The rewrite relation of the following TRS is considered.
There are 227 ruless (increase limit for explicit display).
The evaluation strategy is innermost.There are 352 ruless (increase limit for explicit display).
The dependency pairs are split into 38 components.
There are 101 ruless (increase limit for explicit display).
We restrict the rewrite rules to the following usable rules of the DP problem.
There are 217 ruless (increase limit for explicit display).
[active#(x1)] | = | -1 + x1 |
[U11(x1, x2)] | = | 2 |
[U12(x1, x2)] | = | 2 |
[U13(x1)] | = | -2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U23(x1)] | = | -2 |
[U31(x1, x2)] | = | 2 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | 0 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | -2 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | -2 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 0 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U86(x1)] | = | -2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[cons(x1, x2)] | = | -2 |
[length(x1)] | = | 2 |
[s(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 |
[0] | = | 0 |
[tt] | = | 0 |
[isNatIListKind(x1)] | = | 2 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | 1 |
There are 130 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairsmark#(cons(X1,X2)) | → | active#(cons(mark(X1),X2)) | (336) |
mark#(U13(X)) | → | active#(U13(mark(X))) | (348) |
mark#(U23(X)) | → | active#(U23(mark(X))) | (359) |
mark#(U33(X)) | → | active#(U33(mark(X))) | (369) |
mark#(U46(X)) | → | active#(U46(mark(X))) | (387) |
mark#(U52(X)) | → | active#(U52(mark(X))) | (394) |
mark#(U86(X)) | → | active#(U86(mark(X))) | (418) |
mark#(s(X)) | → | active#(s(mark(X))) | (433) |
mark#(U61(X)) | → | active#(U61(mark(X))) | (397) |
mark#(U71(X)) | → | active#(U71(mark(X))) | (400) |
[active#(x1)] | = | x1 |
[U11(x1, x2)] | = | x1 |
[U12(x1, x2)] | = | x1 |
[U21(x1, x2)] | = | x1 |
[U22(x1, x2)] | = | 2 · x1 |
[U31(x1, x2)] | = | 1 + x1 |
[U32(x1, x2)] | = | 1 + x1 |
[U41(x1, x2, x3)] | = | 1 + x1 |
[U42(x1, x2, x3)] | = | 1 + x1 |
[U43(x1, x2, x3)] | = | 1 + 2 · x1 |
[U44(x1, x2, x3)] | = | 1 + 2 · x1 |
[U45(x1, x2)] | = | 1 + x1 |
[U51(x1, x2)] | = | x1 |
[U81(x1, x2, x3)] | = | 2 · x1 |
[U82(x1, x2, x3)] | = | 2 · x1 |
[U83(x1, x2, x3)] | = | 2 · x1 |
[U84(x1, x2, x3)] | = | x1 |
[U85(x1, x2)] | = | x1 |
[U91(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + x3 |
[U92(x1, x2, x3)] | = | x1 + 2 · x2 + x3 |
[U93(x1, x2, x3)] | = | x1 + 2 · x2 |
[U94(x1, x2)] | = | x1 + 2 · x2 |
[length(x1)] | = | 2 · x1 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | x1 + x2 |
[0] | = | 0 |
[tt] | = | 0 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 0 |
[U33(x1)] | = | 2 · x1 |
[U46(x1)] | = | x1 |
[isNatIList(x1)] | = | 1 |
[U52(x1)] | = | 2 · x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | x1 |
[U61(x1)] | = | x1 |
[U71(x1)] | = | 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | x1 |
active#(U32(tt,V)) | → | mark#(U33(isNatList(V))) | (247) |
mark#(U31(X1,X2)) | → | mark#(X1) | (365) |
mark#(U32(X1,X2)) | → | mark#(X1) | (368) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (374) |
mark#(U42(X1,X2,X3)) | → | mark#(X1) | (377) |
mark#(U43(X1,X2,X3)) | → | mark#(X1) | (380) |
mark#(U44(X1,X2,X3)) | → | mark#(X1) | (383) |
mark#(U45(X1,X2)) | → | mark#(X1) | (386) |
[active#(x1)] | = | -2 + 2 · x1 |
[U11(x1, x2)] | = | 2 |
[U12(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2)] | = | 2 |
[U32(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | 0 |
[zeros] | = | 2 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 2 + 2 · x2 |
[0] | = | 0 |
[tt] | = | 0 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 2 |
[U23(x1)] | = | 2 · x1 |
[isNat(x1)] | = | 2 |
[U33(x1)] | = | -2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | -2 |
[U86(x1)] | = | -2 |
[s(x1)] | = | -2 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 |
There are 108 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairmark#(U32(X1,X2)) | → | active#(U32(mark(X1),X2)) | (366) |
The dependency pairs are split into 1 component.
mark#(U12(X1,X2)) | → | active#(U12(mark(X1),X2)) | (344) |
active#(U11(tt,V1)) | → | mark#(U12(isNatIListKind(V1),V1)) | (230) |
mark#(U12(X1,X2)) | → | mark#(X1) | (346) |
mark#(zeros) | → | active#(zeros) | (335) |
active#(zeros) | → | mark#(cons(0,zeros)) | (228) |
mark#(cons(X1,X2)) | → | mark#(X1) | (338) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (340) |
active#(U12(tt,V1)) | → | mark#(U13(isNatList(V1))) | (233) |
mark#(U13(X)) | → | mark#(X) | (350) |
mark#(U11(X1,X2)) | → | mark#(X1) | (342) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(isNatList(X)) | → | active#(isNatList(X)) | (351) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U21(X1,X2)) | → | mark#(X1) | (354) |
mark#(U22(X1,X2)) | → | mark#(X1) | (357) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (358) |
active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | (321) |
mark#(U61(X)) | → | mark#(X) | (399) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(length(V1))) | → | mark#(U11(isNatIListKind(V1),V1)) | (302) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (363) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(U33(X)) | → | mark#(X) | (371) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(V)) | → | mark#(U31(isNatIListKind(V),V)) | (308) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U51(X1,X2)) | → | mark#(X1) | (393) |
mark#(U71(X)) | → | mark#(X) | (402) |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (405) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U85(X1,X2)) | → | mark#(X1) | (417) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | mark#(X1) | (423) |
mark#(U92(X1,X2,X3)) | → | mark#(X1) | (426) |
mark#(U93(X1,X2,X3)) | → | mark#(X1) | (429) |
mark#(U94(X1,X2)) | → | mark#(X1) | (432) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
mark#(length(X)) | → | mark#(X) | (438) |
active#(isNatKind(s(V1))) | → | mark#(U71(isNatKind(V1))) | (324) |
[active#(x1)] | = | -2 + 2 · x1 |
[U11(x1, x2)] | = | 2 |
[U12(x1, x2)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U31(x1, x2)] | = | 0 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | -2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | -2 + x1 |
[0] | = | 0 |
[tt] | = | 0 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 2 |
[U23(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | 2 + 2 · x1 |
[U46(x1)] | = | -2 + 2 · x1 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | 0 |
[U86(x1)] | = | 2 |
[s(x1)] | = | 2 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 |
There are 104 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair), the pairmark#(U31(X1,X2)) | → | active#(U31(mark(X1),X2)) | (363) |
The dependency pairs are split into 1 component.
active#(U11(tt,V1)) | → | mark#(U12(isNatIListKind(V1),V1)) | (230) |
mark#(U12(X1,X2)) | → | active#(U12(mark(X1),X2)) | (344) |
active#(U12(tt,V1)) | → | mark#(U13(isNatList(V1))) | (233) |
mark#(U13(X)) | → | mark#(X) | (350) |
mark#(zeros) | → | active#(zeros) | (335) |
active#(zeros) | → | mark#(cons(0,zeros)) | (228) |
mark#(cons(X1,X2)) | → | mark#(X1) | (338) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (340) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(U11(X1,X2)) | → | mark#(X1) | (342) |
mark#(U12(X1,X2)) | → | mark#(X1) | (346) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(isNatList(X)) | → | active#(isNatList(X)) | (351) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(U21(X1,X2)) | → | mark#(X1) | (354) |
mark#(U22(X1,X2)) | → | mark#(X1) | (357) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (358) |
active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | (321) |
mark#(U61(X)) | → | mark#(X) | (399) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(length(V1))) | → | mark#(U11(isNatIListKind(V1),V1)) | (302) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U33(X)) | → | mark#(X) | (371) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U51(X1,X2)) | → | mark#(X1) | (393) |
mark#(U71(X)) | → | mark#(X) | (402) |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (405) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U85(X1,X2)) | → | mark#(X1) | (417) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | mark#(X1) | (423) |
mark#(U92(X1,X2,X3)) | → | mark#(X1) | (426) |
mark#(U93(X1,X2,X3)) | → | mark#(X1) | (429) |
mark#(U94(X1,X2)) | → | mark#(X1) | (432) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
mark#(length(X)) | → | mark#(X) | (438) |
active#(isNatKind(s(V1))) | → | mark#(U71(isNatKind(V1))) | (324) |
[active#(x1)] | = | x1 |
[U11(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
[U12(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U21(x1, x2)] | = | x1 + 2 · x2 |
[U22(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U41(x1, x2, x3)] | = | 1 + x2 + 2 · x3 |
[U42(x1, x2, x3)] | = | 1 + x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | 1 + x1 + x2 + 2 · x3 |
[U44(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x3 |
[U45(x1, x2)] | = | 1 + 2 · x2 |
[U51(x1, x2)] | = | 2 · x1 |
[U81(x1, x2, x3)] | = | x1 + 2 · x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | x1 + 2 · x2 + 2 · x3 |
[U85(x1, x2)] | = | x1 + 2 · x2 |
[U91(x1, x2, x3)] | = | 1 + x1 + 2 · x2 + 2 · x3 |
[U92(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x2 + 2 · x3 |
[U93(x1, x2, x3)] | = | 1 + x1 + 2 · x2 |
[U94(x1, x2)] | = | 1 + 2 · x1 + 2 · x2 |
[length(x1)] | = | 1 + 2 · x1 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | x1 + 2 · x2 |
[0] | = | 0 |
[tt] | = | 0 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | x1 |
[isNatList(x1)] | = | 2 · x1 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 2 · x1 |
[U31(x1, x2)] | = | 1 + x1 + 2 · x2 |
[U32(x1, x2)] | = | 1 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | 1 + x1 |
[U46(x1)] | = | x1 |
[isNatIList(x1)] | = | 1 + 2 · x1 |
[U52(x1)] | = | 2 · x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | x1 |
[U61(x1)] | = | x1 |
[U71(x1)] | = | x1 |
[nil] | = | 0 |
[mark#(x1)] | = | x1 |
active#(U11(tt,V1)) | → | mark#(U12(isNatIListKind(V1),V1)) | (230) |
mark#(U11(X1,X2)) | → | mark#(X1) | (342) |
mark#(U33(X)) | → | mark#(X) | (371) |
mark#(U91(X1,X2,X3)) | → | mark#(X1) | (423) |
mark#(U92(X1,X2,X3)) | → | mark#(X1) | (426) |
mark#(U93(X1,X2,X3)) | → | mark#(X1) | (429) |
mark#(U94(X1,X2)) | → | mark#(X1) | (432) |
mark#(length(X)) | → | mark#(X) | (438) |
[active#(x1)] | = | -2 |
[U11(x1, x2)] | = | 0 |
[U12(x1, x2)] | = | 2 + x1 |
[U21(x1, x2)] | = | 1 + x1 |
[U22(x1, x2)] | = | 1 + 2 · x1 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 1 + x1 |
[U81(x1, x2, x3)] | = | 1 + x1 |
[U82(x1, x2, x3)] | = | 1 + x1 |
[U83(x1, x2, x3)] | = | 1 + 2 · x1 |
[U84(x1, x2, x3)] | = | 1 + 2 · x1 |
[U85(x1, x2)] | = | 1 + x1 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 1 |
[length(x1)] | = | -2 |
[mark(x1)] | = | 1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 + 2 · x1 |
[cons(x1, x2)] | = | 1 + 2 · x1 |
[0] | = | 0 |
[tt] | = | 1 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 1 + 2 · x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | 2 + 2 · x1 + x2 |
[U32(x1, x2)] | = | -2 + 2 · x2 |
[U33(x1)] | = | 2 |
[U46(x1)] | = | 1 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 1 + 2 · x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 1 + 2 · x1 |
[U71(x1)] | = | 1 + x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U12(X1,X2)) | → | active#(U12(mark(X1),X2)) | (344) |
mark#(U12(X1,X2)) | → | mark#(X1) | (346) |
[active#(x1)] | = | -2 + x1 |
[U11(x1, x2)] | = | -2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 0 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | 0 |
[zeros] | = | 0 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | -2 + x1 |
[0] | = | 0 |
[tt] | = | 1 |
[U12(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | x1 |
[U32(x1, x2)] | = | -2 + 2 · x1 |
[U33(x1)] | = | 2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | 2 |
[U86(x1)] | = | 1 |
[s(x1)] | = | 1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (93) |
U11(mark(X1),X2) | → | U11(X1,X2) | (92) |
U11(active(X1),X2) | → | U11(X1,X2) | (94) |
U11(X1,active(X2)) | → | U11(X1,X2) | (95) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U43(X1,mark(X2),X3) | → | U43(X1,X2,X3) | (143) |
U43(mark(X1),X2,X3) | → | U43(X1,X2,X3) | (142) |
U43(X1,X2,mark(X3)) | → | U43(X1,X2,X3) | (144) |
U43(active(X1),X2,X3) | → | U43(X1,X2,X3) | (145) |
U43(X1,active(X2),X3) | → | U43(X1,X2,X3) | (146) |
U43(X1,X2,active(X3)) | → | U43(X1,X2,X3) | (147) |
U44(X1,mark(X2),X3) | → | U44(X1,X2,X3) | (149) |
U44(mark(X1),X2,X3) | → | U44(X1,X2,X3) | (148) |
U44(X1,X2,mark(X3)) | → | U44(X1,X2,X3) | (150) |
U44(active(X1),X2,X3) | → | U44(X1,X2,X3) | (151) |
U44(X1,active(X2),X3) | → | U44(X1,X2,X3) | (152) |
U44(X1,X2,active(X3)) | → | U44(X1,X2,X3) | (153) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (173) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (172) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (174) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (175) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (176) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (177) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U12(tt,V1)) | → | mark#(U13(isNatList(V1))) | (233) |
[active#(x1)] | = | -1 + x1 |
[U11(x1, x2)] | = | -2 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | 2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | -2 + x2 |
[0] | = | 0 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 + x1 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 2 |
[U23(x1)] | = | -2 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | 2 + 2 · x1 + x2 |
[U32(x1, x2)] | = | 2 + 2 · x2 |
[U33(x1)] | = | -2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | -2 + 2 · x1 |
[U86(x1)] | = | 0 |
[s(x1)] | = | -2 |
[U61(x1)] | = | -2 + x1 |
[U71(x1)] | = | -2 |
[nil] | = | 0 |
[mark#(x1)] | = | 1 |
U11(X1,mark(X2)) | → | U11(X1,X2) | (93) |
U11(mark(X1),X2) | → | U11(X1,X2) | (92) |
U11(active(X1),X2) | → | U11(X1,X2) | (94) |
U11(X1,active(X2)) | → | U11(X1,X2) | (95) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U43(X1,mark(X2),X3) | → | U43(X1,X2,X3) | (143) |
U43(mark(X1),X2,X3) | → | U43(X1,X2,X3) | (142) |
U43(X1,X2,mark(X3)) | → | U43(X1,X2,X3) | (144) |
U43(active(X1),X2,X3) | → | U43(X1,X2,X3) | (145) |
U43(X1,active(X2),X3) | → | U43(X1,X2,X3) | (146) |
U43(X1,X2,active(X3)) | → | U43(X1,X2,X3) | (147) |
U44(X1,mark(X2),X3) | → | U44(X1,X2,X3) | (149) |
U44(mark(X1),X2,X3) | → | U44(X1,X2,X3) | (148) |
U44(X1,X2,mark(X3)) | → | U44(X1,X2,X3) | (150) |
U44(active(X1),X2,X3) | → | U44(X1,X2,X3) | (151) |
U44(X1,active(X2),X3) | → | U44(X1,X2,X3) | (152) |
U44(X1,X2,active(X3)) | → | U44(X1,X2,X3) | (153) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (173) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (172) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (174) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (175) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (176) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (177) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (340) |
The dependency pairs are split into 1 component.
mark#(zeros) | → | active#(zeros) | (335) |
active#(zeros) | → | mark#(cons(0,zeros)) | (228) |
mark#(cons(X1,X2)) | → | mark#(X1) | (338) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(U13(X)) | → | mark#(X) | (350) |
mark#(isNatList(X)) | → | active#(isNatList(X)) | (351) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U21(X1,X2)) | → | mark#(X1) | (354) |
mark#(U22(X1,X2)) | → | mark#(X1) | (357) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (358) |
active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | (321) |
mark#(U61(X)) | → | mark#(X) | (399) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U51(X1,X2)) | → | mark#(X1) | (393) |
mark#(U71(X)) | → | mark#(X) | (402) |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (405) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U85(X1,X2)) | → | mark#(X1) | (417) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
active#(isNatKind(s(V1))) | → | mark#(U71(isNatKind(V1))) | (324) |
[active#(x1)] | = | 2 |
[U21(x1, x2)] | = | x1 |
[U22(x1, x2)] | = | x1 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | 0 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 2 · x1 |
[U81(x1, x2, x3)] | = | 2 · x1 |
[U82(x1, x2, x3)] | = | 2 · x1 |
[U83(x1, x2, x3)] | = | x1 |
[U84(x1, x2, x3)] | = | 2 · x1 |
[U85(x1, x2)] | = | x1 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | 2 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x1 + x2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 + x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | 2 + x1 |
[U32(x1, x2)] | = | 2 + x2 |
[U33(x1)] | = | 2 |
[U46(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 · x1 |
[U86(x1)] | = | 2 · x1 |
[s(x1)] | = | 2 · x1 |
[U61(x1)] | = | 2 · x1 |
[U71(x1)] | = | 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 + x1 |
mark#(U13(X)) | → | mark#(X) | (350) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | 1 + x1 |
[U41(x1, x2, x3)] | = | 1 |
[U42(x1, x2, x3)] | = | 0 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | 0 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 1 + 2 · x1 |
[U81(x1, x2, x3)] | = | 1 + x1 |
[U82(x1, x2, x3)] | = | 1 + x1 |
[U83(x1, x2, x3)] | = | 1 + 2 · x1 |
[U84(x1, x2, x3)] | = | 1 + x1 |
[U85(x1, x2)] | = | 1 + x1 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 + 2 · x1 |
[zeros] | = | 2 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 1 + 2 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 + 2 · x1 |
[tt] | = | 0 |
[U12(x1, x2)] | = | 2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -1 + x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U32(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | -2 + 2 · x1 |
[U46(x1)] | = | 1 + 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 1 + 2 · x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 1 + 2 · x1 |
[U71(x1)] | = | 1 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(zeros) | → | active#(zeros) | (335) |
The dependency pairs are split into 1 component.
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(cons(X1,X2)) | → | mark#(X1) | (338) |
mark#(isNatList(X)) | → | active#(isNatList(X)) | (351) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U21(X1,X2)) | → | mark#(X1) | (354) |
mark#(U22(X1,X2)) | → | mark#(X1) | (357) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (358) |
active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | (321) |
mark#(U61(X)) | → | mark#(X) | (399) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U51(X1,X2)) | → | mark#(X1) | (393) |
mark#(U71(X)) | → | mark#(X) | (402) |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (405) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U85(X1,X2)) | → | mark#(X1) | (417) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
active#(isNatKind(s(V1))) | → | mark#(U71(isNatKind(V1))) | (324) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[U22(x1, x2)] | = | 1 + 2 · x1 |
[U41(x1, x2, x3)] | = | 1 |
[U42(x1, x2, x3)] | = | 1 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | 1 |
[U45(x1, x2)] | = | 1 |
[U51(x1, x2)] | = | 1 + 2 · x1 |
[U81(x1, x2, x3)] | = | 1 + 2 · x1 |
[U82(x1, x2, x3)] | = | 1 + x1 |
[U83(x1, x2, x3)] | = | 1 + 2 · x1 |
[U84(x1, x2, x3)] | = | 1 + 2 · x1 |
[U85(x1, x2)] | = | 1 + 2 · x1 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | 1 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 1 + 2 · x1 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -1 + x1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 2 + 2 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x1 + x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x1 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 + 2 · x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | 2 |
[U32(x1, x2)] | = | -2 + x2 |
[U33(x1)] | = | 0 |
[U46(x1)] | = | 1 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 1 + x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 1 + x1 |
[U71(x1)] | = | 1 + x1 |
[nil] | = | 2 |
[mark#(x1)] | = | -2 + 2 · x1 |
mark#(cons(X1,X2)) | → | mark#(X1) | (338) |
[active#(x1)] | = | 2 · x1 |
[U21(x1, x2)] | = | 2 · x1 |
[U22(x1, x2)] | = | x1 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | 0 |
[U43(x1, x2, x3)] | = | 0 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | x1 |
[U81(x1, x2, x3)] | = | 1 + 2 · x1 |
[U82(x1, x2, x3)] | = | 1 + x1 |
[U83(x1, x2, x3)] | = | 1 + x1 |
[U84(x1, x2, x3)] | = | 1 + x1 |
[U85(x1, x2)] | = | 1 + 2 · x1 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | 1 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 1 + x1 |
[length(x1)] | = | 1 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | -2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | 0 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 1 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 |
[U32(x1, x2)] | = | -2 |
[U33(x1)] | = | -2 |
[U46(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | x1 |
[U61(x1)] | = | x1 |
[U71(x1)] | = | 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 · x1 |
mark#(U81(X1,X2,X3)) | → | mark#(X1) | (405) |
mark#(U82(X1,X2,X3)) | → | mark#(X1) | (408) |
mark#(U83(X1,X2,X3)) | → | mark#(X1) | (411) |
mark#(U84(X1,X2,X3)) | → | mark#(X1) | (414) |
mark#(U85(X1,X2)) | → | mark#(X1) | (417) |
[active#(x1)] | = | 2 · x1 |
[U21(x1, x2)] | = | 2 + x1 |
[U22(x1, x2)] | = | 2 + x1 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | 0 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | x1 |
[U81(x1, x2, x3)] | = | 0 |
[U82(x1, x2, x3)] | = | 0 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 + 2 · x1 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 + 2 · x1 |
[length(x1)] | = | 2 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | -2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 + 2 · x1 |
[tt] | = | 0 |
[U12(x1, x2)] | = | 2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 + x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | -2 |
[U32(x1, x2)] | = | -2 |
[U33(x1)] | = | -2 |
[U46(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 · x1 |
[U86(x1)] | = | 2 · x1 |
[s(x1)] | = | x1 |
[U61(x1)] | = | 2 · x1 |
[U71(x1)] | = | 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 · x1 |
mark#(U21(X1,X2)) | → | mark#(X1) | (354) |
mark#(U22(X1,X2)) | → | mark#(X1) | (357) |
[active#(x1)] | = | x1 |
[U21(x1, x2)] | = | 2 · x2 |
[U22(x1, x2)] | = | 2 · x2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U81(x1, x2, x3)] | = | x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | x2 + 2 · x3 |
[U83(x1, x2, x3)] | = | x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | x2 + 2 · x3 |
[U85(x1, x2)] | = | 2 · x2 |
[U91(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U92(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U93(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U94(x1, x2)] | = | 2 + 2 · x2 |
[length(x1)] | = | 2 + 2 · x1 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | 2 · x1 + x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 + 2 · x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | 2 + x2 |
[isNatIListKind(x1)] | = | 2 · x1 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 2 · x1 |
[isNatKind(x1)] | = | 2 · x1 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 2 · x1 |
[U31(x1, x2)] | = | 0 |
[U32(x1, x2)] | = | -2 |
[U33(x1)] | = | -2 |
[U46(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | x1 |
[U61(x1)] | = | 2 + x1 |
[U71(x1)] | = | x1 |
[nil] | = | 0 |
[mark#(x1)] | = | x1 |
active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | (321) |
mark#(U61(X)) | → | mark#(X) | (399) |
[active#(x1)] | = | 2 + x1 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 2 + x1 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | -2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 2 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 |
[U32(x1, x2)] | = | -2 |
[U33(x1)] | = | 0 |
[U46(x1)] | = | x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | 2 · x1 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 + x1 |
mark#(U51(X1,X2)) | → | mark#(X1) | (393) |
[active#(x1)] | = | -2 + x1 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | 0 |
[U42(x1, x2, x3)] | = | 0 |
[U43(x1, x2, x3)] | = | 1 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 0 |
[U81(x1, x2, x3)] | = | 1 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | 0 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | 1 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 + 2 · x1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | -2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 + 2 · x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 2 + 2 · x1 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | 2 + x2 |
[U32(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | -2 + x1 |
[U46(x1)] | = | 1 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 1 + 2 · x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | -2 + 2 · x1 |
[U71(x1)] | = | 1 + x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (173) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (172) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (174) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (175) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (176) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (177) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U43(X1,mark(X2),X3) | → | U43(X1,X2,X3) | (143) |
U43(mark(X1),X2,X3) | → | U43(X1,X2,X3) | (142) |
U43(X1,X2,mark(X3)) | → | U43(X1,X2,X3) | (144) |
U43(active(X1),X2,X3) | → | U43(X1,X2,X3) | (145) |
U43(X1,active(X2),X3) | → | U43(X1,X2,X3) | (146) |
U43(X1,X2,active(X3)) | → | U43(X1,X2,X3) | (147) |
U44(X1,mark(X2),X3) | → | U44(X1,X2,X3) | (149) |
U44(mark(X1),X2,X3) | → | U44(X1,X2,X3) | (148) |
U44(X1,X2,mark(X3)) | → | U44(X1,X2,X3) | (150) |
U44(active(X1),X2,X3) | → | U44(X1,X2,X3) | (151) |
U44(X1,active(X2),X3) | → | U44(X1,X2,X3) | (152) |
U44(X1,X2,active(X3)) | → | U44(X1,X2,X3) | (153) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
mark#(isNatKind(X)) | → | active#(isNatKind(X)) | (358) |
The dependency pairs are split into 1 component.
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
mark#(isNatList(X)) | → | active#(isNatList(X)) | (351) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U71(X)) | → | mark#(X) | (402) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | 0 |
[U42(x1, x2, x3)] | = | -2 |
[U43(x1, x2, x3)] | = | -2 |
[U44(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | 1 + x1 |
[U81(x1, x2, x3)] | = | 1 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | 2 + x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | 2 |
[U46(x1)] | = | 1 + 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 1 + 2 · x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | -2 + 2 · x1 |
[U71(x1)] | = | 2 + x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 + 2 · x1 |
mark#(U71(X)) | → | mark#(X) | (402) |
[active#(x1)] | = | 1 · x1 |
[isNatIListKind(x1)] | = | 1 · x1 |
[cons(x1, x2)] | = | 1 + 1 · x2 |
[mark#(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 1 + 1 · x2 |
[isNatKind(x1)] | = | 0 |
[mark(x1)] | = | 1 · x1 |
[U21(x1, x2)] | = | 0 |
[tt] | = | 0 |
[U22(x1, x2)] | = | 0 |
[U23(x1)] | = | 1 · x1 |
[isNat(x1)] | = | 0 |
[isNatList(x1)] | = | 1 · x1 |
[U81(x1, x2, x3)] | = | 1 · x3 |
[U41(x1, x2, x3)] | = | 1 + 1 · x3 |
[U42(x1, x2, x3)] | = | 1 + 1 · x3 |
[U43(x1, x2, x3)] | = | 1 + 1 · x3 |
[U44(x1, x2, x3)] | = | 1 · x3 |
[U45(x1, x2)] | = | 1 · x2 |
[U46(x1)] | = | 1 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[U52(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[U82(x1, x2, x3)] | = | 1 · x3 |
[U83(x1, x2, x3)] | = | 1 · x3 |
[U84(x1, x2, x3)] | = | 1 · x3 |
[U85(x1, x2)] | = | 1 · x2 |
[U86(x1)] | = | 1 · x1 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | 0 |
[U93(x1, x2, x3)] | = | 0 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | 0 |
[zeros] | = | 0 |
[active(x1)] | = | 1 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | 0 |
[U12(x1, x2)] | = | 1 · x2 |
[U13(x1)] | = | 0 |
[U31(x1, x2)] | = | 1 · x2 |
[U32(x1, x2)] | = | 1 · x2 |
[U33(x1)] | = | 0 |
[U61(x1)] | = | 0 |
[U71(x1)] | = | 0 |
[nil] | = | 0 |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (173) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (172) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (174) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (175) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (176) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (177) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U43(X1,mark(X2),X3) | → | U43(X1,X2,X3) | (143) |
U43(mark(X1),X2,X3) | → | U43(X1,X2,X3) | (142) |
U43(X1,X2,mark(X3)) | → | U43(X1,X2,X3) | (144) |
U43(active(X1),X2,X3) | → | U43(X1,X2,X3) | (145) |
U43(X1,active(X2),X3) | → | U43(X1,X2,X3) | (146) |
U43(X1,X2,active(X3)) | → | U43(X1,X2,X3) | (147) |
U44(X1,mark(X2),X3) | → | U44(X1,X2,X3) | (149) |
U44(mark(X1),X2,X3) | → | U44(X1,X2,X3) | (148) |
U44(X1,X2,mark(X3)) | → | U44(X1,X2,X3) | (150) |
U44(active(X1),X2,X3) | → | U44(X1,X2,X3) | (151) |
U44(X1,active(X2),X3) | → | U44(X1,X2,X3) | (152) |
U44(X1,X2,active(X3)) | → | U44(X1,X2,X3) | (153) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(isNatList(cons(V1,V2))) | → | mark#(U81(isNatKind(V1),V1,V2)) | (328) |
active#(U43(tt,V1,V2)) | → | mark#(U44(isNatIListKind(V2),V1,V2)) | (257) |
active#(U51(tt,V2)) | → | mark#(U52(isNatIListKind(V2))) | (267) |
The dependency pairs are split into 1 component.
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U42(tt,V1,V2)) | → | mark#(U43(isNatIListKind(V2),V1,V2)) | (254) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
[active#(x1)] | = | -2 + 2 · x1 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 |
[U43(x1, x2, x3)] | = | 0 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | 2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | 2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | 2 + x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 2 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | 2 + 2 · x1 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | 2 |
[U46(x1)] | = | 0 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | 0 |
[U86(x1)] | = | -2 + 2 · x1 |
[s(x1)] | = | 2 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U43(X1,mark(X2),X3) | → | U43(X1,X2,X3) | (143) |
U43(mark(X1),X2,X3) | → | U43(X1,X2,X3) | (142) |
U43(X1,X2,mark(X3)) | → | U43(X1,X2,X3) | (144) |
U43(active(X1),X2,X3) | → | U43(X1,X2,X3) | (145) |
U43(X1,active(X2),X3) | → | U43(X1,X2,X3) | (146) |
U43(X1,X2,active(X3)) | → | U43(X1,X2,X3) | (147) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U44(X1,mark(X2),X3) | → | U44(X1,X2,X3) | (149) |
U44(mark(X1),X2,X3) | → | U44(X1,X2,X3) | (148) |
U44(X1,X2,mark(X3)) | → | U44(X1,X2,X3) | (150) |
U44(active(X1),X2,X3) | → | U44(X1,X2,X3) | (151) |
U44(X1,active(X2),X3) | → | U44(X1,X2,X3) | (152) |
U44(X1,X2,active(X3)) | → | U44(X1,X2,X3) | (153) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U81(X1,mark(X2),X3) | → | U81(X1,X2,X3) | (173) |
U81(mark(X1),X2,X3) | → | U81(X1,X2,X3) | (172) |
U81(X1,X2,mark(X3)) | → | U81(X1,X2,X3) | (174) |
U81(active(X1),X2,X3) | → | U81(X1,X2,X3) | (175) |
U81(X1,active(X2),X3) | → | U81(X1,X2,X3) | (176) |
U81(X1,X2,active(X3)) | → | U81(X1,X2,X3) | (177) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
mark#(U43(X1,X2,X3)) | → | active#(U43(mark(X1),X2,X3)) | (378) |
The dependency pairs are split into 1 component.
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
active#(isNatIList(cons(V1,V2))) | → | mark#(U41(isNatKind(V1),V1,V2)) | (312) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 1 + x1 |
[U22(x1, x2)] | = | 1 + 2 · x1 |
[U41(x1, x2, x3)] | = | 1 + x1 |
[U42(x1, x2, x3)] | = | 1 + 2 · x1 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | -2 |
[U51(x1, x2)] | = | -2 |
[U81(x1, x2, x3)] | = | 2 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | 1 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 0 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 + 2 · x1 |
[zeros] | = | 2 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | 2 + x1 + x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + x1 + x2 |
[tt] | = | 1 |
[U12(x1, x2)] | = | 2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | 2 |
[U32(x1, x2)] | = | 2 + 2 · x1 |
[U33(x1)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 + x1 |
[U46(x1)] | = | 1 + 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 + 2 · x1 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 2 + x1 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U44(X1,X2,X3)) | → | active#(U44(mark(X1),X2,X3)) | (381) |
mark#(U52(X)) | → | mark#(X) | (396) |
mark#(U81(X1,X2,X3)) | → | active#(U81(mark(X1),X2,X3)) | (403) |
[active#(x1)] | = | -2 + 2 · x1 |
[U21(x1, x2)] | = | 0 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | 1 |
[U51(x1, x2)] | = | -2 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | 1 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | 1 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | 0 |
[mark(x1)] | = | 2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | 2 + x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x1 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 + x1 |
[isNat(x1)] | = | 1 |
[U31(x1, x2)] | = | -2 + 2 · x1 |
[U32(x1, x2)] | = | -2 |
[U33(x1)] | = | 1 + x1 |
[U43(x1, x2, x3)] | = | 2 + 2 · x3 |
[U44(x1, x2, x3)] | = | 2 + x2 + 2 · x3 |
[U46(x1)] | = | -2 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 0 |
[U81(x1, x2, x3)] | = | -2 |
[U86(x1)] | = | -2 + 2 · x1 |
[s(x1)] | = | -2 + 2 · x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U45(X1,mark(X2)) | → | U45(X1,X2) | (155) |
U45(mark(X1),X2) | → | U45(X1,X2) | (154) |
U45(active(X1),X2) | → | U45(X1,X2) | (156) |
U45(X1,active(X2)) | → | U45(X1,X2) | (157) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U44(tt,V1,V2)) | → | mark#(U45(isNat(V1),V2)) | (260) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U45(x1, x2)] | = | 2 |
[U51(x1, x2)] | = | 1 + x1 |
[U82(x1, x2, x3)] | = | 0 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | -2 |
[mark(x1)] | = | x1 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[0] | = | 1 |
[U11(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x2 |
[U32(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | 2 + x1 |
[U43(x1, x2, x3)] | = | -2 + x1 + x2 + 2 · x3 |
[U44(x1, x2, x3)] | = | 2 + x2 |
[U46(x1)] | = | 1 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 1 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U45(X1,X2)) | → | active#(U45(mark(X1),X2)) | (384) |
[active#(x1)] | = | -2 + x1 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2, x3)] | = | 0 |
[U42(x1, x2, x3)] | = | -2 |
[U51(x1, x2)] | = | -2 |
[U82(x1, x2, x3)] | = | -2 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | 0 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + x1 |
[cons(x1, x2)] | = | -2 + x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 1 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 2 · x1 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U32(x1, x2)] | = | -2 + 2 · x2 |
[U33(x1)] | = | 0 |
[U43(x1, x2, x3)] | = | -2 + x1 + 2 · x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x3 |
[U45(x1, x2)] | = | -2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 |
[U86(x1)] | = | 2 |
[s(x1)] | = | -2 |
[U61(x1)] | = | 0 |
[U71(x1)] | = | 0 |
[nil] | = | 2 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U82(X1,mark(X2),X3) | → | U82(X1,X2,X3) | (179) |
U82(mark(X1),X2,X3) | → | U82(X1,X2,X3) | (178) |
U82(X1,X2,mark(X3)) | → | U82(X1,X2,X3) | (180) |
U82(active(X1),X2,X3) | → | U82(X1,X2,X3) | (181) |
U82(X1,active(X2),X3) | → | U82(X1,X2,X3) | (182) |
U82(X1,X2,active(X3)) | → | U82(X1,X2,X3) | (183) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U81(tt,V1,V2)) | → | mark#(U82(isNatKind(V1),V1,V2)) | (273) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 |
[U42(x1, x2, x3)] | = | -2 |
[U51(x1, x2)] | = | -2 |
[U82(x1, x2, x3)] | = | 2 + 2 · x2 + x3 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 1 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 + 2 · x1 |
[zeros] | = | 2 |
[active(x1)] | = | 0 |
[cons(x1, x2)] | = | -2 + 2 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + x1 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x1 |
[isNatIListKind(x1)] | = | 1 |
[U13(x1)] | = | -2 + 2 · x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | -2 + 2 · x1 |
[U43(x1, x2, x3)] | = | 2 + 2 · x1 |
[U44(x1, x2, x3)] | = | 2 + x2 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | 1 + x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | -2 + 2 · x1 |
[U81(x1, x2, x3)] | = | -2 + x1 + 2 · x3 |
[U86(x1)] | = | 1 + x1 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | 0 |
[nil] | = | 2 |
[mark#(x1)] | = | -1 + x1 |
mark#(U82(X1,X2,X3)) | → | active#(U82(mark(X1),X2,X3)) | (406) |
[active#(x1)] | = | -2 + x1 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | 0 |
[U42(x1, x2, x3)] | = | -2 |
[U51(x1, x2)] | = | 0 |
[U83(x1, x2, x3)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 0 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | -2 + x1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x1 + x2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + 2 · x2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x1 |
[U32(x1, x2)] | = | -2 + x2 |
[U33(x1)] | = | 2 |
[U43(x1, x2, x3)] | = | 1 + 2 · x1 + x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x1 |
[U45(x1, x2)] | = | 1 + 2 · x1 |
[U46(x1)] | = | -2 + 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 + x3 |
[U82(x1, x2, x3)] | = | 1 + 2 · x1 |
[U86(x1)] | = | x1 |
[s(x1)] | = | 2 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | -2 + x1 |
[nil] | = | 2 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U83(X1,mark(X2),X3) | → | U83(X1,X2,X3) | (185) |
U83(mark(X1),X2,X3) | → | U83(X1,X2,X3) | (184) |
U83(X1,X2,mark(X3)) | → | U83(X1,X2,X3) | (186) |
U83(active(X1),X2,X3) | → | U83(X1,X2,X3) | (187) |
U83(X1,active(X2),X3) | → | U83(X1,X2,X3) | (188) |
U83(X1,X2,active(X3)) | → | U83(X1,X2,X3) | (189) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U45(tt,V2)) | → | mark#(U46(isNatIList(V2))) | (263) |
active#(U82(tt,V1,V2)) | → | mark#(U83(isNatIListKind(V2),V1,V2)) | (276) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U41(x1, x2, x3)] | = | 1 + 2 · x1 |
[U42(x1, x2, x3)] | = | 0 |
[U51(x1, x2)] | = | -2 |
[U83(x1, x2, x3)] | = | 2 + x2 + 2 · x3 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | 0 |
[mark(x1)] | = | -2 + x1 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | 2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 1 |
[U13(x1)] | = | -2 + 2 · x1 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x2 |
[U32(x1, x2)] | = | -2 + 2 · x2 |
[U33(x1)] | = | 1 |
[U43(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x1 + x2 |
[U45(x1, x2)] | = | -2 + 2 · x2 |
[U46(x1)] | = | 2 + x1 |
[isNatIList(x1)] | = | 2 |
[U52(x1)] | = | -2 + x1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + x3 |
[U82(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[U86(x1)] | = | 1 + 2 · x1 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | 2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U46(X)) | → | mark#(X) | (389) |
mark#(U83(X1,X2,X3)) | → | active#(U83(mark(X1),X2,X3)) | (409) |
mark#(isNatIList(X)) | → | active#(isNatIList(X)) | (390) |
The dependency pairs are split into 1 component.
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | (347) |
active#(isNatIListKind(cons(V1,V2))) | → | mark#(U51(isNatKind(V1),V2)) | (317) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
active#(U41(tt,V1,V2)) | → | mark#(U42(isNatKind(V1),V1,V2)) | (251) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
[active#(x1)] | = | -2 + 2 · x1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 1 |
[U41(x1, x2, x3)] | = | 1 |
[U42(x1, x2, x3)] | = | -2 |
[U51(x1, x2)] | = | -2 |
[U84(x1, x2, x3)] | = | -2 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | 1 |
[U93(x1, x2, x3)] | = | 0 |
[U94(x1, x2)] | = | 1 |
[length(x1)] | = | 1 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 |
[cons(x1, x2)] | = | -2 + 2 · x1 |
[0] | = | 2 |
[U11(x1, x2)] | = | -2 + 2 · x1 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U23(x1)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x2 |
[U32(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | 1 |
[U43(x1, x2, x3)] | = | -2 + x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x3 |
[U45(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 0 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x1 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 |
[U86(x1)] | = | -2 + 2 · x1 |
[s(x1)] | = | -2 + x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U83(tt,V1,V2)) | → | mark#(U84(isNatIListKind(V2),V1,V2)) | (279) |
[active#(x1)] | = | -1 + x1 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | -2 |
[U51(x1, x2)] | = | 0 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | 2 + 2 · x2 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | 2 |
[U43(x1, x2, x3)] | = | 2 + 2 · x1 |
[U44(x1, x2, x3)] | = | -2 + 2 · x3 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 · x1 |
[U52(x1)] | = | -2 |
[U81(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 + x2 |
[U83(x1, x2, x3)] | = | 2 |
[U86(x1)] | = | -2 + x1 |
[s(x1)] | = | -2 |
[U61(x1)] | = | 2 + 2 · x1 |
[U71(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | 1 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U51(X1,mark(X2)) | → | U51(X1,X2) | (163) |
U51(mark(X1),X2) | → | U51(X1,X2) | (162) |
U51(active(X1),X2) | → | U51(X1,X2) | (164) |
U51(X1,active(X2)) | → | U51(X1,X2) | (165) |
U42(X1,mark(X2),X3) | → | U42(X1,X2,X3) | (137) |
U42(mark(X1),X2,X3) | → | U42(X1,X2,X3) | (136) |
U42(X1,X2,mark(X3)) | → | U42(X1,X2,X3) | (138) |
U42(active(X1),X2,X3) | → | U42(X1,X2,X3) | (139) |
U42(X1,active(X2),X3) | → | U42(X1,X2,X3) | (140) |
U42(X1,X2,active(X3)) | → | U42(X1,X2,X3) | (141) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
mark#(U51(X1,X2)) | → | active#(U51(mark(X1),X2)) | (391) |
mark#(U42(X1,X2,X3)) | → | active#(U42(mark(X1),X2,X3)) | (375) |
The dependency pairs are split into 1 component.
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
mark#(U86(X)) | → | mark#(X) | (420) |
mark#(isNat(X)) | → | active#(isNat(X)) | (362) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
[active#(x1)] | = | x1 |
[U21(x1, x2)] | = | 2 |
[U22(x1, x2)] | = | 2 |
[U41(x1, x2, x3)] | = | 1 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | 2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | 2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 + x1 |
[cons(x1, x2)] | = | 2 + 2 · x1 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 + x1 |
[isNat(x1)] | = | 2 |
[U31(x1, x2)] | = | 0 |
[U32(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 + 2 · x1 + x2 |
[U43(x1, x2, x3)] | = | 2 + 2 · x1 |
[U44(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[U45(x1, x2)] | = | -2 + 2 · x2 |
[U46(x1)] | = | -2 |
[isNatIList(x1)] | = | 2 · x1 |
[U51(x1, x2)] | = | -2 + x1 + x2 |
[U52(x1)] | = | 0 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 + x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[U83(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + 2 · x3 |
[U86(x1)] | = | -2 + 2 · x1 |
[s(x1)] | = | -2 + x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 |
[nil] | = | 0 |
[mark#(x1)] | = | 2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (131) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (130) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (132) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (133) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (134) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (135) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U84(X1,mark(X2),X3) | → | U84(X1,X2,X3) | (191) |
U84(mark(X1),X2,X3) | → | U84(X1,X2,X3) | (190) |
U84(X1,X2,mark(X3)) | → | U84(X1,X2,X3) | (192) |
U84(active(X1),X2,X3) | → | U84(X1,X2,X3) | (193) |
U84(X1,active(X2),X3) | → | U84(X1,X2,X3) | (194) |
U84(X1,X2,active(X3)) | → | U84(X1,X2,X3) | (195) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (372) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U84(x1, x2, x3)] | = | 2 + x2 + x3 |
[U85(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 0 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 2 |
[active(x1)] | = | 2 + x1 |
[cons(x1, x2)] | = | 2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 + 2 · x1 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | 2 |
[U41(x1, x2, x3)] | = | 2 + x3 |
[U42(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | -2 + x1 + x2 + x3 |
[U44(x1, x2, x3)] | = | 2 + x1 + x2 + 2 · x3 |
[U45(x1, x2)] | = | -2 + 2 · x2 |
[U46(x1)] | = | -2 |
[isNatIList(x1)] | = | 0 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | 0 |
[U81(x1, x2, x3)] | = | 2 + x2 + x3 |
[U82(x1, x2, x3)] | = | 2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 2 |
[U86(x1)] | = | 1 + x1 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U84(X1,X2,X3)) | → | active#(U84(mark(X1),X2,X3)) | (412) |
[active#(x1)] | = | -2 + x1 |
[U21(x1, x2)] | = | 0 |
[U22(x1, x2)] | = | 2 |
[U85(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | -2 + 2 · x1 |
[zeros] | = | 0 |
[active(x1)] | = | 1 |
[cons(x1, x2)] | = | -2 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U23(x1)] | = | -2 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -1 + x2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | -2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | 2 + 2 · x1 |
[U43(x1, x2, x3)] | = | -1 + 2 · x1 + x2 + x3 |
[U44(x1, x2, x3)] | = | -1 + x2 + x3 |
[U45(x1, x2)] | = | 2 + 2 · x1 + x2 |
[U46(x1)] | = | 1 |
[isNatIList(x1)] | = | 0 |
[U51(x1, x2)] | = | 2 + x2 |
[U52(x1)] | = | -2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 |
[U82(x1, x2, x3)] | = | -1 + x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x3 |
[U84(x1, x2, x3)] | = | -1 + 2 · x1 + 2 · x2 + 2 · x3 |
[U86(x1)] | = | -2 + 2 · x1 |
[s(x1)] | = | -2 + 2 · x1 |
[U61(x1)] | = | -2 + 2 · x1 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | 0 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U85(X1,mark(X2)) | → | U85(X1,X2) | (197) |
U85(mark(X1),X2) | → | U85(X1,X2) | (196) |
U85(active(X1),X2) | → | U85(X1,X2) | (198) |
U85(X1,active(X2)) | → | U85(X1,X2) | (199) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U84(tt,V1,V2)) | → | mark#(U85(isNat(V1),V2)) | (282) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | -2 |
[U22(x1, x2)] | = | -2 |
[U85(x1, x2)] | = | 2 + 2 · x2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | -2 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x2 |
[U32(x1, x2)] | = | 2 + x1 + x2 |
[U33(x1)] | = | 2 |
[U41(x1, x2, x3)] | = | -2 + x1 |
[U42(x1, x2, x3)] | = | -1 + x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x2 |
[U44(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 0 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | -2 |
[U81(x1, x2, x3)] | = | -2 + x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x2 |
[U83(x1, x2, x3)] | = | 2 + x1 |
[U84(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[U86(x1)] | = | 1 + x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | -2 + x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U85(X1,X2)) | → | active#(U85(mark(X1),X2)) | (415) |
[active#(x1)] | = | -2 + 2 · x1 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 1 |
[length(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + 2 · x1 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x1 + x2 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 2 · x1 |
[U13(x1)] | = | 0 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | -2 + 2 · x1 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | -2 + x1 + 2 · x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x2 |
[U44(x1, x2, x3)] | = | -2 + 2 · x3 |
[U45(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 · x1 |
[U51(x1, x2)] | = | -2 + x1 + x2 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 + x3 |
[U82(x1, x2, x3)] | = | 2 + 2 · x1 |
[U83(x1, x2, x3)] | = | -2 + 2 · x2 |
[U84(x1, x2, x3)] | = | -2 + x1 + x3 |
[U85(x1, x2)] | = | 2 + 2 · x1 |
[U86(x1)] | = | 0 |
[s(x1)] | = | -2 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 0 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U85(tt,V2)) | → | mark#(U86(isNatList(V2))) | (285) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 1 |
[U22(x1, x2)] | = | 0 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 + x1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 |
[cons(x1, x2)] | = | -2 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | -2 + 2 · x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + 2 · x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + x1 + x2 |
[U32(x1, x2)] | = | -2 + x1 |
[U33(x1)] | = | 2 |
[U41(x1, x2, x3)] | = | -2 + 2 · x3 |
[U42(x1, x2, x3)] | = | -2 + x1 |
[U43(x1, x2, x3)] | = | 2 + x3 |
[U44(x1, x2, x3)] | = | -2 + x1 |
[U45(x1, x2)] | = | -2 + 2 · x1 |
[U46(x1)] | = | -2 + 2 · x1 |
[isNatIList(x1)] | = | 0 |
[U51(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U52(x1)] | = | -2 + 2 · x1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x3 |
[U82(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x3 |
[U83(x1, x2, x3)] | = | -2 + 2 · x2 |
[U84(x1, x2, x3)] | = | 2 |
[U85(x1, x2)] | = | -2 + 2 · x1 |
[U86(x1)] | = | 2 + 2 · x1 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | -2 + 2 · x1 |
[U71(x1)] | = | -2 + x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U86(X)) | → | mark#(X) | (420) |
[active#(x1)] | = | -1 + x1 |
[U21(x1, x2)] | = | 2 + 2 · x2 |
[U22(x1, x2)] | = | 2 + 2 · x2 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 0 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | 2 + x1 |
[zeros] | = | 0 |
[active(x1)] | = | 2 + 2 · x1 |
[cons(x1, x2)] | = | -2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x2 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 1 + 2 · x1 |
[U31(x1, x2)] | = | -2 + x2 |
[U32(x1, x2)] | = | 2 + x1 |
[U33(x1)] | = | -2 |
[U41(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U42(x1, x2, x3)] | = | -2 + x1 + x3 |
[U43(x1, x2, x3)] | = | -2 + x2 + 2 · x3 |
[U44(x1, x2, x3)] | = | -2 + x3 |
[U45(x1, x2)] | = | -2 + x2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | 2 + x1 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 |
[U82(x1, x2, x3)] | = | -2 + 2 · x2 |
[U83(x1, x2, x3)] | = | -2 + x2 + x3 |
[U84(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[U85(x1, x2)] | = | 2 + x1 + x2 |
[U86(x1)] | = | -2 + x1 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U21(X1,mark(X2)) | → | U21(X1,X2) | (107) |
U21(mark(X1),X2) | → | U21(X1,X2) | (106) |
U21(active(X1),X2) | → | U21(X1,X2) | (108) |
U21(X1,active(X2)) | → | U21(X1,X2) | (109) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1),V1)) | (305) |
The dependency pairs are split into 1 component.
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
mark#(U23(X)) | → | mark#(X) | (361) |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
mark#(U92(X1,X2,X3)) | → | active#(U92(mark(X1),X2,X3)) | (424) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
mark#(U93(X1,X2,X3)) | → | active#(U93(mark(X1),X2,X3)) | (427) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
mark#(U94(X1,X2)) | → | active#(U94(mark(X1),X2)) | (430) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
mark#(s(X)) | → | mark#(X) | (435) |
mark#(U91(X1,X2,X3)) | → | active#(U91(mark(X1),X2,X3)) | (421) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
mark#(length(X)) | → | active#(length(mark(X))) | (436) |
[active#(x1)] | = | -2 |
[U21(x1, x2)] | = | 2 + 2 · x2 |
[U22(x1, x2)] | = | -2 |
[U91(x1, x2, x3)] | = | 1 + x1 |
[U92(x1, x2, x3)] | = | 0 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | -2 |
[mark(x1)] | = | 2 + 2 · x1 |
[zeros] | = | 0 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -1 + 2 · x1 |
[0] | = | 2 |
[U11(x1, x2)] | = | -2 + 2 · x2 |
[tt] | = | 1 |
[U12(x1, x2)] | = | -2 + x1 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U23(x1)] | = | 1 + 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -1 + 2 · x1 + 2 · x2 |
[U32(x1, x2)] | = | -2 + 2 · x2 |
[U33(x1)] | = | 1 |
[U41(x1, x2, x3)] | = | -2 + x1 |
[U42(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x3 |
[U43(x1, x2, x3)] | = | 2 + x1 + 2 · x3 |
[U44(x1, x2, x3)] | = | -1 + 2 · x3 |
[U45(x1, x2)] | = | -2 + 2 · x2 |
[U46(x1)] | = | 0 |
[isNatIList(x1)] | = | 0 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | -2 + x1 |
[U81(x1, x2, x3)] | = | -2 + 2 · x1 |
[U82(x1, x2, x3)] | = | -2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 |
[U84(x1, x2, x3)] | = | 2 + 2 · x3 |
[U85(x1, x2)] | = | -2 + x1 + 2 · x2 |
[U86(x1)] | = | -2 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | 2 + x1 |
[U71(x1)] | = | 2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U21(X1,X2)) | → | active#(U21(mark(X1),X2)) | (352) |
[active#(x1)] | = | -2 + x1 |
[U22(x1, x2)] | = | 2 |
[U91(x1, x2, x3)] | = | 2 |
[U92(x1, x2, x3)] | = | 2 |
[U93(x1, x2, x3)] | = | 2 |
[U94(x1, x2)] | = | -2 |
[length(x1)] | = | 2 |
[mark(x1)] | = | -2 |
[zeros] | = | 0 |
[active(x1)] | = | -1 + 2 · x1 |
[cons(x1, x2)] | = | -2 + 2 · x2 |
[0] | = | 1 |
[U11(x1, x2)] | = | -2 + x1 |
[tt] | = | 2 |
[U12(x1, x2)] | = | -2 + x1 + 2 · x2 |
[isNatIListKind(x1)] | = | x1 |
[U13(x1)] | = | -2 + x1 |
[isNatList(x1)] | = | 0 |
[U21(x1, x2)] | = | 1 + 2 · x1 |
[isNatKind(x1)] | = | 2 · x1 |
[U23(x1)] | = | -2 + 2 · x1 |
[isNat(x1)] | = | 2 · x1 |
[U31(x1, x2)] | = | -1 + x2 |
[U32(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U33(x1)] | = | -2 + x1 |
[U41(x1, x2, x3)] | = | -2 + 2 · x2 |
[U42(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x1 + x2 |
[U44(x1, x2, x3)] | = | -2 + x2 |
[U45(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 + x1 |
[U51(x1, x2)] | = | -2 + 2 · x2 |
[U52(x1)] | = | 1 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 |
[U82(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 |
[U83(x1, x2, x3)] | = | 2 + 2 · x1 |
[U84(x1, x2, x3)] | = | 2 + 2 · x2 + x3 |
[U85(x1, x2)] | = | 2 |
[U86(x1)] | = | 1 |
[s(x1)] | = | -2 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | -2 |
U22(X1,mark(X2)) | → | U22(X1,X2) | (111) |
U22(mark(X1),X2) | → | U22(X1,X2) | (110) |
U22(active(X1),X2) | → | U22(X1,X2) | (112) |
U22(X1,active(X2)) | → | U22(X1,X2) | (113) |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U21(tt,V1)) | → | mark#(U22(isNatKind(V1),V1)) | (237) |
[active#(x1)] | = | -2 |
[U22(x1, x2)] | = | 2 + 2 · x1 + x2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | -2 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | 0 |
[mark(x1)] | = | -2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + x1 + x2 |
[0] | = | 2 |
[U11(x1, x2)] | = | -2 + 2 · x1 |
[tt] | = | 2 |
[U12(x1, x2)] | = | 2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 2 |
[U21(x1, x2)] | = | -2 + 2 · x2 |
[isNatKind(x1)] | = | 2 + 2 · x1 |
[U23(x1)] | = | 1 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U32(x1, x2)] | = | -2 + 2 · x2 |
[U33(x1)] | = | 2 |
[U41(x1, x2, x3)] | = | 2 |
[U42(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x1 |
[U44(x1, x2, x3)] | = | -2 + 2 · x1 + x2 |
[U45(x1, x2)] | = | -2 + 2 · x1 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 + 2 · x1 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | -2 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 + x2 + x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x3 |
[U83(x1, x2, x3)] | = | 2 + x1 + x2 + x3 |
[U84(x1, x2, x3)] | = | -2 + x1 + x2 |
[U85(x1, x2)] | = | -2 + x1 + x2 |
[U86(x1)] | = | -2 |
[s(x1)] | = | 1 + x1 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 2 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U22(X1,X2)) | → | active#(U22(mark(X1),X2)) | (355) |
[active#(x1)] | = | 1 |
[U91(x1, x2, x3)] | = | 1 |
[U92(x1, x2, x3)] | = | 1 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 1 |
[length(x1)] | = | 1 |
[mark(x1)] | = | 2 |
[zeros] | = | 0 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + x2 |
[0] | = | 2 |
[U11(x1, x2)] | = | -1 + 2 · x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | -2 + x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 |
[isNatList(x1)] | = | 2 |
[U21(x1, x2)] | = | -2 + 2 · x2 |
[U22(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[isNatKind(x1)] | = | 0 |
[U23(x1)] | = | 2 · x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 |
[U32(x1, x2)] | = | 2 + x1 + x2 |
[U33(x1)] | = | -2 |
[U41(x1, x2, x3)] | = | -2 + x1 + x2 + 2 · x3 |
[U42(x1, x2, x3)] | = | -1 + x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x3 |
[U45(x1, x2)] | = | -2 + 2 · x1 |
[U46(x1)] | = | -2 + 2 · x1 |
[isNatIList(x1)] | = | 2 |
[U51(x1, x2)] | = | 2 |
[U52(x1)] | = | 2 |
[U81(x1, x2, x3)] | = | 2 + 2 · x1 + x3 |
[U82(x1, x2, x3)] | = | -2 + 2 · x3 |
[U83(x1, x2, x3)] | = | -2 + x2 |
[U84(x1, x2, x3)] | = | -2 + x1 + 2 · x3 |
[U85(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[U86(x1)] | = | 2 |
[s(x1)] | = | x1 |
[U61(x1)] | = | -2 |
[U71(x1)] | = | 0 |
[nil] | = | 0 |
[mark#(x1)] | = | x1 |
active#(U22(tt,V1)) | → | mark#(U23(isNat(V1))) | (240) |
[active#(x1)] | = | -2 |
[U91(x1, x2, x3)] | = | -2 |
[U92(x1, x2, x3)] | = | -2 |
[U93(x1, x2, x3)] | = | 1 |
[U94(x1, x2)] | = | 0 |
[length(x1)] | = | -2 |
[mark(x1)] | = | -2 |
[zeros] | = | 2 |
[active(x1)] | = | -2 + 2 · x1 |
[cons(x1, x2)] | = | -2 + 2 · x1 + 2 · x2 |
[0] | = | 2 |
[U11(x1, x2)] | = | -2 + x2 |
[tt] | = | 0 |
[U12(x1, x2)] | = | 1 + x2 |
[isNatIListKind(x1)] | = | 0 |
[U13(x1)] | = | -2 + x1 |
[isNatList(x1)] | = | 0 |
[U21(x1, x2)] | = | 2 + 2 · x2 |
[U22(x1, x2)] | = | -2 + 2 · x2 |
[isNatKind(x1)] | = | 2 + x1 |
[U23(x1)] | = | 2 + x1 |
[isNat(x1)] | = | 0 |
[U31(x1, x2)] | = | -2 + 2 · x1 + x2 |
[U32(x1, x2)] | = | 2 + 2 · x1 |
[U33(x1)] | = | -2 |
[U41(x1, x2, x3)] | = | 2 + x1 + 2 · x2 + x3 |
[U42(x1, x2, x3)] | = | -2 + 2 · x2 + x3 |
[U43(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U44(x1, x2, x3)] | = | -2 + 2 · x1 + 2 · x2 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 |
[U51(x1, x2)] | = | -2 + x2 |
[U52(x1)] | = | 0 |
[U81(x1, x2, x3)] | = | 2 + 2 · x3 |
[U82(x1, x2, x3)] | = | -2 + x1 + 2 · x2 + x3 |
[U83(x1, x2, x3)] | = | 2 |
[U84(x1, x2, x3)] | = | -2 + 2 · x2 + 2 · x3 |
[U85(x1, x2)] | = | -2 + 2 · x2 |
[U86(x1)] | = | -2 |
[s(x1)] | = | 1 + 2 · x1 |
[U61(x1)] | = | 2 |
[U71(x1)] | = | -2 + 2 · x1 |
[nil] | = | 0 |
[mark#(x1)] | = | -1 + x1 |
mark#(U23(X)) | → | mark#(X) | (361) |
[active#(x1)] | = | -2 + x1 |
[U91(x1, x2, x3)] | = | 2 + 2 · x1 + 2 · x2 + 2 · x3 |
[U92(x1, x2, x3)] | = | 2 + x1 + 2 · x2 + 2 · x3 |
[U93(x1, x2, x3)] | = | 2 + x1 + 2 · x2 |
[U94(x1, x2)] | = | 2 + x1 + 2 · x2 |
[length(x1)] | = | 2 + 2 · x1 |
[mark(x1)] | = | x1 |
[zeros] | = | 0 |
[active(x1)] | = | x1 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[U11(x1, x2)] | = | 2 + 2 · x1 |
[tt] | = | 2 |
[U12(x1, x2)] | = | 2 + 2 · x1 |
[isNatIListKind(x1)] | = | 2 |
[U13(x1)] | = | 2 |
[isNatList(x1)] | = | x1 |
[U21(x1, x2)] | = | 2 + 2 · x1 |
[U22(x1, x2)] | = | 1 + x1 |
[isNatKind(x1)] | = | 2 |
[U23(x1)] | = | 2 |
[isNat(x1)] | = | 2 + 2 · x1 |
[U31(x1, x2)] | = | x1 + x2 |
[U32(x1, x2)] | = | x2 |
[U33(x1)] | = | x1 |
[U41(x1, x2, x3)] | = | 2 + 2 · x2 + 2 · x3 |
[U42(x1, x2, x3)] | = | x1 + x2 + 2 · x3 |
[U43(x1, x2, x3)] | = | 2 |
[U44(x1, x2, x3)] | = | 2 |
[U45(x1, x2)] | = | 2 |
[U46(x1)] | = | 2 |
[isNatIList(x1)] | = | 2 + x1 |
[U51(x1, x2)] | = | x1 |
[U52(x1)] | = | x1 |
[U81(x1, x2, x3)] | = | 2 · x3 |
[U82(x1, x2, x3)] | = | 2 · x3 |
[U83(x1, x2, x3)] | = | 2 · x3 |
[U84(x1, x2, x3)] | = | 2 · x3 |
[U85(x1, x2)] | = | 2 · x2 |
[U86(x1)] | = | 2 · x1 |
[s(x1)] | = | 2 + x1 |
[U61(x1)] | = | x1 |
[U71(x1)] | = | x1 |
[nil] | = | 2 |
[mark#(x1)] | = | -2 + x1 |
active#(U91(tt,L,N)) | → | mark#(U92(isNatIListKind(L),L,N)) | (289) |
prec(U92) | = | 2 | weight(U92) | = | 5 | ||||
prec(U93) | = | 1 | weight(U93) | = | 4 | ||||
prec(U94) | = | 4 | weight(U94) | = | 3 | ||||
prec(length) | = | 3 | weight(length) | = | 2 | ||||
prec(U91) | = | 0 | weight(U91) | = | 1 |
π(mark#) | = | 1 |
π(U92) | = | [] |
π(active#) | = | 1 |
π(U93) | = | [] |
π(U94) | = | [] |
π(s) | = | 1 |
π(length) | = | [] |
π(U91) | = | [] |
π(active) | = | 1 |
π(mark) | = | 1 |
U92(X1,mark(X2),X3) | → | U92(X1,X2,X3) | (209) |
U92(mark(X1),X2,X3) | → | U92(X1,X2,X3) | (208) |
U92(X1,X2,mark(X3)) | → | U92(X1,X2,X3) | (210) |
U92(active(X1),X2,X3) | → | U92(X1,X2,X3) | (211) |
U92(X1,active(X2),X3) | → | U92(X1,X2,X3) | (212) |
U92(X1,X2,active(X3)) | → | U92(X1,X2,X3) | (213) |
U93(X1,mark(X2),X3) | → | U93(X1,X2,X3) | (215) |
U93(mark(X1),X2,X3) | → | U93(X1,X2,X3) | (214) |
U93(X1,X2,mark(X3)) | → | U93(X1,X2,X3) | (216) |
U93(active(X1),X2,X3) | → | U93(X1,X2,X3) | (217) |
U93(X1,active(X2),X3) | → | U93(X1,X2,X3) | (218) |
U93(X1,X2,active(X3)) | → | U93(X1,X2,X3) | (219) |
U94(X1,mark(X2)) | → | U94(X1,X2) | (221) |
U94(mark(X1),X2) | → | U94(X1,X2) | (220) |
U94(active(X1),X2) | → | U94(X1,X2) | (222) |
U94(X1,active(X2)) | → | U94(X1,X2) | (223) |
U91(X1,mark(X2),X3) | → | U91(X1,X2,X3) | (203) |
U91(mark(X1),X2,X3) | → | U91(X1,X2,X3) | (202) |
U91(X1,X2,mark(X3)) | → | U91(X1,X2,X3) | (204) |
U91(active(X1),X2,X3) | → | U91(X1,X2,X3) | (205) |
U91(X1,active(X2),X3) | → | U91(X1,X2,X3) | (206) |
U91(X1,X2,active(X3)) | → | U91(X1,X2,X3) | (207) |
length(active(X)) | → | length(X) | (227) |
length(mark(X)) | → | length(X) | (226) |
active#(U92(tt,L,N)) | → | mark#(U93(isNat(N),L,N)) | (292) |
active#(U93(tt,L,N)) | → | mark#(U94(isNatKind(N),L)) | (295) |
active#(U94(tt,L)) | → | mark#(s(length(L))) | (298) |
active#(length(cons(N,L))) | → | mark#(U91(isNatList(L),L,N)) | (332) |
The dependency pairs are split into 1 component.
mark#(s(X)) | → | mark#(X) | (435) |
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.
s(mark(x0)) |
s(active(x0)) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
mark#(s(X)) | → | mark#(X) | (435) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (441) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (440) |
cons#(active(X1),X2) | → | cons#(X1,X2) | (442) |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (443) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
cons#(X1,mark(X2)) | → | cons#(X1,X2) | (441) |
1 | ≥ | 1 | |
2 | > | 2 | |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (440) |
1 | > | 1 | |
2 | ≥ | 2 | |
cons#(active(X1),X2) | → | cons#(X1,X2) | (442) |
1 | > | 1 | |
2 | ≥ | 2 | |
cons#(X1,active(X2)) | → | cons#(X1,X2) | (443) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (445) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (444) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (446) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (447) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (445) |
1 | ≥ | 1 | |
2 | > | 2 | |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (444) |
1 | > | 1 | |
2 | ≥ | 2 | |
U11#(active(X1),X2) | → | U11#(X1,X2) | (446) |
1 | > | 1 | |
2 | ≥ | 2 | |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (447) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U12#(X1,mark(X2)) | → | U12#(X1,X2) | (449) |
U12#(mark(X1),X2) | → | U12#(X1,X2) | (448) |
U12#(active(X1),X2) | → | U12#(X1,X2) | (450) |
U12#(X1,active(X2)) | → | U12#(X1,X2) | (451) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U12#(X1,mark(X2)) | → | U12#(X1,X2) | (449) |
1 | ≥ | 1 | |
2 | > | 2 | |
U12#(mark(X1),X2) | → | U12#(X1,X2) | (448) |
1 | > | 1 | |
2 | ≥ | 2 | |
U12#(active(X1),X2) | → | U12#(X1,X2) | (450) |
1 | > | 1 | |
2 | ≥ | 2 | |
U12#(X1,active(X2)) | → | U12#(X1,X2) | (451) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNatIListKind#(active(X)) | → | isNatIListKind#(X) | (453) |
isNatIListKind#(mark(X)) | → | isNatIListKind#(X) | (452) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNatIListKind#(active(X)) | → | isNatIListKind#(X) | (453) |
1 | > | 1 | |
isNatIListKind#(mark(X)) | → | isNatIListKind#(X) | (452) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U13#(active(X)) | → | U13#(X) | (455) |
U13#(mark(X)) | → | U13#(X) | (454) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U13#(active(X)) | → | U13#(X) | (455) |
1 | > | 1 | |
U13#(mark(X)) | → | U13#(X) | (454) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNatList#(active(X)) | → | isNatList#(X) | (457) |
isNatList#(mark(X)) | → | isNatList#(X) | (456) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNatList#(active(X)) | → | isNatList#(X) | (457) |
1 | > | 1 | |
isNatList#(mark(X)) | → | isNatList#(X) | (456) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U21#(X1,mark(X2)) | → | U21#(X1,X2) | (459) |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (458) |
U21#(active(X1),X2) | → | U21#(X1,X2) | (460) |
U21#(X1,active(X2)) | → | U21#(X1,X2) | (461) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (459) |
1 | ≥ | 1 | |
2 | > | 2 | |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (458) |
1 | > | 1 | |
2 | ≥ | 2 | |
U21#(active(X1),X2) | → | U21#(X1,X2) | (460) |
1 | > | 1 | |
2 | ≥ | 2 | |
U21#(X1,active(X2)) | → | U21#(X1,X2) | (461) |
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) | (463) |
U22#(mark(X1),X2) | → | U22#(X1,X2) | (462) |
U22#(active(X1),X2) | → | U22#(X1,X2) | (464) |
U22#(X1,active(X2)) | → | U22#(X1,X2) | (465) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (463) |
1 | ≥ | 1 | |
2 | > | 2 | |
U22#(mark(X1),X2) | → | U22#(X1,X2) | (462) |
1 | > | 1 | |
2 | ≥ | 2 | |
U22#(active(X1),X2) | → | U22#(X1,X2) | (464) |
1 | > | 1 | |
2 | ≥ | 2 | |
U22#(X1,active(X2)) | → | U22#(X1,X2) | (465) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNatKind#(active(X)) | → | isNatKind#(X) | (467) |
isNatKind#(mark(X)) | → | isNatKind#(X) | (466) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNatKind#(active(X)) | → | isNatKind#(X) | (467) |
1 | > | 1 | |
isNatKind#(mark(X)) | → | isNatKind#(X) | (466) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U23#(active(X)) | → | U23#(X) | (469) |
U23#(mark(X)) | → | U23#(X) | (468) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U23#(active(X)) | → | U23#(X) | (469) |
1 | > | 1 | |
U23#(mark(X)) | → | U23#(X) | (468) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNat#(active(X)) | → | isNat#(X) | (471) |
isNat#(mark(X)) | → | isNat#(X) | (470) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNat#(active(X)) | → | isNat#(X) | (471) |
1 | > | 1 | |
isNat#(mark(X)) | → | isNat#(X) | (470) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U31#(X1,mark(X2)) | → | U31#(X1,X2) | (473) |
U31#(mark(X1),X2) | → | U31#(X1,X2) | (472) |
U31#(active(X1),X2) | → | U31#(X1,X2) | (474) |
U31#(X1,active(X2)) | → | U31#(X1,X2) | (475) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U31#(X1,mark(X2)) | → | U31#(X1,X2) | (473) |
1 | ≥ | 1 | |
2 | > | 2 | |
U31#(mark(X1),X2) | → | U31#(X1,X2) | (472) |
1 | > | 1 | |
2 | ≥ | 2 | |
U31#(active(X1),X2) | → | U31#(X1,X2) | (474) |
1 | > | 1 | |
2 | ≥ | 2 | |
U31#(X1,active(X2)) | → | U31#(X1,X2) | (475) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U32#(X1,mark(X2)) | → | U32#(X1,X2) | (477) |
U32#(mark(X1),X2) | → | U32#(X1,X2) | (476) |
U32#(active(X1),X2) | → | U32#(X1,X2) | (478) |
U32#(X1,active(X2)) | → | U32#(X1,X2) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U32#(X1,mark(X2)) | → | U32#(X1,X2) | (477) |
1 | ≥ | 1 | |
2 | > | 2 | |
U32#(mark(X1),X2) | → | U32#(X1,X2) | (476) |
1 | > | 1 | |
2 | ≥ | 2 | |
U32#(active(X1),X2) | → | U32#(X1,X2) | (478) |
1 | > | 1 | |
2 | ≥ | 2 | |
U32#(X1,active(X2)) | → | U32#(X1,X2) | (479) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U33#(active(X)) | → | U33#(X) | (481) |
U33#(mark(X)) | → | U33#(X) | (480) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U33#(active(X)) | → | U33#(X) | (481) |
1 | > | 1 | |
U33#(mark(X)) | → | U33#(X) | (480) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (483) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (482) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (484) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (485) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (486) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (483) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (482) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (484) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (485) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (486) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (487) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (489) |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (488) |
U42#(X1,X2,mark(X3)) | → | U42#(X1,X2,X3) | (490) |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (491) |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (492) |
U42#(X1,X2,active(X3)) | → | U42#(X1,X2,X3) | (493) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U42#(X1,mark(X2),X3) | → | U42#(X1,X2,X3) | (489) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U42#(mark(X1),X2,X3) | → | U42#(X1,X2,X3) | (488) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U42#(X1,X2,mark(X3)) | → | U42#(X1,X2,X3) | (490) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U42#(active(X1),X2,X3) | → | U42#(X1,X2,X3) | (491) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U42#(X1,active(X2),X3) | → | U42#(X1,X2,X3) | (492) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U42#(X1,X2,active(X3)) | → | U42#(X1,X2,X3) | (493) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U43#(X1,mark(X2),X3) | → | U43#(X1,X2,X3) | (495) |
U43#(mark(X1),X2,X3) | → | U43#(X1,X2,X3) | (494) |
U43#(X1,X2,mark(X3)) | → | U43#(X1,X2,X3) | (496) |
U43#(active(X1),X2,X3) | → | U43#(X1,X2,X3) | (497) |
U43#(X1,active(X2),X3) | → | U43#(X1,X2,X3) | (498) |
U43#(X1,X2,active(X3)) | → | U43#(X1,X2,X3) | (499) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U43#(X1,mark(X2),X3) | → | U43#(X1,X2,X3) | (495) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U43#(mark(X1),X2,X3) | → | U43#(X1,X2,X3) | (494) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U43#(X1,X2,mark(X3)) | → | U43#(X1,X2,X3) | (496) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U43#(active(X1),X2,X3) | → | U43#(X1,X2,X3) | (497) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U43#(X1,active(X2),X3) | → | U43#(X1,X2,X3) | (498) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U43#(X1,X2,active(X3)) | → | U43#(X1,X2,X3) | (499) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U44#(X1,mark(X2),X3) | → | U44#(X1,X2,X3) | (501) |
U44#(mark(X1),X2,X3) | → | U44#(X1,X2,X3) | (500) |
U44#(X1,X2,mark(X3)) | → | U44#(X1,X2,X3) | (502) |
U44#(active(X1),X2,X3) | → | U44#(X1,X2,X3) | (503) |
U44#(X1,active(X2),X3) | → | U44#(X1,X2,X3) | (504) |
U44#(X1,X2,active(X3)) | → | U44#(X1,X2,X3) | (505) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U44#(X1,mark(X2),X3) | → | U44#(X1,X2,X3) | (501) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U44#(mark(X1),X2,X3) | → | U44#(X1,X2,X3) | (500) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U44#(X1,X2,mark(X3)) | → | U44#(X1,X2,X3) | (502) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U44#(active(X1),X2,X3) | → | U44#(X1,X2,X3) | (503) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U44#(X1,active(X2),X3) | → | U44#(X1,X2,X3) | (504) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U44#(X1,X2,active(X3)) | → | U44#(X1,X2,X3) | (505) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U45#(X1,mark(X2)) | → | U45#(X1,X2) | (507) |
U45#(mark(X1),X2) | → | U45#(X1,X2) | (506) |
U45#(active(X1),X2) | → | U45#(X1,X2) | (508) |
U45#(X1,active(X2)) | → | U45#(X1,X2) | (509) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U45#(X1,mark(X2)) | → | U45#(X1,X2) | (507) |
1 | ≥ | 1 | |
2 | > | 2 | |
U45#(mark(X1),X2) | → | U45#(X1,X2) | (506) |
1 | > | 1 | |
2 | ≥ | 2 | |
U45#(active(X1),X2) | → | U45#(X1,X2) | (508) |
1 | > | 1 | |
2 | ≥ | 2 | |
U45#(X1,active(X2)) | → | U45#(X1,X2) | (509) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U46#(active(X)) | → | U46#(X) | (511) |
U46#(mark(X)) | → | U46#(X) | (510) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U46#(active(X)) | → | U46#(X) | (511) |
1 | > | 1 | |
U46#(mark(X)) | → | U46#(X) | (510) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
isNatIList#(active(X)) | → | isNatIList#(X) | (513) |
isNatIList#(mark(X)) | → | isNatIList#(X) | (512) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
isNatIList#(active(X)) | → | isNatIList#(X) | (513) |
1 | > | 1 | |
isNatIList#(mark(X)) | → | isNatIList#(X) | (512) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U51#(X1,mark(X2)) | → | U51#(X1,X2) | (515) |
U51#(mark(X1),X2) | → | U51#(X1,X2) | (514) |
U51#(active(X1),X2) | → | U51#(X1,X2) | (516) |
U51#(X1,active(X2)) | → | U51#(X1,X2) | (517) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U51#(X1,mark(X2)) | → | U51#(X1,X2) | (515) |
1 | ≥ | 1 | |
2 | > | 2 | |
U51#(mark(X1),X2) | → | U51#(X1,X2) | (514) |
1 | > | 1 | |
2 | ≥ | 2 | |
U51#(active(X1),X2) | → | U51#(X1,X2) | (516) |
1 | > | 1 | |
2 | ≥ | 2 | |
U51#(X1,active(X2)) | → | U51#(X1,X2) | (517) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U52#(active(X)) | → | U52#(X) | (519) |
U52#(mark(X)) | → | U52#(X) | (518) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U52#(active(X)) | → | U52#(X) | (519) |
1 | > | 1 | |
U52#(mark(X)) | → | U52#(X) | (518) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U61#(active(X)) | → | U61#(X) | (521) |
U61#(mark(X)) | → | U61#(X) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U61#(active(X)) | → | U61#(X) | (521) |
1 | > | 1 | |
U61#(mark(X)) | → | U61#(X) | (520) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U71#(active(X)) | → | U71#(X) | (523) |
U71#(mark(X)) | → | U71#(X) | (522) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U71#(active(X)) | → | U71#(X) | (523) |
1 | > | 1 | |
U71#(mark(X)) | → | U71#(X) | (522) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U81#(X1,mark(X2),X3) | → | U81#(X1,X2,X3) | (525) |
U81#(mark(X1),X2,X3) | → | U81#(X1,X2,X3) | (524) |
U81#(X1,X2,mark(X3)) | → | U81#(X1,X2,X3) | (526) |
U81#(active(X1),X2,X3) | → | U81#(X1,X2,X3) | (527) |
U81#(X1,active(X2),X3) | → | U81#(X1,X2,X3) | (528) |
U81#(X1,X2,active(X3)) | → | U81#(X1,X2,X3) | (529) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (525) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U81#(mark(X1),X2,X3) | → | U81#(X1,X2,X3) | (524) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U81#(X1,X2,mark(X3)) | → | U81#(X1,X2,X3) | (526) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U81#(active(X1),X2,X3) | → | U81#(X1,X2,X3) | (527) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U81#(X1,active(X2),X3) | → | U81#(X1,X2,X3) | (528) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U81#(X1,X2,active(X3)) | → | U81#(X1,X2,X3) | (529) |
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) | (531) |
U82#(mark(X1),X2,X3) | → | U82#(X1,X2,X3) | (530) |
U82#(X1,X2,mark(X3)) | → | U82#(X1,X2,X3) | (532) |
U82#(active(X1),X2,X3) | → | U82#(X1,X2,X3) | (533) |
U82#(X1,active(X2),X3) | → | U82#(X1,X2,X3) | (534) |
U82#(X1,X2,active(X3)) | → | U82#(X1,X2,X3) | (535) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (531) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U82#(mark(X1),X2,X3) | → | U82#(X1,X2,X3) | (530) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U82#(X1,X2,mark(X3)) | → | U82#(X1,X2,X3) | (532) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U82#(active(X1),X2,X3) | → | U82#(X1,X2,X3) | (533) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U82#(X1,active(X2),X3) | → | U82#(X1,X2,X3) | (534) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U82#(X1,X2,active(X3)) | → | U82#(X1,X2,X3) | (535) |
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) | (537) |
U83#(mark(X1),X2,X3) | → | U83#(X1,X2,X3) | (536) |
U83#(X1,X2,mark(X3)) | → | U83#(X1,X2,X3) | (538) |
U83#(active(X1),X2,X3) | → | U83#(X1,X2,X3) | (539) |
U83#(X1,active(X2),X3) | → | U83#(X1,X2,X3) | (540) |
U83#(X1,X2,active(X3)) | → | U83#(X1,X2,X3) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (537) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U83#(mark(X1),X2,X3) | → | U83#(X1,X2,X3) | (536) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U83#(X1,X2,mark(X3)) | → | U83#(X1,X2,X3) | (538) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U83#(active(X1),X2,X3) | → | U83#(X1,X2,X3) | (539) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U83#(X1,active(X2),X3) | → | U83#(X1,X2,X3) | (540) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U83#(X1,X2,active(X3)) | → | U83#(X1,X2,X3) | (541) |
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) | (543) |
U84#(mark(X1),X2,X3) | → | U84#(X1,X2,X3) | (542) |
U84#(X1,X2,mark(X3)) | → | U84#(X1,X2,X3) | (544) |
U84#(active(X1),X2,X3) | → | U84#(X1,X2,X3) | (545) |
U84#(X1,active(X2),X3) | → | U84#(X1,X2,X3) | (546) |
U84#(X1,X2,active(X3)) | → | U84#(X1,X2,X3) | (547) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
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) | (543) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U84#(mark(X1),X2,X3) | → | U84#(X1,X2,X3) | (542) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U84#(X1,X2,mark(X3)) | → | U84#(X1,X2,X3) | (544) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U84#(active(X1),X2,X3) | → | U84#(X1,X2,X3) | (545) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U84#(X1,active(X2),X3) | → | U84#(X1,X2,X3) | (546) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U84#(X1,X2,active(X3)) | → | U84#(X1,X2,X3) | (547) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U85#(X1,mark(X2)) | → | U85#(X1,X2) | (549) |
U85#(mark(X1),X2) | → | U85#(X1,X2) | (548) |
U85#(active(X1),X2) | → | U85#(X1,X2) | (550) |
U85#(X1,active(X2)) | → | U85#(X1,X2) | (551) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U85#(X1,mark(X2)) | → | U85#(X1,X2) | (549) |
1 | ≥ | 1 | |
2 | > | 2 | |
U85#(mark(X1),X2) | → | U85#(X1,X2) | (548) |
1 | > | 1 | |
2 | ≥ | 2 | |
U85#(active(X1),X2) | → | U85#(X1,X2) | (550) |
1 | > | 1 | |
2 | ≥ | 2 | |
U85#(X1,active(X2)) | → | U85#(X1,X2) | (551) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U86#(active(X)) | → | U86#(X) | (553) |
U86#(mark(X)) | → | U86#(X) | (552) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U86#(active(X)) | → | U86#(X) | (553) |
1 | > | 1 | |
U86#(mark(X)) | → | U86#(X) | (552) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U91#(X1,mark(X2),X3) | → | U91#(X1,X2,X3) | (555) |
U91#(mark(X1),X2,X3) | → | U91#(X1,X2,X3) | (554) |
U91#(X1,X2,mark(X3)) | → | U91#(X1,X2,X3) | (556) |
U91#(active(X1),X2,X3) | → | U91#(X1,X2,X3) | (557) |
U91#(X1,active(X2),X3) | → | U91#(X1,X2,X3) | (558) |
U91#(X1,X2,active(X3)) | → | U91#(X1,X2,X3) | (559) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U91#(X1,mark(X2),X3) | → | U91#(X1,X2,X3) | (555) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U91#(mark(X1),X2,X3) | → | U91#(X1,X2,X3) | (554) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U91#(X1,X2,mark(X3)) | → | U91#(X1,X2,X3) | (556) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U91#(active(X1),X2,X3) | → | U91#(X1,X2,X3) | (557) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U91#(X1,active(X2),X3) | → | U91#(X1,X2,X3) | (558) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U91#(X1,X2,active(X3)) | → | U91#(X1,X2,X3) | (559) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U92#(X1,mark(X2),X3) | → | U92#(X1,X2,X3) | (561) |
U92#(mark(X1),X2,X3) | → | U92#(X1,X2,X3) | (560) |
U92#(X1,X2,mark(X3)) | → | U92#(X1,X2,X3) | (562) |
U92#(active(X1),X2,X3) | → | U92#(X1,X2,X3) | (563) |
U92#(X1,active(X2),X3) | → | U92#(X1,X2,X3) | (564) |
U92#(X1,X2,active(X3)) | → | U92#(X1,X2,X3) | (565) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U92#(X1,mark(X2),X3) | → | U92#(X1,X2,X3) | (561) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U92#(mark(X1),X2,X3) | → | U92#(X1,X2,X3) | (560) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U92#(X1,X2,mark(X3)) | → | U92#(X1,X2,X3) | (562) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U92#(active(X1),X2,X3) | → | U92#(X1,X2,X3) | (563) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U92#(X1,active(X2),X3) | → | U92#(X1,X2,X3) | (564) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U92#(X1,X2,active(X3)) | → | U92#(X1,X2,X3) | (565) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U93#(X1,mark(X2),X3) | → | U93#(X1,X2,X3) | (567) |
U93#(mark(X1),X2,X3) | → | U93#(X1,X2,X3) | (566) |
U93#(X1,X2,mark(X3)) | → | U93#(X1,X2,X3) | (568) |
U93#(active(X1),X2,X3) | → | U93#(X1,X2,X3) | (569) |
U93#(X1,active(X2),X3) | → | U93#(X1,X2,X3) | (570) |
U93#(X1,X2,active(X3)) | → | U93#(X1,X2,X3) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U93#(X1,mark(X2),X3) | → | U93#(X1,X2,X3) | (567) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U93#(mark(X1),X2,X3) | → | U93#(X1,X2,X3) | (566) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U93#(X1,X2,mark(X3)) | → | U93#(X1,X2,X3) | (568) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 | |
U93#(active(X1),X2,X3) | → | U93#(X1,X2,X3) | (569) |
1 | > | 1 | |
2 | ≥ | 2 | |
3 | ≥ | 3 | |
U93#(X1,active(X2),X3) | → | U93#(X1,X2,X3) | (570) |
1 | ≥ | 1 | |
2 | > | 2 | |
3 | ≥ | 3 | |
U93#(X1,X2,active(X3)) | → | U93#(X1,X2,X3) | (571) |
1 | ≥ | 1 | |
2 | ≥ | 2 | |
3 | > | 3 |
As there is no critical graph in the transitive closure, there are no infinite chains.
U94#(X1,mark(X2)) | → | U94#(X1,X2) | (573) |
U94#(mark(X1),X2) | → | U94#(X1,X2) | (572) |
U94#(active(X1),X2) | → | U94#(X1,X2) | (574) |
U94#(X1,active(X2)) | → | U94#(X1,X2) | (575) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
U94#(X1,mark(X2)) | → | U94#(X1,X2) | (573) |
1 | ≥ | 1 | |
2 | > | 2 | |
U94#(mark(X1),X2) | → | U94#(X1,X2) | (572) |
1 | > | 1 | |
2 | ≥ | 2 | |
U94#(active(X1),X2) | → | U94#(X1,X2) | (574) |
1 | > | 1 | |
2 | ≥ | 2 | |
U94#(X1,active(X2)) | → | U94#(X1,X2) | (575) |
1 | ≥ | 1 | |
2 | > | 2 |
As there is no critical graph in the transitive closure, there are no infinite chains.
s#(active(X)) | → | s#(X) | (577) |
s#(mark(X)) | → | s#(X) | (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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
s#(active(X)) | → | s#(X) | (577) |
1 | > | 1 | |
s#(mark(X)) | → | s#(X) | (576) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
length#(active(X)) | → | length#(X) | (579) |
length#(mark(X)) | → | length#(X) | (578) |
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(zeros) |
active(U11(tt,x0)) |
active(U12(tt,x0)) |
active(U13(tt)) |
active(U21(tt,x0)) |
active(U22(tt,x0)) |
active(U23(tt)) |
active(U31(tt,x0)) |
active(U32(tt,x0)) |
active(U33(tt)) |
active(U41(tt,x0,x1)) |
active(U42(tt,x0,x1)) |
active(U43(tt,x0,x1)) |
active(U44(tt,x0,x1)) |
active(U45(tt,x0)) |
active(U46(tt)) |
active(U51(tt,x0)) |
active(U52(tt)) |
active(U61(tt)) |
active(U71(tt)) |
active(U81(tt,x0,x1)) |
active(U82(tt,x0,x1)) |
active(U83(tt,x0,x1)) |
active(U84(tt,x0,x1)) |
active(U85(tt,x0)) |
active(U86(tt)) |
active(U91(tt,x0,x1)) |
active(U92(tt,x0,x1)) |
active(U93(tt,x0,x1)) |
active(U94(tt,x0)) |
active(isNat(0)) |
active(isNat(length(x0))) |
active(isNat(s(x0))) |
active(isNatIList(x0)) |
active(isNatIListKind(nil)) |
active(isNatIListKind(zeros)) |
active(isNatIListKind(cons(x0,x1))) |
active(isNatKind(0)) |
active(isNatKind(length(x0))) |
active(isNatKind(s(x0))) |
active(isNatList(nil)) |
active(isNatList(cons(x0,x1))) |
active(length(nil)) |
active(length(cons(x0,x1))) |
mark(zeros) |
mark(cons(x0,x1)) |
mark(0) |
mark(U11(x0,x1)) |
mark(tt) |
mark(U12(x0,x1)) |
mark(isNatIListKind(x0)) |
mark(U13(x0)) |
mark(isNatList(x0)) |
mark(U21(x0,x1)) |
mark(U22(x0,x1)) |
mark(isNatKind(x0)) |
mark(U23(x0)) |
mark(isNat(x0)) |
mark(U31(x0,x1)) |
mark(U32(x0,x1)) |
mark(U33(x0)) |
mark(U41(x0,x1,x2)) |
mark(U42(x0,x1,x2)) |
mark(U43(x0,x1,x2)) |
mark(U44(x0,x1,x2)) |
mark(U45(x0,x1)) |
mark(U46(x0)) |
mark(isNatIList(x0)) |
mark(U51(x0,x1)) |
mark(U52(x0)) |
mark(U61(x0)) |
mark(U71(x0)) |
mark(U81(x0,x1,x2)) |
mark(U82(x0,x1,x2)) |
mark(U83(x0,x1,x2)) |
mark(U84(x0,x1,x2)) |
mark(U85(x0,x1)) |
mark(U86(x0)) |
mark(U91(x0,x1,x2)) |
mark(U92(x0,x1,x2)) |
mark(U93(x0,x1,x2)) |
mark(U94(x0,x1)) |
mark(s(x0)) |
mark(length(x0)) |
mark(nil) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
length#(active(X)) | → | length#(X) | (579) |
1 | > | 1 | |
length#(mark(X)) | → | length#(X) | (578) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.