The rewrite relation of the following TRS is considered.
U11(tt,N) | → | activate(N) | (1) |
U21(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
U31(tt) | → | 0 | (3) |
U41(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
and(tt,X) | → | activate(X) | (5) |
isNat(n__0) | → | tt | (6) |
isNat(n__plus(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (7) |
isNat(n__s(V1)) | → | isNat(activate(V1)) | (8) |
isNat(n__x(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (9) |
plus(N,0) | → | U11(isNat(N),N) | (10) |
plus(N,s(M)) | → | U21(and(isNat(M),n__isNat(N)),M,N) | (11) |
x(N,0) | → | U31(isNat(N)) | (12) |
x(N,s(M)) | → | U41(and(isNat(M),n__isNat(N)),M,N) | (13) |
0 | → | n__0 | (14) |
plus(X1,X2) | → | n__plus(X1,X2) | (15) |
isNat(X) | → | n__isNat(X) | (16) |
s(X) | → | n__s(X) | (17) |
x(X1,X2) | → | n__x(X1,X2) | (18) |
activate(n__0) | → | 0 | (19) |
activate(n__plus(X1,X2)) | → | plus(activate(X1),activate(X2)) | (20) |
activate(n__isNat(X)) | → | isNat(X) | (21) |
activate(n__s(X)) | → | s(activate(X)) | (22) |
activate(n__x(X1,X2)) | → | x(activate(X1),activate(X2)) | (23) |
activate(X) | → | X | (24) |
U21#(tt,M,N) | → | plus#(activate(N),activate(M)) | (25) |
and#(tt,X) | → | activate#(X) | (26) |
U11#(tt,N) | → | activate#(N) | (27) |
U41#(tt,M,N) | → | activate#(N) | (28) |
U41#(tt,M,N) | → | activate#(M) | (29) |
isNat#(n__s(V1)) | → | activate#(V1) | (30) |
U41#(tt,M,N) | → | plus#(x(activate(N),activate(M)),activate(N)) | (31) |
x#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (32) |
U41#(tt,M,N) | → | activate#(N) | (28) |
plus#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (33) |
isNat#(n__x(V1,V2)) | → | isNat#(activate(V1)) | (34) |
isNat#(n__x(V1,V2)) | → | activate#(V2) | (35) |
isNat#(n__plus(V1,V2)) | → | isNat#(activate(V1)) | (36) |
isNat#(n__plus(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (37) |
plus#(N,s(M)) | → | U21#(and(isNat(M),n__isNat(N)),M,N) | (38) |
activate#(n__s(X)) | → | activate#(X) | (39) |
plus#(N,s(M)) | → | isNat#(M) | (40) |
activate#(n__s(X)) | → | s#(activate(X)) | (41) |
isNat#(n__plus(V1,V2)) | → | activate#(V1) | (42) |
activate#(n__plus(X1,X2)) | → | plus#(activate(X1),activate(X2)) | (43) |
x#(N,s(M)) | → | isNat#(M) | (44) |
U41#(tt,M,N) | → | x#(activate(N),activate(M)) | (45) |
isNat#(n__x(V1,V2)) | → | activate#(V1) | (46) |
activate#(n__isNat(X)) | → | isNat#(X) | (47) |
x#(N,s(M)) | → | U41#(and(isNat(M),n__isNat(N)),M,N) | (48) |
plus#(N,0) | → | isNat#(N) | (49) |
activate#(n__plus(X1,X2)) | → | activate#(X2) | (50) |
U31#(tt) | → | 0# | (51) |
plus#(N,0) | → | U11#(isNat(N),N) | (52) |
activate#(n__x(X1,X2)) | → | activate#(X2) | (53) |
activate#(n__0) | → | 0# | (54) |
x#(N,0) | → | isNat#(N) | (55) |
isNat#(n__plus(V1,V2)) | → | activate#(V2) | (56) |
isNat#(n__s(V1)) | → | isNat#(activate(V1)) | (57) |
activate#(n__plus(X1,X2)) | → | activate#(X1) | (58) |
activate#(n__x(X1,X2)) | → | activate#(X1) | (59) |
U21#(tt,M,N) | → | activate#(N) | (60) |
U21#(tt,M,N) | → | s#(plus(activate(N),activate(M))) | (61) |
isNat#(n__x(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (62) |
activate#(n__x(X1,X2)) | → | x#(activate(X1),activate(X2)) | (63) |
U21#(tt,M,N) | → | activate#(M) | (64) |
x#(N,0) | → | U31#(isNat(N)) | (65) |
The dependency pairs are split into 1 component.
isNat#(n__plus(V1,V2)) | → | activate#(V1) | (42) |
U21#(tt,M,N) | → | activate#(M) | (64) |
plus#(N,s(M)) | → | isNat#(M) | (40) |
activate#(n__x(X1,X2)) | → | x#(activate(X1),activate(X2)) | (63) |
activate#(n__s(X)) | → | activate#(X) | (39) |
plus#(N,s(M)) | → | U21#(and(isNat(M),n__isNat(N)),M,N) | (38) |
isNat#(n__x(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (62) |
isNat#(n__plus(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (37) |
U21#(tt,M,N) | → | activate#(N) | (60) |
isNat#(n__plus(V1,V2)) | → | isNat#(activate(V1)) | (36) |
activate#(n__x(X1,X2)) | → | activate#(X1) | (59) |
activate#(n__plus(X1,X2)) | → | activate#(X1) | (58) |
isNat#(n__s(V1)) | → | isNat#(activate(V1)) | (57) |
isNat#(n__plus(V1,V2)) | → | activate#(V2) | (56) |
isNat#(n__x(V1,V2)) | → | activate#(V2) | (35) |
isNat#(n__x(V1,V2)) | → | isNat#(activate(V1)) | (34) |
plus#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (33) |
x#(N,0) | → | isNat#(N) | (55) |
activate#(n__x(X1,X2)) | → | activate#(X2) | (53) |
U41#(tt,M,N) | → | activate#(N) | (28) |
x#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (32) |
plus#(N,0) | → | U11#(isNat(N),N) | (52) |
U41#(tt,M,N) | → | plus#(x(activate(N),activate(M)),activate(N)) | (31) |
activate#(n__plus(X1,X2)) | → | activate#(X2) | (50) |
plus#(N,0) | → | isNat#(N) | (49) |
x#(N,s(M)) | → | U41#(and(isNat(M),n__isNat(N)),M,N) | (48) |
isNat#(n__s(V1)) | → | activate#(V1) | (30) |
activate#(n__isNat(X)) | → | isNat#(X) | (47) |
U41#(tt,M,N) | → | activate#(M) | (29) |
U41#(tt,M,N) | → | activate#(N) | (28) |
isNat#(n__x(V1,V2)) | → | activate#(V1) | (46) |
U41#(tt,M,N) | → | x#(activate(N),activate(M)) | (45) |
x#(N,s(M)) | → | isNat#(M) | (44) |
U11#(tt,N) | → | activate#(N) | (27) |
and#(tt,X) | → | activate#(X) | (26) |
U21#(tt,M,N) | → | plus#(activate(N),activate(M)) | (25) |
activate#(n__plus(X1,X2)) | → | plus#(activate(X1),activate(X2)) | (43) |
[0#] | = | 0 |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 4, x3 + 0, 0) |
[U11(x1, x2)] | = | max(x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | x1 + 2 |
[activate(x1)] | = | x1 + 0 |
[and(x1, x2)] | = | max(x2 + 0, 0) |
[plus#(x1, x2)] | = | max(x1 + 2, x2 + 4, 0) |
[activate#(x1)] | = | x1 + 2 |
[x(x1, x2)] | = | max(x1 + 31116, x2 + 31117, 0) |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 17069 |
[x#(x1, x2)] | = | max(x1 + 31118, x2 + 31119, 0) |
[s#(x1)] | = | 0 |
[n__isNat(x1)] | = | x1 + 0 |
[n__plus(x1, x2)] | = | max(x1 + 0, x2 + 4, 0) |
[n__0] | = | 17069 |
[isNat(x1)] | = | x1 + 0 |
[n__x(x1, x2)] | = | max(x1 + 31116, x2 + 31117, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 4, 0) |
[U11#(x1, x2)] | = | max(x1 + 2, x2 + 2, 0) |
[U31(x1)] | = | 17069 |
[U41#(x1, x2, x3)] | = | max(x1 + 31117, x2 + 31119, x3 + 31118, 0) |
[U21#(x1, x2, x3)] | = | max(x1 + 2, x2 + 4, x3 + 2, 0) |
[tt] | = | 3 |
[U41(x1, x2, x3)] | = | max(x1 + 1, x2 + 31117, x3 + 31116, 0) |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | max(x1 + 1, x2 + 2, 0) |
x(X1,X2) | → | n__x(X1,X2) | (18) |
U41(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
plus(X1,X2) | → | n__plus(X1,X2) | (15) |
isNat(n__s(V1)) | → | isNat(activate(V1)) | (8) |
U11(tt,N) | → | activate(N) | (1) |
U31(tt) | → | 0 | (3) |
isNat(X) | → | n__isNat(X) | (16) |
activate(n__isNat(X)) | → | isNat(X) | (21) |
activate(n__0) | → | 0 | (19) |
s(X) | → | n__s(X) | (17) |
activate(n__s(X)) | → | s(activate(X)) | (22) |
and(tt,X) | → | activate(X) | (5) |
plus(N,0) | → | U11(isNat(N),N) | (10) |
isNat(n__plus(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (7) |
activate(n__plus(X1,X2)) | → | plus(activate(X1),activate(X2)) | (20) |
0 | → | n__0 | (14) |
x(N,0) | → | U31(isNat(N)) | (12) |
activate(n__x(X1,X2)) | → | x(activate(X1),activate(X2)) | (23) |
activate(X) | → | X | (24) |
plus(N,s(M)) | → | U21(and(isNat(M),n__isNat(N)),M,N) | (11) |
isNat(n__x(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (9) |
x(N,s(M)) | → | U41(and(isNat(M),n__isNat(N)),M,N) | (13) |
isNat(n__0) | → | tt | (6) |
U21(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
U21#(tt,M,N) | → | activate#(M) | (64) |
plus#(N,s(M)) | → | isNat#(M) | (40) |
isNat#(n__x(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (62) |
isNat#(n__plus(V1,V2)) | → | and#(isNat(activate(V1)),n__isNat(activate(V2))) | (37) |
activate#(n__x(X1,X2)) | → | activate#(X1) | (59) |
isNat#(n__plus(V1,V2)) | → | activate#(V2) | (56) |
isNat#(n__x(V1,V2)) | → | activate#(V2) | (35) |
isNat#(n__x(V1,V2)) | → | isNat#(activate(V1)) | (34) |
x#(N,0) | → | isNat#(N) | (55) |
activate#(n__x(X1,X2)) | → | activate#(X2) | (53) |
U41#(tt,M,N) | → | activate#(N) | (28) |
x#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (32) |
activate#(n__plus(X1,X2)) | → | activate#(X2) | (50) |
U41#(tt,M,N) | → | activate#(M) | (29) |
U41#(tt,M,N) | → | activate#(N) | (28) |
isNat#(n__x(V1,V2)) | → | activate#(V1) | (46) |
x#(N,s(M)) | → | isNat#(M) | (44) |
The dependency pairs are split into 1 component.
U41#(tt,M,N) | → | x#(activate(N),activate(M)) | (45) |
U41#(tt,M,N) | → | plus#(x(activate(N),activate(M)),activate(N)) | (31) |
isNat#(n__s(V1)) | → | activate#(V1) | (30) |
isNat#(n__s(V1)) | → | isNat#(activate(V1)) | (57) |
U11#(tt,N) | → | activate#(N) | (27) |
activate#(n__isNat(X)) | → | isNat#(X) | (47) |
activate#(n__s(X)) | → | activate#(X) | (39) |
and#(tt,X) | → | activate#(X) | (26) |
plus#(N,0) | → | isNat#(N) | (49) |
plus#(N,0) | → | U11#(isNat(N),N) | (52) |
isNat#(n__plus(V1,V2)) | → | activate#(V1) | (42) |
isNat#(n__plus(V1,V2)) | → | isNat#(activate(V1)) | (36) |
activate#(n__plus(X1,X2)) | → | activate#(X1) | (58) |
activate#(n__plus(X1,X2)) | → | plus#(activate(X1),activate(X2)) | (43) |
activate#(n__x(X1,X2)) | → | x#(activate(X1),activate(X2)) | (63) |
plus#(N,s(M)) | → | and#(isNat(M),n__isNat(N)) | (33) |
plus#(N,s(M)) | → | U21#(and(isNat(M),n__isNat(N)),M,N) | (38) |
x#(N,s(M)) | → | U41#(and(isNat(M),n__isNat(N)),M,N) | (48) |
U21#(tt,M,N) | → | activate#(N) | (60) |
U21#(tt,M,N) | → | plus#(activate(N),activate(M)) | (25) |
π(U11) | = | 2 |
π(isNat#) | = | 1 |
π(activate) | = | 1 |
π(and) | = | 2 |
π(plus#) | = | 1 |
π(activate#) | = | 1 |
π(s#) | = | 1 |
π(n__isNat) | = | 1 |
π(isNat) | = | 1 |
π(U11#) | = | 2 |
π(U21#) | = | 3 |
π(and#) | = | 2 |
prec(0#) | = | 0 | status(0#) | = | [] | list-extension(0#) | = | Lex | ||
prec(U21) | = | 4 | status(U21) | = | [3, 2, 1] | list-extension(U21) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(x) | = | 8 | status(x) | = | [2, 1] | list-extension(x) | = | Lex | ||
prec(n__s) | = | 1 | status(n__s) | = | [1] | list-extension(n__s) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(x#) | = | 8 | status(x#) | = | [2, 1] | list-extension(x#) | = | Lex | ||
prec(n__plus) | = | 4 | status(n__plus) | = | [1, 2] | list-extension(n__plus) | = | Lex | ||
prec(n__0) | = | 0 | status(n__0) | = | [] | list-extension(n__0) | = | Lex | ||
prec(n__x) | = | 8 | status(n__x) | = | [2, 1] | list-extension(n__x) | = | Lex | ||
prec(plus) | = | 4 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(U31) | = | 0 | status(U31) | = | [1] | list-extension(U31) | = | Lex | ||
prec(U41#) | = | 8 | status(U41#) | = | [2, 3] | list-extension(U41#) | = | Lex | ||
prec(tt) | = | 0 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U41) | = | 8 | status(U41) | = | [2, 3, 1] | list-extension(U41) | = | Lex | ||
prec(U31#) | = | 0 | status(U31#) | = | [] | list-extension(U31#) | = | Lex |
[0#] | = | 0 |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__0] | = | 0 |
[n__x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U31(x1)] | = | x1 + 0 |
[U41#(x1, x2, x3)] | = | max(x2 + 0, x3 + 0, 0) |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U31#(x1)] | = | 0 |
x(X1,X2) | → | n__x(X1,X2) | (18) |
U41(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
plus(X1,X2) | → | n__plus(X1,X2) | (15) |
isNat(n__s(V1)) | → | isNat(activate(V1)) | (8) |
U11(tt,N) | → | activate(N) | (1) |
U31(tt) | → | 0 | (3) |
isNat(X) | → | n__isNat(X) | (16) |
activate(n__isNat(X)) | → | isNat(X) | (21) |
activate(n__0) | → | 0 | (19) |
s(X) | → | n__s(X) | (17) |
activate(n__s(X)) | → | s(activate(X)) | (22) |
and(tt,X) | → | activate(X) | (5) |
plus(N,0) | → | U11(isNat(N),N) | (10) |
isNat(n__plus(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (7) |
activate(n__plus(X1,X2)) | → | plus(activate(X1),activate(X2)) | (20) |
0 | → | n__0 | (14) |
x(N,0) | → | U31(isNat(N)) | (12) |
activate(n__x(X1,X2)) | → | x(activate(X1),activate(X2)) | (23) |
activate(X) | → | X | (24) |
plus(N,s(M)) | → | U21(and(isNat(M),n__isNat(N)),M,N) | (11) |
isNat(n__x(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (9) |
x(N,s(M)) | → | U41(and(isNat(M),n__isNat(N)),M,N) | (13) |
isNat(n__0) | → | tt | (6) |
U21(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
isNat#(n__s(V1)) | → | activate#(V1) | (30) |
isNat#(n__s(V1)) | → | isNat#(activate(V1)) | (57) |
activate#(n__s(X)) | → | activate#(X) | (39) |
isNat#(n__plus(V1,V2)) | → | activate#(V1) | (42) |
isNat#(n__plus(V1,V2)) | → | isNat#(activate(V1)) | (36) |
activate#(n__plus(X1,X2)) | → | activate#(X1) | (58) |
activate#(n__plus(X1,X2)) | → | plus#(activate(X1),activate(X2)) | (43) |
x#(N,s(M)) | → | U41#(and(isNat(M),n__isNat(N)),M,N) | (48) |
The dependency pairs are split into 1 component.
plus#(N,s(M)) | → | U21#(and(isNat(M),n__isNat(N)),M,N) | (38) |
U21#(tt,M,N) | → | plus#(activate(N),activate(M)) | (25) |
π(U11) | = | 2 |
π(isNat#) | = | 1 |
π(activate) | = | 1 |
π(and) | = | 2 |
π(activate#) | = | 1 |
π(s#) | = | 1 |
π(n__isNat) | = | 1 |
π(isNat) | = | 1 |
π(U11#) | = | 2 |
π(and#) | = | 2 |
prec(0#) | = | 0 | status(0#) | = | [] | list-extension(0#) | = | Lex | ||
prec(U21) | = | 3 | status(U21) | = | [3, 2, 1] | list-extension(U21) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(plus#) | = | 2 | status(plus#) | = | [1, 2] | list-extension(plus#) | = | Lex | ||
prec(x) | = | 8 | status(x) | = | [2, 1] | list-extension(x) | = | Lex | ||
prec(n__s) | = | 1 | status(n__s) | = | [1] | list-extension(n__s) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(x#) | = | 8 | status(x#) | = | [2, 1] | list-extension(x#) | = | Lex | ||
prec(n__plus) | = | 3 | status(n__plus) | = | [1, 2] | list-extension(n__plus) | = | Lex | ||
prec(n__0) | = | 0 | status(n__0) | = | [] | list-extension(n__0) | = | Lex | ||
prec(n__x) | = | 8 | status(n__x) | = | [2, 1] | list-extension(n__x) | = | Lex | ||
prec(plus) | = | 3 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(U31) | = | 0 | status(U31) | = | [1] | list-extension(U31) | = | Lex | ||
prec(U41#) | = | 8 | status(U41#) | = | [2, 3] | list-extension(U41#) | = | Lex | ||
prec(U21#) | = | 2 | status(U21#) | = | [3, 2, 1] | list-extension(U21#) | = | Lex | ||
prec(tt) | = | 0 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U41) | = | 8 | status(U41) | = | [2, 3, 1] | list-extension(U41) | = | Lex | ||
prec(U31#) | = | 0 | status(U31#) | = | [] | list-extension(U31#) | = | Lex |
[0#] | = | 0 |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[plus#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__s(x1)] | = | x1 + 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[n__0] | = | 0 |
[n__x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U31(x1)] | = | x1 + 0 |
[U41#(x1, x2, x3)] | = | max(x2 + 0, x3 + 0, 0) |
[U21#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U31#(x1)] | = | 0 |
x(X1,X2) | → | n__x(X1,X2) | (18) |
U41(tt,M,N) | → | plus(x(activate(N),activate(M)),activate(N)) | (4) |
plus(X1,X2) | → | n__plus(X1,X2) | (15) |
isNat(n__s(V1)) | → | isNat(activate(V1)) | (8) |
U11(tt,N) | → | activate(N) | (1) |
U31(tt) | → | 0 | (3) |
isNat(X) | → | n__isNat(X) | (16) |
activate(n__isNat(X)) | → | isNat(X) | (21) |
activate(n__0) | → | 0 | (19) |
s(X) | → | n__s(X) | (17) |
activate(n__s(X)) | → | s(activate(X)) | (22) |
and(tt,X) | → | activate(X) | (5) |
plus(N,0) | → | U11(isNat(N),N) | (10) |
isNat(n__plus(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (7) |
activate(n__plus(X1,X2)) | → | plus(activate(X1),activate(X2)) | (20) |
0 | → | n__0 | (14) |
x(N,0) | → | U31(isNat(N)) | (12) |
activate(n__x(X1,X2)) | → | x(activate(X1),activate(X2)) | (23) |
activate(X) | → | X | (24) |
plus(N,s(M)) | → | U21(and(isNat(M),n__isNat(N)),M,N) | (11) |
isNat(n__x(V1,V2)) | → | and(isNat(activate(V1)),n__isNat(activate(V2))) | (9) |
x(N,s(M)) | → | U41(and(isNat(M),n__isNat(N)),M,N) | (13) |
isNat(n__0) | → | tt | (6) |
U21(tt,M,N) | → | s(plus(activate(N),activate(M))) | (2) |
plus#(N,s(M)) | → | U21#(and(isNat(M),n__isNat(N)),M,N) | (38) |
U21#(tt,M,N) | → | plus#(activate(N),activate(M)) | (25) |
The dependency pairs are split into 0 components.