The rewrite relation of the following TRS is considered.
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U12(tt)) | → | mark(tt) | (2) |
active(U21(tt)) | → | mark(tt) | (3) |
active(U31(tt,N)) | → | mark(N) | (4) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
active(isNat(0)) | → | mark(tt) | (7) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
mark(tt) | → | active(tt) | (13) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
mark(0) | → | active(0) | (22) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
isNat(mark(X)) | → | isNat(X) | (29) |
isNat(active(X)) | → | isNat(X) | (30) |
U21(mark(X)) | → | U21(X) | (31) |
U21(active(X)) | → | U21(X) | (32) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
s(mark(X)) | → | s(X) | (49) |
s(active(X)) | → | s(X) | (50) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (55) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (56) |
mark#(U11(X1,X2)) | → | U11#(mark(X1),X2) | (57) |
isNat#(active(X)) | → | isNat#(X) | (58) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(plus(X1,X2)) | → | plus#(mark(X1),mark(X2)) | (60) |
active#(plus(N,0)) | → | isNat#(N) | (61) |
active#(isNat(0)) | → | mark#(tt) | (62) |
mark#(s(X)) | → | mark#(X) | (63) |
s#(mark(X)) | → | s#(X) | (64) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
U31#(mark(X1),X2) | → | U31#(X1,X2) | (66) |
mark#(0) | → | active#(0) | (67) |
mark#(U21(X)) | → | mark#(X) | (68) |
active#(U41(tt,M,N)) | → | mark#(U42(isNat(N),M,N)) | (69) |
active#(U11(tt,V2)) | → | isNat#(V2) | (70) |
active#(U11(tt,V2)) | → | U12#(isNat(V2)) | (71) |
mark#(U31(X1,X2)) | → | mark#(X1) | (72) |
mark#(U42(X1,X2,X3)) | → | U42#(mark(X1),X2,X3) | (73) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (74) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (75) |
U21#(active(X)) | → | U21#(X) | (76) |
U12#(mark(X)) | → | U12#(X) | (77) |
mark#(plus(X1,X2)) | → | mark#(X1) | (78) |
mark#(s(X)) | → | s#(mark(X)) | (79) |
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (80) |
active#(U42(tt,M,N)) | → | mark#(s(plus(N,M))) | (81) |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (82) |
U42#(X1,X2,active(X3)) | → | U42#(X1,X2,X3) | (83) |
mark#(U31(X1,X2)) | → | U31#(mark(X1),X2) | (84) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (85) |
active#(plus(N,s(M))) | → | isNat#(M) | (86) |
mark#(U21(X)) | → | U21#(mark(X)) | (87) |
active#(plus(N,s(M))) | → | U41#(isNat(M),M,N) | (88) |
active#(U31(tt,N)) | → | mark#(N) | (89) |
active#(isNat(plus(V1,V2))) | → | U11#(isNat(V1),V2) | (90) |
active#(plus(N,0)) | → | U31#(isNat(N),N) | (91) |
mark#(U21(X)) | → | active#(U21(mark(X))) | (92) |
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U21#(mark(X)) | → | U21#(X) | (94) |
active#(isNat(plus(V1,V2))) | → | isNat#(V1) | (95) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
s#(active(X)) | → | s#(X) | (97) |
active#(U42(tt,M,N)) | → | s#(plus(N,M)) | (98) |
mark#(U42(X1,X2,X3)) | → | mark#(X1) | (99) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
U12#(active(X)) | → | U12#(X) | (101) |
active#(U41(tt,M,N)) | → | U42#(isNat(N),M,N) | (102) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (103) |
active#(isNat(s(V1))) | → | U21#(isNat(V1)) | (104) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (105) |
mark#(s(X)) | → | active#(s(mark(X))) | (106) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (107) |
U31#(X1,active(X2)) | → | U31#(X1,X2) | (108) |
mark#(U12(X)) | → | U12#(mark(X)) | (109) |
active#(U21(tt)) | → | mark#(tt) | (110) |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (111) |
active#(plus(N,0)) | → | mark#(U31(isNat(N),N)) | (112) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U41(X1,X2,X3)) | → | U41#(mark(X1),X2,X3) | (117) |
U42#(X1,X2,mark(X3)) | → | U42#(X1,X2,X3) | (118) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (120) |
mark#(U12(X)) | → | active#(U12(mark(X))) | (121) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (123) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (124) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (125) |
mark#(plus(X1,X2)) | → | mark#(X2) | (126) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (127) |
active#(isNat(s(V1))) | → | isNat#(V1) | (128) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (129) |
isNat#(mark(X)) | → | isNat#(X) | (130) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U12(tt)) | → | mark#(tt) | (132) |
U31#(X1,mark(X2)) | → | U31#(X1,X2) | (133) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (134) |
active#(U42(tt,M,N)) | → | plus#(N,M) | (135) |
U31#(active(X1),X2) | → | U31#(X1,X2) | (136) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(U41(tt,M,N)) | → | isNat#(N) | (138) |
mark#(tt) | → | active#(tt) | (139) |
The dependency pairs are split into 10 components.
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
mark#(U42(X1,X2,X3)) | → | mark#(X1) | (99) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
mark#(U21(X)) | → | active#(U21(mark(X))) | (92) |
active#(U31(tt,N)) | → | mark#(N) | (89) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
mark#(plus(X1,X2)) | → | mark#(X2) | (126) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (125) |
active#(U42(tt,M,N)) | → | mark#(s(plus(N,M))) | (81) |
mark#(U12(X)) | → | active#(U12(mark(X))) | (121) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
mark#(plus(X1,X2)) | → | mark#(X1) | (78) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
mark#(U31(X1,X2)) | → | mark#(X1) | (72) |
mark#(U12(X)) | → | mark#(X) | (116) |
active#(U41(tt,M,N)) | → | mark#(U42(isNat(N),M,N)) | (69) |
mark#(U21(X)) | → | mark#(X) | (68) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
active#(plus(N,0)) | → | mark#(U31(isNat(N),N)) | (112) |
mark#(s(X)) | → | mark#(X) | (63) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(s(X)) | → | active#(s(mark(X))) | (106) |
[U21(x1)] | = | 1 |
[U11(x1, x2)] | = | 30616 |
[s(x1)] | = | 30615 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | 30616 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 28101 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 30616 |
[0] | = | 3 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[isNat(x1)] | = | 30616 |
[plus(x1, x2)] | = | 30616 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 2 |
[U31(x1, x2)] | = | 30616 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | 30616 |
[U31#(x1, x2)] | = | 0 |
s(active(X)) | → | s(X) | (50) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
U21(active(X)) | → | U21(X) | (32) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
U21(mark(X)) | → | U21(X) | (31) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
mark#(U21(X)) | → | active#(U21(mark(X))) | (92) |
mark#(U12(X)) | → | active#(U12(mark(X))) | (121) |
mark#(s(X)) | → | active#(s(mark(X))) | (106) |
The dependency pairs are split into 1 component.
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (125) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
active#(U31(tt,N)) | → | mark#(N) | (89) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(plus(X1,X2)) | → | mark#(X2) | (126) |
mark#(plus(X1,X2)) | → | mark#(X1) | (78) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U42(X1,X2,X3)) | → | mark#(X1) | (99) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
mark#(U31(X1,X2)) | → | mark#(X1) | (72) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
active#(U41(tt,M,N)) | → | mark#(U42(isNat(N),M,N)) | (69) |
active#(plus(N,0)) | → | mark#(U31(isNat(N),N)) | (112) |
mark#(s(X)) | → | mark#(X) | (63) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
active#(U42(tt,M,N)) | → | mark#(s(plus(N,M))) | (81) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | x1 + 29534 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + x2 + x3 + 41124 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 868 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 19496 |
[plus(x1, x2)] | = | x1 + x2 + 31086 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | x1 + x2 + 12457 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 19496 |
[U41(x1, x2, x3)] | = | x1 + x2 + x3 + 41124 |
[U31#(x1, x2)] | = | 0 |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
s(active(X)) | → | s(X) | (50) |
active(U31(tt,N)) | → | mark(N) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U21(tt)) | → | mark(tt) | (3) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
U21(active(X)) | → | U21(X) | (32) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
mark(0) | → | active(0) | (22) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
active(isNat(0)) | → | mark(tt) | (7) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
U21(mark(X)) | → | U21(X) | (31) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
mark(tt) | → | active(tt) | (13) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
active(U12(tt)) | → | mark(tt) | (2) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (125) |
active#(U31(tt,N)) | → | mark#(N) | (89) |
mark#(plus(X1,X2)) | → | mark#(X2) | (126) |
mark#(plus(X1,X2)) | → | mark#(X1) | (78) |
mark#(U42(X1,X2,X3)) | → | mark#(X1) | (99) |
mark#(U31(X1,X2)) | → | mark#(X1) | (72) |
active#(plus(N,0)) | → | mark#(U31(isNat(N),N)) | (112) |
mark#(s(X)) | → | mark#(X) | (63) |
The dependency pairs are split into 1 component.
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
active#(U41(tt,M,N)) | → | mark#(U42(isNat(N),M,N)) | (69) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
active#(U42(tt,M,N)) | → | mark#(s(plus(N,M))) | (81) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 54785 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + x3 + 54785 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | x1 + x2 + 2 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | x1 + x2 + 2 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x3 + 54786 |
[U31#(x1, x2)] | = | 0 |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
s(active(X)) | → | s(X) | (50) |
active(U31(tt,N)) | → | mark(N) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U21(tt)) | → | mark(tt) | (3) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
U21(active(X)) | → | U21(X) | (32) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
mark(0) | → | active(0) | (22) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
active(isNat(0)) | → | mark(tt) | (7) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
U21(mark(X)) | → | U21(X) | (31) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
mark(tt) | → | active(tt) | (13) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
active(U12(tt)) | → | mark(tt) | (2) |
active#(U41(tt,M,N)) | → | mark#(U42(isNat(N),M,N)) | (69) |
active#(U42(tt,M,N)) | → | mark#(s(plus(N,M))) | (81) |
The dependency pairs are split into 1 component.
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + x3 + 11820 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 45545 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | x1 + x2 + 54787 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | x1 + x2 + 3153 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x3 + 54786 |
[U31#(x1, x2)] | = | 0 |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
s(active(X)) | → | s(X) | (50) |
active(U31(tt,N)) | → | mark(N) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U21(tt)) | → | mark(tt) | (3) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
U21(active(X)) | → | U21(X) | (32) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
mark(0) | → | active(0) | (22) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
active(isNat(0)) | → | mark(tt) | (7) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
U21(mark(X)) | → | U21(X) | (31) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
mark(tt) | → | active(tt) | (13) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
active(U12(tt)) | → | mark(tt) | (2) |
active#(plus(N,s(M))) | → | mark#(U41(isNat(M),M,N)) | (115) |
The dependency pairs are split into 1 component.
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x3 + 19622 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | 0 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 1 |
[U31#(x1, x2)] | = | 0 |
s(active(X)) | → | s(X) | (50) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
U21(active(X)) | → | U21(X) | (32) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
isNat(active(X)) | → | isNat(X) | (30) |
U21(mark(X)) | → | U21(X) | (31) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (59) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (119) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 2 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x3 + 3 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | 0 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + x3 + 2 |
[U31#(x1, x2)] | = | 0 |
s(active(X)) | → | s(X) | (50) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
U21(active(X)) | → | U21(X) | (32) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
isNat(active(X)) | → | isNat(X) | (30) |
U21(mark(X)) | → | U21(X) | (31) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (113) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
[U21(x1)] | = | x1 + 0 |
[U11(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x3 + 9049 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 0 |
[plus(x1, x2)] | = | x2 + 23641 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 9048 |
[U31#(x1, x2)] | = | 0 |
s(active(X)) | → | s(X) | (50) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
U21(active(X)) | → | U21(X) | (32) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
isNat(active(X)) | → | isNat(X) | (30) |
U21(mark(X)) | → | U21(X) | (31) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (96) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U21(X)) | → | mark#(X) | (68) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 0 |
[s(x1)] | = | x1 + 2 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x2 + x3 + 3 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 0 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | x2 + 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + x3 + 3 |
[U31#(x1, x2)] | = | 0 |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
s(active(X)) | → | s(X) | (50) |
active(U31(tt,N)) | → | mark(N) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U21(tt)) | → | mark(tt) | (3) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
U21(active(X)) | → | U21(X) | (32) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
mark(0) | → | active(0) | (22) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
active(isNat(0)) | → | mark(tt) | (7) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
U21(mark(X)) | → | U21(X) | (31) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
mark(tt) | → | active(tt) | (13) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
active(U12(tt)) | → | mark(tt) | (2) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNat(V1),V2)) | (131) |
mark#(U21(X)) | → | mark#(X) | (68) |
active#(isNat(s(V1))) | → | mark#(U21(isNat(V1))) | (122) |
The dependency pairs are split into 1 component.
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 3 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x2 + x3 + 4 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | x1 + 1 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | x1 + 1 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 3 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2)] | = | x2 + 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + x3 + 4 |
[U31#(x1, x2)] | = | 0 |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (18) |
s(active(X)) | → | s(X) | (50) |
active(U31(tt,N)) | → | mark(N) | (4) |
mark(isNat(X)) | → | active(isNat(X)) | (15) |
active(isNat(plus(V1,V2))) | → | mark(U11(isNat(V1),V2)) | (8) |
plus(X1,active(X2)) | → | plus(X1,X2) | (54) |
active(U11(tt,V2)) | → | mark(U12(isNat(V2))) | (1) |
active(U21(tt)) | → | mark(tt) | (3) |
mark(U21(X)) | → | active(U21(mark(X))) | (16) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (21) |
U31(X1,active(X2)) | → | U31(X1,X2) | (36) |
U11(X1,active(X2)) | → | U11(X1,X2) | (26) |
mark(U42(X1,X2,X3)) | → | active(U42(mark(X1),X2,X3)) | (19) |
U21(active(X)) | → | U21(X) | (32) |
mark(U31(X1,X2)) | → | active(U31(mark(X1),X2)) | (17) |
U12(mark(X)) | → | U12(X) | (27) |
U31(X1,mark(X2)) | → | U31(X1,X2) | (34) |
mark(0) | → | active(0) | (22) |
U12(active(X)) | → | U12(X) | (28) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (44) |
active(U41(tt,M,N)) | → | mark(U42(isNat(N),M,N)) | (5) |
U31(mark(X1),X2) | → | U31(X1,X2) | (33) |
active(plus(N,0)) | → | mark(U31(isNat(N),N)) | (10) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (39) |
active(isNat(0)) | → | mark(tt) | (7) |
mark(s(X)) | → | active(s(mark(X))) | (20) |
U11(active(X1),X2) | → | U11(X1,X2) | (25) |
s(mark(X)) | → | s(X) | (49) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (52) |
isNat(active(X)) | → | isNat(X) | (30) |
mark(U12(X)) | → | active(U12(mark(X))) | (14) |
U21(mark(X)) | → | U21(X) | (31) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (12) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (45) |
U11(mark(X1),X2) | → | U11(X1,X2) | (23) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (24) |
active(plus(N,s(M))) | → | mark(U41(isNat(M),M,N)) | (11) |
active(isNat(s(V1))) | → | mark(U21(isNat(V1))) | (9) |
mark(tt) | → | active(tt) | (13) |
plus(mark(X1),X2) | → | plus(X1,X2) | (51) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (40) |
active(U42(tt,M,N)) | → | mark(s(plus(N,M))) | (6) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (38) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (48) |
plus(active(X1),X2) | → | plus(X1,X2) | (53) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (47) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (37) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (41) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (42) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (46) |
U31(active(X1),X2) | → | U31(X1,X2) | (35) |
isNat(mark(X)) | → | isNat(X) | (29) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (43) |
active(U12(tt)) | → | mark(tt) | (2) |
mark#(isNat(X)) | → | active#(isNat(X)) | (137) |
active#(U11(tt,V2)) | → | mark#(U12(isNat(V2))) | (65) |
mark#(U12(X)) | → | mark#(X) | (116) |
mark#(U11(X1,X2)) | → | mark#(X1) | (100) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (114) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (97) |
s#(mark(X)) | → | s#(X) | (64) |
[U21(x1)] | = | x1 + 31320 |
[U11(x1, x2)] | = | x1 + 1894 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 2699 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 19098 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 31322 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | x1 + 31319 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 1734 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
s#(active(X)) | → | s#(X) | (97) |
s#(mark(X)) | → | s#(X) | (64) |
The dependency pairs are split into 0 components.
U31#(active(X1),X2) | → | U31#(X1,X2) | (136) |
U31#(X1,mark(X2)) | → | U31#(X1,X2) | (133) |
U31#(mark(X1),X2) | → | U31#(X1,X2) | (66) |
U31#(X1,active(X2)) | → | U31#(X1,X2) | (108) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x2 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 1 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 2 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + 1 |
[U31#(x1, x2)] | = | x1 + x2 + 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U31#(active(X1),X2) | → | U31#(X1,X2) | (136) |
U31#(X1,mark(X2)) | → | U31#(X1,X2) | (133) |
U31#(mark(X1),X2) | → | U31#(X1,X2) | (66) |
U31#(X1,active(X2)) | → | U31#(X1,X2) | (108) |
The dependency pairs are split into 0 components.
plus#(X1,active(X2)) | → | plus#(X1,X2) | (85) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (127) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (120) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (107) |
[U21(x1)] | = | 13704 |
[U11(x1, x2)] | = | 21804 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + x2 + 8684 |
[plus#(x1, x2)] | = | x1 + x2 + 0 |
[U12(x1)] | = | 12384 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 34685 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 13259 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | x1 + 34682 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 3137 |
[U31#(x1, x2)] | = | 0 |
s(active(X)) | → | s(X) | (50) |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
s(mark(X)) | → | s(X) | (49) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (85) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (127) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (120) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (107) |
The dependency pairs are split into 0 components.
U12#(active(X)) | → | U12#(X) | (101) |
U12#(mark(X)) | → | U12#(X) | (77) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 2 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 2 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | x1 + 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 2 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U12#(active(X)) | → | U12#(X) | (101) |
U12#(mark(X)) | → | U12#(X) | (77) |
The dependency pairs are split into 0 components.
isNat#(mark(X)) | → | isNat#(X) | (130) |
isNat#(active(X)) | → | isNat#(X) | (58) |
[U21(x1)] | = | x1 + 2 |
[U11(x1, x2)] | = | x1 + 3 |
[s(x1)] | = | x1 + 3 |
[isNat#(x1)] | = | x1 + 0 |
[U42(x1, x2, x3)] | = | x1 + 2 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 3 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 2 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 2 |
[U41(x1, x2, x3)] | = | x1 + x2 + 2 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
isNat#(mark(X)) | → | isNat#(X) | (130) |
isNat#(active(X)) | → | isNat#(X) | (58) |
The dependency pairs are split into 0 components.
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (103) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (124) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (123) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (74) |
[U21(x1)] | = | x1 + 11452 |
[U11(x1, x2)] | = | x1 + 18243 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 4212 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 815 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 8752 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 45148 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 3507 |
[U11#(x1, x2)] | = | x1 + x2 + 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 27718 |
[U41(x1, x2, x3)] | = | x1 + x2 + 5609 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (103) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (124) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (123) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (74) |
The dependency pairs are split into 0 components.
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (134) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (129) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (75) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (105) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (56) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 2 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 2 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | x1 + x3 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 1 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (134) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (129) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (75) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (56) |
The dependency pairs are split into 1 component.
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (105) |
[U21(x1)] | = | x1 + 767 |
[U11(x1, x2)] | = | x1 + 24227 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 3062 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 14212 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 12341 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 15093 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 15091 |
[U41#(x1, x2, x3)] | = | x2 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 2802 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (105) |
The dependency pairs are split into 0 components.
U42#(X1,X2,active(X3)) | → | U42#(X1,X2,X3) | (83) |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (82) |
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (80) |
U42#(X1,X2,mark(X3)) | → | U42#(X1,X2,X3) | (118) |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (111) |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (55) |
[U21(x1)] | = | x1 + 291 |
[U11(x1, x2)] | = | x1 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 8842 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 615 |
[U42#(x1, x2, x3)] | = | x3 + 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 15093 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 8501 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U42#(X1,X2,active(X3)) | → | U42#(X1,X2,X3) | (83) |
U42#(X1,X2,mark(X3)) | → | U42#(X1,X2,X3) | (118) |
The dependency pairs are split into 1 component.
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (80) |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (82) |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (111) |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (55) |
[U21(x1)] | = | x1 + 49184 |
[U11(x1, x2)] | = | x1 + 27667 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 28541 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 1 |
[U42#(x1, x2, x3)] | = | x1 + x2 + 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 35205 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 49186 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2)] | = | 49184 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 1602 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (80) |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (82) |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (111) |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (55) |
The dependency pairs are split into 0 components.
U21#(mark(X)) | → | U21#(X) | (94) |
U21#(active(X)) | → | U21#(X) | (76) |
[U21(x1)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + 1 |
[s(x1)] | = | x1 + 2 |
[isNat#(x1)] | = | 0 |
[U42(x1, x2, x3)] | = | x1 + 3 |
[plus#(x1, x2)] | = | 0 |
[U12(x1)] | = | 2 |
[U42#(x1, x2, x3)] | = | 0 |
[U12#(x1)] | = | 0 |
[mark#(x1)] | = | 1 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 24329 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 24327 |
[U31(x1, x2)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1)] | = | x1 + 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + 1 |
[U31#(x1, x2)] | = | 0 |
U12(mark(X)) | → | U12(X) | (27) |
U12(active(X)) | → | U12(X) | (28) |
U21#(mark(X)) | → | U21#(X) | (94) |
U21#(active(X)) | → | U21#(X) | (76) |
The dependency pairs are split into 0 components.