The rewrite relation of the following TRS is considered.
There are 243 ruless (increase limit for explicit display).
The evaluation strategy is innermost.There are 383 ruless (increase limit for explicit display).
The dependency pairs are split into 38 components.
There are 109 ruless (increase limit for explicit display).
We restrict the rewrite rules to the following usable rules of the DP problem.
There are 239 ruless (increase limit for explicit display).
[active#(x1)] | = | x1 |
[U101(x1, x2, x3)] | = | 2 |
[U102(x1, x2, x3)] | = | 2 |
[U103(x1, x2, x3)] | = | 2 |
[U104(x1, x2, x3)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U16(x1)] | = | -2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U23(x1)] | = | 0 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | 2 |
[U35(x1, x2)] | = | 2 |
[U36(x1)] | = | 0 |
[U41(x1, x2)] | = | 2 |
[U42(x1)] | = | 2 |
[U51(x1)] | = | -2 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U91(x1, x2)] | = | 2 |
[U92(x1)] | = | -2 |
[plus(x1, x2)] | = | 2 |
[s(x1)] | = | -2 |
[x(x1, x2)] | = | 2 |
[mark(x1)] | = | 2 |
[active(x1)] | = | -2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
There are 156 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairsmark#(U16(X)) | → | active#(U16(mark(X))) | (394) |
mark#(U23(X)) | → | active#(U23(mark(X))) | (403) |
mark#(U36(X)) | → | active#(U36(mark(X))) | (421) |
mark#(s(X)) | → | active#(s(mark(X))) | (457) |
mark#(U92(X)) | → | active#(U92(mark(X))) | (463) |
mark#(U51(X)) | → | active#(U51(mark(X))) | (430) |
[active#(x1)] | = | -1 + x1 |
[U101(x1, x2, x3)] | = | 2 |
[U102(x1, x2, x3)] | = | 2 |
[U103(x1, x2, x3)] | = | 2 |
[U104(x1, x2, x3)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | 2 |
[U35(x1, x2)] | = | 2 |
[U41(x1, x2)] | = | 2 |
[U42(x1)] | = | -2 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | -2 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U91(x1, x2)] | = | 2 |
[plus(x1, x2)] | = | 2 |
[x(x1, x2)] | = | 2 |
[mark(x1)] | = | -2 |
[active(x1)] | = | 2 + 2 · x1 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[U16(x1)] | = | 2 |
[U23(x1)] | = | 2 |
[U36(x1)] | = | -2 + x1 |
[s(x1)] | = | -2 + x1 |
[U92(x1)] | = | 0 |
[U51(x1)] | = | -2 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
There are 144 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairsmark#(U42(X)) | → | active#(U42(mark(X))) | (427) |
mark#(U62(X)) | → | active#(U62(mark(X))) | (436) |
prec(U102) | = | 4 | stat(U102) | = | lex | |
prec(U101) | = | 4 | stat(U101) | = | lex | |
prec(tt) | = | 3 | stat(tt) | = | mul | |
prec(isNatKind) | = | 3 | stat(isNatKind) | = | lex | |
prec(U103) | = | 4 | stat(U103) | = | lex | |
prec(isNat) | = | 3 | stat(isNat) | = | lex | |
prec(U104) | = | 4 | stat(U104) | = | lex | |
prec(plus) | = | 3 | stat(plus) | = | lex | |
prec(x) | = | 4 | stat(x) | = | lex | |
prec(U71) | = | 1 | stat(U71) | = | lex | |
prec(U72) | = | 0 | stat(U72) | = | mul | |
prec(U81) | = | 3 | stat(U81) | = | lex | |
prec(U82) | = | 3 | stat(U82) | = | lex | |
prec(U83) | = | 3 | stat(U83) | = | lex | |
prec(U84) | = | 3 | stat(U84) | = | lex | |
prec(s) | = | 2 | stat(s) | = | mul | |
prec(U91) | = | 3 | stat(U91) | = | mul | |
prec(U92) | = | 3 | stat(U92) | = | mul | |
prec(0) | = | 3 | stat(0) | = | mul |
π(mark#) | = | 1 |
π(U102) | = | [2,3,1] |
π(active#) | = | 1 |
π(mark) | = | 1 |
π(U101) | = | [2,3,1] |
π(tt) | = | [] |
π(isNatKind) | = | [] |
π(U103) | = | [2,3,1] |
π(isNat) | = | [] |
π(U104) | = | [2,3,1] |
π(plus) | = | [2,1] |
π(x) | = | [2,1] |
π(U11) | = | 1 |
π(U12) | = | 1 |
π(U13) | = | 1 |
π(U14) | = | 1 |
π(U15) | = | 1 |
π(U16) | = | 1 |
π(U21) | = | 1 |
π(U22) | = | 1 |
π(U23) | = | 1 |
π(U31) | = | 1 |
π(U32) | = | 1 |
π(U33) | = | 1 |
π(U34) | = | 1 |
π(U35) | = | 1 |
π(U36) | = | 1 |
π(U41) | = | 1 |
π(U42) | = | 1 |
π(U61) | = | 1 |
π(U62) | = | 1 |
π(U71) | = | [2,1] |
π(U72) | = | [1,2] |
π(U81) | = | [2,3,1] |
π(U82) | = | [2,3,1] |
π(U83) | = | [2,3,1] |
π(U84) | = | [2,3,1] |
π(s) | = | [1] |
π(U91) | = | [1] |
π(U92) | = | [1] |
π(0) | = | [] |
π(U51) | = | 1 |
π(active) | = | 1 |
mark#(U102(X1,X2,X3)) | → | mark#(X1) | (362) |
active#(U104(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (253) |
active#(U71(tt,N)) | → | mark#(U72(isNatKind(N),N)) | (304) |
active#(U72(tt,N)) | → | mark#(N) | (307) |
mark#(U101(X1,X2,X3)) | → | mark#(X1) | (358) |
active#(U84(tt,M,N)) | → | mark#(s(plus(N,M))) | (317) |
active#(plus(N,0)) | → | mark#(U71(isNat(N),N)) | (344) |
active#(plus(N,s(M))) | → | mark#(U81(isNat(M),M,N)) | (347) |
active#(x(N,0)) | → | mark#(U91(isNat(N),N)) | (350) |
active#(x(N,s(M))) | → | mark#(U101(isNat(M),M,N)) | (353) |
mark#(U91(X1,X2)) | → | mark#(X1) | (462) |
mark#(U103(X1,X2,X3)) | → | mark#(X1) | (366) |
mark#(U104(X1,X2,X3)) | → | mark#(X1) | (370) |
mark#(plus(X1,X2)) | → | mark#(X1) | (373) |
mark#(plus(X1,X2)) | → | mark#(X2) | (374) |
mark#(x(X1,X2)) | → | mark#(X1) | (377) |
mark#(x(X1,X2)) | → | mark#(X2) | (378) |
mark#(U71(X1,X2)) | → | mark#(X1) | (441) |
mark#(U72(X1,X2)) | → | mark#(X1) | (444) |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (447) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (450) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (453) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (456) |
mark#(s(X)) | → | mark#(X) | (459) |
mark#(U92(X)) | → | mark#(X) | (465) |
The dependency pairs are split into 1 component.
active#(U101(tt,M,N)) | → | mark#(U102(isNatKind(M),M,N)) | (244) |
mark#(U102(X1,X2,X3)) | → | active#(U102(mark(X1),X2,X3)) | (360) |
active#(U102(tt,M,N)) | → | mark#(U103(isNat(N),M,N)) | (247) |
mark#(U103(X1,X2,X3)) | → | active#(U103(mark(X1),X2,X3)) | (364) |
active#(U103(tt,M,N)) | → | mark#(U104(isNatKind(N),M,N)) | (250) |
mark#(U104(X1,X2,X3)) | → | active#(U104(mark(X1),X2,X3)) | (368) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(U101(X1,X2,X3)) | → | active#(U101(mark(X1),X2,X3)) | (356) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U34(tt,V1,V2)) | → | mark#(U35(isNat(V1),V2)) | (288) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
mark#(U36(X)) | → | mark#(X) | (423) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (371) |
active#(U61(tt,V2)) | → | mark#(U62(isNatKind(V2))) | (300) |
mark#(U62(X)) | → | mark#(X) | (438) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (375) |
active#(U81(tt,M,N)) | → | mark#(U82(isNatKind(M),M,N)) | (308) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (448) |
active#(U82(tt,M,N)) | → | mark#(U83(isNat(N),M,N)) | (311) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (451) |
active#(U83(tt,M,N)) | → | mark#(U84(isNatKind(N),M,N)) | (314) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (454) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
mark#(U61(X1,X2)) | → | active#(U61(mark(X1),X2)) | (433) |
mark#(U61(X1,X2)) | → | mark#(X1) | (435) |
mark#(U71(X1,X2)) | → | active#(U71(mark(X1),X2)) | (439) |
mark#(U72(X1,X2)) | → | active#(U72(mark(X1),X2)) | (442) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (445) |
mark#(U91(X1,X2)) | → | active#(U91(mark(X1),X2)) | (460) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
active#(isNatKind(x(V1,V2))) | → | mark#(U61(isNatKind(V1),V2)) | (341) |
[active#(x1)] | = | x1 |
[U101(x1, x2, x3)] | = | 2 |
[U102(x1, x2, x3)] | = | 2 |
[U103(x1, x2, x3)] | = | 2 |
[U104(x1, x2, x3)] | = | -2 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | 2 |
[U35(x1, x2)] | = | 2 |
[U41(x1, x2)] | = | 2 |
[U61(x1, x2)] | = | 2 |
[U71(x1, x2)] | = | -2 |
[U72(x1, x2)] | = | -2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 0 |
[U91(x1, x2)] | = | 2 |
[plus(x1, x2)] | = | 0 |
[x(x1, x2)] | = | 0 |
[mark(x1)] | = | 2 + 2 · x1 |
[active(x1)] | = | -2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[U16(x1)] | = | 2 |
[U23(x1)] | = | -2 + x1 |
[U36(x1)] | = | -2 |
[U42(x1)] | = | -2 + x1 |
[U62(x1)] | = | -2 + x1 |
[s(x1)] | = | -2 + x1 |
[U92(x1)] | = | -2 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
There are 140 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairsmark#(U104(X1,X2,X3)) | → | active#(U104(mark(X1),X2,X3)) | (368) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (371) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (375) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (454) |
mark#(U71(X1,X2)) | → | active#(U71(mark(X1),X2)) | (439) |
mark#(U72(X1,X2)) | → | active#(U72(mark(X1),X2)) | (442) |
The dependency pairs are split into 1 component.
mark#(U102(X1,X2,X3)) | → | active#(U102(mark(X1),X2,X3)) | (360) |
active#(U101(tt,M,N)) | → | mark#(U102(isNatKind(M),M,N)) | (244) |
active#(U102(tt,M,N)) | → | mark#(U103(isNat(N),M,N)) | (247) |
mark#(U103(X1,X2,X3)) | → | active#(U103(mark(X1),X2,X3)) | (364) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(U101(X1,X2,X3)) | → | active#(U101(mark(X1),X2,X3)) | (356) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U34(tt,V1,V2)) | → | mark#(U35(isNat(V1),V2)) | (288) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
mark#(U36(X)) | → | mark#(X) | (423) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
active#(U61(tt,V2)) | → | mark#(U62(isNatKind(V2))) | (300) |
mark#(U62(X)) | → | mark#(X) | (438) |
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
active#(U81(tt,M,N)) | → | mark#(U82(isNatKind(M),M,N)) | (308) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (448) |
active#(U82(tt,M,N)) | → | mark#(U83(isNat(N),M,N)) | (311) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (451) |
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
mark#(U61(X1,X2)) | → | active#(U61(mark(X1),X2)) | (433) |
mark#(U61(X1,X2)) | → | mark#(X1) | (435) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (445) |
mark#(U91(X1,X2)) | → | active#(U91(mark(X1),X2)) | (460) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
active#(isNatKind(x(V1,V2))) | → | mark#(U61(isNatKind(V1),V2)) | (341) |
[active#(x1)] | = | -1 + 2 · x1 |
[U101(x1, x2, x3)] | = | 1 |
[U102(x1, x2, x3)] | = | 1 |
[U103(x1, x2, x3)] | = | -2 |
[U11(x1, x2, x3)] | = | 1 |
[U12(x1, x2, x3)] | = | 1 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | 1 |
[U15(x1, x2)] | = | 1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 1 |
[U31(x1, x2, x3)] | = | 1 |
[U32(x1, x2, x3)] | = | 1 |
[U33(x1, x2, x3)] | = | 1 |
[U34(x1, x2, x3)] | = | 1 |
[U35(x1, x2)] | = | 1 |
[U41(x1, x2)] | = | 1 |
[U61(x1, x2)] | = | 1 |
[U81(x1, x2, x3)] | = | 1 |
[U82(x1, x2, x3)] | = | 1 |
[U83(x1, x2, x3)] | = | 0 |
[U91(x1, x2)] | = | -2 |
[mark(x1)] | = | 2 |
[active(x1)] | = | -2 + x1 |
[tt] | = | 2 |
[isNatKind(x1)] | = | 1 |
[isNat(x1)] | = | 1 |
[U104(x1, x2, x3)] | = | 2 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | -2 + 2 · x1 |
[U16(x1)] | = | 0 |
[U23(x1)] | = | 2 |
[U36(x1)] | = | -2 + x1 |
[U42(x1)] | = | -2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U72(x1, x2)] | = | 2 + 2 · x1 |
[U84(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + x3 |
[s(x1)] | = | -2 + 2 · x1 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | 2 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
There are 112 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairsmark#(U103(X1,X2,X3)) | → | active#(U103(mark(X1),X2,X3)) | (364) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (451) |
mark#(U91(X1,X2)) | → | active#(U91(mark(X1),X2)) | (460) |
The dependency pairs are split into 1 component.
active#(U101(tt,M,N)) | → | mark#(U102(isNatKind(M),M,N)) | (244) |
mark#(U102(X1,X2,X3)) | → | active#(U102(mark(X1),X2,X3)) | (360) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(U101(X1,X2,X3)) | → | active#(U101(mark(X1),X2,X3)) | (356) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U34(tt,V1,V2)) | → | mark#(U35(isNat(V1),V2)) | (288) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
mark#(U36(X)) | → | mark#(X) | (423) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
active#(U61(tt,V2)) | → | mark#(U62(isNatKind(V2))) | (300) |
mark#(U62(X)) | → | mark#(X) | (438) |
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
active#(U81(tt,M,N)) | → | mark#(U82(isNatKind(M),M,N)) | (308) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (448) |
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
mark#(U61(X1,X2)) | → | active#(U61(mark(X1),X2)) | (433) |
mark#(U61(X1,X2)) | → | mark#(X1) | (435) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (445) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
active#(isNatKind(x(V1,V2))) | → | mark#(U61(isNatKind(V1),V2)) | (341) |
[active#(x1)] | = | -1 + x1 |
[U101(x1, x2, x3)] | = | 2 |
[U102(x1, x2, x3)] | = | 0 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | 2 |
[U35(x1, x2)] | = | 2 |
[U41(x1, x2)] | = | 2 |
[U61(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 |
[mark(x1)] | = | 2 |
[active(x1)] | = | 2 + x1 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | -1 + x2 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | 0 |
[plus(x1, x2)] | = | -2 + x1 |
[x(x1, x2)] | = | -2 + x1 |
[U16(x1)] | = | 2 + 2 · x1 |
[U23(x1)] | = | -2 |
[U36(x1)] | = | -2 + x1 |
[U42(x1)] | = | 1 |
[U62(x1)] | = | 2 + x1 |
[U71(x1, x2)] | = | 2 + x1 + 2 · x2 |
[U72(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U83(x1, x2, x3)] | = | 2 · x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[s(x1)] | = | 2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
U102(X1,mark(X2),X3) | → | U102(X1,X2,X3) | (91) |
U102(mark(X1),X2,X3) | → | U102(X1,X2,X3) | (90) |
U102(X1,X2,mark(X3)) | → | U102(X1,X2,X3) | (92) |
U102(active(X1),X2,X3) | → | U102(X1,X2,X3) | (93) |
U102(X1,active(X2),X3) | → | U102(X1,X2,X3) | (94) |
U102(X1,X2,active(X3)) | → | U102(X1,X2,X3) | (95) |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U101(X1,mark(X2),X3) | → | U101(X1,X2,X3) | (85) |
U101(mark(X1),X2,X3) | → | U101(X1,X2,X3) | (84) |
U101(X1,X2,mark(X3)) | → | U101(X1,X2,X3) | (86) |
U101(active(X1),X2,X3) | → | U101(X1,X2,X3) | (87) |
U101(X1,active(X2),X3) | → | U101(X1,X2,X3) | (88) |
U101(X1,X2,active(X3)) | → | U101(X1,X2,X3) | (89) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U34(X1,mark(X2),X3) | → | U34(X1,X2,X3) | (179) |
U34(mark(X1),X2,X3) | → | U34(X1,X2,X3) | (178) |
U34(X1,X2,mark(X3)) | → | U34(X1,X2,X3) | (180) |
U34(active(X1),X2,X3) | → | U34(X1,X2,X3) | (181) |
U34(X1,active(X2),X3) | → | U34(X1,X2,X3) | (182) |
U34(X1,X2,active(X3)) | → | U34(X1,X2,X3) | (183) |
U35(X1,mark(X2)) | → | U35(X1,X2) | (185) |
U35(mark(X1),X2) | → | U35(X1,X2) | (184) |
U35(active(X1),X2) | → | U35(X1,X2) | (186) |
U35(X1,active(X2)) | → | U35(X1,X2) | (187) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (219) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (218) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (220) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (221) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (222) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (223) |
U61(X1,mark(X2)) | → | U61(X1,X2) | (199) |
U61(mark(X1),X2) | → | U61(X1,X2) | (198) |
U61(active(X1),X2) | → | U61(X1,X2) | (200) |
U61(X1,active(X2)) | → | U61(X1,X2) | (201) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (213) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (212) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (214) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (215) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (216) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (217) |
mark#(U102(X1,X2,X3)) | → | active#(U102(mark(X1),X2,X3)) | (360) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (448) |
The dependency pairs are split into 1 component.
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(U101(X1,X2,X3)) | → | active#(U101(mark(X1),X2,X3)) | (356) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U34(tt,V1,V2)) | → | mark#(U35(isNat(V1),V2)) | (288) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
mark#(U36(X)) | → | mark#(X) | (423) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
active#(U61(tt,V2)) | → | mark#(U62(isNatKind(V2))) | (300) |
mark#(U62(X)) | → | mark#(X) | (438) |
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
mark#(U61(X1,X2)) | → | active#(U61(mark(X1),X2)) | (433) |
mark#(U61(X1,X2)) | → | mark#(X1) | (435) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (445) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
active#(isNatKind(x(V1,V2))) | → | mark#(U61(isNatKind(V1),V2)) | (341) |
[active#(x1)] | = | -2 |
[U101(x1, x2, x3)] | = | 1 + x1 + x2 + x3 |
[U11(x1, x2, x3)] | = | 1 + 2 · x1 |
[U12(x1, x2, x3)] | = | 1 + 2 · x1 |
[U13(x1, x2, x3)] | = | 1 + 2 · x1 |
[U14(x1, x2, x3)] | = | 1 + 2 · x1 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | 1 + 2 · x1 |
[U32(x1, x2, x3)] | = | 1 + 2 · x1 |
[U33(x1, x2, x3)] | = | 1 + 2 · x1 |
[U34(x1, x2, x3)] | = | 1 + 2 · x1 |
[U35(x1, x2)] | = | 1 + 2 · x1 |
[U41(x1, x2)] | = | 1 + 2 · x1 |
[U61(x1, x2)] | = | 1 + 2 · x1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 + x3 |
[mark(x1)] | = | 0 |
[U102(x1, x2, x3)] | = | -1 + 2 · x1 + x3 |
[active(x1)] | = | -1 + x1 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | 2 + x2 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | 2 + 2 · x1 |
[plus(x1, x2)] | = | -1 + 2 · x1 + 2 · x2 |
[x(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U16(x1)] | = | 1 + x1 |
[U23(x1)] | = | 1 + x1 |
[U36(x1)] | = | 1 + 2 · x1 |
[U42(x1)] | = | 1 + x1 |
[U62(x1)] | = | 1 + 2 · x1 |
[U71(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U72(x1, x2)] | = | -2 + 2 · x1 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | 2 + x1 |
[U92(x1)] | = | 0 |
[U51(x1)] | = | 1 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (445) |
[active#(x1)] | = | 1 + x1 |
[U101(x1, x2, x3)] | = | 0 |
[U11(x1, x2, x3)] | = | 1 |
[U12(x1, x2, x3)] | = | 1 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | 1 |
[U15(x1, x2)] | = | 1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 1 |
[U31(x1, x2, x3)] | = | 1 |
[U32(x1, x2, x3)] | = | 1 |
[U33(x1, x2, x3)] | = | 1 |
[U34(x1, x2, x3)] | = | 1 |
[U35(x1, x2)] | = | 1 |
[U41(x1, x2)] | = | 1 |
[U61(x1, x2)] | = | 1 |
[mark(x1)] | = | 2 |
[U102(x1, x2, x3)] | = | -2 + 2 · x2 |
[active(x1)] | = | -2 + 2 · x1 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U103(x1, x2, x3)] | = | -2 + x3 |
[isNat(x1)] | = | 1 |
[U104(x1, x2, x3)] | = | -1 + x2 + x3 |
[plus(x1, x2)] | = | -1 + x2 |
[x(x1, x2)] | = | -2 + x1 + x2 |
[U16(x1)] | = | -2 + 2 · x1 |
[U23(x1)] | = | 2 |
[U36(x1)] | = | -2 + 2 · x1 |
[U42(x1)] | = | -2 + 2 · x1 |
[U62(x1)] | = | -2 + 2 · x1 |
[U71(x1, x2)] | = | -2 + 2 · x1 |
[U72(x1, x2)] | = | -2 + 2 · x1 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[U82(x1, x2, x3)] | = | -2 + x3 |
[U83(x1, x2, x3)] | = | -1 + x2 + x3 |
[U84(x1, x2, x3)] | = | 2 + 2 · x1 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | 2 + x2 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U101(X1,mark(X2),X3) | → | U101(X1,X2,X3) | (85) |
U101(mark(X1),X2,X3) | → | U101(X1,X2,X3) | (84) |
U101(X1,X2,mark(X3)) | → | U101(X1,X2,X3) | (86) |
U101(active(X1),X2,X3) | → | U101(X1,X2,X3) | (87) |
U101(X1,active(X2),X3) | → | U101(X1,X2,X3) | (88) |
U101(X1,X2,active(X3)) | → | U101(X1,X2,X3) | (89) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U34(X1,mark(X2),X3) | → | U34(X1,X2,X3) | (179) |
U34(mark(X1),X2,X3) | → | U34(X1,X2,X3) | (178) |
U34(X1,X2,mark(X3)) | → | U34(X1,X2,X3) | (180) |
U34(active(X1),X2,X3) | → | U34(X1,X2,X3) | (181) |
U34(X1,active(X2),X3) | → | U34(X1,X2,X3) | (182) |
U34(X1,X2,active(X3)) | → | U34(X1,X2,X3) | (183) |
U35(X1,mark(X2)) | → | U35(X1,X2) | (185) |
U35(mark(X1),X2) | → | U35(X1,X2) | (184) |
U35(active(X1),X2) | → | U35(X1,X2) | (186) |
U35(X1,active(X2)) | → | U35(X1,X2) | (187) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
U61(X1,mark(X2)) | → | U61(X1,X2) | (199) |
U61(mark(X1),X2) | → | U61(X1,X2) | (198) |
U61(active(X1),X2) | → | U61(X1,X2) | (200) |
U61(X1,active(X2)) | → | U61(X1,X2) | (201) |
mark#(U101(X1,X2,X3)) | → | active#(U101(mark(X1),X2,X3)) | (356) |
[active#(x1)] | = |
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[U11(x1, x2, x3)] | = |
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[tt] | = |
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[mark#(x1)] | = |
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[U12(x1, x2, x3)] | = |
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[isNatKind(x1)] | = |
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[mark(x1)] | = |
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[U13(x1, x2, x3)] | = |
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[U14(x1, x2, x3)] | = |
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[U15(x1, x2)] | = |
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[isNat(x1)] | = |
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[U16(x1)] | = |
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[U21(x1, x2)] | = |
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[U22(x1, x2)] | = |
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[U23(x1)] | = |
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[plus(x1, x2)] | = |
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[U41(x1, x2)] | = |
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[U31(x1, x2, x3)] | = |
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[U32(x1, x2, x3)] | = |
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[U33(x1, x2, x3)] | = |
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[U34(x1, x2, x3)] | = |
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[U35(x1, x2)] | = |
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[U36(x1)] | = |
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[U42(x1)] | = |
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[U61(x1, x2)] | = |
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[U62(x1)] | = |
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[U51(x1)] | = |
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[s(x1)] | = |
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[x(x1, x2)] | = |
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[U102(x1, x2, x3)] | = |
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[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U61(X1,X2)) | → | mark#(X1) | (435) |
[active#(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
active#(U61(tt,V2)) | → | mark#(U62(isNatKind(V2))) | (300) |
[active#(x1)] | = | -1 + 2 · x1 |
[U11(x1, x2, x3)] | = | 1 |
[U12(x1, x2, x3)] | = | 1 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | 1 |
[U15(x1, x2)] | = | 1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 1 |
[U31(x1, x2, x3)] | = | 1 |
[U32(x1, x2, x3)] | = | 1 |
[U33(x1, x2, x3)] | = | 1 |
[U34(x1, x2, x3)] | = | 1 |
[U35(x1, x2)] | = | 1 |
[U41(x1, x2)] | = | 1 |
[U61(x1, x2)] | = | -2 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | -2 + x2 + x3 |
[active(x1)] | = | 2 + x1 |
[U101(x1, x2, x3)] | = | 2 + x2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U103(x1, x2, x3)] | = | 2 + x2 + x3 |
[isNat(x1)] | = | 1 |
[U104(x1, x2, x3)] | = | 2 |
[plus(x1, x2)] | = | 2 |
[x(x1, x2)] | = | -2 + x1 |
[U16(x1)] | = | -2 |
[U23(x1)] | = | -2 |
[U36(x1)] | = | -2 + x1 |
[U42(x1)] | = | -2 + x1 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | 2 + x1 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 + x2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[U84(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[s(x1)] | = | 2 |
[U91(x1, x2)] | = | 2 + x2 |
[U92(x1)] | = | 0 |
[U51(x1)] | = | -2 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U34(X1,mark(X2),X3) | → | U34(X1,X2,X3) | (179) |
U34(mark(X1),X2,X3) | → | U34(X1,X2,X3) | (178) |
U34(X1,X2,mark(X3)) | → | U34(X1,X2,X3) | (180) |
U34(active(X1),X2,X3) | → | U34(X1,X2,X3) | (181) |
U34(X1,active(X2),X3) | → | U34(X1,X2,X3) | (182) |
U34(X1,X2,active(X3)) | → | U34(X1,X2,X3) | (183) |
U35(X1,mark(X2)) | → | U35(X1,X2) | (185) |
U35(mark(X1),X2) | → | U35(X1,X2) | (184) |
U35(active(X1),X2) | → | U35(X1,X2) | (186) |
U35(X1,active(X2)) | → | U35(X1,X2) | (187) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
U61(X1,mark(X2)) | → | U61(X1,X2) | (199) |
U61(mark(X1),X2) | → | U61(X1,X2) | (198) |
U61(active(X1),X2) | → | U61(X1,X2) | (200) |
U61(X1,active(X2)) | → | U61(X1,X2) | (201) |
mark#(U61(X1,X2)) | → | active#(U61(mark(X1),X2)) | (433) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U34(tt,V1,V2)) | → | mark#(U35(isNat(V1),V2)) | (288) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
mark#(U36(X)) | → | mark#(X) | (423) |
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
mark#(U62(X)) | → | mark#(X) | (438) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 1 + 2 · x1 |
[U12(x1, x2, x3)] | = | 1 + 2 · x1 |
[U13(x1, x2, x3)] | = | 1 + 2 · x1 |
[U14(x1, x2, x3)] | = | 1 + 2 · x1 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | 1 + x1 |
[U31(x1, x2, x3)] | = | 1 + 2 · x1 |
[U32(x1, x2, x3)] | = | 1 + 2 · x1 |
[U33(x1, x2, x3)] | = | 1 + 2 · x1 |
[U34(x1, x2, x3)] | = | 1 + 2 · x1 |
[U35(x1, x2)] | = | 1 + x1 |
[U41(x1, x2)] | = | 1 + x1 |
[mark(x1)] | = | -2 + 2 · x1 |
[U102(x1, x2, x3)] | = | -2 + x2 |
[active(x1)] | = | 2 + 2 · x1 |
[U101(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | 0 |
[U16(x1)] | = | 1 + x1 |
[U23(x1)] | = | 1 + 2 · x1 |
[U36(x1)] | = | 1 + 2 · x1 |
[U42(x1)] | = | 1 + x1 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 2 + x1 |
[U71(x1, x2)] | = | -2 + 2 · x1 |
[U72(x1, x2)] | = | -2 + x1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 + 2 · x2 + x3 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 + x3 |
[s(x1)] | = | -2 + 2 · x1 |
[U91(x1, x2)] | = | -2 + 2 · x2 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | 1 + x1 |
[0] | = | 2 |
[mark#(x1)] | = | -2 + 2 · x1 |
mark#(U62(X)) | → | mark#(X) | (438) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U31(X1,X2,X3)) | → | mark#(X1) | (408) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U32(X1,X2,X3)) | → | mark#(X1) | (411) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
active#(U35(tt,V2)) | → | mark#(U36(isNat(V2))) | (291) |
[active#(x1)] | = | -2 + 2 · x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | 2 |
[U35(x1, x2)] | = | -2 |
[U41(x1, x2)] | = | 2 |
[mark(x1)] | = | -2 + 2 · x1 |
[U102(x1, x2, x3)] | = | 2 + 2 · x1 |
[active(x1)] | = | 2 |
[U101(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | -2 + 2 · x3 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | -2 + 2 · x1 |
[plus(x1, x2)] | = | -2 + x1 |
[x(x1, x2)] | = | -2 + x1 |
[U16(x1)] | = | -2 + x1 |
[U23(x1)] | = | -2 + 2 · x1 |
[U36(x1)] | = | -2 + 2 · x1 |
[U42(x1)] | = | -2 + 2 · x1 |
[U61(x1, x2)] | = | -1 + x2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | -1 + x1 + 2 · x2 |
[U72(x1, x2)] | = | 2 + 2 · x1 |
[U81(x1, x2, x3)] | = | 1 + x2 + x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x2 |
[U83(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[U84(x1, x2, x3)] | = | 2 + 2 · x3 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x1 |
[U92(x1)] | = | -2 + 2 · x1 |
[U51(x1)] | = | -2 + 2 · x1 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U34(X1,mark(X2),X3) | → | U34(X1,X2,X3) | (179) |
U34(mark(X1),X2,X3) | → | U34(X1,X2,X3) | (178) |
U34(X1,X2,mark(X3)) | → | U34(X1,X2,X3) | (180) |
U34(active(X1),X2,X3) | → | U34(X1,X2,X3) | (181) |
U34(X1,active(X2),X3) | → | U34(X1,X2,X3) | (182) |
U34(X1,X2,active(X3)) | → | U34(X1,X2,X3) | (183) |
U35(X1,mark(X2)) | → | U35(X1,X2) | (185) |
U35(mark(X1),X2) | → | U35(X1,X2) | (184) |
U35(active(X1),X2) | → | U35(X1,X2) | (186) |
U35(X1,active(X2)) | → | U35(X1,X2) | (187) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
mark#(U35(X1,X2)) | → | active#(U35(mark(X1),X2)) | (418) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 1 + x1 |
[U12(x1, x2, x3)] | = | 1 + 2 · x1 |
[U13(x1, x2, x3)] | = | 1 + 2 · x1 |
[U14(x1, x2, x3)] | = | 1 + x1 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | -2 |
[U32(x1, x2, x3)] | = | 1 |
[U33(x1, x2, x3)] | = | 1 + 2 · x1 |
[U34(x1, x2, x3)] | = | 1 + 2 · x1 |
[U41(x1, x2)] | = | 1 + 2 · x1 |
[mark(x1)] | = | 0 |
[U102(x1, x2, x3)] | = | 1 + 2 · x1 + x2 + x3 |
[active(x1)] | = | 1 + x1 |
[U101(x1, x2, x3)] | = | -2 + 2 · x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | 2 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | 2 + 2 · x3 |
[plus(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[x(x1, x2)] | = | -2 + 2 · x1 |
[U16(x1)] | = | 1 + x1 |
[U23(x1)] | = | 1 + 2 · x1 |
[U35(x1, x2)] | = | 1 + 2 · x1 |
[U36(x1)] | = | 2 + 2 · x1 |
[U42(x1)] | = | 1 + x1 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 1 |
[U71(x1, x2)] | = | -1 + 2 · x2 |
[U72(x1, x2)] | = | -2 + x1 |
[U81(x1, x2, x3)] | = | 2 + x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 + x3 |
[U84(x1, x2, x3)] | = | 2 + x2 |
[s(x1)] | = | 0 |
[U91(x1, x2)] | = | -2 + x2 |
[U92(x1)] | = | 1 |
[U51(x1)] | = | 1 + 2 · x1 |
[0] | = | 1 |
[mark#(x1)] | = | -1 + x1 |
mark#(U36(X)) | → | mark#(X) | (423) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U13(X1,X2,X3)) | → | mark#(X1) | (387) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U12(X1,X2,X3)) | → | mark#(X1) | (384) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U34(X1,X2,X3)) | → | mark#(X1) | (417) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U21(X1,X2)) | → | mark#(X1) | (399) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U11(X1,X2,X3)) | → | mark#(X1) | (381) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U35(X1,X2)) | → | mark#(X1) | (420) |
The dependency pairs are split into 1 component.
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U33(tt,V1,V2)) | → | mark#(U34(isNatKind(V2),V1,V2)) | (285) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
[active#(x1)] | = | -1 + 2 · x1 |
[U11(x1, x2, x3)] | = | 1 |
[U12(x1, x2, x3)] | = | 1 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | 1 |
[U15(x1, x2)] | = | 1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 1 |
[U31(x1, x2, x3)] | = | 1 |
[U32(x1, x2, x3)] | = | 1 |
[U33(x1, x2, x3)] | = | 1 |
[U34(x1, x2, x3)] | = | -2 |
[U41(x1, x2)] | = | 1 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[active(x1)] | = | -2 |
[U101(x1, x2, x3)] | = | -2 + x1 + x2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U103(x1, x2, x3)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 1 |
[U104(x1, x2, x3)] | = | -2 + x2 + x3 |
[plus(x1, x2)] | = | -2 + x1 |
[x(x1, x2)] | = | -2 + x2 |
[U16(x1)] | = | -2 |
[U23(x1)] | = | -2 + x1 |
[U35(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U36(x1)] | = | 1 |
[U42(x1)] | = | -2 |
[U61(x1, x2)] | = | 2 + 2 · x1 |
[U62(x1)] | = | -2 |
[U71(x1, x2)] | = | -1 + x1 + x2 |
[U72(x1, x2)] | = | -2 + 2 · x1 |
[U81(x1, x2, x3)] | = | -2 + x1 + x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + x3 |
[U84(x1, x2, x3)] | = | -2 + 2 · x2 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x1 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U34(X1,mark(X2),X3) | → | U34(X1,X2,X3) | (179) |
U34(mark(X1),X2,X3) | → | U34(X1,X2,X3) | (178) |
U34(X1,X2,mark(X3)) | → | U34(X1,X2,X3) | (180) |
U34(active(X1),X2,X3) | → | U34(X1,X2,X3) | (181) |
U34(X1,active(X2),X3) | → | U34(X1,X2,X3) | (182) |
U34(X1,X2,active(X3)) | → | U34(X1,X2,X3) | (183) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
mark#(U34(X1,X2,X3)) | → | active#(U34(mark(X1),X2,X3)) | (415) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U31(tt,V1,V2)) | → | mark#(U32(isNatKind(V1),V1,V2)) | (279) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
[active#(x1)] | = | -1 + x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | 2 |
[U33(x1, x2, x3)] | = | 0 |
[U41(x1, x2)] | = | 2 |
[mark(x1)] | = | 2 |
[U102(x1, x2, x3)] | = | -2 + x3 |
[active(x1)] | = | -2 + 2 · x1 |
[U101(x1, x2, x3)] | = | -2 + x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | -2 + 2 · x3 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | 2 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | -2 |
[U16(x1)] | = | -2 |
[U23(x1)] | = | -2 |
[U34(x1, x2, x3)] | = | -2 + 2 · x1 |
[U35(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U36(x1)] | = | 2 |
[U42(x1)] | = | 2 |
[U61(x1, x2)] | = | 2 + 2 · x2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | 2 + x2 |
[U72(x1, x2)] | = | -2 + x2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x3 |
[U84(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + 2 · x3 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | 2 + 2 · x2 |
[U92(x1)] | = | -2 + 2 · x1 |
[U51(x1)] | = | -2 |
[0] | = | 0 |
[mark#(x1)] | = | 1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U33(X1,mark(X2),X3) | → | U33(X1,X2,X3) | (173) |
U33(mark(X1),X2,X3) | → | U33(X1,X2,X3) | (172) |
U33(X1,X2,mark(X3)) | → | U33(X1,X2,X3) | (174) |
U33(active(X1),X2,X3) | → | U33(X1,X2,X3) | (175) |
U33(X1,active(X2),X3) | → | U33(X1,X2,X3) | (176) |
U33(X1,X2,active(X3)) | → | U33(X1,X2,X3) | (177) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
mark#(U33(X1,X2,X3)) | → | active#(U33(mark(X1),X2,X3)) | (412) |
[mark#(x1)] | = |
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[U12(x1, x2, x3)] | = |
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[active#(x1)] | = |
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[mark(x1)] | = |
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[U11(x1, x2, x3)] | = |
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[tt] | = |
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[isNatKind(x1)] | = |
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[U13(x1, x2, x3)] | = |
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[U14(x1, x2, x3)] | = |
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[U15(x1, x2)] | = |
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[isNat(x1)] | = |
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[U16(x1)] | = |
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[plus(x1, x2)] | = |
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[U41(x1, x2)] | = |
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[U21(x1, x2)] | = |
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[U22(x1, x2)] | = |
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[U23(x1)] | = |
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[U31(x1, x2, x3)] | = |
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[U32(x1, x2, x3)] | = |
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[U33(x1, x2, x3)] | = |
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[U42(x1)] | = |
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[U51(x1)] | = |
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[s(x1)] | = |
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[x(x1, x2)] | = |
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[U102(x1, x2, x3)] | = |
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[active(x1)] | = |
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[U101(x1, x2, x3)] | = |
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[U103(x1, x2, x3)] | = |
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[U104(x1, x2, x3)] | = |
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[U34(x1, x2, x3)] | = |
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[U35(x1, x2)] | = |
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[U36(x1)] | = |
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[U61(x1, x2)] | = |
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[U62(x1)] | = |
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[U71(x1, x2)] | = |
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[U72(x1, x2)] | = |
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[U81(x1, x2, x3)] | = |
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[U82(x1, x2, x3)] | = |
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[U83(x1, x2, x3)] | = |
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[U84(x1, x2, x3)] | = |
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[U91(x1, x2)] | = |
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[U92(x1)] | = |
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[0] | = |
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active#(U32(tt,V1,V2)) | → | mark#(U33(isNatKind(V2),V1,V2)) | (282) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 0 |
[U12(x1, x2, x3)] | = | -2 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | 1 + x1 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U21(x1, x2)] | = | 0 |
[U22(x1, x2)] | = | 1 + x1 |
[U31(x1, x2, x3)] | = | -2 |
[U32(x1, x2, x3)] | = | -2 |
[U41(x1, x2)] | = | 1 + x1 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | -2 + 2 · x1 + x2 + x3 |
[active(x1)] | = | -2 + 2 · x1 |
[U101(x1, x2, x3)] | = | 2 + x2 + x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | 2 + x3 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[plus(x1, x2)] | = | 2 + x1 |
[x(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U16(x1)] | = | 1 + 2 · x1 |
[U23(x1)] | = | 1 + x1 |
[U33(x1, x2, x3)] | = | 2 + x1 + x2 |
[U34(x1, x2, x3)] | = | 2 + x2 + x3 |
[U35(x1, x2)] | = | -2 + 2 · x2 |
[U36(x1)] | = | 1 |
[U42(x1)] | = | 1 + x1 |
[U61(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U62(x1)] | = | 1 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[U83(x1, x2, x3)] | = | -2 + x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[s(x1)] | = | -2 |
[U91(x1, x2)] | = | -2 + 2 · x1 |
[U92(x1)] | = | 0 |
[U51(x1)] | = | 1 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U33(X1,X2,X3)) | → | mark#(X1) | (414) |
[active#(x1)] | = | x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | -2 |
[U41(x1, x2)] | = | 2 |
[mark(x1)] | = | 2 |
[U102(x1, x2, x3)] | = | 2 + x2 |
[active(x1)] | = | -2 + x1 |
[U101(x1, x2, x3)] | = | 2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | 2 + x2 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[plus(x1, x2)] | = | -2 + x1 + x2 |
[x(x1, x2)] | = | -2 + x1 |
[U16(x1)] | = | -2 + x1 |
[U23(x1)] | = | 2 |
[U33(x1, x2, x3)] | = | -2 + 2 · x2 |
[U34(x1, x2, x3)] | = | -2 + x1 + x2 + 2 · x3 |
[U35(x1, x2)] | = | -2 + x1 + x2 |
[U36(x1)] | = | 2 |
[U42(x1)] | = | -2 + x1 |
[U61(x1, x2)] | = | 2 + 2 · x1 |
[U62(x1)] | = | 0 |
[U71(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U72(x1, x2)] | = | -2 + x2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | -1 + x1 + x2 + x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | 2 + 2 · x2 |
[s(x1)] | = | -1 + x1 |
[U91(x1, x2)] | = | -2 + x1 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | 0 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U32(X1,mark(X2),X3) | → | U32(X1,X2,X3) | (167) |
U32(mark(X1),X2,X3) | → | U32(X1,X2,X3) | (166) |
U32(X1,X2,mark(X3)) | → | U32(X1,X2,X3) | (168) |
U32(active(X1),X2,X3) | → | U32(X1,X2,X3) | (169) |
U32(X1,active(X2),X3) | → | U32(X1,X2,X3) | (170) |
U32(X1,X2,active(X3)) | → | U32(X1,X2,X3) | (171) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
mark#(U32(X1,X2,X3)) | → | active#(U32(mark(X1),X2,X3)) | (409) |
The dependency pairs are split into 1 component.
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNat(x(V1,V2))) | → | mark#(U31(isNatKind(V1),V1,V2)) | (331) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
[active#(x1)] | = | -2 + 2 · x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2, x3)] | = | -2 |
[U41(x1, x2)] | = | 2 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | -2 + 2 · x1 + x3 |
[active(x1)] | = | -2 + x1 |
[U101(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | -2 + 2 · x1 + x3 |
[plus(x1, x2)] | = | -2 |
[x(x1, x2)] | = | 2 |
[U16(x1)] | = | -2 + x1 |
[U23(x1)] | = | 2 + x1 |
[U32(x1, x2, x3)] | = | -2 + x1 + x2 + 2 · x3 |
[U33(x1, x2, x3)] | = | 2 + x1 |
[U34(x1, x2, x3)] | = | 2 + x1 + x3 |
[U35(x1, x2)] | = | -2 + x2 |
[U36(x1)] | = | 0 |
[U42(x1)] | = | -2 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 0 |
[U71(x1, x2)] | = | -2 + 2 · x2 |
[U72(x1, x2)] | = | -2 + x1 + x2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x2 |
[U82(x1, x2, x3)] | = | -2 + x1 + x3 |
[U83(x1, x2, x3)] | = | 2 + x1 + x2 + x3 |
[U84(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | -2 + x2 |
[U92(x1)] | = | 0 |
[U51(x1)] | = | 2 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
U31(X1,mark(X2),X3) | → | U31(X1,X2,X3) | (161) |
U31(mark(X1),X2,X3) | → | U31(X1,X2,X3) | (160) |
U31(X1,X2,mark(X3)) | → | U31(X1,X2,X3) | (162) |
U31(active(X1),X2,X3) | → | U31(X1,X2,X3) | (163) |
U31(X1,active(X2),X3) | → | U31(X1,X2,X3) | (164) |
U31(X1,X2,active(X3)) | → | U31(X1,X2,X3) | (165) |
mark#(U31(X1,X2,X3)) | → | active#(U31(mark(X1),X2,X3)) | (406) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
mark#(U16(X)) | → | mark#(X) | (396) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (363) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
mark#(U42(X)) | → | mark#(X) | (429) |
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U22(X1,X2)) | → | mark#(X1) | (402) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
mark#(U14(X1,X2,X3)) | → | mark#(X1) | (390) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
active#(U15(tt,V2)) | → | mark#(U16(isNat(V2))) | (268) |
[active#(x1)] | = | x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U15(x1, x2)] | = | 1 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2)] | = | 2 |
[mark(x1)] | = | 2 |
[U102(x1, x2, x3)] | = | -2 + x1 + 2 · x3 |
[active(x1)] | = | 0 |
[U101(x1, x2, x3)] | = | 2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | 2 + x1 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U16(x1)] | = | -2 + 2 · x1 |
[U23(x1)] | = | -2 + 2 · x1 |
[U31(x1, x2, x3)] | = | -2 + 2 · x2 |
[U32(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + x3 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[U35(x1, x2)] | = | -2 + 2 · x1 |
[U36(x1)] | = | -2 + 2 · x1 |
[U42(x1)] | = | -2 + x1 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | -2 + 2 · x1 |
[U71(x1, x2)] | = | 2 + x1 |
[U72(x1, x2)] | = | 2 + 2 · x1 + x2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 + 2 · x1 |
[U83(x1, x2, x3)] | = | -1 + x1 + 2 · x2 |
[U84(x1, x2, x3)] | = | 2 |
[s(x1)] | = | 2 |
[U91(x1, x2)] | = | -2 + x1 + x2 |
[U92(x1)] | = | 1 + x1 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U15(X1,mark(X2)) | → | U15(X1,X2) | (145) |
U15(mark(X1),X2) | → | U15(X1,X2) | (144) |
U15(active(X1),X2) | → | U15(X1,X2) | (146) |
U15(X1,active(X2)) | → | U15(X1,X2) | (147) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
mark#(U15(X1,X2)) | → | active#(U15(mark(X1),X2)) | (391) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | -2 |
[U12(x1, x2, x3)] | = | -2 |
[U13(x1, x2, x3)] | = | -2 |
[U14(x1, x2, x3)] | = | 1 |
[U21(x1, x2)] | = | 0 |
[U22(x1, x2)] | = | 0 |
[U41(x1, x2)] | = | 1 + 2 · x1 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | 2 + 2 · x3 |
[active(x1)] | = | 2 |
[U101(x1, x2, x3)] | = | 2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | -2 + x3 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | 2 + 2 · x3 |
[plus(x1, x2)] | = | -1 + x1 + x2 |
[x(x1, x2)] | = | 2 |
[U15(x1, x2)] | = | 1 + x1 |
[U16(x1)] | = | 2 + 2 · x1 |
[U23(x1)] | = | 1 + x1 |
[U31(x1, x2, x3)] | = | 2 |
[U32(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U33(x1, x2, x3)] | = | -2 + x2 |
[U34(x1, x2, x3)] | = | -2 + 2 · x3 |
[U35(x1, x2)] | = | -2 + 2 · x1 |
[U36(x1)] | = | 2 |
[U42(x1)] | = | 1 + x1 |
[U61(x1, x2)] | = | -2 + x1 |
[U62(x1)] | = | -2 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 |
[U82(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[U83(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + x3 |
[U84(x1, x2, x3)] | = | 2 + x1 |
[s(x1)] | = | 2 |
[U91(x1, x2)] | = | -2 + x1 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | 1 + 2 · x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U16(X)) | → | mark#(X) | (396) |
[mark#(x1)] | = |
|
||||||||||||||||
[U12(x1, x2, x3)] | = |
|
||||||||||||||||
[active#(x1)] | = |
|
||||||||||||||||
[mark(x1)] | = |
|
||||||||||||||||
[U11(x1, x2, x3)] | = |
|
||||||||||||||||
[tt] | = |
|
||||||||||||||||
[isNatKind(x1)] | = |
|
||||||||||||||||
[U13(x1, x2, x3)] | = |
|
||||||||||||||||
[U14(x1, x2, x3)] | = |
|
||||||||||||||||
[U15(x1, x2)] | = |
|
||||||||||||||||
[isNat(x1)] | = |
|
||||||||||||||||
[plus(x1, x2)] | = |
|
||||||||||||||||
[U41(x1, x2)] | = |
|
||||||||||||||||
[U21(x1, x2)] | = |
|
||||||||||||||||
[U22(x1, x2)] | = |
|
||||||||||||||||
[U23(x1)] | = |
|
||||||||||||||||
[U42(x1)] | = |
|
||||||||||||||||
[U51(x1)] | = |
|
||||||||||||||||
[s(x1)] | = |
|
||||||||||||||||
[U102(x1, x2, x3)] | = |
|
||||||||||||||||
[active(x1)] | = |
|
||||||||||||||||
[U101(x1, x2, x3)] | = |
|
||||||||||||||||
[U103(x1, x2, x3)] | = |
|
||||||||||||||||
[U104(x1, x2, x3)] | = |
|
||||||||||||||||
[x(x1, x2)] | = |
|
||||||||||||||||
[U16(x1)] | = |
|
||||||||||||||||
[U31(x1, x2, x3)] | = |
|
||||||||||||||||
[U32(x1, x2, x3)] | = |
|
||||||||||||||||
[U33(x1, x2, x3)] | = |
|
||||||||||||||||
[U34(x1, x2, x3)] | = |
|
||||||||||||||||
[U35(x1, x2)] | = |
|
||||||||||||||||
[U36(x1)] | = |
|
||||||||||||||||
[U61(x1, x2)] | = |
|
||||||||||||||||
[U62(x1)] | = |
|
||||||||||||||||
[U71(x1, x2)] | = |
|
||||||||||||||||
[U72(x1, x2)] | = |
|
||||||||||||||||
[U81(x1, x2, x3)] | = |
|
||||||||||||||||
[U82(x1, x2, x3)] | = |
|
||||||||||||||||
[U83(x1, x2, x3)] | = |
|
||||||||||||||||
[U84(x1, x2, x3)] | = |
|
||||||||||||||||
[U91(x1, x2)] | = |
|
||||||||||||||||
[U92(x1)] | = |
|
||||||||||||||||
[0] | = |
|
active#(U41(tt,V2)) | → | mark#(U42(isNatKind(V2))) | (295) |
[active#(x1)] | = | -2 + 2 · x1 |
[U11(x1, x2, x3)] | = | 2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | 2 |
[U14(x1, x2, x3)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2)] | = | -2 |
[mark(x1)] | = | 1 |
[U102(x1, x2, x3)] | = | 2 |
[active(x1)] | = | -2 |
[U101(x1, x2, x3)] | = | -2 + 2 · x2 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U103(x1, x2, x3)] | = | 2 |
[isNat(x1)] | = | 2 |
[U104(x1, x2, x3)] | = | -2 + x2 |
[plus(x1, x2)] | = | 2 + x1 |
[x(x1, x2)] | = | -1 + x2 |
[U15(x1, x2)] | = | -2 |
[U16(x1)] | = | 1 + 2 · x1 |
[U23(x1)] | = | -2 + 2 · x1 |
[U31(x1, x2, x3)] | = | -1 + x1 + x2 |
[U32(x1, x2, x3)] | = | 2 + 2 · x2 |
[U33(x1, x2, x3)] | = | 2 + x3 |
[U34(x1, x2, x3)] | = | -2 + x1 |
[U35(x1, x2)] | = | -2 + 2 · x1 |
[U36(x1)] | = | 2 |
[U42(x1)] | = | -2 + 2 · x1 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 1 + x1 |
[U71(x1, x2)] | = | -2 + x1 |
[U72(x1, x2)] | = | -1 + x1 + x2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 0 |
[U84(x1, x2, x3)] | = | 2 |
[s(x1)] | = | 2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x2 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | -2 |
[0] | = | 0 |
[mark#(x1)] | = | 2 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U41(X1,mark(X2)) | → | U41(X1,X2) | (191) |
U41(mark(X1),X2) | → | U41(X1,X2) | (190) |
U41(active(X1),X2) | → | U41(X1,X2) | (192) |
U41(X1,active(X2)) | → | U41(X1,X2) | (193) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
mark#(U41(X1,X2)) | → | active#(U41(mark(X1),X2)) | (424) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 1 |
[U12(x1, x2, x3)] | = | -2 |
[U13(x1, x2, x3)] | = | -2 |
[U14(x1, x2, x3)] | = | -2 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | -2 |
[mark(x1)] | = | -2 + x1 |
[U102(x1, x2, x3)] | = | -2 + 2 · x1 + x2 + 2 · x3 |
[active(x1)] | = | -2 + x1 |
[U101(x1, x2, x3)] | = | -2 + x3 |
[tt] | = | 1 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | -2 + 2 · x2 + x3 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + 2 · x2 + x3 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | 2 + x1 |
[U15(x1, x2)] | = | 1 + x1 |
[U16(x1)] | = | -2 + 2 · x1 |
[U23(x1)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | 2 + 2 · x1 |
[U32(x1, x2, x3)] | = | -2 + 2 · x2 |
[U33(x1, x2, x3)] | = | -2 + 2 · x2 |
[U34(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + x3 |
[U35(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U36(x1)] | = | -2 + x1 |
[U41(x1, x2)] | = | 1 + 2 · x1 |
[U42(x1)] | = | 2 + 2 · x1 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U72(x1, x2)] | = | -2 + 2 · x2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 + x2 + x3 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | -2 + 2 · x1 |
[U84(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[s(x1)] | = | 0 |
[U91(x1, x2)] | = | 2 |
[U92(x1)] | = | -2 |
[U51(x1)] | = | 1 + 2 · x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U42(X)) | → | mark#(X) | (429) |
[active#(x1)] | = | -2 + x1 |
[U11(x1, x2, x3)] | = | -2 |
[U12(x1, x2, x3)] | = | 2 |
[U13(x1, x2, x3)] | = | -2 |
[U14(x1, x2, x3)] | = | 2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[mark(x1)] | = | -2 + 2 · x1 |
[U102(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[active(x1)] | = | -2 + x1 |
[U101(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + x3 |
[tt] | = | 2 |
[isNatKind(x1)] | = | 2 + 2 · x1 |
[U103(x1, x2, x3)] | = | -2 + x2 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | 2 |
[plus(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
[x(x1, x2)] | = | -2 + x1 |
[U15(x1, x2)] | = | 2 + 2 · x1 |
[U16(x1)] | = | 0 |
[U23(x1)] | = | 2 + 2 · x1 |
[U31(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U32(x1, x2, x3)] | = | 2 + 2 · x1 |
[U33(x1, x2, x3)] | = | -2 + 2 · x3 |
[U34(x1, x2, x3)] | = | -2 + 2 · x3 |
[U35(x1, x2)] | = | 2 |
[U36(x1)] | = | -2 |
[U41(x1, x2)] | = | 2 + x1 + x2 |
[U42(x1)] | = | 1 |
[U61(x1, x2)] | = | -2 + x2 |
[U62(x1)] | = | -2 + x1 |
[U71(x1, x2)] | = | -2 + 2 · x2 |
[U72(x1, x2)] | = | -2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -1 + 2 · x1 + 2 · x2 + x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[U84(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[s(x1)] | = | 2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U92(x1)] | = | 1 + 2 · x1 |
[U51(x1)] | = | 2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | -2 + x1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
active#(isNatKind(plus(V1,V2))) | → | mark#(U41(isNatKind(V1),V2)) | (335) |
active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | (338) |
The dependency pairs are split into 1 component.
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(isNat(X)) | → | active#(isNat(X)) | (367) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
mark#(U51(X)) | → | mark#(X) | (432) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | -2 |
[U12(x1, x2, x3)] | = | -2 |
[U13(x1, x2, x3)] | = | 1 |
[U14(x1, x2, x3)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[mark(x1)] | = | -2 |
[U102(x1, x2, x3)] | = | 2 + 2 · x2 |
[active(x1)] | = | -2 + x1 |
[U101(x1, x2, x3)] | = | -2 + 2 · x3 |
[tt] | = | 1 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | 2 + 2 · x1 + x2 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + x1 + 2 · x2 |
[plus(x1, x2)] | = | -2 + 2 · x1 |
[x(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U15(x1, x2)] | = | 1 + x1 |
[U16(x1)] | = | 0 |
[U23(x1)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U32(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1, x2, x3)] | = | 2 |
[U34(x1, x2, x3)] | = | -2 + x1 |
[U35(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U36(x1)] | = | 0 |
[U41(x1, x2)] | = | 1 + x1 + x2 |
[U42(x1)] | = | 2 |
[U61(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | 2 |
[U72(x1, x2)] | = | -2 + 2 · x2 |
[U81(x1, x2, x3)] | = | 2 + x1 |
[U82(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | 2 + 2 · x3 |
[s(x1)] | = | 2 |
[U91(x1, x2)] | = | -2 + 2 · x2 |
[U92(x1)] | = | -2 |
[U51(x1)] | = | 2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U51(X)) | → | mark#(X) | (432) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 0 |
[U12(x1, x2, x3)] | = | 0 |
[U13(x1, x2, x3)] | = | -2 |
[U14(x1, x2, x3)] | = | 0 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[mark(x1)] | = | 2 |
[U102(x1, x2, x3)] | = | 2 + 2 · x1 |
[active(x1)] | = | 2 + x1 |
[U101(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | -2 + x2 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + x2 |
[plus(x1, x2)] | = | -2 + x1 |
[x(x1, x2)] | = | 2 + 2 · x1 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U16(x1)] | = | -2 + 2 · x1 |
[U23(x1)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | -2 + 2 · x2 |
[U32(x1, x2, x3)] | = | 2 + 2 · x3 |
[U33(x1, x2, x3)] | = | -2 + x2 |
[U34(x1, x2, x3)] | = | -2 + 2 · x2 |
[U35(x1, x2)] | = | -1 + x1 |
[U36(x1)] | = | -2 + 2 · x1 |
[U41(x1, x2)] | = | 2 + 2 · x1 |
[U42(x1)] | = | 2 |
[U61(x1, x2)] | = | -2 + x2 |
[U62(x1)] | = | 0 |
[U71(x1, x2)] | = | -2 + x2 |
[U72(x1, x2)] | = | -2 + 2 · x1 |
[U81(x1, x2, x3)] | = | -2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 |
[U84(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x3 |
[s(x1)] | = | -2 + x1 |
[U91(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U92(x1)] | = | 2 |
[U51(x1)] | = | 1 |
[0] | = | 0 |
[mark#(x1)] | = | -2 + 2 · x1 |
mark#(U41(X1,X2)) | → | mark#(X1) | (426) |
[active#(x1)] | = | -1 + x1 |
[U11(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U12(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U13(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U14(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U21(x1, x2)] | = | 2 + 2 · x2 |
[U22(x1, x2)] | = | 2 + 2 · x2 |
[mark(x1)] | = | 2 · x1 |
[U102(x1, x2, x3)] | = | 2 + x1 |
[active(x1)] | = | x1 |
[U101(x1, x2, x3)] | = | -2 + x3 |
[tt] | = | 2 |
[isNatKind(x1)] | = | 1 |
[U103(x1, x2, x3)] | = | -2 + x2 |
[isNat(x1)] | = | 1 + 2 · x1 |
[U104(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[plus(x1, x2)] | = | 1 + 2 · x1 + x2 |
[x(x1, x2)] | = | -1 + 2 · x1 |
[U15(x1, x2)] | = | 1 + x1 + 2 · x2 |
[U16(x1)] | = | -2 |
[U23(x1)] | = | 1 + x1 |
[U31(x1, x2, x3)] | = | 2 + x1 + 2 · x3 |
[U32(x1, x2, x3)] | = | 2 + x1 + 2 · x2 |
[U33(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + 2 · x3 |
[U34(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + x3 |
[U35(x1, x2)] | = | -2 + x1 |
[U36(x1)] | = | 0 |
[U41(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U42(x1)] | = | 1 + 2 · x1 |
[U61(x1, x2)] | = | -2 + 2 · x1 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | -2 + x2 |
[U72(x1, x2)] | = | -2 + x2 |
[U81(x1, x2, x3)] | = | -2 + x2 |
[U82(x1, x2, x3)] | = | x1 + x2 |
[U83(x1, x2, x3)] | = | 1 + 2 · x1 + x2 |
[U84(x1, x2, x3)] | = | -2 + x2 + x3 |
[s(x1)] | = | 1 + x1 |
[U91(x1, x2)] | = | 2 + x1 |
[U92(x1)] | = | -2 + x1 |
[U51(x1)] | = | -2 + x1 |
[0] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U11(X1,mark(X2),X3) | → | U11(X1,X2,X3) | (121) |
U11(mark(X1),X2,X3) | → | U11(X1,X2,X3) | (120) |
U11(X1,X2,mark(X3)) | → | U11(X1,X2,X3) | (122) |
U11(active(X1),X2,X3) | → | U11(X1,X2,X3) | (123) |
U11(X1,active(X2),X3) | → | U11(X1,X2,X3) | (124) |
U11(X1,X2,active(X3)) | → | U11(X1,X2,X3) | (125) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (151) |
U21(mark(X1),X2) | → | U21(X1,X2) | (150) |
U21(active(X1),X2) | → | U21(X1,X2) | (152) |
U21(X1,active(X2)) | → | U21(X1,X2) | (153) |
active#(isNat(plus(V1,V2))) | → | mark#(U11(isNatKind(V1),V1,V2)) | (325) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (328) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2,X3)) | → | active#(U12(mark(X1),X2,X3)) | (382) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
mark#(U13(X1,X2,X3)) | → | active#(U13(mark(X1),X2,X3)) | (385) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
mark#(U14(X1,X2,X3)) | → | active#(U14(mark(X1),X2,X3)) | (388) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (400) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
[active#(x1)] | = | -2 |
[U11(x1, x2, x3)] | = | 2 + x2 + 2 · x3 |
[U12(x1, x2, x3)] | = | -2 |
[U13(x1, x2, x3)] | = | -2 |
[U14(x1, x2, x3)] | = | -2 |
[U21(x1, x2)] | = | 2 + x2 |
[U22(x1, x2)] | = | -2 |
[mark(x1)] | = | 0 |
[U102(x1, x2, x3)] | = | -2 + 2 · x2 |
[active(x1)] | = | 2 |
[U101(x1, x2, x3)] | = | -2 + x1 + x3 |
[tt] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U103(x1, x2, x3)] | = | 2 + x1 + 2 · x3 |
[isNat(x1)] | = | 0 |
[U104(x1, x2, x3)] | = | -2 + x2 |
[plus(x1, x2)] | = | 2 |
[x(x1, x2)] | = | 2 |
[U15(x1, x2)] | = | 1 + 2 · x1 |
[U16(x1)] | = | -2 |
[U23(x1)] | = | 1 + 2 · x1 |
[U31(x1, x2, x3)] | = | -2 + 2 · x2 |
[U32(x1, x2, x3)] | = | -1 + 2 · x2 + x3 |
[U33(x1, x2, x3)] | = | -2 + 2 · x3 |
[U34(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[U35(x1, x2)] | = | 2 + x1 + x2 |
[U36(x1)] | = | -2 |
[U41(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U42(x1)] | = | 2 |
[U61(x1, x2)] | = | 2 |
[U62(x1)] | = | 2 |
[U71(x1, x2)] | = | x1 |
[U72(x1, x2)] | = | 2 + x1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | -2 + x1 |
[U84(x1, x2, x3)] | = | -2 + 2 · x2 |
[s(x1)] | = | 1 |
[U91(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U92(x1)] | = | 1 |
[U51(x1)] | = | -2 |
[0] | = | 0 |
[mark#(x1)] | = | -2 + 2 · x1 |
mark#(U11(X1,X2,X3)) | → | active#(U11(mark(X1),X2,X3)) | (379) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (397) |
prec(U12) | = | 1 | weight(U12) | = | 4 | ||||
prec(U11) | = | 6 | weight(U11) | = | 5 | ||||
prec(U13) | = | 4 | weight(U13) | = | 3 | ||||
prec(U14) | = | 3 | weight(U14) | = | 2 | ||||
prec(isNat) | = | 0 | weight(isNat) | = | 1 | ||||
prec(U21) | = | 5 | weight(U21) | = | 3 | ||||
prec(U22) | = | 2 | weight(U22) | = | 2 |
π(mark#) | = | 1 |
π(U12) | = | [] |
π(active#) | = | 1 |
π(U11) | = | [] |
π(U13) | = | [] |
π(U14) | = | [] |
π(U15) | = | 1 |
π(isNat) | = | [] |
π(U21) | = | [] |
π(U22) | = | [] |
π(U23) | = | 1 |
π(mark) | = | 1 |
π(active) | = | 1 |
U12(X1,mark(X2),X3) | → | U12(X1,X2,X3) | (127) |
U12(mark(X1),X2,X3) | → | U12(X1,X2,X3) | (126) |
U12(X1,X2,mark(X3)) | → | U12(X1,X2,X3) | (128) |
U12(active(X1),X2,X3) | → | U12(X1,X2,X3) | (129) |
U12(X1,active(X2),X3) | → | U12(X1,X2,X3) | (130) |
U12(X1,X2,active(X3)) | → | U12(X1,X2,X3) | (131) |
U13(X1,mark(X2),X3) | → | U13(X1,X2,X3) | (133) |
U13(mark(X1),X2,X3) | → | U13(X1,X2,X3) | (132) |
U13(X1,X2,mark(X3)) | → | U13(X1,X2,X3) | (134) |
U13(active(X1),X2,X3) | → | U13(X1,X2,X3) | (135) |
U13(X1,active(X2),X3) | → | U13(X1,X2,X3) | (136) |
U13(X1,X2,active(X3)) | → | U13(X1,X2,X3) | (137) |
U14(X1,mark(X2),X3) | → | U14(X1,X2,X3) | (139) |
U14(mark(X1),X2,X3) | → | U14(X1,X2,X3) | (138) |
U14(X1,X2,mark(X3)) | → | U14(X1,X2,X3) | (140) |
U14(active(X1),X2,X3) | → | U14(X1,X2,X3) | (141) |
U14(X1,active(X2),X3) | → | U14(X1,X2,X3) | (142) |
U14(X1,X2,active(X3)) | → | U14(X1,X2,X3) | (143) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (155) |
U22(mark(X1),X2) | → | U22(X1,X2) | (154) |
U22(active(X1),X2) | → | U22(X1,X2) | (156) |
U22(X1,active(X2)) | → | U22(X1,X2) | (157) |
active#(U11(tt,V1,V2)) | → | mark#(U12(isNatKind(V1),V1,V2)) | (256) |
active#(U12(tt,V1,V2)) | → | mark#(U13(isNatKind(V2),V1,V2)) | (259) |
active#(U13(tt,V1,V2)) | → | mark#(U14(isNatKind(V2),V1,V2)) | (262) |
active#(U14(tt,V1,V2)) | → | mark#(U15(isNat(V1),V2)) | (265) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (272) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (275) |
The dependency pairs are split into 1 component.
mark#(U23(X)) | → | mark#(X) | (405) |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
U15(mark(x0),x1) |
U15(x0,mark(x1)) |
U15(active(x0),x1) |
U15(x0,active(x1)) |
U23(mark(x0)) |
U23(active(x0)) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
mark#(U23(X)) | → | mark#(X) | (405) |
1 | > | 1 | |
mark#(U15(X1,X2)) | → | mark#(X1) | (393) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U101#(X1,mark(X2),X3) | → | U101#(X1,X2,X3) | (468) |
U101#(mark(X1),X2,X3) | → | U101#(X1,X2,X3) | (467) |
U101#(X1,X2,mark(X3)) | → | U101#(X1,X2,X3) | (469) |
U101#(active(X1),X2,X3) | → | U101#(X1,X2,X3) | (470) |
U101#(X1,active(X2),X3) | → | U101#(X1,X2,X3) | (471) |
U101#(X1,X2,active(X3)) | → | U101#(X1,X2,X3) | (472) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U101#(X1,mark(X2),X3) | → | U101#(X1,X2,X3) | (468) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U101#(mark(X1),X2,X3) | → | U101#(X1,X2,X3) | (467) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U101#(X1,X2,mark(X3)) | → | U101#(X1,X2,X3) | (469) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U101#(active(X1),X2,X3) | → | U101#(X1,X2,X3) | (470) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U101#(X1,active(X2),X3) | → | U101#(X1,X2,X3) | (471) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U101#(X1,X2,active(X3)) | → | U101#(X1,X2,X3) | (472) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U102#(X1,mark(X2),X3) | → | U102#(X1,X2,X3) | (474) |
U102#(mark(X1),X2,X3) | → | U102#(X1,X2,X3) | (473) |
U102#(X1,X2,mark(X3)) | → | U102#(X1,X2,X3) | (475) |
U102#(active(X1),X2,X3) | → | U102#(X1,X2,X3) | (476) |
U102#(X1,active(X2),X3) | → | U102#(X1,X2,X3) | (477) |
U102#(X1,X2,active(X3)) | → | U102#(X1,X2,X3) | (478) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U102#(X1,mark(X2),X3) | → | U102#(X1,X2,X3) | (474) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U102#(mark(X1),X2,X3) | → | U102#(X1,X2,X3) | (473) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U102#(X1,X2,mark(X3)) | → | U102#(X1,X2,X3) | (475) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U102#(active(X1),X2,X3) | → | U102#(X1,X2,X3) | (476) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U102#(X1,active(X2),X3) | → | U102#(X1,X2,X3) | (477) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U102#(X1,X2,active(X3)) | → | U102#(X1,X2,X3) | (478) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNatKind#(active(X)) | → | isNatKind#(X) | (480) |
isNatKind#(mark(X)) | → | isNatKind#(X) | (479) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNatKind#(active(X)) | → | isNatKind#(X) | (480) |
1 | > | 1 | |
isNatKind#(mark(X)) | → | isNatKind#(X) | (479) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U103#(X1,mark(X2),X3) | → | U103#(X1,X2,X3) | (482) |
U103#(mark(X1),X2,X3) | → | U103#(X1,X2,X3) | (481) |
U103#(X1,X2,mark(X3)) | → | U103#(X1,X2,X3) | (483) |
U103#(active(X1),X2,X3) | → | U103#(X1,X2,X3) | (484) |
U103#(X1,active(X2),X3) | → | U103#(X1,X2,X3) | (485) |
U103#(X1,X2,active(X3)) | → | U103#(X1,X2,X3) | (486) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U103#(X1,mark(X2),X3) | → | U103#(X1,X2,X3) | (482) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U103#(mark(X1),X2,X3) | → | U103#(X1,X2,X3) | (481) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U103#(X1,X2,mark(X3)) | → | U103#(X1,X2,X3) | (483) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U103#(active(X1),X2,X3) | → | U103#(X1,X2,X3) | (484) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U103#(X1,active(X2),X3) | → | U103#(X1,X2,X3) | (485) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U103#(X1,X2,active(X3)) | → | U103#(X1,X2,X3) | (486) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNat#(active(X)) | → | isNat#(X) | (488) |
isNat#(mark(X)) | → | isNat#(X) | (487) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNat#(active(X)) | → | isNat#(X) | (488) |
1 | > | 1 | |
isNat#(mark(X)) | → | isNat#(X) | (487) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U104#(X1,mark(X2),X3) | → | U104#(X1,X2,X3) | (490) |
U104#(mark(X1),X2,X3) | → | U104#(X1,X2,X3) | (489) |
U104#(X1,X2,mark(X3)) | → | U104#(X1,X2,X3) | (491) |
U104#(active(X1),X2,X3) | → | U104#(X1,X2,X3) | (492) |
U104#(X1,active(X2),X3) | → | U104#(X1,X2,X3) | (493) |
U104#(X1,X2,active(X3)) | → | U104#(X1,X2,X3) | (494) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U104#(X1,mark(X2),X3) | → | U104#(X1,X2,X3) | (490) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U104#(mark(X1),X2,X3) | → | U104#(X1,X2,X3) | (489) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U104#(X1,X2,mark(X3)) | → | U104#(X1,X2,X3) | (491) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U104#(active(X1),X2,X3) | → | U104#(X1,X2,X3) | (492) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U104#(X1,active(X2),X3) | → | U104#(X1,X2,X3) | (493) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U104#(X1,X2,active(X3)) | → | U104#(X1,X2,X3) | (494) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (496) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (495) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (497) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (498) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (496) |
1 | ≥ | 1 | |
2 | > | 2 | |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (495) |
1 | > | 1 | |
2 | ≥ | 2 | |
plus#(active(X1),X2) | → | plus#(X1,X2) | (497) |
1 | > | 1 | |
2 | ≥ | 2 | |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (498) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
x#(X1,mark(X2)) | → | x#(X1,X2) | (500) |
x#(mark(X1),X2) | → | x#(X1,X2) | (499) |
x#(active(X1),X2) | → | x#(X1,X2) | (501) |
x#(X1,active(X2)) | → | x#(X1,X2) | (502) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
x#(X1,mark(X2)) | → | x#(X1,X2) | (500) |
1 | ≥ | 1 | |
2 | > | 2 | |
x#(mark(X1),X2) | → | x#(X1,X2) | (499) |
1 | > | 1 | |
2 | ≥ | 2 | |
x#(active(X1),X2) | → | x#(X1,X2) | (501) |
1 | > | 1 | |
2 | ≥ | 2 | |
x#(X1,active(X2)) | → | x#(X1,X2) | (502) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U11#(X1,mark(X2),X3) | → | U11#(X1,X2,X3) | (504) |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (503) |
U11#(X1,X2,mark(X3)) | → | U11#(X1,X2,X3) | (505) |
U11#(active(X1),X2,X3) | → | U11#(X1,X2,X3) | (506) |
U11#(X1,active(X2),X3) | → | U11#(X1,X2,X3) | (507) |
U11#(X1,X2,active(X3)) | → | U11#(X1,X2,X3) | (508) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U11#(X1,mark(X2),X3) | → | U11#(X1,X2,X3) | (504) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (503) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U11#(X1,X2,mark(X3)) | → | U11#(X1,X2,X3) | (505) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U11#(active(X1),X2,X3) | → | U11#(X1,X2,X3) | (506) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U11#(X1,active(X2),X3) | → | U11#(X1,X2,X3) | (507) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U11#(X1,X2,active(X3)) | → | U11#(X1,X2,X3) | (508) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U12#(X1,mark(X2),X3) | → | U12#(X1,X2,X3) | (510) |
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (509) |
U12#(X1,X2,mark(X3)) | → | U12#(X1,X2,X3) | (511) |
U12#(active(X1),X2,X3) | → | U12#(X1,X2,X3) | (512) |
U12#(X1,active(X2),X3) | → | U12#(X1,X2,X3) | (513) |
U12#(X1,X2,active(X3)) | → | U12#(X1,X2,X3) | (514) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U12#(X1,mark(X2),X3) | → | U12#(X1,X2,X3) | (510) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U12#(mark(X1),X2,X3) | → | U12#(X1,X2,X3) | (509) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U12#(X1,X2,mark(X3)) | → | U12#(X1,X2,X3) | (511) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U12#(active(X1),X2,X3) | → | U12#(X1,X2,X3) | (512) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U12#(X1,active(X2),X3) | → | U12#(X1,X2,X3) | (513) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U12#(X1,X2,active(X3)) | → | U12#(X1,X2,X3) | (514) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U13#(X1,mark(X2),X3) | → | U13#(X1,X2,X3) | (516) |
U13#(mark(X1),X2,X3) | → | U13#(X1,X2,X3) | (515) |
U13#(X1,X2,mark(X3)) | → | U13#(X1,X2,X3) | (517) |
U13#(active(X1),X2,X3) | → | U13#(X1,X2,X3) | (518) |
U13#(X1,active(X2),X3) | → | U13#(X1,X2,X3) | (519) |
U13#(X1,X2,active(X3)) | → | U13#(X1,X2,X3) | (520) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U13#(X1,mark(X2),X3) | → | U13#(X1,X2,X3) | (516) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U13#(mark(X1),X2,X3) | → | U13#(X1,X2,X3) | (515) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U13#(X1,X2,mark(X3)) | → | U13#(X1,X2,X3) | (517) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U13#(active(X1),X2,X3) | → | U13#(X1,X2,X3) | (518) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U13#(X1,active(X2),X3) | → | U13#(X1,X2,X3) | (519) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U13#(X1,X2,active(X3)) | → | U13#(X1,X2,X3) | (520) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U14#(X1,mark(X2),X3) | → | U14#(X1,X2,X3) | (522) |
U14#(mark(X1),X2,X3) | → | U14#(X1,X2,X3) | (521) |
U14#(X1,X2,mark(X3)) | → | U14#(X1,X2,X3) | (523) |
U14#(active(X1),X2,X3) | → | U14#(X1,X2,X3) | (524) |
U14#(X1,active(X2),X3) | → | U14#(X1,X2,X3) | (525) |
U14#(X1,X2,active(X3)) | → | U14#(X1,X2,X3) | (526) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U14#(X1,mark(X2),X3) | → | U14#(X1,X2,X3) | (522) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U14#(mark(X1),X2,X3) | → | U14#(X1,X2,X3) | (521) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U14#(X1,X2,mark(X3)) | → | U14#(X1,X2,X3) | (523) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U14#(active(X1),X2,X3) | → | U14#(X1,X2,X3) | (524) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U14#(X1,active(X2),X3) | → | U14#(X1,X2,X3) | (525) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U14#(X1,X2,active(X3)) | → | U14#(X1,X2,X3) | (526) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U15#(X1,mark(X2)) | → | U15#(X1,X2) | (528) |
U15#(mark(X1),X2) | → | U15#(X1,X2) | (527) |
U15#(active(X1),X2) | → | U15#(X1,X2) | (529) |
U15#(X1,active(X2)) | → | U15#(X1,X2) | (530) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U15#(X1,mark(X2)) | → | U15#(X1,X2) | (528) |
1 | ≥ | 1 | |
2 | > | 2 | |
U15#(mark(X1),X2) | → | U15#(X1,X2) | (527) |
1 | > | 1 | |
2 | ≥ | 2 | |
U15#(active(X1),X2) | → | U15#(X1,X2) | (529) |
1 | > | 1 | |
2 | ≥ | 2 | |
U15#(X1,active(X2)) | → | U15#(X1,X2) | (530) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U16#(active(X)) | → | U16#(X) | (532) |
U16#(mark(X)) | → | U16#(X) | (531) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U16#(active(X)) | → | U16#(X) | (532) |
1 | > | 1 | |
U16#(mark(X)) | → | U16#(X) | (531) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U21#(X1,mark(X2)) | → | U21#(X1,X2) | (534) |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (533) |
U21#(active(X1),X2) | → | U21#(X1,X2) | (535) |
U21#(X1,active(X2)) | → | U21#(X1,X2) | (536) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U21#(X1,mark(X2)) | → | U21#(X1,X2) | (534) |
1 | ≥ | 1 | |
2 | > | 2 | |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (533) |
1 | > | 1 | |
2 | ≥ | 2 | |
U21#(active(X1),X2) | → | U21#(X1,X2) | (535) |
1 | > | 1 | |
2 | ≥ | 2 | |
U21#(X1,active(X2)) | → | U21#(X1,X2) | (536) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U22#(X1,mark(X2)) | → | U22#(X1,X2) | (538) |
U22#(mark(X1),X2) | → | U22#(X1,X2) | (537) |
U22#(active(X1),X2) | → | U22#(X1,X2) | (539) |
U22#(X1,active(X2)) | → | U22#(X1,X2) | (540) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U22#(X1,mark(X2)) | → | U22#(X1,X2) | (538) |
1 | ≥ | 1 | |
2 | > | 2 | |
U22#(mark(X1),X2) | → | U22#(X1,X2) | (537) |
1 | > | 1 | |
2 | ≥ | 2 | |
U22#(active(X1),X2) | → | U22#(X1,X2) | (539) |
1 | > | 1 | |
2 | ≥ | 2 | |
U22#(X1,active(X2)) | → | U22#(X1,X2) | (540) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U23#(active(X)) | → | U23#(X) | (542) |
U23#(mark(X)) | → | U23#(X) | (541) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U23#(active(X)) | → | U23#(X) | (542) |
1 | > | 1 | |
U23#(mark(X)) | → | U23#(X) | (541) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U31#(X1,mark(X2),X3) | → | U31#(X1,X2,X3) | (544) |
U31#(mark(X1),X2,X3) | → | U31#(X1,X2,X3) | (543) |
U31#(X1,X2,mark(X3)) | → | U31#(X1,X2,X3) | (545) |
U31#(active(X1),X2,X3) | → | U31#(X1,X2,X3) | (546) |
U31#(X1,active(X2),X3) | → | U31#(X1,X2,X3) | (547) |
U31#(X1,X2,active(X3)) | → | U31#(X1,X2,X3) | (548) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U31#(X1,mark(X2),X3) | → | U31#(X1,X2,X3) | (544) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U31#(mark(X1),X2,X3) | → | U31#(X1,X2,X3) | (543) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U31#(X1,X2,mark(X3)) | → | U31#(X1,X2,X3) | (545) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U31#(active(X1),X2,X3) | → | U31#(X1,X2,X3) | (546) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U31#(X1,active(X2),X3) | → | U31#(X1,X2,X3) | (547) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U31#(X1,X2,active(X3)) | → | U31#(X1,X2,X3) | (548) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U32#(X1,mark(X2),X3) | → | U32#(X1,X2,X3) | (550) |
U32#(mark(X1),X2,X3) | → | U32#(X1,X2,X3) | (549) |
U32#(X1,X2,mark(X3)) | → | U32#(X1,X2,X3) | (551) |
U32#(active(X1),X2,X3) | → | U32#(X1,X2,X3) | (552) |
U32#(X1,active(X2),X3) | → | U32#(X1,X2,X3) | (553) |
U32#(X1,X2,active(X3)) | → | U32#(X1,X2,X3) | (554) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U32#(X1,mark(X2),X3) | → | U32#(X1,X2,X3) | (550) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U32#(mark(X1),X2,X3) | → | U32#(X1,X2,X3) | (549) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U32#(X1,X2,mark(X3)) | → | U32#(X1,X2,X3) | (551) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U32#(active(X1),X2,X3) | → | U32#(X1,X2,X3) | (552) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U32#(X1,active(X2),X3) | → | U32#(X1,X2,X3) | (553) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U32#(X1,X2,active(X3)) | → | U32#(X1,X2,X3) | (554) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U33#(X1,mark(X2),X3) | → | U33#(X1,X2,X3) | (556) |
U33#(mark(X1),X2,X3) | → | U33#(X1,X2,X3) | (555) |
U33#(X1,X2,mark(X3)) | → | U33#(X1,X2,X3) | (557) |
U33#(active(X1),X2,X3) | → | U33#(X1,X2,X3) | (558) |
U33#(X1,active(X2),X3) | → | U33#(X1,X2,X3) | (559) |
U33#(X1,X2,active(X3)) | → | U33#(X1,X2,X3) | (560) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U33#(X1,mark(X2),X3) | → | U33#(X1,X2,X3) | (556) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U33#(mark(X1),X2,X3) | → | U33#(X1,X2,X3) | (555) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U33#(X1,X2,mark(X3)) | → | U33#(X1,X2,X3) | (557) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U33#(active(X1),X2,X3) | → | U33#(X1,X2,X3) | (558) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U33#(X1,active(X2),X3) | → | U33#(X1,X2,X3) | (559) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U33#(X1,X2,active(X3)) | → | U33#(X1,X2,X3) | (560) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U34#(X1,mark(X2),X3) | → | U34#(X1,X2,X3) | (562) |
U34#(mark(X1),X2,X3) | → | U34#(X1,X2,X3) | (561) |
U34#(X1,X2,mark(X3)) | → | U34#(X1,X2,X3) | (563) |
U34#(active(X1),X2,X3) | → | U34#(X1,X2,X3) | (564) |
U34#(X1,active(X2),X3) | → | U34#(X1,X2,X3) | (565) |
U34#(X1,X2,active(X3)) | → | U34#(X1,X2,X3) | (566) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U34#(X1,mark(X2),X3) | → | U34#(X1,X2,X3) | (562) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U34#(mark(X1),X2,X3) | → | U34#(X1,X2,X3) | (561) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U34#(X1,X2,mark(X3)) | → | U34#(X1,X2,X3) | (563) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U34#(active(X1),X2,X3) | → | U34#(X1,X2,X3) | (564) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U34#(X1,active(X2),X3) | → | U34#(X1,X2,X3) | (565) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U34#(X1,X2,active(X3)) | → | U34#(X1,X2,X3) | (566) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U35#(X1,mark(X2)) | → | U35#(X1,X2) | (568) |
U35#(mark(X1),X2) | → | U35#(X1,X2) | (567) |
U35#(active(X1),X2) | → | U35#(X1,X2) | (569) |
U35#(X1,active(X2)) | → | U35#(X1,X2) | (570) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U35#(X1,mark(X2)) | → | U35#(X1,X2) | (568) |
1 | ≥ | 1 | |
2 | > | 2 | |
U35#(mark(X1),X2) | → | U35#(X1,X2) | (567) |
1 | > | 1 | |
2 | ≥ | 2 | |
U35#(active(X1),X2) | → | U35#(X1,X2) | (569) |
1 | > | 1 | |
2 | ≥ | 2 | |
U35#(X1,active(X2)) | → | U35#(X1,X2) | (570) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U36#(active(X)) | → | U36#(X) | (572) |
U36#(mark(X)) | → | U36#(X) | (571) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U36#(active(X)) | → | U36#(X) | (572) |
1 | > | 1 | |
U36#(mark(X)) | → | U36#(X) | (571) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U41#(X1,mark(X2)) | → | U41#(X1,X2) | (574) |
U41#(mark(X1),X2) | → | U41#(X1,X2) | (573) |
U41#(active(X1),X2) | → | U41#(X1,X2) | (575) |
U41#(X1,active(X2)) | → | U41#(X1,X2) | (576) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U41#(X1,mark(X2)) | → | U41#(X1,X2) | (574) |
1 | ≥ | 1 | |
2 | > | 2 | |
U41#(mark(X1),X2) | → | U41#(X1,X2) | (573) |
1 | > | 1 | |
2 | ≥ | 2 | |
U41#(active(X1),X2) | → | U41#(X1,X2) | (575) |
1 | > | 1 | |
2 | ≥ | 2 | |
U41#(X1,active(X2)) | → | U41#(X1,X2) | (576) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U42#(active(X)) | → | U42#(X) | (578) |
U42#(mark(X)) | → | U42#(X) | (577) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U42#(active(X)) | → | U42#(X) | (578) |
1 | > | 1 | |
U42#(mark(X)) | → | U42#(X) | (577) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U51#(active(X)) | → | U51#(X) | (580) |
U51#(mark(X)) | → | U51#(X) | (579) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U51#(active(X)) | → | U51#(X) | (580) |
1 | > | 1 | |
U51#(mark(X)) | → | U51#(X) | (579) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U61#(X1,mark(X2)) | → | U61#(X1,X2) | (582) |
U61#(mark(X1),X2) | → | U61#(X1,X2) | (581) |
U61#(active(X1),X2) | → | U61#(X1,X2) | (583) |
U61#(X1,active(X2)) | → | U61#(X1,X2) | (584) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U61#(X1,mark(X2)) | → | U61#(X1,X2) | (582) |
1 | ≥ | 1 | |
2 | > | 2 | |
U61#(mark(X1),X2) | → | U61#(X1,X2) | (581) |
1 | > | 1 | |
2 | ≥ | 2 | |
U61#(active(X1),X2) | → | U61#(X1,X2) | (583) |
1 | > | 1 | |
2 | ≥ | 2 | |
U61#(X1,active(X2)) | → | U61#(X1,X2) | (584) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U62#(active(X)) | → | U62#(X) | (586) |
U62#(mark(X)) | → | U62#(X) | (585) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U62#(active(X)) | → | U62#(X) | (586) |
1 | > | 1 | |
U62#(mark(X)) | → | U62#(X) | (585) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U71#(X1,mark(X2)) | → | U71#(X1,X2) | (588) |
U71#(mark(X1),X2) | → | U71#(X1,X2) | (587) |
U71#(active(X1),X2) | → | U71#(X1,X2) | (589) |
U71#(X1,active(X2)) | → | U71#(X1,X2) | (590) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U71#(X1,mark(X2)) | → | U71#(X1,X2) | (588) |
1 | ≥ | 1 | |
2 | > | 2 | |
U71#(mark(X1),X2) | → | U71#(X1,X2) | (587) |
1 | > | 1 | |
2 | ≥ | 2 | |
U71#(active(X1),X2) | → | U71#(X1,X2) | (589) |
1 | > | 1 | |
2 | ≥ | 2 | |
U71#(X1,active(X2)) | → | U71#(X1,X2) | (590) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U72#(X1,mark(X2)) | → | U72#(X1,X2) | (592) |
U72#(mark(X1),X2) | → | U72#(X1,X2) | (591) |
U72#(active(X1),X2) | → | U72#(X1,X2) | (593) |
U72#(X1,active(X2)) | → | U72#(X1,X2) | (594) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U72#(X1,mark(X2)) | → | U72#(X1,X2) | (592) |
1 | ≥ | 1 | |
2 | > | 2 | |
U72#(mark(X1),X2) | → | U72#(X1,X2) | (591) |
1 | > | 1 | |
2 | ≥ | 2 | |
U72#(active(X1),X2) | → | U72#(X1,X2) | (593) |
1 | > | 1 | |
2 | ≥ | 2 | |
U72#(X1,active(X2)) | → | U72#(X1,X2) | (594) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U81#(X1,mark(X2),X3) | → | U81#(X1,X2,X3) | (596) |
U81#(mark(X1),X2,X3) | → | U81#(X1,X2,X3) | (595) |
U81#(X1,X2,mark(X3)) | → | U81#(X1,X2,X3) | (597) |
U81#(active(X1),X2,X3) | → | U81#(X1,X2,X3) | (598) |
U81#(X1,active(X2),X3) | → | U81#(X1,X2,X3) | (599) |
U81#(X1,X2,active(X3)) | → | U81#(X1,X2,X3) | (600) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U81#(X1,mark(X2),X3) | → | U81#(X1,X2,X3) | (596) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U81#(mark(X1),X2,X3) | → | U81#(X1,X2,X3) | (595) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U81#(X1,X2,mark(X3)) | → | U81#(X1,X2,X3) | (597) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U81#(active(X1),X2,X3) | → | U81#(X1,X2,X3) | (598) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U81#(X1,active(X2),X3) | → | U81#(X1,X2,X3) | (599) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U81#(X1,X2,active(X3)) | → | U81#(X1,X2,X3) | (600) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U82#(X1,mark(X2),X3) | → | U82#(X1,X2,X3) | (602) |
U82#(mark(X1),X2,X3) | → | U82#(X1,X2,X3) | (601) |
U82#(X1,X2,mark(X3)) | → | U82#(X1,X2,X3) | (603) |
U82#(active(X1),X2,X3) | → | U82#(X1,X2,X3) | (604) |
U82#(X1,active(X2),X3) | → | U82#(X1,X2,X3) | (605) |
U82#(X1,X2,active(X3)) | → | U82#(X1,X2,X3) | (606) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U82#(X1,mark(X2),X3) | → | U82#(X1,X2,X3) | (602) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U82#(mark(X1),X2,X3) | → | U82#(X1,X2,X3) | (601) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U82#(X1,X2,mark(X3)) | → | U82#(X1,X2,X3) | (603) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U82#(active(X1),X2,X3) | → | U82#(X1,X2,X3) | (604) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U82#(X1,active(X2),X3) | → | U82#(X1,X2,X3) | (605) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U82#(X1,X2,active(X3)) | → | U82#(X1,X2,X3) | (606) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U83#(X1,mark(X2),X3) | → | U83#(X1,X2,X3) | (608) |
U83#(mark(X1),X2,X3) | → | U83#(X1,X2,X3) | (607) |
U83#(X1,X2,mark(X3)) | → | U83#(X1,X2,X3) | (609) |
U83#(active(X1),X2,X3) | → | U83#(X1,X2,X3) | (610) |
U83#(X1,active(X2),X3) | → | U83#(X1,X2,X3) | (611) |
U83#(X1,X2,active(X3)) | → | U83#(X1,X2,X3) | (612) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U83#(X1,mark(X2),X3) | → | U83#(X1,X2,X3) | (608) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U83#(mark(X1),X2,X3) | → | U83#(X1,X2,X3) | (607) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U83#(X1,X2,mark(X3)) | → | U83#(X1,X2,X3) | (609) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U83#(active(X1),X2,X3) | → | U83#(X1,X2,X3) | (610) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U83#(X1,active(X2),X3) | → | U83#(X1,X2,X3) | (611) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U83#(X1,X2,active(X3)) | → | U83#(X1,X2,X3) | (612) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U84#(X1,mark(X2),X3) | → | U84#(X1,X2,X3) | (614) |
U84#(mark(X1),X2,X3) | → | U84#(X1,X2,X3) | (613) |
U84#(X1,X2,mark(X3)) | → | U84#(X1,X2,X3) | (615) |
U84#(active(X1),X2,X3) | → | U84#(X1,X2,X3) | (616) |
U84#(X1,active(X2),X3) | → | U84#(X1,X2,X3) | (617) |
U84#(X1,X2,active(X3)) | → | U84#(X1,X2,X3) | (618) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U84#(X1,mark(X2),X3) | → | U84#(X1,X2,X3) | (614) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U84#(mark(X1),X2,X3) | → | U84#(X1,X2,X3) | (613) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U84#(X1,X2,mark(X3)) | → | U84#(X1,X2,X3) | (615) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U84#(active(X1),X2,X3) | → | U84#(X1,X2,X3) | (616) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U84#(X1,active(X2),X3) | → | U84#(X1,X2,X3) | (617) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U84#(X1,X2,active(X3)) | → | U84#(X1,X2,X3) | (618) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
s#(active(X)) | → | s#(X) | (620) |
s#(mark(X)) | → | s#(X) | (619) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
s#(active(X)) | → | s#(X) | (620) |
1 | > | 1 | |
s#(mark(X)) | → | s#(X) | (619) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U91#(X1,mark(X2)) | → | U91#(X1,X2) | (622) |
U91#(mark(X1),X2) | → | U91#(X1,X2) | (621) |
U91#(active(X1),X2) | → | U91#(X1,X2) | (623) |
U91#(X1,active(X2)) | → | U91#(X1,X2) | (624) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U91#(X1,mark(X2)) | → | U91#(X1,X2) | (622) |
1 | ≥ | 1 | |
2 | > | 2 | |
U91#(mark(X1),X2) | → | U91#(X1,X2) | (621) |
1 | > | 1 | |
2 | ≥ | 2 | |
U91#(active(X1),X2) | → | U91#(X1,X2) | (623) |
1 | > | 1 | |
2 | ≥ | 2 | |
U91#(X1,active(X2)) | → | U91#(X1,X2) | (624) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U92#(active(X)) | → | U92#(X) | (626) |
U92#(mark(X)) | → | U92#(X) | (625) |
We restrict the rewrite rules to the following usable rules of the DP problem.
There are no rules.
We restrict the innermost strategy to the following left hand sides.
active(U101(tt,x0,x1)) |
active(U102(tt,x0,x1)) |
active(U103(tt,x0,x1)) |
active(U104(tt,x0,x1)) |
active(U11(tt,x0,x1)) |
active(U12(tt,x0,x1)) |
active(U13(tt,x0,x1)) |
active(U14(tt,x0,x1)) |
active(U15(tt,x0)) |
active(U16(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0,x1)) |
active(U32(tt,x0,x1)) |
active(U33(tt,x0,x1)) |
active(U34(tt,x0,x1)) |
active(U35(tt,x0)) |
active(U36(tt)) |
active(U41(tt,x0)) |
active(U42(tt)) |
active(U51(tt)) |
active(U61(tt,x0)) |
active(U62(tt)) |
active(U71(tt,x0)) |
active(U72(tt,x0)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U91(tt,x0)) |
active(U92(tt)) |
active(isNat(0)) |
active(isNat(plus(x0,x1))) |
active(isNat(s(x0))) |
active(isNat(x(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(plus(x0,x1))) |
active(isNatKind(s(x0))) |
active(isNatKind(x(x0,x1))) |
active(plus(x0,0)) |
active(plus(x0,s(x1))) |
active(x(x0,0)) |
active(x(x0,s(x1))) |
mark(U101(x0,x1,x2)) |
mark(tt) |
mark(U102(x0,x1,x2)) |
mark(isNatKind(x0)) |
mark(U103(x0,x1,x2)) |
mark(isNat(x0)) |
mark(U104(x0,x1,x2)) |
mark(plus(x0,x1)) |
mark(x(x0,x1)) |
mark(U11(x0,x1,x2)) |
mark(U12(x0,x1,x2)) |
mark(U13(x0,x1,x2)) |
mark(U14(x0,x1,x2)) |
mark(U15(x0,x1)) |
mark(U16(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(U23(x0)) |
mark(U31(x0,x1,x2)) |
mark(U32(x0,x1,x2)) |
mark(U33(x0,x1,x2)) |
mark(U34(x0,x1,x2)) |
mark(U35(x0,x1)) |
mark(U36(x0)) |
mark(U41(x0,x1)) |
mark(U42(x0)) |
mark(U51(x0)) |
mark(U61(x0,x1)) |
mark(U62(x0)) |
mark(U71(x0,x1)) |
mark(U72(x0,x1)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(s(x0)) |
mark(U91(x0,x1)) |
mark(U92(x0)) |
mark(0) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U92#(active(X)) | → | U92#(X) | (626) |
1 | > | 1 | |
U92#(mark(X)) | → | U92#(X) | (625) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.