,M,N) | (3) |
mark(s(X)) | → | s(mark(X)) | (16) |
a__U21(X1,X2,X3) | → | U21(X1,X2,X3) | (21) |
a__U12(X1,X2,X3) | → | U12(X1,X2,X3) | (19) |
mark(0) | → | 0 | (17) |
a__U22(X1,X2,X3) | → | U22(X1,X2,X3) | (22) |
a__plus(N,0) | → | mark(N) | (5) |
mark(U12(X1,X2,X3)) | → | a__U12(mark(X1),X2,X3) | (10) |
a__x(N,0) | → | 0 | (7) |
a__plus(X1,X2) | → | plus(X1,X2) | (20) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (14) |
mark(U21(X1,X2,X3)) | → | a__U21(mark(X1),X2,X3) | (12) |
a__x(X1,X2) | → | x(X1,X2) | (23) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (11) |
mark(U11(X1,X2,X3)) | → | a__U11(mark(X1),X2,X3) | (9) |
mark(U22(X1,X2,X3)) | → | a__U22(mark(X1),X2,X3) | (13) |
a__plus(N,s(M)) | → | a__U11(tt,M,N) | (6) |
a__U12(tt,M,N) | → | s(a__plus(mark(N),mark(M))) | (2) |
a__x#(N,s(M)) | → | a__U21#(tt,M,N) | (30) |
a__U21#(tt,M,N) | → | a__U22#(tt,M,N) | (43) |
mark#(s(X)) | → | mark#(X) | (34) |
mark#(U12(X1,X2,X3)) | → | a__U12#(mark(X1),X2,X3) | (41) |
mark#(plus(X1,X2)) | → | mark#(X1) | (36) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (27) |
mark#(U11(X1,X2,X3)) | → | a__U11#(mark(X1),X2,X3) | (35) |
mark#(U22(X1,X2,X3)) | → | a__U22#(mark(X1),X2,X3) | (37) |
The dependency pairs are split into 1 component.
a__U11#(tt,M,N) | → | a__U12#(tt,M,N) | (39) |
a__plus#(N,s(M)) | → | a__U11#(tt,M,N) | (49) |
a__U12#(tt,M,N) | → | a__plus#(mark(N),mark(M)) | (46) |
π(a__U11#) | = | 2 |
π(a__U12#) | = | 2 |
π(a__plus#) | = | 2 |
π(mark#) | = | 1 |
π(mark) | = | 1 |
prec(a__plus) | = | 4 | status(a__plus) | = | [1, 2] | list-extension(a__plus) | = | Lex | ||
prec(U21) | = | 5 | status(U21) | = | [3, 2, 1] | list-extension(U21) | = | Lex | ||
prec(U11) | = | 4 | status(U11) | = | [3, 2, 1] | list-extension(U11) | = | Lex | ||
prec(s) | = | 3 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__x#) | = | 4 | status(a__x#) | = | [1, 2] | list-extension(a__x#) | = | Lex | ||
prec(a__U22) | = | 5 | status(a__U22) | = | [3, 2, 1] | list-extension(a__U22) | = | Lex | ||
prec(a__x) | = | 5 | status(a__x) | = | [1, 2] | list-extension(a__x) | = | Lex | ||
prec(U12) | = | 4 | status(U12) | = | [3, 2, 1] | list-extension(U12) | = | Lex | ||
prec(x) | = | 5 | status(x) | = | [1, 2] | list-extension(x) | = | Lex | ||
prec(a__U21#) | = | 4 | status(a__U21#) | = | [3, 2, 1] | list-extension(a__U21#) | = | Lex | ||
prec(0) | = | 1 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__U21) | = | 5 | status(a__U21) | = | [3, 2, 1] | list-extension(a__U21) | = | Lex | ||
prec(a__U11) | = | 4 | status(a__U11) | = | [3, 2, 1] | list-extension(a__U11) | = | Lex | ||
prec(a__U12) | = | 4 | status(a__U12) | = | [3, 2, 1] | list-extension(a__U12) | = | Lex | ||
prec(plus) | = | 4 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(a__U22#) | = | 4 | status(a__U22#) | = | [3, 2] | list-extension(a__U22#) | = | Lex | ||
prec(tt) | = | 2 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U22) | = | 5 | status(U22) | = | [3, 2, 1] | list-extension(U22) | = | Lex |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U11(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[a__x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U22(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U12(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U21#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[0] | = | 0 |
[a__U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__U11(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[a__U12(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__U22#(x1, x2, x3)] | = | max(x2 + 0, x3 + 0, 0) |
[tt] | = | 0 |
[U22(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
a__U11(X1,X2,X3) | → | U11(X1,X2,X3) | (18) |
a__U22(tt,M,N) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (4) |
mark(tt) | → | tt | (15) |
a__x(N,s(M)) | → | a__U21(tt,M,N) | (8) |
a__U11(tt,M,N) | → | a__U12(tt,M,N) | (1) |
a__U21(tt,M,N) | → | a__U22(tt,M,N) | (3) |
mark(s(X)) | → | s(mark(X)) | (16) |
a__U21(X1,X2,X3) | → | U21(X1,X2,X3) | (21) |
a__U12(X1,X2,X3) | → | U12(X1,X2,X3) | (19) |
mark(0) | → | 0 | (17) |
a__U22(X1,X2,X3) | → | U22(X1,X2,X3) | (22) |
a__plus(N,0) | → | mark(N) | (5) |
mark(U12(X1,X2,X3)) | → | a__U12(mark(X1),X2,X3) | (10) |
a__x(N,0) | → | 0 | (7) |
a__plus(X1,X2) | → | plus(X1,X2) | (20) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (14) |
mark(U21(X1,X2,X3)) | → | a__U21(mark(X1),X2,X3) | (12) |
a__x(X1,X2) | → | x(X1,X2) | (23) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (11) |
mark(U11(X1,X2,X3)) | → | a__U11(mark(X1),X2,X3) | (9) |
mark(U22(X1,X2,X3)) | → | a__U22(mark(X1),X2,X3) | (13) |
a__plus(N,s(M)) | → | a__U11(tt,M,N) | (6) |
a__U12(tt,M,N) | → | s(a__plus(mark(N),mark(M))) | (2) |
a__plus#(N,s(M)) | → | a__U11#(tt,M,N) | (49) |
The dependency pairs are split into 0 components.