The rewrite relation of the following TRS is considered.
active(U11(tt,N)) | → | mark(N) | (1) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active(and(tt,X)) | → | mark(X) | (3) |
active(isNat(0)) | → | mark(tt) | (4) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (9) |
mark(tt) | → | active(tt) | (10) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (11) |
mark(s(X)) | → | active(s(mark(X))) | (12) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (13) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (14) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
mark(0) | → | active(0) | (16) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
s(mark(X)) | → | s(X) | (27) |
s(active(X)) | → | s(X) | (28) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
isNat(mark(X)) | → | isNat(X) | (37) |
isNat(active(X)) | → | isNat(X) | (38) |
active#(U21(tt,M,N)) | → | s#(plus(N,M)) | (39) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (40) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (41) |
mark#(tt) | → | active#(tt) | (42) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (43) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (44) |
s#(active(X)) | → | s#(X) | (45) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (47) |
active#(U11(tt,N)) | → | mark#(N) | (48) |
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (49) |
active#(plus(N,s(M))) | → | isNat#(N) | (50) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (51) |
active#(isNat(plus(V1,V2))) | → | and#(isNat(V1),isNat(V2)) | (52) |
isNat#(mark(X)) | → | isNat#(X) | (53) |
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(plus(N,s(M))) | → | U21#(and(isNat(M),isNat(N)),M,N) | (55) |
active#(isNat(plus(V1,V2))) | → | isNat#(V2) | (56) |
mark#(0) | → | active#(0) | (57) |
mark#(plus(X1,X2)) | → | mark#(X2) | (58) |
active#(isNat(s(V1))) | → | isNat#(V1) | (59) |
mark#(plus(X1,X2)) | → | plus#(mark(X1),mark(X2)) | (60) |
active#(plus(N,s(M))) | → | isNat#(M) | (61) |
mark#(s(X)) | → | mark#(X) | (62) |
mark#(s(X)) | → | s#(mark(X)) | (63) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (64) |
mark#(plus(X1,X2)) | → | mark#(X1) | (65) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (66) |
active#(plus(N,s(M))) | → | and#(isNat(M),isNat(N)) | (67) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (69) |
active#(and(tt,X)) | → | mark#(X) | (70) |
and#(X1,active(X2)) | → | and#(X1,X2) | (71) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (72) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (73) |
isNat#(active(X)) | → | isNat#(X) | (74) |
active#(isNat(plus(V1,V2))) | → | isNat#(V1) | (75) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(plus(N,0)) | → | U11#(isNat(N),N) | (77) |
and#(active(X1),X2) | → | and#(X1,X2) | (78) |
s#(mark(X)) | → | s#(X) | (79) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(s(X)) | → | active#(s(mark(X))) | (81) |
active#(plus(N,0)) | → | isNat#(N) | (82) |
mark#(and(X1,X2)) | → | and#(mark(X1),X2) | (83) |
active#(isNat(0)) | → | mark#(tt) | (84) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (86) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (87) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
and#(mark(X1),X2) | → | and#(X1,X2) | (89) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (90) |
mark#(U11(X1,X2)) | → | mark#(X1) | (91) |
active#(U21(tt,M,N)) | → | plus#(N,M) | (92) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (94) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
mark#(U11(X1,X2)) | → | U11#(mark(X1),X2) | (96) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (97) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (98) |
mark#(U21(X1,X2,X3)) | → | U21#(mark(X1),X2,X3) | (99) |
The dependency pairs are split into 7 components.
active#(and(tt,X)) | → | mark#(X) | (70) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | mark#(X1) | (65) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (94) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
mark#(s(X)) | → | mark#(X) | (62) |
mark#(U11(X1,X2)) | → | mark#(X1) | (91) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(plus(X1,X2)) | → | mark#(X2) | (58) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (86) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (87) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
mark#(s(X)) | → | active#(s(mark(X))) | (81) |
active#(U11(tt,N)) | → | mark#(N) | (48) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
[U21(x1, x2, x3)] | = | 5855 |
[U11(x1, x2)] | = | 5855 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 5855 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | 5855 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[isNat(x1)] | = | 5855 |
[plus(x1, x2)] | = | 5855 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
mark#(s(X)) | → | active#(s(mark(X))) | (81) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (94) |
active#(U11(tt,N)) | → | mark#(N) | (48) |
active#(and(tt,X)) | → | mark#(X) | (70) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (86) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(s(X)) | → | mark#(X) | (62) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (87) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(U11(X1,X2)) | → | mark#(X1) | (91) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | mark#(X2) | (58) |
mark#(plus(X1,X2)) | → | mark#(X1) | (65) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
[U21(x1, x2, x3)] | = | x1 + x2 + x3 + 677 |
[U11(x1, x2)] | = | x1 + x2 + 841 |
[s(x1)] | = | x1 + 591 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 756 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 86 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
mark(0) | → | active(0) | (16) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
mark(tt) | → | active(tt) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (14) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
mark(s(X)) | → | active(s(mark(X))) | (12) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (11) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (9) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active#(U11(tt,N)) | → | mark#(N) | (48) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (86) |
mark#(s(X)) | → | mark#(X) | (62) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (87) |
mark#(U11(X1,X2)) | → | mark#(X1) | (91) |
mark#(plus(X1,X2)) | → | mark#(X2) | (58) |
mark#(plus(X1,X2)) | → | mark#(X1) | (65) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (94) |
active#(and(tt,X)) | → | mark#(X) | (70) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
[U21(x1, x2, x3)] | = | x1 + x3 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
mark(0) | → | active(0) | (16) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
mark(tt) | → | active(tt) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (14) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
mark(s(X)) | → | active(s(mark(X))) | (12) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (11) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (9) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (94) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(and(tt,X)) | → | mark#(X) | (70) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
[U21(x1, x2, x3)] | = | x1 + x3 + 2 |
[U11(x1, x2)] | = | x1 + x2 + 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
mark(0) | → | active(0) | (16) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
mark(tt) | → | active(tt) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (14) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
mark(s(X)) | → | active(s(mark(X))) | (12) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (11) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (9) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (93) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(and(tt,X)) | → | mark#(X) | (70) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
[U21(x1, x2, x3)] | = | x2 + x3 + 77330 |
[U11(x1, x2)] | = | x2 + 5599 |
[s(x1)] | = | x1 + 27858 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 14137 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 35333 |
[plus(x1, x2)] | = | x1 + x2 + 49472 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 21653 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
mark(0) | → | active(0) | (16) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
plus(X1,active(X2)) | → | plus(X1,X2) | (32) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
mark(tt) | → | active(tt) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (30) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (14) |
plus(active(X1),X2) | → | plus(X1,X2) | (31) |
mark(s(X)) | → | active(s(mark(X))) | (12) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (11) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (9) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus(mark(X1),X2) | → | plus(X1,X2) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
mark#(isNat(X)) | → | active#(isNat(X)) | (54) |
active#(and(tt,X)) | → | mark#(X) | (70) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (46) |
mark#(and(X1,X2)) | → | mark#(X1) | (80) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (88) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (85) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (76) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (95) |
The dependency pairs are split into 0 components.
U11#(X1,active(X2)) | → | U11#(X1,X2) | (66) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (64) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (51) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (47) |
[U21(x1, x2, x3)] | = | x3 + 2987 |
[U11(x1, x2)] | = | x2 + 1521 |
[s(x1)] | = | 2987 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 405 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 28872 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | 2987 |
[U11#(x1, x2)] | = | x1 + x2 + 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 11820 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (66) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (64) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (51) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (47) |
The dependency pairs are split into 0 components.
isNat#(mark(X)) | → | isNat#(X) | (53) |
isNat#(active(X)) | → | isNat#(X) | (74) |
[U21(x1, x2, x3)] | = | x3 + 1 |
[U11(x1, x2)] | = | x2 + 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | x1 + 0 |
[and(x1, x2)] | = | x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 28872 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 25984 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
isNat#(mark(X)) | → | isNat#(X) | (53) |
isNat#(active(X)) | → | isNat#(X) | (74) |
The dependency pairs are split into 0 components.
plus#(active(X1),X2) | → | plus#(X1,X2) | (72) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (97) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (43) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (41) |
[U21(x1, x2, x3)] | = | x3 + 15360 |
[U11(x1, x2)] | = | x2 + 12063 |
[s(x1)] | = | 6812 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 12701 |
[plus#(x1, x2)] | = | x1 + 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 37154 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | 39090 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 5586 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (72) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (97) |
The dependency pairs are split into 1 component.
plus#(X1,active(X2)) | → | plus#(X1,X2) | (43) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (41) |
[U21(x1, x2, x3)] | = | x3 + 1 |
[U11(x1, x2)] | = | x2 + 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 1 |
[plus#(x1, x2)] | = | x2 + 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 18748 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 42385 |
[plus(x1, x2)] | = | 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 5969 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (43) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (41) |
The dependency pairs are split into 0 components.
and#(X1,active(X2)) | → | and#(X1,X2) | (71) |
and#(mark(X1),X2) | → | and#(X1,X2) | (89) |
and#(active(X1),X2) | → | and#(X1,X2) | (78) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (40) |
[U21(x1, x2, x3)] | = | x3 + 31985 |
[U11(x1, x2)] | = | x2 + 30808 |
[s(x1)] | = | 3801 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 21095 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 2204 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 21310 |
[plus(x1, x2)] | = | 38405 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 2607 |
[and#(x1, x2)] | = | x2 + 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
and#(X1,active(X2)) | → | and#(X1,X2) | (71) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (40) |
The dependency pairs are split into 1 component.
and#(mark(X1),X2) | → | and#(X1,X2) | (89) |
and#(active(X1),X2) | → | and#(X1,X2) | (78) |
[U21(x1, x2, x3)] | = | x3 + 16760 |
[U11(x1, x2)] | = | x2 + 7362 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 11495 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 16264 |
[plus(x1, x2)] | = | 27507 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 10114 |
[and#(x1, x2)] | = | x1 + 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
and#(mark(X1),X2) | → | and#(X1,X2) | (89) |
and#(active(X1),X2) | → | and#(X1,X2) | (78) |
The dependency pairs are split into 0 components.
s#(mark(X)) | → | s#(X) | (79) |
s#(active(X)) | → | s#(X) | (45) |
[U21(x1, x2, x3)] | = | x3 + 34866 |
[U11(x1, x2)] | = | x2 + 6133 |
[s(x1)] | = | 28733 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 7343 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 6134 |
[isNat(x1)] | = | x1 + 13363 |
[plus(x1, x2)] | = | 40999 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
s#(mark(X)) | → | s#(X) | (79) |
s#(active(X)) | → | s#(X) | (45) |
The dependency pairs are split into 0 components.
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (98) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (69) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (90) |
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (49) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (44) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (73) |
[U21(x1, x2, x3)] | = | x3 + 970 |
[U11(x1, x2)] | = | x2 + 2421 |
[s(x1)] | = | 970 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2720 |
[plus#(x1, x2)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 15243 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[isNat(x1)] | = | x1 + 37749 |
[plus(x1, x2)] | = | 3448 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[tt] | = | 24817 |
[and#(x1, x2)] | = | 0 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (18) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (21) |
and(X1,active(X2)) | → | and(X1,X2) | (36) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (19) |
U11(mark(X1),X2) | → | U11(X1,X2) | (17) |
s(mark(X)) | → | s(X) | (27) |
and(X1,mark(X2)) | → | and(X1,X2) | (34) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (22) |
s(active(X)) | → | s(X) | (28) |
and(mark(X1),X2) | → | and(X1,X2) | (33) |
U11(X1,active(X2)) | → | U11(X1,X2) | (20) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (25) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (23) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (24) |
isNat(active(X)) | → | isNat(X) | (38) |
isNat(mark(X)) | → | isNat(X) | (37) |
and(active(X1),X2) | → | and(X1,X2) | (35) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (98) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (69) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (90) |
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (49) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (44) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (73) |
The dependency pairs are split into 0 components.