The rewrite relation of the following TRS is considered.
active(U11(tt,M,N)) | → | mark(U12(tt,M,N)) | (1) |
active(U12(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active(plus(N,0)) | → | mark(N) | (3) |
active(plus(N,s(M))) | → | mark(U11(tt,M,N)) | (4) |
active(U11(X1,X2,X3)) | → | U11(active(X1),X2,X3) | (5) |
active(U12(X1,X2,X3)) | → | U12(active(X1),X2,X3) | (6) |
active(s(X)) | → | s(active(X)) | (7) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (8) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (9) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
s(mark(X)) | → | mark(s(X)) | (12) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
proper(U11(X1,X2,X3)) | → | U11(proper(X1),proper(X2),proper(X3)) | (15) |
proper(tt) | → | ok(tt) | (16) |
proper(U12(X1,X2,X3)) | → | U12(proper(X1),proper(X2),proper(X3)) | (17) |
proper(s(X)) | → | s(proper(X)) | (18) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (19) |
proper(0) | → | ok(0) | (20) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
top(mark(X)) | → | top(proper(X)) | (25) |
top(ok(X)) | → | top(active(X)) | (26) |
active#(U12(tt,M,N)) | → | plus#(N,M) | (27) |
top#(ok(X)) | → | active#(X) | (28) |
proper#(U11(X1,X2,X3)) | → | proper#(X1) | (29) |
proper#(U11(X1,X2,X3)) | → | proper#(X3) | (30) |
active#(plus(N,s(M))) | → | U11#(tt,M,N) | (31) |
active#(plus(X1,X2)) | → | plus#(X1,active(X2)) | (32) |
proper#(s(X)) | → | proper#(X) | (33) |
top#(mark(X)) | → | top#(proper(X)) | (34) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (35) |
s#(mark(X)) | → | s#(X) | (36) |
proper#(U12(X1,X2,X3)) | → | proper#(X3) | (37) |
proper#(U12(X1,X2,X3)) | → | proper#(X2) | (38) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (39) |
active#(U11(tt,M,N)) | → | U12#(tt,M,N) | (40) |
top#(mark(X)) | → | proper#(X) | (41) |
U11#(ok(X1),ok(X2),ok(X3)) | → | U11#(X1,X2,X3) | (42) |
proper#(plus(X1,X2)) | → | plus#(proper(X1),proper(X2)) | (43) |
U12#(ok(X1),ok(X2),ok(X3)) | → | U12#(X1,X2,X3) | (44) |
active#(plus(X1,X2)) | → | active#(X2) | (45) |
proper#(s(X)) | → | s#(proper(X)) | (46) |
s#(ok(X)) | → | s#(X) | (47) |
active#(plus(X1,X2)) | → | active#(X1) | (48) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (49) |
top#(ok(X)) | → | top#(active(X)) | (50) |
proper#(U12(X1,X2,X3)) | → | proper#(X1) | (51) |
proper#(U11(X1,X2,X3)) | → | U11#(proper(X1),proper(X2),proper(X3)) | (52) |
proper#(plus(X1,X2)) | → | proper#(X2) | (53) |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (54) |
active#(plus(X1,X2)) | → | plus#(active(X1),X2) | (55) |
active#(U11(X1,X2,X3)) | → | active#(X1) | (56) |
proper#(plus(X1,X2)) | → | proper#(X1) | (57) |
proper#(U11(X1,X2,X3)) | → | proper#(X2) | (58) |
proper#(U12(X1,X2,X3)) | → | U12#(proper(X1),proper(X2),proper(X3)) | (59) |
active#(s(X)) | → | active#(X) | (60) |
active#(U12(X1,X2,X3)) | → | U12#(active(X1),X2,X3) | (61) |
active#(U12(tt,M,N)) | → | s#(plus(N,M)) | (62) |
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (63) |
active#(s(X)) | → | s#(active(X)) | (64) |
active#(U12(X1,X2,X3)) | → | active#(X1) | (65) |
active#(U11(X1,X2,X3)) | → | U11#(active(X1),X2,X3) | (66) |
The dependency pairs are split into 7 components.
top#(mark(X)) | → | top#(proper(X)) | (34) |
top#(ok(X)) | → | top#(active(X)) | (50) |
π(top) | = | 1 |
π(proper) | = | 1 |
π(ok) | = | 1 |
π(proper#) | = | 1 |
π(active) | = | 1 |
prec(U11) | = | 6 | status(U11) | = | [1, 2] | list-extension(U11) | = | Lex | ||
prec(s) | = | 4 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(plus#) | = | 0 | status(plus#) | = | [] | list-extension(plus#) | = | Lex | ||
prec(top#) | = | 0 | status(top#) | = | [1] | list-extension(top#) | = | Lex | ||
prec(U12) | = | 5 | status(U12) | = | [3, 2, 1] | list-extension(U12) | = | Lex | ||
prec(U12#) | = | 0 | status(U12#) | = | [2, 3, 1] | list-extension(U12#) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(mark) | = | 1 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
prec(plus) | = | 6 | status(plus) | = | [2, 1] | list-extension(plus) | = | Lex | ||
prec(U11#) | = | 0 | status(U11#) | = | [3, 2] | list-extension(U11#) | = | Lex | ||
prec(active#) | = | 0 | status(active#) | = | [] | list-extension(active#) | = | Lex | ||
prec(tt) | = | 2 | status(tt) | = | [] | list-extension(tt) | = | Lex |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 12619 |
[plus#(x1, x2)] | = | x2 + 1 |
[top#(x1)] | = | x1 + 1 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[0] | = | 36068 |
[s#(x1)] | = | 1 |
[mark(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | x2 + x3 + 1 |
[active#(x1)] | = | 1 |
[tt] | = | 12619 |
proper(s(X)) | → | s(proper(X)) | (18) |
active(plus(N,s(M))) | → | mark(U11(tt,M,N)) | (4) |
proper(U11(X1,X2,X3)) | → | U11(proper(X1),proper(X2),proper(X3)) | (15) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (8) |
active(U11(tt,M,N)) | → | mark(U12(tt,M,N)) | (1) |
active(plus(N,0)) | → | mark(N) | (3) |
proper(tt) | → | ok(tt) | (16) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (19) |
proper(U12(X1,X2,X3)) | → | U12(proper(X1),proper(X2),proper(X3)) | (17) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
active(U11(X1,X2,X3)) | → | U11(active(X1),X2,X3) | (5) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
active(s(X)) | → | s(active(X)) | (7) |
proper(0) | → | ok(0) | (20) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (9) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
active(U12(X1,X2,X3)) | → | U12(active(X1),X2,X3) | (6) |
active(U12(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (34) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (50) |
[U11(x1, x2, x3)] | = | x1 + 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[U12(x1, x2, x3)] | = | x1 + 0 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 14588 |
[ok(x1)] | = | x1 + 14587 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 14586 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
proper(s(X)) | → | s(proper(X)) | (18) |
active(plus(N,s(M))) | → | mark(U11(tt,M,N)) | (4) |
proper(U11(X1,X2,X3)) | → | U11(proper(X1),proper(X2),proper(X3)) | (15) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (8) |
active(U11(tt,M,N)) | → | mark(U12(tt,M,N)) | (1) |
active(plus(N,0)) | → | mark(N) | (3) |
proper(tt) | → | ok(tt) | (16) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (19) |
proper(U12(X1,X2,X3)) | → | U12(proper(X1),proper(X2),proper(X3)) | (17) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
active(U11(X1,X2,X3)) | → | U11(active(X1),X2,X3) | (5) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
active(s(X)) | → | s(active(X)) | (7) |
proper(0) | → | ok(0) | (20) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (9) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
active(U12(X1,X2,X3)) | → | U12(active(X1),X2,X3) | (6) |
active(U12(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
top#(ok(X)) | → | top#(active(X)) | (50) |
The dependency pairs are split into 0 components.
proper#(U12(X1,X2,X3)) | → | proper#(X2) | (38) |
proper#(U12(X1,X2,X3)) | → | proper#(X3) | (37) |
proper#(U11(X1,X2,X3)) | → | proper#(X2) | (58) |
proper#(plus(X1,X2)) | → | proper#(X1) | (57) |
proper#(s(X)) | → | proper#(X) | (33) |
proper#(plus(X1,X2)) | → | proper#(X2) | (53) |
proper#(U12(X1,X2,X3)) | → | proper#(X1) | (51) |
proper#(U11(X1,X2,X3)) | → | proper#(X3) | (30) |
proper#(U11(X1,X2,X3)) | → | proper#(X1) | (29) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 2 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
proper#(U12(X1,X2,X3)) | → | proper#(X2) | (38) |
proper#(U12(X1,X2,X3)) | → | proper#(X3) | (37) |
proper#(U11(X1,X2,X3)) | → | proper#(X2) | (58) |
proper#(plus(X1,X2)) | → | proper#(X1) | (57) |
proper#(s(X)) | → | proper#(X) | (33) |
proper#(plus(X1,X2)) | → | proper#(X2) | (53) |
proper#(U12(X1,X2,X3)) | → | proper#(X1) | (51) |
proper#(U11(X1,X2,X3)) | → | proper#(X3) | (30) |
proper#(U11(X1,X2,X3)) | → | proper#(X1) | (29) |
The dependency pairs are split into 0 components.
active#(U12(X1,X2,X3)) | → | active#(X1) | (65) |
active#(s(X)) | → | active#(X) | (60) |
active#(U11(X1,X2,X3)) | → | active#(X1) | (56) |
active#(plus(X1,X2)) | → | active#(X1) | (48) |
active#(plus(X1,X2)) | → | active#(X2) | (45) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 25311 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 2 |
[active#(x1)] | = | x1 + 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
active#(U12(X1,X2,X3)) | → | active#(X1) | (65) |
active#(s(X)) | → | active#(X) | (60) |
active#(U11(X1,X2,X3)) | → | active#(X1) | (56) |
active#(plus(X1,X2)) | → | active#(X1) | (48) |
active#(plus(X1,X2)) | → | active#(X2) | (45) |
The dependency pairs are split into 0 components.
s#(mark(X)) | → | s#(X) | (36) |
s#(ok(X)) | → | s#(X) | (47) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 55803 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 2 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
s#(ok(X)) | → | s#(X) | (47) |
The dependency pairs are split into 1 component.
s#(mark(X)) | → | s#(X) | (36) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
s#(mark(X)) | → | s#(X) | (36) |
The dependency pairs are split into 0 components.
U11#(ok(X1),ok(X2),ok(X3)) | → | U11#(X1,X2,X3) | (42) |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (54) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | x3 + 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
U11#(ok(X1),ok(X2),ok(X3)) | → | U11#(X1,X2,X3) | (42) |
The dependency pairs are split into 1 component.
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (54) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | x1 + 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (54) |
The dependency pairs are split into 0 components.
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (39) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (35) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (49) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | x1 + x2 + 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (39) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (35) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (49) |
The dependency pairs are split into 0 components.
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (63) |
U12#(ok(X1),ok(X2),ok(X3)) | → | U12#(X1,X2,X3) | (44) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | x2 + x3 + 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 31490 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
U12#(ok(X1),ok(X2),ok(X3)) | → | U12#(X1,X2,X3) | (44) |
The dependency pairs are split into 1 component.
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (63) |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U12(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U12#(x1, x2, x3)] | = | x1 + 0 |
[proper(x1)] | = | 0 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 11453 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 3 |
[active#(x1)] | = | 0 |
[tt] | = | 1 |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (21) |
U12(ok(X1),ok(X2),ok(X3)) | → | ok(U12(X1,X2,X3)) | (22) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (10) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (14) |
s(mark(X)) | → | mark(s(X)) | (12) |
s(ok(X)) | → | ok(s(X)) | (23) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (24) |
U12(mark(X1),X2,X3) | → | mark(U12(X1,X2,X3)) | (11) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (13) |
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (63) |
The dependency pairs are split into 0 components.