100.54/26.76 WORST_CASE(Omega(n^1), O(n^1)) 100.54/26.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 100.54/26.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 100.54/26.78 100.54/26.78 100.54/26.78 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 100.54/26.78 100.54/26.78 (0) CpxTRS 100.54/26.78 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 69 ms] 100.54/26.78 (2) CpxTRS 100.54/26.78 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 466 ms] 100.54/26.78 (4) CpxTRS 100.54/26.78 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 100.54/26.78 (6) CdtProblem 100.54/26.78 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 100.54/26.78 (8) CdtProblem 100.54/26.78 (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 100.54/26.78 (10) CdtProblem 100.54/26.78 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9 ms] 100.54/26.78 (12) CdtProblem 100.54/26.78 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 772 ms] 100.54/26.78 (14) CdtProblem 100.54/26.78 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 313 ms] 100.54/26.78 (16) CdtProblem 100.54/26.78 (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 100.54/26.78 (18) BOUNDS(1, 1) 100.54/26.78 (19) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 100.54/26.78 (20) CpxTRS 100.54/26.78 (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 100.54/26.78 (22) typed CpxTrs 100.54/26.78 (23) OrderProof [LOWER BOUND(ID), 13 ms] 100.54/26.78 (24) typed CpxTrs 100.54/26.78 (25) RewriteLemmaProof [LOWER BOUND(ID), 811 ms] 100.54/26.78 (26) BEST 100.54/26.78 (27) proven lower bound 100.54/26.78 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 100.54/26.78 (29) BOUNDS(n^1, INF) 100.54/26.78 (30) typed CpxTrs 100.54/26.78 (31) RewriteLemmaProof [LOWER BOUND(ID), 523 ms] 100.54/26.78 (32) typed CpxTrs 100.54/26.78 (33) RewriteLemmaProof [LOWER BOUND(ID), 396 ms] 100.54/26.78 (34) typed CpxTrs 100.54/26.78 (35) RewriteLemmaProof [LOWER BOUND(ID), 343 ms] 100.54/26.78 (36) typed CpxTrs 100.54/26.78 (37) RewriteLemmaProof [LOWER BOUND(ID), 207 ms] 100.54/26.78 (38) typed CpxTrs 100.54/26.78 (39) RewriteLemmaProof [LOWER BOUND(ID), 374 ms] 100.54/26.78 (40) typed CpxTrs 100.54/26.78 (41) RewriteLemmaProof [LOWER BOUND(ID), 204 ms] 100.54/26.78 (42) typed CpxTrs 100.54/26.78 (43) RewriteLemmaProof [LOWER BOUND(ID), 379 ms] 100.54/26.78 (44) typed CpxTrs 100.54/26.78 (45) RewriteLemmaProof [LOWER BOUND(ID), 174 ms] 100.54/26.78 (46) typed CpxTrs 100.54/26.78 (47) RewriteLemmaProof [LOWER BOUND(ID), 337 ms] 100.54/26.78 (48) typed CpxTrs 100.54/26.78 (49) RewriteLemmaProof [LOWER BOUND(ID), 200 ms] 100.54/26.78 (50) typed CpxTrs 100.54/26.78 (51) RewriteLemmaProof [LOWER BOUND(ID), 275 ms] 100.54/26.78 (52) typed CpxTrs 100.54/26.78 (53) RewriteLemmaProof [LOWER BOUND(ID), 161 ms] 100.54/26.78 (54) typed CpxTrs 100.54/26.78 (55) RewriteLemmaProof [LOWER BOUND(ID), 272 ms] 100.54/26.78 (56) typed CpxTrs 100.54/26.78 (57) RewriteLemmaProof [LOWER BOUND(ID), 121 ms] 100.54/26.78 (58) typed CpxTrs 100.54/26.78 (59) RewriteLemmaProof [LOWER BOUND(ID), 283 ms] 100.54/26.78 (60) typed CpxTrs 100.54/26.78 (61) RewriteLemmaProof [LOWER BOUND(ID), 137 ms] 100.54/26.78 (62) typed CpxTrs 100.54/26.78 (63) RewriteLemmaProof [LOWER BOUND(ID), 378 ms] 100.54/26.78 (64) typed CpxTrs 100.54/26.78 (65) RewriteLemmaProof [LOWER BOUND(ID), 328 ms] 100.54/26.78 (66) typed CpxTrs 100.54/26.78 (67) RewriteLemmaProof [LOWER BOUND(ID), 374 ms] 100.54/26.78 (68) typed CpxTrs 100.54/26.78 (69) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] 100.54/26.78 (70) typed CpxTrs 100.54/26.78 (71) RewriteLemmaProof [LOWER BOUND(ID), 167 ms] 100.54/26.78 (72) typed CpxTrs 100.54/26.78 (73) RewriteLemmaProof [LOWER BOUND(ID), 376 ms] 100.54/26.78 (74) typed CpxTrs 100.54/26.78 (75) RewriteLemmaProof [LOWER BOUND(ID), 331 ms] 100.54/26.78 (76) typed CpxTrs 100.54/26.78 (77) RewriteLemmaProof [LOWER BOUND(ID), 259 ms] 100.54/26.78 (78) typed CpxTrs 100.54/26.78 (79) RewriteLemmaProof [LOWER BOUND(ID), 207 ms] 100.54/26.78 (80) typed CpxTrs 100.54/26.78 (81) RewriteLemmaProof [LOWER BOUND(ID), 429 ms] 100.54/26.78 (82) typed CpxTrs 100.54/26.78 (83) RewriteLemmaProof [LOWER BOUND(ID), 443 ms] 100.54/26.78 (84) typed CpxTrs 100.54/26.78 (85) RewriteLemmaProof [LOWER BOUND(ID), 498 ms] 100.54/26.78 (86) typed CpxTrs 100.54/26.78 (87) RewriteLemmaProof [LOWER BOUND(ID), 326 ms] 100.54/26.78 (88) typed CpxTrs 100.54/26.78 (89) RewriteLemmaProof [LOWER BOUND(ID), 118 ms] 100.54/26.78 (90) typed CpxTrs 100.54/26.78 (91) RewriteLemmaProof [LOWER BOUND(ID), 428 ms] 100.54/26.78 (92) typed CpxTrs 100.54/26.78 (93) RewriteLemmaProof [LOWER BOUND(ID), 423 ms] 100.54/26.78 (94) typed CpxTrs 100.54/26.78 (95) RewriteLemmaProof [LOWER BOUND(ID), 450 ms] 100.54/26.78 (96) typed CpxTrs 100.54/26.78 (97) RewriteLemmaProof [LOWER BOUND(ID), 295 ms] 100.54/26.78 (98) typed CpxTrs 100.54/26.78 (99) RewriteLemmaProof [LOWER BOUND(ID), 156 ms] 100.54/26.78 (100) typed CpxTrs 100.54/26.78 (101) RewriteLemmaProof [LOWER BOUND(ID), 169 ms] 100.54/26.78 (102) typed CpxTrs 100.54/26.78 (103) RewriteLemmaProof [LOWER BOUND(ID), 132 ms] 100.54/26.78 (104) typed CpxTrs 100.54/26.78 (105) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] 100.54/26.78 (106) typed CpxTrs 100.54/26.78 100.54/26.78 100.54/26.78 ---------------------------------------- 100.54/26.78 100.54/26.78 (0) 100.54/26.78 Obligation: 100.54/26.78 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 100.54/26.78 100.54/26.78 100.54/26.78 The TRS R consists of the following rules: 100.54/26.78 100.54/26.78 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 100.54/26.78 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 100.54/26.78 active(U106(tt)) -> mark(tt) 100.54/26.78 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 100.54/26.78 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 100.54/26.78 active(U112(tt)) -> mark(tt) 100.54/26.78 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 100.54/26.78 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 100.54/26.78 active(U122(tt)) -> mark(tt) 100.54/26.78 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 100.54/26.78 active(U131(tt)) -> mark(tt) 100.54/26.78 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 100.54/26.78 active(U141(tt)) -> mark(tt) 100.54/26.78 active(U151(tt)) -> mark(tt) 100.54/26.78 active(U161(tt)) -> mark(tt) 100.54/26.78 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 100.54/26.78 active(U172(tt)) -> mark(tt) 100.54/26.78 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 100.54/26.78 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 100.54/26.78 active(U183(tt)) -> mark(tt) 100.54/26.78 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 100.54/26.78 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 100.54/26.78 active(U193(tt)) -> mark(tt) 100.54/26.78 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 100.54/26.78 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 100.54/26.78 active(U206(tt)) -> mark(tt) 100.54/26.78 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 100.54/26.78 active(U211(tt)) -> mark(tt) 100.54/26.78 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 100.54/26.78 active(U221(tt)) -> mark(tt) 100.54/26.78 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 100.54/26.78 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 100.54/26.78 active(U232(tt)) -> mark(tt) 100.54/26.78 active(U24(tt, X)) -> mark(X) 100.54/26.78 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 100.54/26.78 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 100.54/26.78 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 100.54/26.78 active(U246(tt)) -> mark(tt) 100.54/26.78 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 100.54/26.78 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 100.54/26.78 active(U256(tt)) -> mark(tt) 100.54/26.78 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 100.54/26.78 active(U262(tt)) -> mark(tt) 100.54/26.78 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 100.54/26.78 active(U272(tt)) -> mark(tt) 100.54/26.78 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 100.54/26.78 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 100.54/26.78 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 100.54/26.78 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 100.54/26.78 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 100.54/26.78 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 100.54/26.78 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 100.54/26.78 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 100.54/26.78 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 100.54/26.78 active(U304(tt, Y)) -> mark(Y) 100.54/26.78 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 100.54/26.78 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 100.54/26.78 active(U312(tt, XS)) -> mark(pair(nil, XS)) 100.54/26.78 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 100.54/26.78 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 100.54/26.78 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 100.54/26.78 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 100.54/26.78 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 100.54/26.78 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 100.54/26.78 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 100.54/26.78 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 100.54/26.78 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 100.54/26.78 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 100.54/26.78 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 100.54/26.78 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 100.54/26.78 active(U334(tt, XS)) -> mark(XS) 100.54/26.78 active(U34(tt, N)) -> mark(N) 100.54/26.78 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 100.54/26.78 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 100.54/26.78 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 100.54/26.78 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 100.54/26.78 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 100.54/26.78 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 100.54/26.78 active(U46(tt)) -> mark(tt) 100.54/26.78 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 100.54/26.78 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 100.54/26.78 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 100.54/26.78 active(U56(tt)) -> mark(tt) 100.54/26.78 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 100.54/26.78 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 100.54/26.78 active(U63(tt)) -> mark(tt) 100.54/26.78 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 100.54/26.78 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 100.54/26.78 active(U73(tt)) -> mark(tt) 100.54/26.78 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 100.54/26.78 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 100.54/26.78 active(U83(tt)) -> mark(tt) 100.54/26.78 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 100.54/26.78 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 100.54/26.78 active(U93(tt)) -> mark(tt) 100.54/26.78 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 100.54/26.78 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 100.54/26.78 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 100.54/26.78 active(isLNat(nil)) -> mark(tt) 100.54/26.78 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 100.54/26.78 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 100.54/26.78 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 100.54/26.78 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 100.54/26.78 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(isLNatKind(nil)) -> mark(tt) 100.54/26.78 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 100.54/26.78 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 100.54/26.78 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 100.54/26.78 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 100.54/26.78 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 100.54/26.78 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 100.54/26.78 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 100.54/26.78 active(isNatural(0)) -> mark(tt) 100.54/26.78 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 100.54/26.78 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 100.54/26.78 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(isNaturalKind(0)) -> mark(tt) 100.54/26.78 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 100.54/26.78 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 100.54/26.78 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 100.54/26.78 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 100.54/26.78 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 100.54/26.78 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 100.54/26.78 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 100.54/26.78 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 100.54/26.78 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 100.54/26.78 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 100.54/26.78 active(splitAt(0, XS)) -> mark(U311(isLNat(XS), XS)) 100.54/26.78 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 100.54/26.78 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 100.54/26.78 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 100.54/26.78 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 100.54/26.78 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 100.54/26.78 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 100.54/26.78 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 100.54/26.78 active(U105(X1, X2)) -> U105(active(X1), X2) 100.54/26.78 active(U106(X)) -> U106(active(X)) 100.54/26.78 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 100.54/26.78 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 100.54/26.78 active(U111(X1, X2)) -> U111(active(X1), X2) 100.54/26.78 active(U112(X)) -> U112(active(X)) 100.54/26.78 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 100.54/26.78 active(U121(X1, X2)) -> U121(active(X1), X2) 100.54/26.78 active(U122(X)) -> U122(active(X)) 100.54/26.78 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 100.54/26.78 active(U131(X)) -> U131(active(X)) 100.54/26.78 active(snd(X)) -> snd(active(X)) 100.54/26.78 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 100.54/26.78 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 100.54/26.78 active(U141(X)) -> U141(active(X)) 100.54/26.78 active(U151(X)) -> U151(active(X)) 100.54/26.78 active(U161(X)) -> U161(active(X)) 100.54/26.78 active(U171(X1, X2)) -> U171(active(X1), X2) 100.54/26.78 active(U172(X)) -> U172(active(X)) 100.54/26.78 active(U181(X1, X2)) -> U181(active(X1), X2) 100.54/26.78 active(U182(X1, X2)) -> U182(active(X1), X2) 100.54/26.78 active(U183(X)) -> U183(active(X)) 100.54/26.78 active(U191(X1, X2)) -> U191(active(X1), X2) 100.54/26.78 active(U192(X1, X2)) -> U192(active(X1), X2) 100.54/26.78 active(U193(X)) -> U193(active(X)) 100.54/26.78 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 100.54/26.78 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 100.54/26.78 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 100.54/26.78 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 100.54/26.78 active(U205(X1, X2)) -> U205(active(X1), X2) 100.54/26.78 active(U206(X)) -> U206(active(X)) 100.54/26.78 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 100.54/26.78 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 100.54/26.78 active(U211(X)) -> U211(active(X)) 100.54/26.78 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 100.54/26.78 active(U221(X)) -> U221(active(X)) 100.54/26.78 active(U24(X1, X2)) -> U24(active(X1), X2) 100.54/26.78 active(U231(X1, X2)) -> U231(active(X1), X2) 100.54/26.78 active(U232(X)) -> U232(active(X)) 100.54/26.78 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 100.54/26.78 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 100.54/26.78 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 100.54/26.78 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 100.54/26.78 active(U245(X1, X2)) -> U245(active(X1), X2) 100.54/26.78 active(U246(X)) -> U246(active(X)) 100.54/26.78 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 100.54/26.78 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 100.54/26.78 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 100.54/26.78 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 100.54/26.78 active(U255(X1, X2)) -> U255(active(X1), X2) 100.54/26.78 active(U256(X)) -> U256(active(X)) 100.54/26.78 active(U261(X1, X2)) -> U261(active(X1), X2) 100.54/26.78 active(U262(X)) -> U262(active(X)) 100.54/26.78 active(U271(X1, X2)) -> U271(active(X1), X2) 100.54/26.78 active(U272(X)) -> U272(active(X)) 100.54/26.78 active(U281(X1, X2)) -> U281(active(X1), X2) 100.54/26.78 active(U282(X1, X2)) -> U282(active(X1), X2) 100.54/26.78 active(cons(X1, X2)) -> cons(active(X1), X2) 100.54/26.78 active(natsFrom(X)) -> natsFrom(active(X)) 100.54/26.78 active(s(X)) -> s(active(X)) 100.54/26.78 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 100.54/26.78 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 100.54/26.78 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 100.54/26.78 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 100.54/26.78 active(head(X)) -> head(active(X)) 100.54/26.78 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 100.54/26.78 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 100.54/26.78 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 100.54/26.78 active(U302(X1, X2)) -> U302(active(X1), X2) 100.54/26.78 active(U303(X1, X2)) -> U303(active(X1), X2) 100.54/26.78 active(U304(X1, X2)) -> U304(active(X1), X2) 100.54/26.78 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 100.54/26.78 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 100.54/26.78 active(U311(X1, X2)) -> U311(active(X1), X2) 100.54/26.78 active(U312(X1, X2)) -> U312(active(X1), X2) 100.54/26.78 active(pair(X1, X2)) -> pair(active(X1), X2) 100.54/26.78 active(pair(X1, X2)) -> pair(X1, active(X2)) 100.54/26.78 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 100.54/26.78 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 100.54/26.78 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 100.54/26.78 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 100.54/26.78 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 100.54/26.78 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 100.54/26.78 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 100.54/26.78 active(U327(X1, X2)) -> U327(active(X1), X2) 100.54/26.78 active(U34(X1, X2)) -> U34(active(X1), X2) 100.54/26.78 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 100.54/26.78 active(U332(X1, X2)) -> U332(active(X1), X2) 100.54/26.78 active(U333(X1, X2)) -> U333(active(X1), X2) 100.54/26.78 active(U334(X1, X2)) -> U334(active(X1), X2) 100.54/26.78 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 100.54/26.78 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 100.54/26.78 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 100.54/26.78 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 100.54/26.78 active(fst(X)) -> fst(active(X)) 100.54/26.78 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 100.54/26.78 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 100.54/26.78 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 100.54/26.78 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 100.54/26.78 active(U45(X1, X2)) -> U45(active(X1), X2) 100.54/26.78 active(U46(X)) -> U46(active(X)) 100.54/26.78 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 100.54/26.78 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 100.54/26.78 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 100.54/26.78 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 100.54/26.78 active(U55(X1, X2)) -> U55(active(X1), X2) 100.54/26.78 active(U56(X)) -> U56(active(X)) 100.54/26.78 active(U61(X1, X2)) -> U61(active(X1), X2) 100.54/26.78 active(U62(X1, X2)) -> U62(active(X1), X2) 100.54/26.78 active(U63(X)) -> U63(active(X)) 100.54/26.78 active(U71(X1, X2)) -> U71(active(X1), X2) 100.54/26.78 active(U72(X1, X2)) -> U72(active(X1), X2) 100.54/26.78 active(U73(X)) -> U73(active(X)) 100.54/26.78 active(U81(X1, X2)) -> U81(active(X1), X2) 100.54/26.78 active(U82(X1, X2)) -> U82(active(X1), X2) 100.54/26.78 active(U83(X)) -> U83(active(X)) 100.54/26.78 active(U91(X1, X2)) -> U91(active(X1), X2) 100.54/26.78 active(U92(X1, X2)) -> U92(active(X1), X2) 100.54/26.78 active(U93(X)) -> U93(active(X)) 100.54/26.78 active(tail(X)) -> tail(active(X)) 100.54/26.78 active(take(X1, X2)) -> take(active(X1), X2) 100.54/26.78 active(take(X1, X2)) -> take(X1, active(X2)) 100.54/26.78 active(sel(X1, X2)) -> sel(active(X1), X2) 100.54/26.78 active(sel(X1, X2)) -> sel(X1, active(X2)) 100.54/26.78 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 100.54/26.78 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 100.54/26.78 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 100.54/26.78 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 100.54/26.78 U105(mark(X1), X2) -> mark(U105(X1, X2)) 100.54/26.78 U106(mark(X)) -> mark(U106(X)) 100.54/26.78 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 100.54/26.78 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 100.54/26.78 U111(mark(X1), X2) -> mark(U111(X1, X2)) 100.54/26.78 U112(mark(X)) -> mark(U112(X)) 100.54/26.78 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 100.54/26.78 U121(mark(X1), X2) -> mark(U121(X1, X2)) 100.54/26.78 U122(mark(X)) -> mark(U122(X)) 100.54/26.78 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 100.54/26.78 U131(mark(X)) -> mark(U131(X)) 100.54/26.78 snd(mark(X)) -> mark(snd(X)) 100.54/26.78 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 100.54/26.78 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 100.54/26.78 U141(mark(X)) -> mark(U141(X)) 100.54/26.78 U151(mark(X)) -> mark(U151(X)) 100.54/26.78 U161(mark(X)) -> mark(U161(X)) 100.54/26.78 U171(mark(X1), X2) -> mark(U171(X1, X2)) 100.54/26.78 U172(mark(X)) -> mark(U172(X)) 100.54/26.78 U181(mark(X1), X2) -> mark(U181(X1, X2)) 100.54/26.78 U182(mark(X1), X2) -> mark(U182(X1, X2)) 100.54/26.78 U183(mark(X)) -> mark(U183(X)) 100.54/26.78 U191(mark(X1), X2) -> mark(U191(X1, X2)) 100.54/26.78 U192(mark(X1), X2) -> mark(U192(X1, X2)) 100.54/26.78 U193(mark(X)) -> mark(U193(X)) 100.54/26.78 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 100.54/26.78 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 100.54/26.78 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 100.54/26.78 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 100.54/26.78 U205(mark(X1), X2) -> mark(U205(X1, X2)) 100.54/26.78 U206(mark(X)) -> mark(U206(X)) 100.54/26.78 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 100.54/26.78 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 100.54/26.78 U211(mark(X)) -> mark(U211(X)) 100.54/26.78 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 100.54/26.78 U221(mark(X)) -> mark(U221(X)) 100.54/26.78 U24(mark(X1), X2) -> mark(U24(X1, X2)) 100.54/26.78 U231(mark(X1), X2) -> mark(U231(X1, X2)) 100.54/26.78 U232(mark(X)) -> mark(U232(X)) 100.54/26.78 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 100.54/26.78 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 100.54/26.78 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 100.54/26.78 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 100.54/26.78 U245(mark(X1), X2) -> mark(U245(X1, X2)) 100.54/26.78 U246(mark(X)) -> mark(U246(X)) 100.54/26.78 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 100.54/26.78 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 100.54/26.78 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 100.54/26.78 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 100.54/26.78 U255(mark(X1), X2) -> mark(U255(X1, X2)) 100.54/26.78 U256(mark(X)) -> mark(U256(X)) 100.54/26.78 U261(mark(X1), X2) -> mark(U261(X1, X2)) 100.54/26.78 U262(mark(X)) -> mark(U262(X)) 100.54/26.78 U271(mark(X1), X2) -> mark(U271(X1, X2)) 100.54/26.78 U272(mark(X)) -> mark(U272(X)) 100.54/26.78 U281(mark(X1), X2) -> mark(U281(X1, X2)) 100.54/26.78 U282(mark(X1), X2) -> mark(U282(X1, X2)) 100.54/26.78 cons(mark(X1), X2) -> mark(cons(X1, X2)) 100.54/26.78 natsFrom(mark(X)) -> mark(natsFrom(X)) 100.54/26.78 s(mark(X)) -> mark(s(X)) 100.54/26.78 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 100.54/26.78 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 100.54/26.78 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 100.54/26.78 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 100.54/26.78 head(mark(X)) -> mark(head(X)) 100.54/26.78 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 100.54/26.78 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 100.54/26.78 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 100.54/26.78 U302(mark(X1), X2) -> mark(U302(X1, X2)) 100.54/26.78 U303(mark(X1), X2) -> mark(U303(X1, X2)) 100.54/26.78 U304(mark(X1), X2) -> mark(U304(X1, X2)) 100.54/26.78 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 100.54/26.78 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 100.54/26.78 U311(mark(X1), X2) -> mark(U311(X1, X2)) 100.54/26.78 U312(mark(X1), X2) -> mark(U312(X1, X2)) 100.54/26.78 pair(mark(X1), X2) -> mark(pair(X1, X2)) 100.54/26.78 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 100.54/26.78 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 100.54/26.78 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 100.54/26.78 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 100.54/26.78 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 100.54/26.78 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 100.54/26.78 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 100.54/26.78 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 100.54/26.78 U327(mark(X1), X2) -> mark(U327(X1, X2)) 100.54/26.78 U34(mark(X1), X2) -> mark(U34(X1, X2)) 100.54/26.78 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 100.54/26.78 U332(mark(X1), X2) -> mark(U332(X1, X2)) 100.54/26.78 U333(mark(X1), X2) -> mark(U333(X1, X2)) 100.54/26.78 U334(mark(X1), X2) -> mark(U334(X1, X2)) 100.54/26.78 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 100.54/26.78 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 100.54/26.78 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 100.54/26.78 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 100.54/26.78 fst(mark(X)) -> mark(fst(X)) 100.54/26.78 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 100.54/26.78 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 100.54/26.78 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 100.54/26.78 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 100.54/26.78 U45(mark(X1), X2) -> mark(U45(X1, X2)) 100.54/26.78 U46(mark(X)) -> mark(U46(X)) 100.54/26.78 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 100.54/26.78 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 100.54/26.78 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 100.54/26.78 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 100.54/26.78 U55(mark(X1), X2) -> mark(U55(X1, X2)) 100.54/26.78 U56(mark(X)) -> mark(U56(X)) 100.54/26.78 U61(mark(X1), X2) -> mark(U61(X1, X2)) 100.54/26.78 U62(mark(X1), X2) -> mark(U62(X1, X2)) 100.54/26.78 U63(mark(X)) -> mark(U63(X)) 100.54/26.78 U71(mark(X1), X2) -> mark(U71(X1, X2)) 100.54/26.78 U72(mark(X1), X2) -> mark(U72(X1, X2)) 100.54/26.78 U73(mark(X)) -> mark(U73(X)) 100.54/26.78 U81(mark(X1), X2) -> mark(U81(X1, X2)) 100.54/26.78 U82(mark(X1), X2) -> mark(U82(X1, X2)) 100.54/26.78 U83(mark(X)) -> mark(U83(X)) 100.54/26.78 U91(mark(X1), X2) -> mark(U91(X1, X2)) 100.54/26.78 U92(mark(X1), X2) -> mark(U92(X1, X2)) 100.54/26.78 U93(mark(X)) -> mark(U93(X)) 100.54/26.78 tail(mark(X)) -> mark(tail(X)) 100.54/26.78 take(mark(X1), X2) -> mark(take(X1, X2)) 100.54/26.78 take(X1, mark(X2)) -> mark(take(X1, X2)) 100.54/26.78 sel(mark(X1), X2) -> mark(sel(X1, X2)) 100.54/26.78 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 100.54/26.78 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(tt) -> ok(tt) 100.54/26.78 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 100.54/26.78 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 100.54/26.78 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 100.54/26.78 proper(isNatural(X)) -> isNatural(proper(X)) 100.54/26.78 proper(U106(X)) -> U106(proper(X)) 100.54/26.78 proper(isLNat(X)) -> isLNat(proper(X)) 100.54/26.78 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 100.54/26.78 proper(U112(X)) -> U112(proper(X)) 100.54/26.78 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 100.54/26.78 proper(U122(X)) -> U122(proper(X)) 100.54/26.78 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U131(X)) -> U131(proper(X)) 100.54/26.78 proper(snd(X)) -> snd(proper(X)) 100.54/26.78 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 100.54/26.78 proper(U141(X)) -> U141(proper(X)) 100.54/26.78 proper(U151(X)) -> U151(proper(X)) 100.54/26.78 proper(U161(X)) -> U161(proper(X)) 100.54/26.78 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 100.54/26.78 proper(U172(X)) -> U172(proper(X)) 100.54/26.78 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 100.54/26.78 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 100.54/26.78 proper(U183(X)) -> U183(proper(X)) 100.54/26.78 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 100.54/26.78 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 100.54/26.78 proper(U193(X)) -> U193(proper(X)) 100.54/26.78 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 100.54/26.78 proper(U206(X)) -> U206(proper(X)) 100.54/26.78 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U211(X)) -> U211(proper(X)) 100.54/26.78 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U221(X)) -> U221(proper(X)) 100.54/26.78 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 100.54/26.78 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 100.54/26.78 proper(U232(X)) -> U232(proper(X)) 100.54/26.78 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 100.54/26.78 proper(U246(X)) -> U246(proper(X)) 100.54/26.78 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 100.54/26.78 proper(U256(X)) -> U256(proper(X)) 100.54/26.78 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 100.54/26.78 proper(U262(X)) -> U262(proper(X)) 100.54/26.78 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 100.54/26.78 proper(U272(X)) -> U272(proper(X)) 100.54/26.78 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 100.54/26.78 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 100.54/26.78 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 100.54/26.78 proper(natsFrom(X)) -> natsFrom(proper(X)) 100.54/26.78 proper(s(X)) -> s(proper(X)) 100.54/26.78 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(head(X)) -> head(proper(X)) 100.54/26.78 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 100.54/26.78 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 100.54/26.78 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 100.54/26.78 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 100.54/26.78 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 100.54/26.78 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 100.54/26.78 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 100.54/26.78 proper(nil) -> ok(nil) 100.54/26.78 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.78 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 100.54/26.78 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 100.54/26.78 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 100.54/26.78 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 100.54/26.78 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 100.54/26.78 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(fst(X)) -> fst(proper(X)) 100.54/26.78 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 100.54/26.78 proper(U46(X)) -> U46(proper(X)) 100.54/26.78 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 100.54/26.78 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 100.54/26.78 proper(U56(X)) -> U56(proper(X)) 100.54/26.78 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 100.54/26.78 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 100.54/26.78 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 100.54/26.78 proper(U63(X)) -> U63(proper(X)) 100.54/26.78 proper(isPLNat(X)) -> isPLNat(proper(X)) 100.54/26.78 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 100.54/26.78 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 100.54/26.78 proper(U73(X)) -> U73(proper(X)) 100.54/26.78 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 100.54/26.78 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 100.54/26.78 proper(U83(X)) -> U83(proper(X)) 100.54/26.78 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 100.54/26.78 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 100.54/26.78 proper(U93(X)) -> U93(proper(X)) 100.54/26.78 proper(tail(X)) -> tail(proper(X)) 100.54/26.78 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 100.54/26.78 proper(0) -> ok(0) 100.54/26.78 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 100.54/26.78 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 100.54/26.78 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 100.54/26.78 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 100.54/26.78 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 100.54/26.78 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 100.54/26.78 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 100.54/26.78 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 100.54/26.78 isNatural(ok(X)) -> ok(isNatural(X)) 100.54/26.78 U106(ok(X)) -> ok(U106(X)) 100.54/26.78 isLNat(ok(X)) -> ok(isLNat(X)) 100.54/26.78 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 100.54/26.78 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 100.54/26.78 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 100.54/26.78 U112(ok(X)) -> ok(U112(X)) 100.54/26.78 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 100.54/26.78 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 100.54/26.78 U122(ok(X)) -> ok(U122(X)) 100.54/26.78 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 100.54/26.78 U131(ok(X)) -> ok(U131(X)) 100.54/26.78 snd(ok(X)) -> ok(snd(X)) 100.54/26.78 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 100.54/26.78 U141(ok(X)) -> ok(U141(X)) 100.54/26.78 U151(ok(X)) -> ok(U151(X)) 100.54/26.78 U161(ok(X)) -> ok(U161(X)) 100.54/26.78 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 100.54/26.78 U172(ok(X)) -> ok(U172(X)) 100.54/26.78 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 100.54/26.78 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 100.54/26.78 U183(ok(X)) -> ok(U183(X)) 100.54/26.78 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 100.54/26.78 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 100.54/26.78 U193(ok(X)) -> ok(U193(X)) 100.54/26.78 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 100.54/26.78 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 100.54/26.78 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 100.54/26.78 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 100.54/26.78 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 100.54/26.78 U206(ok(X)) -> ok(U206(X)) 100.54/26.78 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 100.54/26.78 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 100.54/26.78 U211(ok(X)) -> ok(U211(X)) 100.54/26.78 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 100.54/26.78 U221(ok(X)) -> ok(U221(X)) 100.54/26.78 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 100.54/26.78 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 100.54/26.78 U232(ok(X)) -> ok(U232(X)) 100.54/26.78 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 100.54/26.78 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 100.54/26.78 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 100.54/26.78 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 100.54/26.78 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 100.54/26.78 U246(ok(X)) -> ok(U246(X)) 100.54/26.78 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 100.54/26.78 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 100.54/26.78 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 100.54/26.78 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 100.54/26.78 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 100.54/26.78 U256(ok(X)) -> ok(U256(X)) 100.54/26.78 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 100.54/26.78 U262(ok(X)) -> ok(U262(X)) 100.54/26.78 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 100.54/26.78 U272(ok(X)) -> ok(U272(X)) 100.54/26.78 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 100.54/26.78 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 100.54/26.78 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 100.54/26.78 natsFrom(ok(X)) -> ok(natsFrom(X)) 100.54/26.78 s(ok(X)) -> ok(s(X)) 100.54/26.78 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 100.54/26.78 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 100.54/26.78 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 100.54/26.78 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 100.54/26.78 head(ok(X)) -> ok(head(X)) 100.54/26.78 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 100.54/26.78 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 100.54/26.78 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 100.54/26.78 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 100.54/26.78 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 100.54/26.78 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 100.54/26.78 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 100.54/26.78 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 100.54/26.78 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 100.54/26.78 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 100.54/26.78 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 100.54/26.78 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 100.54/26.78 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 100.54/26.78 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 100.54/26.78 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 100.54/26.78 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 100.54/26.78 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 100.54/26.78 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 100.54/26.78 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 100.54/26.78 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 100.54/26.78 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 100.54/26.78 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 100.54/26.78 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 100.54/26.78 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 100.54/26.78 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 100.54/26.78 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 100.54/26.78 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 100.54/26.78 fst(ok(X)) -> ok(fst(X)) 100.54/26.78 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 100.54/26.78 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 100.54/26.78 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 100.54/26.78 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 100.54/26.78 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 100.54/26.78 U46(ok(X)) -> ok(U46(X)) 100.54/26.78 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 100.54/26.78 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 100.54/26.78 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 100.54/26.78 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 100.54/26.78 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 100.54/26.78 U56(ok(X)) -> ok(U56(X)) 100.54/26.78 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 100.54/26.78 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 100.54/26.78 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 100.54/26.78 U63(ok(X)) -> ok(U63(X)) 100.54/26.78 isPLNat(ok(X)) -> ok(isPLNat(X)) 100.54/26.78 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 100.54/26.78 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 100.54/26.78 U73(ok(X)) -> ok(U73(X)) 100.54/26.78 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 100.54/26.78 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 100.54/26.78 U83(ok(X)) -> ok(U83(X)) 100.54/26.78 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 100.54/26.78 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 100.54/26.78 U93(ok(X)) -> ok(U93(X)) 100.54/26.78 tail(ok(X)) -> ok(tail(X)) 100.54/26.78 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 100.54/26.78 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 100.54/26.78 top(mark(X)) -> top(proper(X)) 100.54/26.78 top(ok(X)) -> top(active(X)) 100.54/26.78 100.54/26.78 S is empty. 100.54/26.78 Rewrite Strategy: FULL 100.54/26.78 ---------------------------------------- 100.54/26.78 100.54/26.78 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 100.54/26.78 The following defined symbols can occur below the 0th argument of top: active, proper 100.54/26.78 The following defined symbols can occur below the 0th argument of active: active, proper 100.54/26.79 The following defined symbols can occur below the 0th argument of proper: active, proper 100.54/26.79 100.54/26.79 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 100.54/26.79 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 100.54/26.79 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 100.54/26.79 active(U106(tt)) -> mark(tt) 100.54/26.79 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 100.54/26.79 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 100.54/26.79 active(U112(tt)) -> mark(tt) 100.54/26.79 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 100.54/26.79 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 100.54/26.79 active(U122(tt)) -> mark(tt) 100.54/26.79 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 100.54/26.79 active(U131(tt)) -> mark(tt) 100.54/26.79 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 100.54/26.79 active(U141(tt)) -> mark(tt) 100.54/26.79 active(U151(tt)) -> mark(tt) 100.54/26.79 active(U161(tt)) -> mark(tt) 100.54/26.79 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 100.54/26.79 active(U172(tt)) -> mark(tt) 100.54/26.79 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 100.54/26.79 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 100.54/26.79 active(U183(tt)) -> mark(tt) 100.54/26.79 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 100.54/26.79 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 100.54/26.79 active(U193(tt)) -> mark(tt) 100.54/26.79 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 100.54/26.79 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 100.54/26.79 active(U206(tt)) -> mark(tt) 100.54/26.79 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 100.54/26.79 active(U211(tt)) -> mark(tt) 100.54/26.79 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 100.54/26.79 active(U221(tt)) -> mark(tt) 100.54/26.79 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 100.54/26.79 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 100.54/26.79 active(U232(tt)) -> mark(tt) 100.54/26.79 active(U24(tt, X)) -> mark(X) 100.54/26.79 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 100.54/26.79 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 100.54/26.79 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 100.54/26.79 active(U246(tt)) -> mark(tt) 100.54/26.79 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 100.54/26.79 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 100.54/26.79 active(U256(tt)) -> mark(tt) 100.54/26.79 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 100.54/26.79 active(U262(tt)) -> mark(tt) 100.54/26.79 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 100.54/26.79 active(U272(tt)) -> mark(tt) 100.54/26.79 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 100.54/26.79 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 100.54/26.79 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 100.54/26.79 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 100.54/26.79 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 100.54/26.79 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 100.54/26.79 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 100.54/26.79 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 100.54/26.79 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 100.54/26.79 active(U304(tt, Y)) -> mark(Y) 100.54/26.79 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 100.54/26.79 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 100.54/26.79 active(U312(tt, XS)) -> mark(pair(nil, XS)) 100.54/26.79 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 100.54/26.79 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 100.54/26.79 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 100.54/26.79 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 100.54/26.79 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 100.54/26.79 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 100.54/26.79 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 100.54/26.79 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 100.54/26.79 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 100.54/26.79 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 100.54/26.79 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 100.54/26.79 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 100.54/26.79 active(U334(tt, XS)) -> mark(XS) 100.54/26.79 active(U34(tt, N)) -> mark(N) 100.54/26.79 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 100.54/26.79 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 100.54/26.79 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 100.54/26.79 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 100.54/26.79 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 100.54/26.79 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 100.54/26.79 active(U46(tt)) -> mark(tt) 100.54/26.79 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 100.54/26.79 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 100.54/26.79 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 100.54/26.79 active(U56(tt)) -> mark(tt) 100.54/26.79 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 100.54/26.79 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 100.54/26.79 active(U63(tt)) -> mark(tt) 100.54/26.79 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 100.54/26.79 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 100.54/26.79 active(U73(tt)) -> mark(tt) 100.54/26.79 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 100.54/26.79 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 100.54/26.79 active(U83(tt)) -> mark(tt) 100.54/26.79 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 100.54/26.79 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 100.54/26.79 active(U93(tt)) -> mark(tt) 100.54/26.79 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 100.54/26.79 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 100.54/26.79 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 100.54/26.79 active(isLNat(nil)) -> mark(tt) 100.54/26.79 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 100.54/26.79 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 100.54/26.79 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 100.54/26.79 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 100.54/26.79 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(isLNatKind(nil)) -> mark(tt) 100.54/26.79 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 100.54/26.79 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 100.54/26.79 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 100.54/26.79 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 100.54/26.79 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 100.54/26.79 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 100.54/26.79 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 100.54/26.79 active(isNatural(0)) -> mark(tt) 100.54/26.79 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 100.54/26.79 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 100.54/26.79 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(isNaturalKind(0)) -> mark(tt) 100.54/26.79 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 100.54/26.79 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 100.54/26.79 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 100.54/26.79 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 100.54/26.79 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 100.54/26.79 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 100.54/26.79 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 100.54/26.79 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 100.54/26.79 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 100.54/26.79 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 100.54/26.79 active(splitAt(0, XS)) -> mark(U311(isLNat(XS), XS)) 100.54/26.79 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 100.54/26.79 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 100.54/26.79 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 100.54/26.79 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 100.54/26.79 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 100.54/26.79 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 100.54/26.79 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 100.54/26.79 active(U105(X1, X2)) -> U105(active(X1), X2) 100.54/26.79 active(U106(X)) -> U106(active(X)) 100.54/26.79 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 100.54/26.79 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 100.54/26.79 active(U111(X1, X2)) -> U111(active(X1), X2) 100.54/26.79 active(U112(X)) -> U112(active(X)) 100.54/26.79 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 100.54/26.79 active(U121(X1, X2)) -> U121(active(X1), X2) 100.54/26.79 active(U122(X)) -> U122(active(X)) 100.54/26.79 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 100.54/26.79 active(U131(X)) -> U131(active(X)) 100.54/26.79 active(snd(X)) -> snd(active(X)) 100.54/26.79 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 100.54/26.79 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 100.54/26.79 active(U141(X)) -> U141(active(X)) 100.54/26.79 active(U151(X)) -> U151(active(X)) 100.54/26.79 active(U161(X)) -> U161(active(X)) 100.54/26.79 active(U171(X1, X2)) -> U171(active(X1), X2) 100.54/26.79 active(U172(X)) -> U172(active(X)) 100.54/26.79 active(U181(X1, X2)) -> U181(active(X1), X2) 100.54/26.79 active(U182(X1, X2)) -> U182(active(X1), X2) 100.54/26.79 active(U183(X)) -> U183(active(X)) 100.54/26.79 active(U191(X1, X2)) -> U191(active(X1), X2) 100.54/26.79 active(U192(X1, X2)) -> U192(active(X1), X2) 100.54/26.79 active(U193(X)) -> U193(active(X)) 100.54/26.79 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 100.54/26.79 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 100.54/26.79 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 100.54/26.79 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 100.54/26.79 active(U205(X1, X2)) -> U205(active(X1), X2) 100.54/26.79 active(U206(X)) -> U206(active(X)) 100.54/26.79 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 100.54/26.79 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 100.54/26.79 active(U211(X)) -> U211(active(X)) 100.54/26.79 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 100.54/26.79 active(U221(X)) -> U221(active(X)) 100.54/26.79 active(U24(X1, X2)) -> U24(active(X1), X2) 100.54/26.79 active(U231(X1, X2)) -> U231(active(X1), X2) 100.54/26.79 active(U232(X)) -> U232(active(X)) 100.54/26.79 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 100.54/26.79 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 100.54/26.79 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 100.54/26.79 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 100.54/26.79 active(U245(X1, X2)) -> U245(active(X1), X2) 100.54/26.79 active(U246(X)) -> U246(active(X)) 100.54/26.79 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 100.54/26.79 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 100.54/26.79 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 100.54/26.79 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 100.54/26.79 active(U255(X1, X2)) -> U255(active(X1), X2) 100.54/26.79 active(U256(X)) -> U256(active(X)) 100.54/26.79 active(U261(X1, X2)) -> U261(active(X1), X2) 100.54/26.79 active(U262(X)) -> U262(active(X)) 100.54/26.79 active(U271(X1, X2)) -> U271(active(X1), X2) 100.54/26.79 active(U272(X)) -> U272(active(X)) 100.54/26.79 active(U281(X1, X2)) -> U281(active(X1), X2) 100.54/26.79 active(U282(X1, X2)) -> U282(active(X1), X2) 100.54/26.79 active(cons(X1, X2)) -> cons(active(X1), X2) 100.54/26.79 active(natsFrom(X)) -> natsFrom(active(X)) 100.54/26.79 active(s(X)) -> s(active(X)) 100.54/26.79 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 100.54/26.79 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 100.54/26.79 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 100.54/26.79 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 100.54/26.79 active(head(X)) -> head(active(X)) 100.54/26.79 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 100.54/26.79 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 100.54/26.79 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 100.54/26.79 active(U302(X1, X2)) -> U302(active(X1), X2) 100.54/26.79 active(U303(X1, X2)) -> U303(active(X1), X2) 100.54/26.79 active(U304(X1, X2)) -> U304(active(X1), X2) 100.54/26.79 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 100.54/26.79 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 100.54/26.79 active(U311(X1, X2)) -> U311(active(X1), X2) 100.54/26.79 active(U312(X1, X2)) -> U312(active(X1), X2) 100.54/26.79 active(pair(X1, X2)) -> pair(active(X1), X2) 100.54/26.79 active(pair(X1, X2)) -> pair(X1, active(X2)) 100.54/26.79 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 100.54/26.79 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 100.54/26.79 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 100.54/26.79 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 100.54/26.79 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 100.54/26.79 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 100.54/26.79 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 100.54/26.79 active(U327(X1, X2)) -> U327(active(X1), X2) 100.54/26.79 active(U34(X1, X2)) -> U34(active(X1), X2) 100.54/26.79 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 100.54/26.79 active(U332(X1, X2)) -> U332(active(X1), X2) 100.54/26.79 active(U333(X1, X2)) -> U333(active(X1), X2) 100.54/26.79 active(U334(X1, X2)) -> U334(active(X1), X2) 100.54/26.79 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 100.54/26.79 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 100.54/26.79 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 100.54/26.79 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 100.54/26.79 active(fst(X)) -> fst(active(X)) 100.54/26.79 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 100.54/26.79 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 100.54/26.79 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 100.54/26.79 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 100.54/26.79 active(U45(X1, X2)) -> U45(active(X1), X2) 100.54/26.79 active(U46(X)) -> U46(active(X)) 100.54/26.79 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 100.54/26.79 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 100.54/26.79 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 100.54/26.79 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 100.54/26.79 active(U55(X1, X2)) -> U55(active(X1), X2) 100.54/26.79 active(U56(X)) -> U56(active(X)) 100.54/26.79 active(U61(X1, X2)) -> U61(active(X1), X2) 100.54/26.79 active(U62(X1, X2)) -> U62(active(X1), X2) 100.54/26.79 active(U63(X)) -> U63(active(X)) 100.54/26.79 active(U71(X1, X2)) -> U71(active(X1), X2) 100.54/26.79 active(U72(X1, X2)) -> U72(active(X1), X2) 100.54/26.79 active(U73(X)) -> U73(active(X)) 100.54/26.79 active(U81(X1, X2)) -> U81(active(X1), X2) 100.54/26.79 active(U82(X1, X2)) -> U82(active(X1), X2) 100.54/26.79 active(U83(X)) -> U83(active(X)) 100.54/26.79 active(U91(X1, X2)) -> U91(active(X1), X2) 100.54/26.79 active(U92(X1, X2)) -> U92(active(X1), X2) 100.54/26.79 active(U93(X)) -> U93(active(X)) 100.54/26.79 active(tail(X)) -> tail(active(X)) 100.54/26.79 active(take(X1, X2)) -> take(active(X1), X2) 100.54/26.79 active(take(X1, X2)) -> take(X1, active(X2)) 100.54/26.79 active(sel(X1, X2)) -> sel(active(X1), X2) 100.54/26.79 active(sel(X1, X2)) -> sel(X1, active(X2)) 100.54/26.79 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 100.54/26.79 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 100.54/26.79 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 100.54/26.79 proper(isNatural(X)) -> isNatural(proper(X)) 100.54/26.79 proper(U106(X)) -> U106(proper(X)) 100.54/26.79 proper(isLNat(X)) -> isLNat(proper(X)) 100.54/26.79 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 100.54/26.79 proper(U112(X)) -> U112(proper(X)) 100.54/26.79 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 100.54/26.79 proper(U122(X)) -> U122(proper(X)) 100.54/26.79 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U131(X)) -> U131(proper(X)) 100.54/26.79 proper(snd(X)) -> snd(proper(X)) 100.54/26.79 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 100.54/26.79 proper(U141(X)) -> U141(proper(X)) 100.54/26.79 proper(U151(X)) -> U151(proper(X)) 100.54/26.79 proper(U161(X)) -> U161(proper(X)) 100.54/26.79 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 100.54/26.79 proper(U172(X)) -> U172(proper(X)) 100.54/26.79 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 100.54/26.79 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 100.54/26.79 proper(U183(X)) -> U183(proper(X)) 100.54/26.79 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 100.54/26.79 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 100.54/26.79 proper(U193(X)) -> U193(proper(X)) 100.54/26.79 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 100.54/26.79 proper(U206(X)) -> U206(proper(X)) 100.54/26.79 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U211(X)) -> U211(proper(X)) 100.54/26.79 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U221(X)) -> U221(proper(X)) 100.54/26.79 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 100.54/26.79 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 100.54/26.79 proper(U232(X)) -> U232(proper(X)) 100.54/26.79 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 100.54/26.79 proper(U246(X)) -> U246(proper(X)) 100.54/26.79 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 100.54/26.79 proper(U256(X)) -> U256(proper(X)) 100.54/26.79 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 100.54/26.79 proper(U262(X)) -> U262(proper(X)) 100.54/26.79 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 100.54/26.79 proper(U272(X)) -> U272(proper(X)) 100.54/26.79 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 100.54/26.79 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 100.54/26.79 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 100.54/26.79 proper(natsFrom(X)) -> natsFrom(proper(X)) 100.54/26.79 proper(s(X)) -> s(proper(X)) 100.54/26.79 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(head(X)) -> head(proper(X)) 100.54/26.79 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 100.54/26.79 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 100.54/26.79 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 100.54/26.79 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 100.54/26.79 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 100.54/26.79 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 100.54/26.79 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 100.54/26.79 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 100.54/26.79 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 100.54/26.79 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 100.54/26.79 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 100.54/26.79 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 100.54/26.79 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 100.54/26.79 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(fst(X)) -> fst(proper(X)) 100.54/26.79 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 100.54/26.79 proper(U46(X)) -> U46(proper(X)) 100.54/26.79 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 100.54/26.79 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 100.54/26.79 proper(U56(X)) -> U56(proper(X)) 100.54/26.79 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 100.54/26.79 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 100.54/26.79 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 100.54/26.79 proper(U63(X)) -> U63(proper(X)) 100.54/26.79 proper(isPLNat(X)) -> isPLNat(proper(X)) 100.54/26.79 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 100.54/26.79 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 100.54/26.79 proper(U73(X)) -> U73(proper(X)) 100.54/26.79 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 100.54/26.79 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 100.54/26.79 proper(U83(X)) -> U83(proper(X)) 100.54/26.79 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 100.54/26.79 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 100.54/26.79 proper(U93(X)) -> U93(proper(X)) 100.54/26.79 proper(tail(X)) -> tail(proper(X)) 100.54/26.79 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 100.54/26.79 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 100.54/26.79 100.54/26.79 ---------------------------------------- 100.54/26.79 100.54/26.79 (2) 100.54/26.79 Obligation: 100.54/26.79 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 100.54/26.79 100.54/26.79 100.54/26.79 The TRS R consists of the following rules: 100.54/26.79 100.54/26.79 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 100.54/26.79 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 100.54/26.79 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 100.54/26.79 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 100.54/26.79 U105(mark(X1), X2) -> mark(U105(X1, X2)) 100.54/26.79 U106(mark(X)) -> mark(U106(X)) 100.54/26.79 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 100.54/26.79 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 100.54/26.79 U111(mark(X1), X2) -> mark(U111(X1, X2)) 100.54/26.79 U112(mark(X)) -> mark(U112(X)) 100.54/26.79 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 100.54/26.79 U121(mark(X1), X2) -> mark(U121(X1, X2)) 100.54/26.79 U122(mark(X)) -> mark(U122(X)) 100.54/26.79 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 100.54/26.79 U131(mark(X)) -> mark(U131(X)) 100.54/26.79 snd(mark(X)) -> mark(snd(X)) 100.54/26.79 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 100.54/26.79 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 100.54/26.79 U141(mark(X)) -> mark(U141(X)) 100.54/26.79 U151(mark(X)) -> mark(U151(X)) 100.54/26.79 U161(mark(X)) -> mark(U161(X)) 100.54/26.79 U171(mark(X1), X2) -> mark(U171(X1, X2)) 100.54/26.79 U172(mark(X)) -> mark(U172(X)) 100.54/26.79 U181(mark(X1), X2) -> mark(U181(X1, X2)) 100.54/26.79 U182(mark(X1), X2) -> mark(U182(X1, X2)) 100.54/26.79 U183(mark(X)) -> mark(U183(X)) 100.54/26.79 U191(mark(X1), X2) -> mark(U191(X1, X2)) 100.54/26.79 U192(mark(X1), X2) -> mark(U192(X1, X2)) 100.54/26.79 U193(mark(X)) -> mark(U193(X)) 100.54/26.79 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 100.54/26.79 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 100.54/26.79 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 100.54/26.79 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 100.54/26.79 U205(mark(X1), X2) -> mark(U205(X1, X2)) 100.54/26.79 U206(mark(X)) -> mark(U206(X)) 100.54/26.79 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 100.54/26.79 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 100.54/26.79 U211(mark(X)) -> mark(U211(X)) 100.54/26.79 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 100.54/26.79 U221(mark(X)) -> mark(U221(X)) 100.54/26.79 U24(mark(X1), X2) -> mark(U24(X1, X2)) 100.54/26.79 U231(mark(X1), X2) -> mark(U231(X1, X2)) 100.54/26.79 U232(mark(X)) -> mark(U232(X)) 100.54/26.79 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 100.54/26.79 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 100.54/26.79 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 100.54/26.79 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 100.54/26.79 U245(mark(X1), X2) -> mark(U245(X1, X2)) 100.54/26.79 U246(mark(X)) -> mark(U246(X)) 100.54/26.79 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 100.54/26.79 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 100.54/26.79 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 100.54/26.79 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 100.54/26.79 U255(mark(X1), X2) -> mark(U255(X1, X2)) 100.54/26.79 U256(mark(X)) -> mark(U256(X)) 100.54/26.79 U261(mark(X1), X2) -> mark(U261(X1, X2)) 100.54/26.79 U262(mark(X)) -> mark(U262(X)) 100.54/26.79 U271(mark(X1), X2) -> mark(U271(X1, X2)) 100.54/26.79 U272(mark(X)) -> mark(U272(X)) 100.54/26.79 U281(mark(X1), X2) -> mark(U281(X1, X2)) 100.54/26.79 U282(mark(X1), X2) -> mark(U282(X1, X2)) 100.54/26.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 100.54/26.79 natsFrom(mark(X)) -> mark(natsFrom(X)) 100.54/26.79 s(mark(X)) -> mark(s(X)) 100.54/26.79 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 100.54/26.79 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 100.54/26.79 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 100.54/26.79 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 100.54/26.79 head(mark(X)) -> mark(head(X)) 100.54/26.79 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 100.54/26.79 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 100.54/26.79 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 100.54/26.79 U302(mark(X1), X2) -> mark(U302(X1, X2)) 100.54/26.79 U303(mark(X1), X2) -> mark(U303(X1, X2)) 100.54/26.79 U304(mark(X1), X2) -> mark(U304(X1, X2)) 100.54/26.79 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 100.54/26.79 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 100.54/26.79 U311(mark(X1), X2) -> mark(U311(X1, X2)) 100.54/26.79 U312(mark(X1), X2) -> mark(U312(X1, X2)) 100.54/26.79 pair(mark(X1), X2) -> mark(pair(X1, X2)) 100.54/26.79 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 100.54/26.79 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 100.54/26.79 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 100.54/26.79 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 100.54/26.79 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 100.54/26.79 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 100.54/26.79 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 100.54/26.79 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 100.54/26.79 U327(mark(X1), X2) -> mark(U327(X1, X2)) 100.54/26.79 U34(mark(X1), X2) -> mark(U34(X1, X2)) 100.54/26.79 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 100.54/26.79 U332(mark(X1), X2) -> mark(U332(X1, X2)) 100.54/26.79 U333(mark(X1), X2) -> mark(U333(X1, X2)) 100.54/26.79 U334(mark(X1), X2) -> mark(U334(X1, X2)) 100.54/26.79 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 100.54/26.79 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 100.54/26.79 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 100.54/26.79 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 100.54/26.79 fst(mark(X)) -> mark(fst(X)) 100.54/26.79 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 100.54/26.79 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 100.54/26.79 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 100.54/26.79 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 100.54/26.79 U45(mark(X1), X2) -> mark(U45(X1, X2)) 100.54/26.79 U46(mark(X)) -> mark(U46(X)) 100.54/26.79 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 100.54/26.79 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 100.54/26.79 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 100.54/26.79 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 100.54/26.79 U55(mark(X1), X2) -> mark(U55(X1, X2)) 100.54/26.79 U56(mark(X)) -> mark(U56(X)) 100.54/26.79 U61(mark(X1), X2) -> mark(U61(X1, X2)) 100.54/26.79 U62(mark(X1), X2) -> mark(U62(X1, X2)) 100.54/26.79 U63(mark(X)) -> mark(U63(X)) 100.54/26.79 U71(mark(X1), X2) -> mark(U71(X1, X2)) 100.54/26.79 U72(mark(X1), X2) -> mark(U72(X1, X2)) 100.54/26.79 U73(mark(X)) -> mark(U73(X)) 100.54/26.79 U81(mark(X1), X2) -> mark(U81(X1, X2)) 100.54/26.79 U82(mark(X1), X2) -> mark(U82(X1, X2)) 100.54/26.79 U83(mark(X)) -> mark(U83(X)) 100.54/26.79 U91(mark(X1), X2) -> mark(U91(X1, X2)) 100.54/26.79 U92(mark(X1), X2) -> mark(U92(X1, X2)) 100.54/26.79 U93(mark(X)) -> mark(U93(X)) 100.54/26.79 tail(mark(X)) -> mark(tail(X)) 100.54/26.79 take(mark(X1), X2) -> mark(take(X1, X2)) 100.54/26.79 take(X1, mark(X2)) -> mark(take(X1, X2)) 100.54/26.79 sel(mark(X1), X2) -> mark(sel(X1, X2)) 100.54/26.79 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 100.54/26.79 proper(tt) -> ok(tt) 100.54/26.79 proper(nil) -> ok(nil) 100.54/26.79 proper(0) -> ok(0) 100.54/26.79 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 100.54/26.79 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 100.54/26.79 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 100.54/26.79 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 100.54/26.79 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 100.54/26.79 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 100.54/26.79 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 100.54/26.79 isNatural(ok(X)) -> ok(isNatural(X)) 100.54/26.79 U106(ok(X)) -> ok(U106(X)) 100.54/26.79 isLNat(ok(X)) -> ok(isLNat(X)) 100.54/26.79 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 100.54/26.79 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 100.54/26.79 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 100.54/26.79 U112(ok(X)) -> ok(U112(X)) 100.54/26.79 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 100.54/26.79 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 100.54/26.79 U122(ok(X)) -> ok(U122(X)) 100.54/26.79 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 100.54/26.79 U131(ok(X)) -> ok(U131(X)) 100.54/26.79 snd(ok(X)) -> ok(snd(X)) 100.54/26.79 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 100.54/26.79 U141(ok(X)) -> ok(U141(X)) 100.54/26.79 U151(ok(X)) -> ok(U151(X)) 100.54/26.79 U161(ok(X)) -> ok(U161(X)) 100.54/26.79 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 100.54/26.79 U172(ok(X)) -> ok(U172(X)) 100.54/26.79 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 100.54/26.79 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 100.54/26.79 U183(ok(X)) -> ok(U183(X)) 100.54/26.79 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 100.54/26.79 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 100.54/26.79 U193(ok(X)) -> ok(U193(X)) 100.54/26.79 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 100.54/26.79 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 100.54/26.79 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 100.54/26.79 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 100.54/26.79 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 100.54/26.79 U206(ok(X)) -> ok(U206(X)) 100.54/26.79 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 100.54/26.79 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 100.54/26.79 U211(ok(X)) -> ok(U211(X)) 100.54/26.79 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 100.54/26.79 U221(ok(X)) -> ok(U221(X)) 100.54/26.79 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 100.54/26.79 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 100.54/26.79 U232(ok(X)) -> ok(U232(X)) 100.54/26.79 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 100.54/26.79 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 100.54/26.79 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 100.54/26.79 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 100.54/26.79 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 100.54/26.79 U246(ok(X)) -> ok(U246(X)) 100.54/26.79 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 100.54/26.79 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 100.54/26.79 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 100.54/26.79 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 100.54/26.79 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 100.54/26.79 U256(ok(X)) -> ok(U256(X)) 100.54/26.79 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 100.54/26.79 U262(ok(X)) -> ok(U262(X)) 100.54/26.79 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 100.54/26.79 U272(ok(X)) -> ok(U272(X)) 100.54/26.79 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 100.54/26.79 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 100.54/26.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 100.54/26.79 natsFrom(ok(X)) -> ok(natsFrom(X)) 100.54/26.79 s(ok(X)) -> ok(s(X)) 100.54/26.79 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 100.54/26.79 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 100.54/26.79 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 100.54/26.79 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 100.54/26.79 head(ok(X)) -> ok(head(X)) 100.54/26.79 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 100.54/26.79 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 100.54/26.79 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 100.54/26.79 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 100.54/26.79 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 100.54/26.79 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 100.54/26.79 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 100.54/26.79 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 100.54/26.79 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 100.54/26.79 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 100.54/26.79 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 100.54/26.79 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 100.54/26.79 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 100.54/26.79 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 100.54/26.79 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 100.54/26.79 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 100.54/26.79 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 100.54/26.79 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 100.54/26.79 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 100.54/26.79 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 100.54/26.79 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 100.54/26.79 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 100.54/26.79 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 100.54/26.79 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 100.54/26.79 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 100.54/26.79 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 100.54/26.79 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 100.54/26.79 fst(ok(X)) -> ok(fst(X)) 100.54/26.79 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 100.54/26.79 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 100.54/26.79 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 100.54/26.79 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 100.54/26.79 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 100.54/26.79 U46(ok(X)) -> ok(U46(X)) 100.54/26.79 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 100.54/26.79 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 100.54/26.79 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 100.54/26.79 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 100.54/26.79 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 100.54/26.79 U56(ok(X)) -> ok(U56(X)) 100.54/26.79 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 100.54/26.79 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 100.54/26.79 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 100.54/26.79 U63(ok(X)) -> ok(U63(X)) 100.54/26.79 isPLNat(ok(X)) -> ok(isPLNat(X)) 100.54/26.79 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 100.54/26.79 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 100.54/26.79 U73(ok(X)) -> ok(U73(X)) 100.54/26.79 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 100.54/26.79 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 100.54/26.79 U83(ok(X)) -> ok(U83(X)) 100.54/26.79 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 100.54/26.79 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 100.54/26.79 U93(ok(X)) -> ok(U93(X)) 100.54/26.79 tail(ok(X)) -> ok(tail(X)) 100.54/26.79 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 100.54/26.79 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 100.54/26.79 top(mark(X)) -> top(proper(X)) 100.54/26.79 top(ok(X)) -> top(active(X)) 100.54/26.79 100.54/26.79 S is empty. 100.54/26.79 Rewrite Strategy: FULL 100.54/26.79 ---------------------------------------- 100.54/26.79 100.54/26.79 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 100.54/26.79 Converted rc-obligation to irc-obligation. 100.54/26.79 100.54/26.79 As the TRS is a non-duplicating overlay system, we have rc = irc. 100.54/26.79 ---------------------------------------- 100.54/26.79 100.54/26.79 (4) 100.54/26.79 Obligation: 100.54/26.79 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 100.54/26.79 100.54/26.79 100.54/26.79 The TRS R consists of the following rules: 100.54/26.79 100.54/26.79 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 100.54/26.79 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 100.54/26.79 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 100.54/26.79 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 100.54/26.79 U105(mark(X1), X2) -> mark(U105(X1, X2)) 100.54/26.79 U106(mark(X)) -> mark(U106(X)) 100.54/26.79 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 100.54/26.79 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 100.54/26.79 U111(mark(X1), X2) -> mark(U111(X1, X2)) 100.54/26.79 U112(mark(X)) -> mark(U112(X)) 100.54/26.79 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 100.54/26.79 U121(mark(X1), X2) -> mark(U121(X1, X2)) 100.54/26.79 U122(mark(X)) -> mark(U122(X)) 100.54/26.79 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 100.54/26.79 U131(mark(X)) -> mark(U131(X)) 100.54/26.79 snd(mark(X)) -> mark(snd(X)) 100.54/26.79 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 100.54/26.79 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 100.54/26.79 U141(mark(X)) -> mark(U141(X)) 100.54/26.79 U151(mark(X)) -> mark(U151(X)) 100.54/26.79 U161(mark(X)) -> mark(U161(X)) 100.54/26.79 U171(mark(X1), X2) -> mark(U171(X1, X2)) 100.54/26.79 U172(mark(X)) -> mark(U172(X)) 100.54/26.79 U181(mark(X1), X2) -> mark(U181(X1, X2)) 100.54/26.79 U182(mark(X1), X2) -> mark(U182(X1, X2)) 100.54/26.79 U183(mark(X)) -> mark(U183(X)) 100.54/26.79 U191(mark(X1), X2) -> mark(U191(X1, X2)) 100.54/26.79 U192(mark(X1), X2) -> mark(U192(X1, X2)) 100.54/26.79 U193(mark(X)) -> mark(U193(X)) 100.54/26.79 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 100.54/26.79 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 100.54/26.79 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 100.54/26.79 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 100.54/26.79 U205(mark(X1), X2) -> mark(U205(X1, X2)) 100.54/26.79 U206(mark(X)) -> mark(U206(X)) 100.54/26.79 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 100.54/26.79 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 100.54/26.79 U211(mark(X)) -> mark(U211(X)) 100.54/26.79 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 100.54/26.79 U221(mark(X)) -> mark(U221(X)) 100.54/26.79 U24(mark(X1), X2) -> mark(U24(X1, X2)) 100.54/26.79 U231(mark(X1), X2) -> mark(U231(X1, X2)) 100.54/26.79 U232(mark(X)) -> mark(U232(X)) 100.54/26.79 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 100.54/26.79 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 100.54/26.79 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 100.54/26.79 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 100.54/26.79 U245(mark(X1), X2) -> mark(U245(X1, X2)) 100.54/26.79 U246(mark(X)) -> mark(U246(X)) 100.54/26.79 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 100.54/26.79 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 100.54/26.79 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 100.54/26.79 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 100.54/26.79 U255(mark(X1), X2) -> mark(U255(X1, X2)) 100.54/26.79 U256(mark(X)) -> mark(U256(X)) 100.54/26.79 U261(mark(X1), X2) -> mark(U261(X1, X2)) 100.54/26.79 U262(mark(X)) -> mark(U262(X)) 100.54/26.79 U271(mark(X1), X2) -> mark(U271(X1, X2)) 100.54/26.79 U272(mark(X)) -> mark(U272(X)) 100.54/26.79 U281(mark(X1), X2) -> mark(U281(X1, X2)) 100.54/26.79 U282(mark(X1), X2) -> mark(U282(X1, X2)) 100.54/26.79 cons(mark(X1), X2) -> mark(cons(X1, X2)) 100.54/26.79 natsFrom(mark(X)) -> mark(natsFrom(X)) 100.54/26.79 s(mark(X)) -> mark(s(X)) 100.54/26.79 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 100.54/26.79 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 100.54/26.79 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 100.54/26.79 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 100.54/26.79 head(mark(X)) -> mark(head(X)) 100.54/26.79 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 100.54/26.79 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 100.54/26.79 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 100.54/26.79 U302(mark(X1), X2) -> mark(U302(X1, X2)) 100.54/26.79 U303(mark(X1), X2) -> mark(U303(X1, X2)) 100.54/26.79 U304(mark(X1), X2) -> mark(U304(X1, X2)) 100.54/26.79 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 100.54/26.79 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 100.54/26.79 U311(mark(X1), X2) -> mark(U311(X1, X2)) 100.54/26.79 U312(mark(X1), X2) -> mark(U312(X1, X2)) 100.54/26.79 pair(mark(X1), X2) -> mark(pair(X1, X2)) 100.54/26.79 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 100.54/26.79 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 100.54/26.79 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 100.54/26.79 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 100.54/26.79 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 100.54/26.79 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 100.54/26.79 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 100.54/26.79 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 100.54/26.79 U327(mark(X1), X2) -> mark(U327(X1, X2)) 100.54/26.79 U34(mark(X1), X2) -> mark(U34(X1, X2)) 100.54/26.79 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 100.54/26.79 U332(mark(X1), X2) -> mark(U332(X1, X2)) 100.54/26.79 U333(mark(X1), X2) -> mark(U333(X1, X2)) 100.54/26.79 U334(mark(X1), X2) -> mark(U334(X1, X2)) 100.54/26.79 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 100.54/26.79 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 100.54/26.79 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 100.54/26.79 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 100.54/26.79 fst(mark(X)) -> mark(fst(X)) 100.54/26.79 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 100.54/26.79 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 100.54/26.79 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 100.54/26.79 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 100.54/26.79 U45(mark(X1), X2) -> mark(U45(X1, X2)) 100.54/26.79 U46(mark(X)) -> mark(U46(X)) 100.54/26.79 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 100.54/26.79 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 100.54/26.79 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 100.54/26.79 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 100.54/26.79 U55(mark(X1), X2) -> mark(U55(X1, X2)) 100.54/26.79 U56(mark(X)) -> mark(U56(X)) 100.54/26.79 U61(mark(X1), X2) -> mark(U61(X1, X2)) 100.54/26.79 U62(mark(X1), X2) -> mark(U62(X1, X2)) 100.54/26.79 U63(mark(X)) -> mark(U63(X)) 100.54/26.79 U71(mark(X1), X2) -> mark(U71(X1, X2)) 100.54/26.79 U72(mark(X1), X2) -> mark(U72(X1, X2)) 100.54/26.79 U73(mark(X)) -> mark(U73(X)) 100.54/26.79 U81(mark(X1), X2) -> mark(U81(X1, X2)) 100.54/26.79 U82(mark(X1), X2) -> mark(U82(X1, X2)) 100.54/26.79 U83(mark(X)) -> mark(U83(X)) 100.54/26.79 U91(mark(X1), X2) -> mark(U91(X1, X2)) 100.54/26.79 U92(mark(X1), X2) -> mark(U92(X1, X2)) 100.54/26.79 U93(mark(X)) -> mark(U93(X)) 100.54/26.79 tail(mark(X)) -> mark(tail(X)) 100.54/26.79 take(mark(X1), X2) -> mark(take(X1, X2)) 100.54/26.79 take(X1, mark(X2)) -> mark(take(X1, X2)) 100.54/26.79 sel(mark(X1), X2) -> mark(sel(X1, X2)) 100.54/26.79 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 100.54/26.79 proper(tt) -> ok(tt) 100.54/26.79 proper(nil) -> ok(nil) 100.54/26.79 proper(0) -> ok(0) 100.54/26.79 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 100.54/26.79 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 100.54/26.79 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 100.54/26.79 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 100.54/26.79 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 100.54/26.79 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 100.54/26.79 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 100.54/26.79 isNatural(ok(X)) -> ok(isNatural(X)) 100.54/26.79 U106(ok(X)) -> ok(U106(X)) 100.54/26.79 isLNat(ok(X)) -> ok(isLNat(X)) 100.54/26.79 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 100.54/26.79 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 100.54/26.79 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 100.54/26.79 U112(ok(X)) -> ok(U112(X)) 100.54/26.79 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 100.54/26.79 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 100.54/26.79 U122(ok(X)) -> ok(U122(X)) 100.54/26.79 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 100.54/26.79 U131(ok(X)) -> ok(U131(X)) 100.54/26.79 snd(ok(X)) -> ok(snd(X)) 100.54/26.79 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 100.54/26.79 U141(ok(X)) -> ok(U141(X)) 100.54/26.79 U151(ok(X)) -> ok(U151(X)) 100.54/26.79 U161(ok(X)) -> ok(U161(X)) 100.54/26.79 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 100.54/26.79 U172(ok(X)) -> ok(U172(X)) 100.54/26.79 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 100.54/26.79 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 100.54/26.79 U183(ok(X)) -> ok(U183(X)) 100.54/26.79 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 100.54/26.79 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 100.54/26.79 U193(ok(X)) -> ok(U193(X)) 100.54/26.79 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 100.54/26.79 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 100.54/26.79 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 100.54/26.79 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 100.54/26.79 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 100.54/26.79 U206(ok(X)) -> ok(U206(X)) 100.54/26.79 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 100.54/26.79 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 100.54/26.79 U211(ok(X)) -> ok(U211(X)) 100.54/26.79 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 100.54/26.79 U221(ok(X)) -> ok(U221(X)) 100.54/26.79 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 100.54/26.79 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 100.54/26.79 U232(ok(X)) -> ok(U232(X)) 100.54/26.79 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 100.54/26.79 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 100.54/26.79 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 100.54/26.79 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 100.54/26.79 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 100.54/26.79 U246(ok(X)) -> ok(U246(X)) 100.54/26.79 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 100.54/26.79 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 100.54/26.79 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 100.54/26.79 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 100.54/26.79 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 100.54/26.79 U256(ok(X)) -> ok(U256(X)) 100.54/26.79 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 100.54/26.79 U262(ok(X)) -> ok(U262(X)) 100.54/26.79 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 100.54/26.79 U272(ok(X)) -> ok(U272(X)) 100.54/26.79 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 100.54/26.79 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 100.54/26.79 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 100.54/26.79 natsFrom(ok(X)) -> ok(natsFrom(X)) 100.54/26.79 s(ok(X)) -> ok(s(X)) 100.54/26.79 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 100.54/26.79 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 100.54/26.79 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 100.54/26.79 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 100.54/26.79 head(ok(X)) -> ok(head(X)) 100.54/26.79 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 100.54/26.79 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 100.54/26.79 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 100.54/26.79 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 100.54/26.79 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 100.54/26.79 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 100.54/26.79 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 100.54/26.79 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 100.54/26.79 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 100.54/26.79 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 100.54/26.79 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 100.54/26.79 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 100.54/26.79 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 100.54/26.79 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 100.54/26.79 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 100.54/26.79 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 100.54/26.79 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 100.54/26.79 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 100.54/26.79 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 100.54/26.79 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 100.54/26.79 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 100.54/26.79 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 100.54/26.79 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 100.54/26.79 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 100.54/26.79 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 100.54/26.79 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 100.54/26.79 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 100.54/26.79 fst(ok(X)) -> ok(fst(X)) 100.54/26.79 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 100.54/26.79 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 100.54/26.79 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 100.54/26.79 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 100.54/26.79 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 100.54/26.79 U46(ok(X)) -> ok(U46(X)) 100.54/26.79 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 100.54/26.79 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 100.54/26.79 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 100.54/26.79 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 100.54/26.79 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 100.54/26.79 U56(ok(X)) -> ok(U56(X)) 100.54/26.79 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 100.54/26.79 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 100.54/26.79 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 100.54/26.79 U63(ok(X)) -> ok(U63(X)) 100.54/26.79 isPLNat(ok(X)) -> ok(isPLNat(X)) 100.54/26.79 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 100.54/26.79 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 100.54/26.79 U73(ok(X)) -> ok(U73(X)) 100.54/26.79 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 100.54/26.79 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 100.54/26.79 U83(ok(X)) -> ok(U83(X)) 100.54/26.79 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 100.54/26.79 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 100.54/26.79 U93(ok(X)) -> ok(U93(X)) 100.54/26.79 tail(ok(X)) -> ok(tail(X)) 100.54/26.79 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 100.54/26.79 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 100.54/26.79 top(mark(X)) -> top(proper(X)) 100.54/26.79 top(ok(X)) -> top(active(X)) 100.54/26.79 100.54/26.79 S is empty. 100.54/26.79 Rewrite Strategy: INNERMOST 100.54/26.79 ---------------------------------------- 100.54/26.79 100.54/26.79 (5) CpxTrsToCdtProof (UPPER BOUND(ID)) 100.54/26.79 Converted Cpx (relative) TRS to CDT 100.54/26.79 ---------------------------------------- 100.54/26.79 100.54/26.79 (6) 100.54/26.79 Obligation: 100.54/26.79 Complexity Dependency Tuples Problem 100.54/26.79 100.54/26.79 Rules: 100.54/26.79 U101(mark(z0), z1, z2) -> mark(U101(z0, z1, z2)) 100.54/26.79 U101(ok(z0), ok(z1), ok(z2)) -> ok(U101(z0, z1, z2)) 100.54/26.79 U102(mark(z0), z1, z2) -> mark(U102(z0, z1, z2)) 100.54/26.79 U102(ok(z0), ok(z1), ok(z2)) -> ok(U102(z0, z1, z2)) 100.54/26.79 U103(mark(z0), z1, z2) -> mark(U103(z0, z1, z2)) 100.54/26.79 U103(ok(z0), ok(z1), ok(z2)) -> ok(U103(z0, z1, z2)) 100.54/26.79 U104(mark(z0), z1, z2) -> mark(U104(z0, z1, z2)) 100.54/26.79 U104(ok(z0), ok(z1), ok(z2)) -> ok(U104(z0, z1, z2)) 100.54/26.79 U105(mark(z0), z1) -> mark(U105(z0, z1)) 100.54/26.79 U105(ok(z0), ok(z1)) -> ok(U105(z0, z1)) 100.54/26.79 U106(mark(z0)) -> mark(U106(z0)) 100.54/26.79 U106(ok(z0)) -> ok(U106(z0)) 100.54/26.79 U11(mark(z0), z1, z2) -> mark(U11(z0, z1, z2)) 100.54/26.79 U11(ok(z0), ok(z1), ok(z2)) -> ok(U11(z0, z1, z2)) 100.54/26.79 U12(mark(z0), z1, z2) -> mark(U12(z0, z1, z2)) 100.54/26.79 U12(ok(z0), ok(z1), ok(z2)) -> ok(U12(z0, z1, z2)) 100.54/26.79 U111(mark(z0), z1) -> mark(U111(z0, z1)) 100.54/26.79 U111(ok(z0), ok(z1)) -> ok(U111(z0, z1)) 100.54/26.79 U112(mark(z0)) -> mark(U112(z0)) 100.54/26.79 U112(ok(z0)) -> ok(U112(z0)) 100.54/26.79 U13(mark(z0), z1, z2) -> mark(U13(z0, z1, z2)) 100.54/26.79 U13(ok(z0), ok(z1), ok(z2)) -> ok(U13(z0, z1, z2)) 100.54/26.79 U121(mark(z0), z1) -> mark(U121(z0, z1)) 100.54/26.79 U121(ok(z0), ok(z1)) -> ok(U121(z0, z1)) 100.54/26.79 U122(mark(z0)) -> mark(U122(z0)) 100.54/26.79 U122(ok(z0)) -> ok(U122(z0)) 100.54/26.79 U14(mark(z0), z1, z2) -> mark(U14(z0, z1, z2)) 100.54/26.79 U14(ok(z0), ok(z1), ok(z2)) -> ok(U14(z0, z1, z2)) 100.54/26.79 U131(mark(z0)) -> mark(U131(z0)) 100.54/26.79 U131(ok(z0)) -> ok(U131(z0)) 100.54/26.79 snd(mark(z0)) -> mark(snd(z0)) 100.54/26.79 snd(ok(z0)) -> ok(snd(z0)) 100.54/26.79 splitAt(mark(z0), z1) -> mark(splitAt(z0, z1)) 100.54/26.79 splitAt(z0, mark(z1)) -> mark(splitAt(z0, z1)) 100.54/26.79 splitAt(ok(z0), ok(z1)) -> ok(splitAt(z0, z1)) 100.54/26.79 U141(mark(z0)) -> mark(U141(z0)) 100.54/26.79 U141(ok(z0)) -> ok(U141(z0)) 100.54/26.79 U151(mark(z0)) -> mark(U151(z0)) 100.54/26.79 U151(ok(z0)) -> ok(U151(z0)) 100.54/26.79 U161(mark(z0)) -> mark(U161(z0)) 100.54/26.79 U161(ok(z0)) -> ok(U161(z0)) 100.54/26.79 U171(mark(z0), z1) -> mark(U171(z0, z1)) 100.54/26.79 U171(ok(z0), ok(z1)) -> ok(U171(z0, z1)) 100.54/26.79 U172(mark(z0)) -> mark(U172(z0)) 100.54/26.79 U172(ok(z0)) -> ok(U172(z0)) 100.54/26.79 U181(mark(z0), z1) -> mark(U181(z0, z1)) 100.54/26.79 U181(ok(z0), ok(z1)) -> ok(U181(z0, z1)) 100.54/26.79 U182(mark(z0), z1) -> mark(U182(z0, z1)) 100.54/26.79 U182(ok(z0), ok(z1)) -> ok(U182(z0, z1)) 100.54/26.79 U183(mark(z0)) -> mark(U183(z0)) 100.54/26.79 U183(ok(z0)) -> ok(U183(z0)) 100.54/26.79 U191(mark(z0), z1) -> mark(U191(z0, z1)) 100.54/26.79 U191(ok(z0), ok(z1)) -> ok(U191(z0, z1)) 100.54/26.79 U192(mark(z0), z1) -> mark(U192(z0, z1)) 100.54/26.79 U192(ok(z0), ok(z1)) -> ok(U192(z0, z1)) 100.54/26.79 U193(mark(z0)) -> mark(U193(z0)) 100.54/26.79 U193(ok(z0)) -> ok(U193(z0)) 100.54/26.79 U201(mark(z0), z1, z2) -> mark(U201(z0, z1, z2)) 100.54/26.79 U201(ok(z0), ok(z1), ok(z2)) -> ok(U201(z0, z1, z2)) 100.54/26.79 U202(mark(z0), z1, z2) -> mark(U202(z0, z1, z2)) 100.54/26.79 U202(ok(z0), ok(z1), ok(z2)) -> ok(U202(z0, z1, z2)) 100.54/26.79 U203(mark(z0), z1, z2) -> mark(U203(z0, z1, z2)) 100.54/26.79 U203(ok(z0), ok(z1), ok(z2)) -> ok(U203(z0, z1, z2)) 100.54/26.79 U204(mark(z0), z1, z2) -> mark(U204(z0, z1, z2)) 100.54/26.79 U204(ok(z0), ok(z1), ok(z2)) -> ok(U204(z0, z1, z2)) 100.54/26.79 U205(mark(z0), z1) -> mark(U205(z0, z1)) 100.54/26.79 U205(ok(z0), ok(z1)) -> ok(U205(z0, z1)) 100.54/26.79 U206(mark(z0)) -> mark(U206(z0)) 100.54/26.79 U206(ok(z0)) -> ok(U206(z0)) 100.54/26.79 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 100.54/26.79 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 100.54/26.79 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 100.54/26.79 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 100.54/26.79 U211(mark(z0)) -> mark(U211(z0)) 100.54/26.79 U211(ok(z0)) -> ok(U211(z0)) 100.54/26.79 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 100.54/26.79 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 100.54/26.79 U221(mark(z0)) -> mark(U221(z0)) 100.54/26.79 U221(ok(z0)) -> ok(U221(z0)) 100.54/26.79 U24(mark(z0), z1) -> mark(U24(z0, z1)) 100.54/26.79 U24(ok(z0), ok(z1)) -> ok(U24(z0, z1)) 100.54/26.79 U231(mark(z0), z1) -> mark(U231(z0, z1)) 100.54/26.79 U231(ok(z0), ok(z1)) -> ok(U231(z0, z1)) 100.54/26.79 U232(mark(z0)) -> mark(U232(z0)) 100.54/26.79 U232(ok(z0)) -> ok(U232(z0)) 100.54/26.79 U241(mark(z0), z1, z2) -> mark(U241(z0, z1, z2)) 100.54/26.79 U241(ok(z0), ok(z1), ok(z2)) -> ok(U241(z0, z1, z2)) 100.54/26.79 U242(mark(z0), z1, z2) -> mark(U242(z0, z1, z2)) 100.54/26.79 U242(ok(z0), ok(z1), ok(z2)) -> ok(U242(z0, z1, z2)) 100.54/26.79 U243(mark(z0), z1, z2) -> mark(U243(z0, z1, z2)) 100.54/26.79 U243(ok(z0), ok(z1), ok(z2)) -> ok(U243(z0, z1, z2)) 100.54/26.79 U244(mark(z0), z1, z2) -> mark(U244(z0, z1, z2)) 100.54/26.79 U244(ok(z0), ok(z1), ok(z2)) -> ok(U244(z0, z1, z2)) 100.54/26.79 U245(mark(z0), z1) -> mark(U245(z0, z1)) 100.54/26.79 U245(ok(z0), ok(z1)) -> ok(U245(z0, z1)) 100.54/26.79 U246(mark(z0)) -> mark(U246(z0)) 100.54/26.79 U246(ok(z0)) -> ok(U246(z0)) 100.54/26.79 U251(mark(z0), z1, z2) -> mark(U251(z0, z1, z2)) 100.54/26.79 U251(ok(z0), ok(z1), ok(z2)) -> ok(U251(z0, z1, z2)) 100.54/26.79 U252(mark(z0), z1, z2) -> mark(U252(z0, z1, z2)) 100.54/26.79 U252(ok(z0), ok(z1), ok(z2)) -> ok(U252(z0, z1, z2)) 100.54/26.79 U253(mark(z0), z1, z2) -> mark(U253(z0, z1, z2)) 100.54/26.79 U253(ok(z0), ok(z1), ok(z2)) -> ok(U253(z0, z1, z2)) 100.54/26.79 U254(mark(z0), z1, z2) -> mark(U254(z0, z1, z2)) 100.54/26.79 U254(ok(z0), ok(z1), ok(z2)) -> ok(U254(z0, z1, z2)) 100.54/26.79 U255(mark(z0), z1) -> mark(U255(z0, z1)) 100.54/26.79 U255(ok(z0), ok(z1)) -> ok(U255(z0, z1)) 100.54/26.79 U256(mark(z0)) -> mark(U256(z0)) 100.54/26.79 U256(ok(z0)) -> ok(U256(z0)) 100.54/26.79 U261(mark(z0), z1) -> mark(U261(z0, z1)) 100.54/26.79 U261(ok(z0), ok(z1)) -> ok(U261(z0, z1)) 100.54/26.79 U262(mark(z0)) -> mark(U262(z0)) 100.54/26.79 U262(ok(z0)) -> ok(U262(z0)) 100.54/26.79 U271(mark(z0), z1) -> mark(U271(z0, z1)) 100.54/26.79 U271(ok(z0), ok(z1)) -> ok(U271(z0, z1)) 100.54/26.79 U272(mark(z0)) -> mark(U272(z0)) 100.54/26.79 U272(ok(z0)) -> ok(U272(z0)) 100.54/26.79 U281(mark(z0), z1) -> mark(U281(z0, z1)) 100.54/26.79 U281(ok(z0), ok(z1)) -> ok(U281(z0, z1)) 100.54/26.79 U282(mark(z0), z1) -> mark(U282(z0, z1)) 100.54/26.79 U282(ok(z0), ok(z1)) -> ok(U282(z0, z1)) 100.54/26.79 cons(mark(z0), z1) -> mark(cons(z0, z1)) 100.54/26.79 cons(ok(z0), ok(z1)) -> ok(cons(z0, z1)) 100.54/26.79 natsFrom(mark(z0)) -> mark(natsFrom(z0)) 100.54/26.79 natsFrom(ok(z0)) -> ok(natsFrom(z0)) 100.54/26.79 s(mark(z0)) -> mark(s(z0)) 100.54/26.79 s(ok(z0)) -> ok(s(z0)) 100.54/26.79 U291(mark(z0), z1, z2) -> mark(U291(z0, z1, z2)) 100.54/26.79 U291(ok(z0), ok(z1), ok(z2)) -> ok(U291(z0, z1, z2)) 100.54/26.79 U292(mark(z0), z1, z2) -> mark(U292(z0, z1, z2)) 100.54/26.79 U292(ok(z0), ok(z1), ok(z2)) -> ok(U292(z0, z1, z2)) 100.54/26.79 U293(mark(z0), z1, z2) -> mark(U293(z0, z1, z2)) 100.54/26.79 U293(ok(z0), ok(z1), ok(z2)) -> ok(U293(z0, z1, z2)) 100.54/26.79 U294(mark(z0), z1, z2) -> mark(U294(z0, z1, z2)) 100.54/26.79 U294(ok(z0), ok(z1), ok(z2)) -> ok(U294(z0, z1, z2)) 100.54/26.79 head(mark(z0)) -> mark(head(z0)) 100.54/26.79 head(ok(z0)) -> ok(head(z0)) 100.54/26.79 afterNth(mark(z0), z1) -> mark(afterNth(z0, z1)) 100.54/26.79 afterNth(z0, mark(z1)) -> mark(afterNth(z0, z1)) 100.54/26.79 afterNth(ok(z0), ok(z1)) -> ok(afterNth(z0, z1)) 100.54/26.79 U301(mark(z0), z1, z2) -> mark(U301(z0, z1, z2)) 100.54/26.79 U301(ok(z0), ok(z1), ok(z2)) -> ok(U301(z0, z1, z2)) 100.54/26.79 U302(mark(z0), z1) -> mark(U302(z0, z1)) 100.54/26.79 U302(ok(z0), ok(z1)) -> ok(U302(z0, z1)) 100.54/26.79 U303(mark(z0), z1) -> mark(U303(z0, z1)) 100.54/26.79 U303(ok(z0), ok(z1)) -> ok(U303(z0, z1)) 100.54/26.79 U304(mark(z0), z1) -> mark(U304(z0, z1)) 100.54/26.79 U304(ok(z0), ok(z1)) -> ok(U304(z0, z1)) 100.54/26.79 U31(mark(z0), z1, z2) -> mark(U31(z0, z1, z2)) 100.54/26.79 U31(ok(z0), ok(z1), ok(z2)) -> ok(U31(z0, z1, z2)) 100.54/26.79 U32(mark(z0), z1, z2) -> mark(U32(z0, z1, z2)) 100.54/26.79 U32(ok(z0), ok(z1), ok(z2)) -> ok(U32(z0, z1, z2)) 100.54/26.79 U311(mark(z0), z1) -> mark(U311(z0, z1)) 100.54/26.79 U311(ok(z0), ok(z1)) -> ok(U311(z0, z1)) 100.54/26.79 U312(mark(z0), z1) -> mark(U312(z0, z1)) 100.54/26.79 U312(ok(z0), ok(z1)) -> ok(U312(z0, z1)) 100.54/26.79 pair(mark(z0), z1) -> mark(pair(z0, z1)) 100.54/26.79 pair(z0, mark(z1)) -> mark(pair(z0, z1)) 100.54/26.79 pair(ok(z0), ok(z1)) -> ok(pair(z0, z1)) 100.54/26.79 U33(mark(z0), z1, z2) -> mark(U33(z0, z1, z2)) 100.54/26.79 U33(ok(z0), ok(z1), ok(z2)) -> ok(U33(z0, z1, z2)) 100.54/26.79 U321(mark(z0), z1, z2, z3) -> mark(U321(z0, z1, z2, z3)) 100.54/26.79 U321(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U321(z0, z1, z2, z3)) 100.54/26.79 U322(mark(z0), z1, z2, z3) -> mark(U322(z0, z1, z2, z3)) 100.54/26.79 U322(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U322(z0, z1, z2, z3)) 100.54/26.79 U323(mark(z0), z1, z2, z3) -> mark(U323(z0, z1, z2, z3)) 100.54/26.79 U323(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U323(z0, z1, z2, z3)) 100.54/26.79 U324(mark(z0), z1, z2, z3) -> mark(U324(z0, z1, z2, z3)) 100.54/26.79 U324(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U324(z0, z1, z2, z3)) 100.54/26.79 U325(mark(z0), z1, z2, z3) -> mark(U325(z0, z1, z2, z3)) 100.54/26.79 U325(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U325(z0, z1, z2, z3)) 100.54/26.79 U326(mark(z0), z1, z2, z3) -> mark(U326(z0, z1, z2, z3)) 100.54/26.79 U326(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U326(z0, z1, z2, z3)) 100.54/26.79 U327(mark(z0), z1) -> mark(U327(z0, z1)) 100.54/26.79 U327(ok(z0), ok(z1)) -> ok(U327(z0, z1)) 100.54/26.79 U34(mark(z0), z1) -> mark(U34(z0, z1)) 100.54/26.79 U34(ok(z0), ok(z1)) -> ok(U34(z0, z1)) 100.54/26.79 U331(mark(z0), z1, z2) -> mark(U331(z0, z1, z2)) 100.54/26.79 U331(ok(z0), ok(z1), ok(z2)) -> ok(U331(z0, z1, z2)) 100.54/26.79 U332(mark(z0), z1) -> mark(U332(z0, z1)) 100.54/26.79 U332(ok(z0), ok(z1)) -> ok(U332(z0, z1)) 100.54/26.79 U333(mark(z0), z1) -> mark(U333(z0, z1)) 100.54/26.79 U333(ok(z0), ok(z1)) -> ok(U333(z0, z1)) 100.54/26.79 U334(mark(z0), z1) -> mark(U334(z0, z1)) 100.54/26.79 U334(ok(z0), ok(z1)) -> ok(U334(z0, z1)) 100.54/26.79 U341(mark(z0), z1, z2) -> mark(U341(z0, z1, z2)) 100.54/26.79 U341(ok(z0), ok(z1), ok(z2)) -> ok(U341(z0, z1, z2)) 100.54/26.79 U342(mark(z0), z1, z2) -> mark(U342(z0, z1, z2)) 100.54/26.79 U342(ok(z0), ok(z1), ok(z2)) -> ok(U342(z0, z1, z2)) 100.54/26.79 U343(mark(z0), z1, z2) -> mark(U343(z0, z1, z2)) 100.54/26.79 U343(ok(z0), ok(z1), ok(z2)) -> ok(U343(z0, z1, z2)) 100.54/26.79 U344(mark(z0), z1, z2) -> mark(U344(z0, z1, z2)) 100.54/26.79 U344(ok(z0), ok(z1), ok(z2)) -> ok(U344(z0, z1, z2)) 100.54/26.79 fst(mark(z0)) -> mark(fst(z0)) 100.54/26.79 fst(ok(z0)) -> ok(fst(z0)) 100.54/26.79 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 100.54/26.79 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 100.54/26.79 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 100.54/26.79 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 100.54/26.79 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 100.54/26.79 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 100.54/26.79 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 100.54/26.79 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 100.54/26.79 U45(mark(z0), z1) -> mark(U45(z0, z1)) 100.54/26.79 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 100.54/26.79 U46(mark(z0)) -> mark(U46(z0)) 100.54/26.79 U46(ok(z0)) -> ok(U46(z0)) 100.54/26.79 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 100.54/26.79 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 100.54/26.79 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 100.54/26.79 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 100.54/26.79 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 100.54/26.79 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 100.54/26.79 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 100.54/26.79 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 100.54/26.79 U55(mark(z0), z1) -> mark(U55(z0, z1)) 100.54/26.79 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 100.54/26.79 U56(mark(z0)) -> mark(U56(z0)) 100.54/26.79 U56(ok(z0)) -> ok(U56(z0)) 100.54/26.79 U61(mark(z0), z1) -> mark(U61(z0, z1)) 100.54/26.79 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 100.54/26.79 U62(mark(z0), z1) -> mark(U62(z0, z1)) 100.54/26.79 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 100.54/26.79 U63(mark(z0)) -> mark(U63(z0)) 100.54/26.79 U63(ok(z0)) -> ok(U63(z0)) 100.54/26.79 U71(mark(z0), z1) -> mark(U71(z0, z1)) 100.54/26.79 U71(ok(z0), ok(z1)) -> ok(U71(z0, z1)) 100.54/26.79 U72(mark(z0), z1) -> mark(U72(z0, z1)) 100.54/26.79 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 100.54/26.79 U73(mark(z0)) -> mark(U73(z0)) 100.54/26.79 U73(ok(z0)) -> ok(U73(z0)) 100.54/26.79 U81(mark(z0), z1) -> mark(U81(z0, z1)) 100.54/26.79 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 100.54/26.79 U82(mark(z0), z1) -> mark(U82(z0, z1)) 100.54/26.79 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 100.54/26.79 U83(mark(z0)) -> mark(U83(z0)) 100.54/26.79 U83(ok(z0)) -> ok(U83(z0)) 100.54/26.79 U91(mark(z0), z1) -> mark(U91(z0, z1)) 100.54/26.79 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 100.54/26.79 U92(mark(z0), z1) -> mark(U92(z0, z1)) 100.54/26.79 U92(ok(z0), ok(z1)) -> ok(U92(z0, z1)) 100.54/26.79 U93(mark(z0)) -> mark(U93(z0)) 100.54/26.79 U93(ok(z0)) -> ok(U93(z0)) 100.54/26.79 tail(mark(z0)) -> mark(tail(z0)) 100.54/26.79 tail(ok(z0)) -> ok(tail(z0)) 100.54/26.79 take(mark(z0), z1) -> mark(take(z0, z1)) 100.54/26.79 take(z0, mark(z1)) -> mark(take(z0, z1)) 100.54/26.79 take(ok(z0), ok(z1)) -> ok(take(z0, z1)) 100.54/26.79 sel(mark(z0), z1) -> mark(sel(z0, z1)) 100.54/26.79 sel(z0, mark(z1)) -> mark(sel(z0, z1)) 100.54/26.79 sel(ok(z0), ok(z1)) -> ok(sel(z0, z1)) 100.54/26.79 proper(tt) -> ok(tt) 100.54/26.79 proper(nil) -> ok(nil) 100.54/26.79 proper(0) -> ok(0) 100.54/26.79 isNaturalKind(ok(z0)) -> ok(isNaturalKind(z0)) 100.54/26.79 isLNatKind(ok(z0)) -> ok(isLNatKind(z0)) 100.54/26.79 isNatural(ok(z0)) -> ok(isNatural(z0)) 100.54/26.79 isLNat(ok(z0)) -> ok(isLNat(z0)) 100.54/26.79 isPLNatKind(ok(z0)) -> ok(isPLNatKind(z0)) 100.54/26.79 isPLNat(ok(z0)) -> ok(isPLNat(z0)) 100.54/26.79 top(mark(z0)) -> top(proper(z0)) 100.54/26.79 top(ok(z0)) -> top(active(z0)) 100.54/26.79 Tuples: 100.54/26.79 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.54/26.79 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.54/26.79 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.54/26.79 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.54/26.79 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.54/26.79 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.54/26.79 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.54/26.79 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.54/26.79 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.54/26.79 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.54/26.79 U106'(mark(z0)) -> c10(U106'(z0)) 100.54/26.79 U106'(ok(z0)) -> c11(U106'(z0)) 100.54/26.79 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.54/26.79 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.54/26.79 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.54/26.79 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.54/26.79 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.54/26.79 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.54/26.79 U112'(mark(z0)) -> c18(U112'(z0)) 100.54/26.79 U112'(ok(z0)) -> c19(U112'(z0)) 100.54/26.79 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.54/26.79 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.54/26.79 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.54/26.79 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.54/26.79 U122'(mark(z0)) -> c24(U122'(z0)) 100.54/26.79 U122'(ok(z0)) -> c25(U122'(z0)) 100.54/26.79 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.54/26.79 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.54/26.79 U131'(mark(z0)) -> c28(U131'(z0)) 100.54/26.79 U131'(ok(z0)) -> c29(U131'(z0)) 100.54/26.79 SND(mark(z0)) -> c30(SND(z0)) 100.54/26.79 SND(ok(z0)) -> c31(SND(z0)) 100.54/26.79 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.54/26.79 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.54/26.79 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.54/26.79 U141'(mark(z0)) -> c35(U141'(z0)) 100.54/26.79 U141'(ok(z0)) -> c36(U141'(z0)) 100.54/26.79 U151'(mark(z0)) -> c37(U151'(z0)) 100.54/26.79 U151'(ok(z0)) -> c38(U151'(z0)) 100.54/26.79 U161'(mark(z0)) -> c39(U161'(z0)) 100.54/26.79 U161'(ok(z0)) -> c40(U161'(z0)) 100.54/26.79 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.54/26.79 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.54/26.79 U172'(mark(z0)) -> c43(U172'(z0)) 100.54/26.79 U172'(ok(z0)) -> c44(U172'(z0)) 100.54/26.79 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.54/26.79 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.54/26.79 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.54/26.79 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.54/26.79 U183'(mark(z0)) -> c49(U183'(z0)) 100.54/26.79 U183'(ok(z0)) -> c50(U183'(z0)) 100.54/26.79 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.54/26.79 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.54/26.79 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.54/26.79 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.54/26.79 U193'(mark(z0)) -> c55(U193'(z0)) 100.54/26.79 U193'(ok(z0)) -> c56(U193'(z0)) 100.54/26.79 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.54/26.79 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.54/26.79 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.54/26.79 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.54/26.79 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.54/26.79 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.54/26.79 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.54/26.79 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.54/26.79 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.54/26.79 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.54/26.79 U206'(mark(z0)) -> c67(U206'(z0)) 100.54/26.79 U206'(ok(z0)) -> c68(U206'(z0)) 100.54/26.79 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.54/26.79 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.54/26.79 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.54/26.79 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.54/26.79 U211'(mark(z0)) -> c73(U211'(z0)) 100.54/26.79 U211'(ok(z0)) -> c74(U211'(z0)) 100.54/26.79 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.54/26.79 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.54/26.79 U221'(mark(z0)) -> c77(U221'(z0)) 100.54/26.79 U221'(ok(z0)) -> c78(U221'(z0)) 100.54/26.79 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.54/26.79 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.54/26.79 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.54/26.79 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.54/26.79 U232'(mark(z0)) -> c83(U232'(z0)) 100.54/26.79 U232'(ok(z0)) -> c84(U232'(z0)) 100.54/26.79 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.54/26.79 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.54/26.79 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.54/26.79 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.54/26.79 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.54/26.79 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.54/26.79 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.54/26.79 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.54/26.79 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.54/26.79 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.54/26.79 U246'(mark(z0)) -> c95(U246'(z0)) 100.54/26.79 U246'(ok(z0)) -> c96(U246'(z0)) 100.54/26.79 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.54/26.79 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.54/26.79 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.54/26.79 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.54/26.79 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.54/26.79 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.54/26.79 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.54/26.79 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.54/26.79 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.54/26.79 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.54/26.79 U256'(mark(z0)) -> c107(U256'(z0)) 100.54/26.79 U256'(ok(z0)) -> c108(U256'(z0)) 100.54/26.79 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.54/26.79 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.54/26.79 U262'(mark(z0)) -> c111(U262'(z0)) 100.54/26.79 U262'(ok(z0)) -> c112(U262'(z0)) 100.54/26.79 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.54/26.79 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.54/26.79 U272'(mark(z0)) -> c115(U272'(z0)) 100.54/26.79 U272'(ok(z0)) -> c116(U272'(z0)) 100.54/26.79 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.54/26.79 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.54/26.79 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.54/26.79 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.54/26.79 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.54/26.79 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.54/26.79 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.54/26.79 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.54/26.79 S(mark(z0)) -> c125(S(z0)) 100.54/26.79 S(ok(z0)) -> c126(S(z0)) 100.54/26.79 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.54/26.79 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.54/26.79 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.54/26.79 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.54/26.79 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.54/26.79 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.54/26.79 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.54/26.79 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.54/26.79 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.54/26.79 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.54/26.79 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.54/26.79 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.54/26.79 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.54/26.79 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.54/26.79 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.54/26.79 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.54/26.79 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.54/26.79 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.54/26.79 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.54/26.79 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.54/26.79 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.54/26.79 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.54/26.79 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.54/26.79 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.54/26.79 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.54/26.79 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.54/26.79 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.54/26.79 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.54/26.79 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.54/26.79 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.54/26.79 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.54/26.79 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.54/26.79 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.54/26.79 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.54/26.79 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.54/26.79 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.54/26.79 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.54/26.79 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.54/26.79 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.54/26.79 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.54/26.79 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.54/26.79 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.54/26.79 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.54/26.79 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.54/26.79 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.54/26.79 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.54/26.79 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.54/26.79 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.54/26.79 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.54/26.79 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.54/26.79 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.54/26.79 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.54/26.79 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.54/26.79 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.54/26.79 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.54/26.79 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.54/26.79 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.54/26.79 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.54/26.79 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.54/26.79 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.54/26.79 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.54/26.79 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.54/26.79 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.54/26.79 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.54/26.79 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.54/26.79 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.54/26.79 FST(mark(z0)) -> c193(FST(z0)) 100.54/26.79 FST(ok(z0)) -> c194(FST(z0)) 100.54/26.79 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.54/26.79 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.54/26.79 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.54/26.79 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.54/26.79 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.54/26.79 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.54/26.79 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.54/26.79 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.54/26.79 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.54/26.79 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.54/26.79 U46'(mark(z0)) -> c205(U46'(z0)) 100.54/26.79 U46'(ok(z0)) -> c206(U46'(z0)) 100.54/26.79 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.54/26.79 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.54/26.79 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.54/26.79 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.54/26.79 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.54/26.79 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.54/26.79 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.54/26.79 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.54/26.79 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.54/26.79 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.54/26.79 U56'(mark(z0)) -> c217(U56'(z0)) 100.54/26.79 U56'(ok(z0)) -> c218(U56'(z0)) 100.54/26.79 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.54/26.79 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.54/26.79 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.54/26.79 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.54/26.79 U63'(mark(z0)) -> c223(U63'(z0)) 100.54/26.79 U63'(ok(z0)) -> c224(U63'(z0)) 100.54/26.79 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.54/26.79 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.54/26.79 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.54/26.79 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.54/26.79 U73'(mark(z0)) -> c229(U73'(z0)) 100.54/26.79 U73'(ok(z0)) -> c230(U73'(z0)) 100.54/26.79 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.54/26.79 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.54/26.79 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.54/26.79 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.54/26.79 U83'(mark(z0)) -> c235(U83'(z0)) 100.54/26.79 U83'(ok(z0)) -> c236(U83'(z0)) 100.54/26.79 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.54/26.79 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.54/26.79 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.54/26.79 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.54/26.79 U93'(mark(z0)) -> c241(U93'(z0)) 100.54/26.79 U93'(ok(z0)) -> c242(U93'(z0)) 100.54/26.79 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.54/26.79 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.54/26.79 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.54/26.79 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.54/26.79 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.54/26.79 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.54/26.79 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.54/26.79 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.54/26.79 PROPER(tt) -> c251 100.54/26.79 PROPER(nil) -> c252 100.54/26.79 PROPER(0) -> c253 100.54/26.79 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.54/26.79 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.54/26.79 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.54/26.79 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.54/26.79 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.54/26.79 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.54/26.79 TOP(mark(z0)) -> c260(TOP(proper(z0)), PROPER(z0)) 100.54/26.79 TOP(ok(z0)) -> c261(TOP(active(z0))) 100.54/26.79 S tuples: 100.54/26.79 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.54/26.79 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.54/26.79 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.54/26.79 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.54/26.79 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.54/26.79 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.54/26.79 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.54/26.79 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.54/26.79 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.54/26.79 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.54/26.79 U106'(mark(z0)) -> c10(U106'(z0)) 100.54/26.79 U106'(ok(z0)) -> c11(U106'(z0)) 100.54/26.79 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.54/26.79 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.54/26.79 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.54/26.79 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.54/26.79 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.54/26.79 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.54/26.79 U112'(mark(z0)) -> c18(U112'(z0)) 100.54/26.79 U112'(ok(z0)) -> c19(U112'(z0)) 100.54/26.79 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.54/26.79 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.54/26.79 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.54/26.79 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.54/26.79 U122'(mark(z0)) -> c24(U122'(z0)) 100.54/26.79 U122'(ok(z0)) -> c25(U122'(z0)) 100.54/26.79 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.54/26.79 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.54/26.79 U131'(mark(z0)) -> c28(U131'(z0)) 100.54/26.79 U131'(ok(z0)) -> c29(U131'(z0)) 100.54/26.79 SND(mark(z0)) -> c30(SND(z0)) 100.54/26.79 SND(ok(z0)) -> c31(SND(z0)) 100.54/26.79 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.54/26.79 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.54/26.79 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.54/26.79 U141'(mark(z0)) -> c35(U141'(z0)) 100.54/26.79 U141'(ok(z0)) -> c36(U141'(z0)) 100.54/26.79 U151'(mark(z0)) -> c37(U151'(z0)) 100.54/26.79 U151'(ok(z0)) -> c38(U151'(z0)) 100.54/26.79 U161'(mark(z0)) -> c39(U161'(z0)) 100.54/26.79 U161'(ok(z0)) -> c40(U161'(z0)) 100.54/26.79 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.54/26.79 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.54/26.79 U172'(mark(z0)) -> c43(U172'(z0)) 100.54/26.79 U172'(ok(z0)) -> c44(U172'(z0)) 100.54/26.79 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.54/26.79 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.54/26.79 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.54/26.79 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.54/26.79 U183'(mark(z0)) -> c49(U183'(z0)) 100.54/26.79 U183'(ok(z0)) -> c50(U183'(z0)) 100.54/26.79 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.54/26.79 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.54/26.79 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.54/26.79 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.54/26.79 U193'(mark(z0)) -> c55(U193'(z0)) 100.54/26.79 U193'(ok(z0)) -> c56(U193'(z0)) 100.54/26.79 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.54/26.79 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.54/26.79 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.54/26.79 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.54/26.79 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.54/26.79 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.54/26.79 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.54/26.79 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.54/26.79 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.54/26.79 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.54/26.79 U206'(mark(z0)) -> c67(U206'(z0)) 100.54/26.79 U206'(ok(z0)) -> c68(U206'(z0)) 100.54/26.79 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.54/26.79 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.54/26.79 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.54/26.79 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.54/26.79 U211'(mark(z0)) -> c73(U211'(z0)) 100.54/26.79 U211'(ok(z0)) -> c74(U211'(z0)) 100.54/26.79 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.54/26.79 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.54/26.79 U221'(mark(z0)) -> c77(U221'(z0)) 100.54/26.79 U221'(ok(z0)) -> c78(U221'(z0)) 100.54/26.79 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.54/26.79 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.54/26.79 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.54/26.79 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.54/26.79 U232'(mark(z0)) -> c83(U232'(z0)) 100.54/26.79 U232'(ok(z0)) -> c84(U232'(z0)) 100.54/26.79 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.54/26.79 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.54/26.79 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.54/26.79 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.54/26.79 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.54/26.79 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.54/26.79 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.54/26.79 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.54/26.79 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.54/26.79 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.54/26.79 U246'(mark(z0)) -> c95(U246'(z0)) 100.54/26.79 U246'(ok(z0)) -> c96(U246'(z0)) 100.54/26.79 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.54/26.79 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.54/26.79 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.54/26.79 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.54/26.79 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.54/26.79 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.54/26.79 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.54/26.79 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.54/26.79 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.54/26.79 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.54/26.79 U256'(mark(z0)) -> c107(U256'(z0)) 100.54/26.79 U256'(ok(z0)) -> c108(U256'(z0)) 100.54/26.79 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.54/26.79 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.54/26.79 U262'(mark(z0)) -> c111(U262'(z0)) 100.54/26.79 U262'(ok(z0)) -> c112(U262'(z0)) 100.54/26.79 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.54/26.79 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.54/26.79 U272'(mark(z0)) -> c115(U272'(z0)) 100.54/26.79 U272'(ok(z0)) -> c116(U272'(z0)) 100.54/26.79 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.54/26.79 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.54/26.79 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.54/26.79 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.54/26.79 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.54/26.79 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.54/26.79 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.54/26.79 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.54/26.79 S(mark(z0)) -> c125(S(z0)) 100.54/26.79 S(ok(z0)) -> c126(S(z0)) 100.54/26.79 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.54/26.79 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.54/26.79 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.54/26.79 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.54/26.79 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.54/26.80 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.54/26.80 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.54/26.80 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.54/26.80 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.54/26.80 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.54/26.80 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.54/26.80 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.54/26.80 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.54/26.80 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.54/26.80 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.54/26.80 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.54/26.80 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.54/26.80 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.54/26.80 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.54/26.80 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.54/26.80 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.54/26.80 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.54/26.80 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.54/26.80 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.54/26.80 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.54/26.80 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.54/26.80 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.54/26.80 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.54/26.80 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.54/26.80 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.54/26.80 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.54/26.80 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.54/26.80 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.54/26.80 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.54/26.80 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.54/26.80 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.54/26.80 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.54/26.80 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.54/26.80 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.54/26.80 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.54/26.80 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.54/26.80 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.54/26.80 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.54/26.80 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.54/26.80 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.54/26.80 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.54/26.80 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.54/26.80 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.54/26.80 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.54/26.80 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.54/26.80 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.54/26.80 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.54/26.80 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.54/26.80 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.54/26.80 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.54/26.80 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.54/26.80 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.54/26.80 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.54/26.80 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.54/26.80 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.54/26.80 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.54/26.80 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.54/26.80 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.54/26.80 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.54/26.80 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.54/26.80 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.54/26.80 FST(mark(z0)) -> c193(FST(z0)) 100.54/26.80 FST(ok(z0)) -> c194(FST(z0)) 100.54/26.80 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.54/26.80 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.54/26.80 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.54/26.80 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.54/26.80 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.54/26.80 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.54/26.80 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.54/26.80 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.54/26.80 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.54/26.80 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.54/26.80 U46'(mark(z0)) -> c205(U46'(z0)) 100.54/26.80 U46'(ok(z0)) -> c206(U46'(z0)) 100.54/26.80 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.54/26.80 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.54/26.80 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.54/26.80 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.54/26.80 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.54/26.80 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.54/26.80 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.54/26.80 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.54/26.80 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.54/26.80 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.54/26.80 U56'(mark(z0)) -> c217(U56'(z0)) 100.54/26.80 U56'(ok(z0)) -> c218(U56'(z0)) 100.54/26.80 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.54/26.80 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.54/26.80 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.54/26.80 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.54/26.80 U63'(mark(z0)) -> c223(U63'(z0)) 100.54/26.80 U63'(ok(z0)) -> c224(U63'(z0)) 100.54/26.80 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.54/26.80 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.54/26.80 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.54/26.80 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.54/26.80 U73'(mark(z0)) -> c229(U73'(z0)) 100.54/26.80 U73'(ok(z0)) -> c230(U73'(z0)) 100.54/26.80 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.54/26.80 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.54/26.80 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.54/26.80 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.54/26.80 U83'(mark(z0)) -> c235(U83'(z0)) 100.54/26.80 U83'(ok(z0)) -> c236(U83'(z0)) 100.54/26.80 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.54/26.80 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.54/26.80 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.54/26.80 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.54/26.80 U93'(mark(z0)) -> c241(U93'(z0)) 100.54/26.80 U93'(ok(z0)) -> c242(U93'(z0)) 100.54/26.80 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.54/26.80 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.54/26.80 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.54/26.80 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.54/26.80 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.54/26.80 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.54/26.80 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.54/26.80 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.54/26.80 PROPER(tt) -> c251 100.54/26.80 PROPER(nil) -> c252 100.54/26.80 PROPER(0) -> c253 100.54/26.80 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.54/26.80 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.54/26.80 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.54/26.80 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.54/26.80 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.54/26.80 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.54/26.80 TOP(mark(z0)) -> c260(TOP(proper(z0)), PROPER(z0)) 100.54/26.80 TOP(ok(z0)) -> c261(TOP(active(z0))) 100.54/26.80 K tuples:none 100.54/26.80 Defined Rule Symbols: U101_3, U102_3, U103_3, U104_3, U105_2, U106_1, U11_3, U12_3, U111_2, U112_1, U13_3, U121_2, U122_1, U14_3, U131_1, snd_1, splitAt_2, U141_1, U151_1, U161_1, U171_2, U172_1, U181_2, U182_2, U183_1, U191_2, U192_2, U193_1, U201_3, U202_3, U203_3, U204_3, U205_2, U206_1, U21_3, U22_3, U211_1, U23_3, U221_1, U24_2, U231_2, U232_1, U241_3, U242_3, U243_3, U244_3, U245_2, U246_1, U251_3, U252_3, U253_3, U254_3, U255_2, U256_1, U261_2, U262_1, U271_2, U272_1, U281_2, U282_2, cons_2, natsFrom_1, s_1, U291_3, U292_3, U293_3, U294_3, head_1, afterNth_2, U301_3, U302_2, U303_2, U304_2, U31_3, U32_3, U311_2, U312_2, pair_2, U33_3, U321_4, U322_4, U323_4, U324_4, U325_4, U326_4, U327_2, U34_2, U331_3, U332_2, U333_2, U334_2, U341_3, U342_3, U343_3, U344_3, fst_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_2, U72_2, U73_1, U81_2, U82_2, U83_1, U91_2, U92_2, U93_1, tail_1, take_2, sel_2, proper_1, isNaturalKind_1, isLNatKind_1, isNatural_1, isLNat_1, isPLNatKind_1, isPLNat_1, top_1 100.54/26.80 100.54/26.80 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, PROPER_1, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.54/26.80 100.54/26.80 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c251, c252, c253, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_2, c261_1 100.54/26.80 100.54/26.80 100.54/26.80 ---------------------------------------- 100.54/26.80 100.54/26.80 (7) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 100.54/26.80 Removed 4 trailing nodes: 100.54/26.80 PROPER(tt) -> c251 100.54/26.80 PROPER(nil) -> c252 100.54/26.80 TOP(ok(z0)) -> c261(TOP(active(z0))) 100.54/26.80 PROPER(0) -> c253 100.54/26.80 100.54/26.80 ---------------------------------------- 100.54/26.80 100.54/26.80 (8) 100.54/26.80 Obligation: 100.54/26.80 Complexity Dependency Tuples Problem 100.54/26.80 100.54/26.80 Rules: 100.54/26.80 U101(mark(z0), z1, z2) -> mark(U101(z0, z1, z2)) 100.54/26.80 U101(ok(z0), ok(z1), ok(z2)) -> ok(U101(z0, z1, z2)) 100.54/26.80 U102(mark(z0), z1, z2) -> mark(U102(z0, z1, z2)) 100.54/26.80 U102(ok(z0), ok(z1), ok(z2)) -> ok(U102(z0, z1, z2)) 100.54/26.80 U103(mark(z0), z1, z2) -> mark(U103(z0, z1, z2)) 100.54/26.80 U103(ok(z0), ok(z1), ok(z2)) -> ok(U103(z0, z1, z2)) 100.54/26.80 U104(mark(z0), z1, z2) -> mark(U104(z0, z1, z2)) 100.54/26.80 U104(ok(z0), ok(z1), ok(z2)) -> ok(U104(z0, z1, z2)) 100.54/26.80 U105(mark(z0), z1) -> mark(U105(z0, z1)) 100.54/26.80 U105(ok(z0), ok(z1)) -> ok(U105(z0, z1)) 100.54/26.80 U106(mark(z0)) -> mark(U106(z0)) 100.54/26.80 U106(ok(z0)) -> ok(U106(z0)) 100.54/26.80 U11(mark(z0), z1, z2) -> mark(U11(z0, z1, z2)) 100.54/26.80 U11(ok(z0), ok(z1), ok(z2)) -> ok(U11(z0, z1, z2)) 100.54/26.80 U12(mark(z0), z1, z2) -> mark(U12(z0, z1, z2)) 100.54/26.80 U12(ok(z0), ok(z1), ok(z2)) -> ok(U12(z0, z1, z2)) 100.54/26.80 U111(mark(z0), z1) -> mark(U111(z0, z1)) 100.54/26.80 U111(ok(z0), ok(z1)) -> ok(U111(z0, z1)) 100.54/26.80 U112(mark(z0)) -> mark(U112(z0)) 100.54/26.80 U112(ok(z0)) -> ok(U112(z0)) 100.54/26.80 U13(mark(z0), z1, z2) -> mark(U13(z0, z1, z2)) 100.54/26.80 U13(ok(z0), ok(z1), ok(z2)) -> ok(U13(z0, z1, z2)) 100.54/26.80 U121(mark(z0), z1) -> mark(U121(z0, z1)) 100.54/26.80 U121(ok(z0), ok(z1)) -> ok(U121(z0, z1)) 100.54/26.80 U122(mark(z0)) -> mark(U122(z0)) 100.54/26.80 U122(ok(z0)) -> ok(U122(z0)) 100.54/26.80 U14(mark(z0), z1, z2) -> mark(U14(z0, z1, z2)) 100.54/26.80 U14(ok(z0), ok(z1), ok(z2)) -> ok(U14(z0, z1, z2)) 100.54/26.80 U131(mark(z0)) -> mark(U131(z0)) 100.54/26.80 U131(ok(z0)) -> ok(U131(z0)) 100.54/26.80 snd(mark(z0)) -> mark(snd(z0)) 100.54/26.80 snd(ok(z0)) -> ok(snd(z0)) 100.54/26.80 splitAt(mark(z0), z1) -> mark(splitAt(z0, z1)) 100.54/26.80 splitAt(z0, mark(z1)) -> mark(splitAt(z0, z1)) 100.54/26.80 splitAt(ok(z0), ok(z1)) -> ok(splitAt(z0, z1)) 100.54/26.80 U141(mark(z0)) -> mark(U141(z0)) 100.54/26.80 U141(ok(z0)) -> ok(U141(z0)) 100.54/26.80 U151(mark(z0)) -> mark(U151(z0)) 100.54/26.80 U151(ok(z0)) -> ok(U151(z0)) 100.54/26.80 U161(mark(z0)) -> mark(U161(z0)) 100.54/26.80 U161(ok(z0)) -> ok(U161(z0)) 100.54/26.80 U171(mark(z0), z1) -> mark(U171(z0, z1)) 100.54/26.80 U171(ok(z0), ok(z1)) -> ok(U171(z0, z1)) 100.54/26.80 U172(mark(z0)) -> mark(U172(z0)) 100.54/26.80 U172(ok(z0)) -> ok(U172(z0)) 100.54/26.80 U181(mark(z0), z1) -> mark(U181(z0, z1)) 100.54/26.80 U181(ok(z0), ok(z1)) -> ok(U181(z0, z1)) 100.54/26.80 U182(mark(z0), z1) -> mark(U182(z0, z1)) 100.54/26.80 U182(ok(z0), ok(z1)) -> ok(U182(z0, z1)) 100.54/26.80 U183(mark(z0)) -> mark(U183(z0)) 100.54/26.80 U183(ok(z0)) -> ok(U183(z0)) 100.54/26.80 U191(mark(z0), z1) -> mark(U191(z0, z1)) 100.54/26.80 U191(ok(z0), ok(z1)) -> ok(U191(z0, z1)) 100.54/26.80 U192(mark(z0), z1) -> mark(U192(z0, z1)) 100.54/26.80 U192(ok(z0), ok(z1)) -> ok(U192(z0, z1)) 100.54/26.80 U193(mark(z0)) -> mark(U193(z0)) 100.54/26.80 U193(ok(z0)) -> ok(U193(z0)) 100.54/26.80 U201(mark(z0), z1, z2) -> mark(U201(z0, z1, z2)) 100.54/26.80 U201(ok(z0), ok(z1), ok(z2)) -> ok(U201(z0, z1, z2)) 100.54/26.80 U202(mark(z0), z1, z2) -> mark(U202(z0, z1, z2)) 100.54/26.80 U202(ok(z0), ok(z1), ok(z2)) -> ok(U202(z0, z1, z2)) 100.54/26.80 U203(mark(z0), z1, z2) -> mark(U203(z0, z1, z2)) 100.54/26.80 U203(ok(z0), ok(z1), ok(z2)) -> ok(U203(z0, z1, z2)) 100.54/26.80 U204(mark(z0), z1, z2) -> mark(U204(z0, z1, z2)) 100.54/26.80 U204(ok(z0), ok(z1), ok(z2)) -> ok(U204(z0, z1, z2)) 100.54/26.80 U205(mark(z0), z1) -> mark(U205(z0, z1)) 100.54/26.80 U205(ok(z0), ok(z1)) -> ok(U205(z0, z1)) 100.54/26.80 U206(mark(z0)) -> mark(U206(z0)) 100.54/26.80 U206(ok(z0)) -> ok(U206(z0)) 100.54/26.80 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 100.54/26.80 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 100.54/26.80 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 100.54/26.80 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 100.54/26.80 U211(mark(z0)) -> mark(U211(z0)) 100.54/26.80 U211(ok(z0)) -> ok(U211(z0)) 100.54/26.80 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 100.54/26.80 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 100.54/26.80 U221(mark(z0)) -> mark(U221(z0)) 100.54/26.80 U221(ok(z0)) -> ok(U221(z0)) 100.54/26.80 U24(mark(z0), z1) -> mark(U24(z0, z1)) 100.54/26.80 U24(ok(z0), ok(z1)) -> ok(U24(z0, z1)) 100.54/26.80 U231(mark(z0), z1) -> mark(U231(z0, z1)) 100.54/26.80 U231(ok(z0), ok(z1)) -> ok(U231(z0, z1)) 100.54/26.80 U232(mark(z0)) -> mark(U232(z0)) 100.54/26.80 U232(ok(z0)) -> ok(U232(z0)) 100.54/26.80 U241(mark(z0), z1, z2) -> mark(U241(z0, z1, z2)) 100.54/26.80 U241(ok(z0), ok(z1), ok(z2)) -> ok(U241(z0, z1, z2)) 100.54/26.80 U242(mark(z0), z1, z2) -> mark(U242(z0, z1, z2)) 100.54/26.80 U242(ok(z0), ok(z1), ok(z2)) -> ok(U242(z0, z1, z2)) 100.54/26.80 U243(mark(z0), z1, z2) -> mark(U243(z0, z1, z2)) 100.54/26.80 U243(ok(z0), ok(z1), ok(z2)) -> ok(U243(z0, z1, z2)) 100.54/26.80 U244(mark(z0), z1, z2) -> mark(U244(z0, z1, z2)) 100.54/26.80 U244(ok(z0), ok(z1), ok(z2)) -> ok(U244(z0, z1, z2)) 100.54/26.80 U245(mark(z0), z1) -> mark(U245(z0, z1)) 100.54/26.80 U245(ok(z0), ok(z1)) -> ok(U245(z0, z1)) 100.54/26.80 U246(mark(z0)) -> mark(U246(z0)) 100.54/26.80 U246(ok(z0)) -> ok(U246(z0)) 100.54/26.80 U251(mark(z0), z1, z2) -> mark(U251(z0, z1, z2)) 100.54/26.80 U251(ok(z0), ok(z1), ok(z2)) -> ok(U251(z0, z1, z2)) 100.54/26.80 U252(mark(z0), z1, z2) -> mark(U252(z0, z1, z2)) 100.54/26.80 U252(ok(z0), ok(z1), ok(z2)) -> ok(U252(z0, z1, z2)) 100.54/26.80 U253(mark(z0), z1, z2) -> mark(U253(z0, z1, z2)) 100.54/26.80 U253(ok(z0), ok(z1), ok(z2)) -> ok(U253(z0, z1, z2)) 100.54/26.80 U254(mark(z0), z1, z2) -> mark(U254(z0, z1, z2)) 100.54/26.80 U254(ok(z0), ok(z1), ok(z2)) -> ok(U254(z0, z1, z2)) 100.54/26.80 U255(mark(z0), z1) -> mark(U255(z0, z1)) 100.54/26.80 U255(ok(z0), ok(z1)) -> ok(U255(z0, z1)) 100.54/26.80 U256(mark(z0)) -> mark(U256(z0)) 100.54/26.80 U256(ok(z0)) -> ok(U256(z0)) 100.54/26.80 U261(mark(z0), z1) -> mark(U261(z0, z1)) 100.54/26.80 U261(ok(z0), ok(z1)) -> ok(U261(z0, z1)) 100.54/26.80 U262(mark(z0)) -> mark(U262(z0)) 100.54/26.80 U262(ok(z0)) -> ok(U262(z0)) 100.54/26.80 U271(mark(z0), z1) -> mark(U271(z0, z1)) 100.54/26.80 U271(ok(z0), ok(z1)) -> ok(U271(z0, z1)) 100.54/26.80 U272(mark(z0)) -> mark(U272(z0)) 100.54/26.80 U272(ok(z0)) -> ok(U272(z0)) 100.54/26.80 U281(mark(z0), z1) -> mark(U281(z0, z1)) 100.54/26.80 U281(ok(z0), ok(z1)) -> ok(U281(z0, z1)) 100.54/26.80 U282(mark(z0), z1) -> mark(U282(z0, z1)) 100.54/26.80 U282(ok(z0), ok(z1)) -> ok(U282(z0, z1)) 100.54/26.80 cons(mark(z0), z1) -> mark(cons(z0, z1)) 100.54/26.80 cons(ok(z0), ok(z1)) -> ok(cons(z0, z1)) 100.54/26.81 natsFrom(mark(z0)) -> mark(natsFrom(z0)) 100.54/26.81 natsFrom(ok(z0)) -> ok(natsFrom(z0)) 100.54/26.81 s(mark(z0)) -> mark(s(z0)) 100.54/26.81 s(ok(z0)) -> ok(s(z0)) 100.54/26.81 U291(mark(z0), z1, z2) -> mark(U291(z0, z1, z2)) 100.54/26.81 U291(ok(z0), ok(z1), ok(z2)) -> ok(U291(z0, z1, z2)) 100.54/26.81 U292(mark(z0), z1, z2) -> mark(U292(z0, z1, z2)) 100.54/26.81 U292(ok(z0), ok(z1), ok(z2)) -> ok(U292(z0, z1, z2)) 100.54/26.81 U293(mark(z0), z1, z2) -> mark(U293(z0, z1, z2)) 100.54/26.81 U293(ok(z0), ok(z1), ok(z2)) -> ok(U293(z0, z1, z2)) 100.54/26.81 U294(mark(z0), z1, z2) -> mark(U294(z0, z1, z2)) 100.54/26.81 U294(ok(z0), ok(z1), ok(z2)) -> ok(U294(z0, z1, z2)) 100.54/26.81 head(mark(z0)) -> mark(head(z0)) 100.54/26.81 head(ok(z0)) -> ok(head(z0)) 100.54/26.81 afterNth(mark(z0), z1) -> mark(afterNth(z0, z1)) 100.54/26.81 afterNth(z0, mark(z1)) -> mark(afterNth(z0, z1)) 100.54/26.81 afterNth(ok(z0), ok(z1)) -> ok(afterNth(z0, z1)) 100.54/26.81 U301(mark(z0), z1, z2) -> mark(U301(z0, z1, z2)) 100.54/26.81 U301(ok(z0), ok(z1), ok(z2)) -> ok(U301(z0, z1, z2)) 100.54/26.81 U302(mark(z0), z1) -> mark(U302(z0, z1)) 100.54/26.81 U302(ok(z0), ok(z1)) -> ok(U302(z0, z1)) 100.54/26.81 U303(mark(z0), z1) -> mark(U303(z0, z1)) 100.54/26.81 U303(ok(z0), ok(z1)) -> ok(U303(z0, z1)) 100.54/26.81 U304(mark(z0), z1) -> mark(U304(z0, z1)) 100.54/26.81 U304(ok(z0), ok(z1)) -> ok(U304(z0, z1)) 100.54/26.81 U31(mark(z0), z1, z2) -> mark(U31(z0, z1, z2)) 100.54/26.81 U31(ok(z0), ok(z1), ok(z2)) -> ok(U31(z0, z1, z2)) 100.54/26.81 U32(mark(z0), z1, z2) -> mark(U32(z0, z1, z2)) 100.54/26.81 U32(ok(z0), ok(z1), ok(z2)) -> ok(U32(z0, z1, z2)) 100.54/26.81 U311(mark(z0), z1) -> mark(U311(z0, z1)) 100.54/26.81 U311(ok(z0), ok(z1)) -> ok(U311(z0, z1)) 100.54/26.81 U312(mark(z0), z1) -> mark(U312(z0, z1)) 100.54/26.81 U312(ok(z0), ok(z1)) -> ok(U312(z0, z1)) 100.54/26.81 pair(mark(z0), z1) -> mark(pair(z0, z1)) 100.54/26.81 pair(z0, mark(z1)) -> mark(pair(z0, z1)) 100.54/26.81 pair(ok(z0), ok(z1)) -> ok(pair(z0, z1)) 100.54/26.81 U33(mark(z0), z1, z2) -> mark(U33(z0, z1, z2)) 100.54/26.81 U33(ok(z0), ok(z1), ok(z2)) -> ok(U33(z0, z1, z2)) 100.54/26.81 U321(mark(z0), z1, z2, z3) -> mark(U321(z0, z1, z2, z3)) 100.54/26.81 U321(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U321(z0, z1, z2, z3)) 100.54/26.81 U322(mark(z0), z1, z2, z3) -> mark(U322(z0, z1, z2, z3)) 100.54/26.81 U322(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U322(z0, z1, z2, z3)) 100.54/26.81 U323(mark(z0), z1, z2, z3) -> mark(U323(z0, z1, z2, z3)) 100.54/26.81 U323(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U323(z0, z1, z2, z3)) 100.54/26.81 U324(mark(z0), z1, z2, z3) -> mark(U324(z0, z1, z2, z3)) 100.54/26.81 U324(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U324(z0, z1, z2, z3)) 100.54/26.81 U325(mark(z0), z1, z2, z3) -> mark(U325(z0, z1, z2, z3)) 100.54/26.81 U325(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U325(z0, z1, z2, z3)) 100.54/26.81 U326(mark(z0), z1, z2, z3) -> mark(U326(z0, z1, z2, z3)) 100.54/26.81 U326(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U326(z0, z1, z2, z3)) 100.54/26.81 U327(mark(z0), z1) -> mark(U327(z0, z1)) 100.54/26.81 U327(ok(z0), ok(z1)) -> ok(U327(z0, z1)) 100.54/26.81 U34(mark(z0), z1) -> mark(U34(z0, z1)) 100.54/26.81 U34(ok(z0), ok(z1)) -> ok(U34(z0, z1)) 100.54/26.81 U331(mark(z0), z1, z2) -> mark(U331(z0, z1, z2)) 100.54/26.81 U331(ok(z0), ok(z1), ok(z2)) -> ok(U331(z0, z1, z2)) 100.54/26.81 U332(mark(z0), z1) -> mark(U332(z0, z1)) 100.54/26.81 U332(ok(z0), ok(z1)) -> ok(U332(z0, z1)) 100.54/26.81 U333(mark(z0), z1) -> mark(U333(z0, z1)) 100.54/26.81 U333(ok(z0), ok(z1)) -> ok(U333(z0, z1)) 100.54/26.81 U334(mark(z0), z1) -> mark(U334(z0, z1)) 100.54/26.81 U334(ok(z0), ok(z1)) -> ok(U334(z0, z1)) 100.54/26.81 U341(mark(z0), z1, z2) -> mark(U341(z0, z1, z2)) 100.54/26.81 U341(ok(z0), ok(z1), ok(z2)) -> ok(U341(z0, z1, z2)) 100.54/26.81 U342(mark(z0), z1, z2) -> mark(U342(z0, z1, z2)) 100.54/26.81 U342(ok(z0), ok(z1), ok(z2)) -> ok(U342(z0, z1, z2)) 100.54/26.81 U343(mark(z0), z1, z2) -> mark(U343(z0, z1, z2)) 100.54/26.81 U343(ok(z0), ok(z1), ok(z2)) -> ok(U343(z0, z1, z2)) 100.54/26.81 U344(mark(z0), z1, z2) -> mark(U344(z0, z1, z2)) 100.54/26.81 U344(ok(z0), ok(z1), ok(z2)) -> ok(U344(z0, z1, z2)) 100.54/26.81 fst(mark(z0)) -> mark(fst(z0)) 100.54/26.81 fst(ok(z0)) -> ok(fst(z0)) 100.54/26.81 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 100.54/26.81 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 100.54/26.81 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 100.54/26.81 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 100.54/26.81 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 100.54/26.81 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 100.54/26.81 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 100.54/26.81 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 100.54/26.81 U45(mark(z0), z1) -> mark(U45(z0, z1)) 100.54/26.81 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 100.54/26.81 U46(mark(z0)) -> mark(U46(z0)) 100.54/26.81 U46(ok(z0)) -> ok(U46(z0)) 100.54/26.81 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 100.54/26.81 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 100.54/26.81 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 100.54/26.81 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 100.54/26.81 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 100.54/26.81 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 100.54/26.81 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 100.54/26.81 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 100.54/26.81 U55(mark(z0), z1) -> mark(U55(z0, z1)) 100.54/26.81 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 100.54/26.81 U56(mark(z0)) -> mark(U56(z0)) 100.54/26.81 U56(ok(z0)) -> ok(U56(z0)) 100.54/26.81 U61(mark(z0), z1) -> mark(U61(z0, z1)) 100.54/26.81 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 100.54/26.81 U62(mark(z0), z1) -> mark(U62(z0, z1)) 100.54/26.81 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 100.54/26.81 U63(mark(z0)) -> mark(U63(z0)) 100.54/26.81 U63(ok(z0)) -> ok(U63(z0)) 100.54/26.81 U71(mark(z0), z1) -> mark(U71(z0, z1)) 100.54/26.81 U71(ok(z0), ok(z1)) -> ok(U71(z0, z1)) 100.54/26.81 U72(mark(z0), z1) -> mark(U72(z0, z1)) 100.54/26.81 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 100.54/26.81 U73(mark(z0)) -> mark(U73(z0)) 100.54/26.81 U73(ok(z0)) -> ok(U73(z0)) 100.54/26.81 U81(mark(z0), z1) -> mark(U81(z0, z1)) 100.54/26.81 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 100.54/26.81 U82(mark(z0), z1) -> mark(U82(z0, z1)) 100.54/26.81 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 100.54/26.81 U83(mark(z0)) -> mark(U83(z0)) 100.54/26.81 U83(ok(z0)) -> ok(U83(z0)) 100.54/26.81 U91(mark(z0), z1) -> mark(U91(z0, z1)) 100.54/26.81 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 100.54/26.81 U92(mark(z0), z1) -> mark(U92(z0, z1)) 100.54/26.81 U92(ok(z0), ok(z1)) -> ok(U92(z0, z1)) 100.54/26.81 U93(mark(z0)) -> mark(U93(z0)) 100.54/26.81 U93(ok(z0)) -> ok(U93(z0)) 100.54/26.81 tail(mark(z0)) -> mark(tail(z0)) 100.54/26.81 tail(ok(z0)) -> ok(tail(z0)) 100.54/26.81 take(mark(z0), z1) -> mark(take(z0, z1)) 100.54/26.81 take(z0, mark(z1)) -> mark(take(z0, z1)) 100.54/26.81 take(ok(z0), ok(z1)) -> ok(take(z0, z1)) 100.54/26.81 sel(mark(z0), z1) -> mark(sel(z0, z1)) 100.54/26.81 sel(z0, mark(z1)) -> mark(sel(z0, z1)) 100.54/26.81 sel(ok(z0), ok(z1)) -> ok(sel(z0, z1)) 100.54/26.81 proper(tt) -> ok(tt) 100.54/26.81 proper(nil) -> ok(nil) 100.54/26.81 proper(0) -> ok(0) 100.54/26.81 isNaturalKind(ok(z0)) -> ok(isNaturalKind(z0)) 100.54/26.81 isLNatKind(ok(z0)) -> ok(isLNatKind(z0)) 100.54/26.81 isNatural(ok(z0)) -> ok(isNatural(z0)) 100.54/26.81 isLNat(ok(z0)) -> ok(isLNat(z0)) 100.54/26.81 isPLNatKind(ok(z0)) -> ok(isPLNatKind(z0)) 100.54/26.81 isPLNat(ok(z0)) -> ok(isPLNat(z0)) 100.54/26.81 top(mark(z0)) -> top(proper(z0)) 100.54/26.81 top(ok(z0)) -> top(active(z0)) 100.54/26.81 Tuples: 100.54/26.81 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.54/26.81 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.54/26.81 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.54/26.81 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.54/26.81 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.54/26.81 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.54/26.81 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.54/26.81 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.54/26.81 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.54/26.81 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.54/26.81 U106'(mark(z0)) -> c10(U106'(z0)) 100.54/26.81 U106'(ok(z0)) -> c11(U106'(z0)) 100.54/26.81 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.54/26.81 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.54/26.81 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.54/26.81 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.54/26.81 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.54/26.81 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.54/26.81 U112'(mark(z0)) -> c18(U112'(z0)) 100.54/26.81 U112'(ok(z0)) -> c19(U112'(z0)) 100.54/26.81 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.54/26.81 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.54/26.81 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.54/26.81 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.54/26.81 U122'(mark(z0)) -> c24(U122'(z0)) 100.54/26.81 U122'(ok(z0)) -> c25(U122'(z0)) 100.54/26.81 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.54/26.81 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.54/26.81 U131'(mark(z0)) -> c28(U131'(z0)) 100.54/26.81 U131'(ok(z0)) -> c29(U131'(z0)) 100.54/26.81 SND(mark(z0)) -> c30(SND(z0)) 100.54/26.81 SND(ok(z0)) -> c31(SND(z0)) 100.54/26.81 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.54/26.81 U141'(mark(z0)) -> c35(U141'(z0)) 100.54/26.81 U141'(ok(z0)) -> c36(U141'(z0)) 100.54/26.81 U151'(mark(z0)) -> c37(U151'(z0)) 100.54/26.81 U151'(ok(z0)) -> c38(U151'(z0)) 100.54/26.81 U161'(mark(z0)) -> c39(U161'(z0)) 100.54/26.81 U161'(ok(z0)) -> c40(U161'(z0)) 100.54/26.81 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.54/26.81 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.54/26.81 U172'(mark(z0)) -> c43(U172'(z0)) 100.54/26.81 U172'(ok(z0)) -> c44(U172'(z0)) 100.54/26.81 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.54/26.81 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.54/26.81 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.54/26.81 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.54/26.81 U183'(mark(z0)) -> c49(U183'(z0)) 100.54/26.81 U183'(ok(z0)) -> c50(U183'(z0)) 100.54/26.81 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.54/26.81 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.54/26.81 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.54/26.81 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.54/26.81 U193'(mark(z0)) -> c55(U193'(z0)) 100.54/26.81 U193'(ok(z0)) -> c56(U193'(z0)) 100.54/26.81 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.54/26.81 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.54/26.81 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.54/26.81 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.54/26.81 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.54/26.81 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.54/26.81 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.54/26.81 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.54/26.81 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.54/26.81 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.54/26.81 U206'(mark(z0)) -> c67(U206'(z0)) 100.54/26.81 U206'(ok(z0)) -> c68(U206'(z0)) 100.54/26.81 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.54/26.81 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.54/26.81 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.54/26.81 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.54/26.81 U211'(mark(z0)) -> c73(U211'(z0)) 100.54/26.81 U211'(ok(z0)) -> c74(U211'(z0)) 100.54/26.81 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.54/26.81 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.54/26.81 U221'(mark(z0)) -> c77(U221'(z0)) 100.54/26.81 U221'(ok(z0)) -> c78(U221'(z0)) 100.54/26.81 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.54/26.81 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.54/26.81 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.54/26.81 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.54/26.81 U232'(mark(z0)) -> c83(U232'(z0)) 100.54/26.81 U232'(ok(z0)) -> c84(U232'(z0)) 100.54/26.81 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.54/26.81 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.54/26.81 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.54/26.81 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.54/26.81 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.54/26.81 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.54/26.81 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.54/26.81 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.54/26.81 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.54/26.81 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.54/26.81 U246'(mark(z0)) -> c95(U246'(z0)) 100.54/26.81 U246'(ok(z0)) -> c96(U246'(z0)) 100.54/26.81 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.54/26.81 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.54/26.81 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.54/26.81 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.54/26.81 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.54/26.81 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.54/26.81 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.54/26.81 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.54/26.81 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.54/26.81 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.54/26.81 U256'(mark(z0)) -> c107(U256'(z0)) 100.54/26.81 U256'(ok(z0)) -> c108(U256'(z0)) 100.54/26.81 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.54/26.81 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.54/26.81 U262'(mark(z0)) -> c111(U262'(z0)) 100.54/26.81 U262'(ok(z0)) -> c112(U262'(z0)) 100.54/26.81 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.54/26.81 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.54/26.81 U272'(mark(z0)) -> c115(U272'(z0)) 100.54/26.81 U272'(ok(z0)) -> c116(U272'(z0)) 100.54/26.81 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.54/26.81 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.54/26.81 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.54/26.81 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.54/26.81 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.54/26.81 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.54/26.81 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.54/26.81 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.54/26.81 S(mark(z0)) -> c125(S(z0)) 100.54/26.81 S(ok(z0)) -> c126(S(z0)) 100.54/26.81 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.54/26.81 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.54/26.81 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.54/26.81 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.54/26.81 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.54/26.81 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.54/26.81 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.54/26.81 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.54/26.81 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.54/26.81 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.54/26.81 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.54/26.81 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.54/26.81 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.54/26.81 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.54/26.81 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.54/26.81 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.54/26.81 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.54/26.81 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.54/26.81 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.54/26.81 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.54/26.81 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.54/26.81 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.54/26.81 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.54/26.81 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.54/26.81 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.54/26.81 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.54/26.81 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.54/26.81 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.54/26.81 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.54/26.81 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.54/26.81 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.54/26.81 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.54/26.81 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.54/26.81 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.54/26.81 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.54/26.81 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.54/26.81 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.54/26.81 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.54/26.81 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.54/26.81 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.54/26.81 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.54/26.81 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.54/26.81 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.54/26.81 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.54/26.81 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.54/26.81 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.54/26.81 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.54/26.81 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.54/26.81 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.54/26.81 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.54/26.81 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.54/26.81 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.54/26.81 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.54/26.81 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.54/26.81 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.54/26.81 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.54/26.81 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.54/26.81 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.54/26.81 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.54/26.81 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.54/26.81 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.54/26.81 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.54/26.81 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.54/26.81 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.54/26.81 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.54/26.81 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.54/26.81 FST(mark(z0)) -> c193(FST(z0)) 100.54/26.81 FST(ok(z0)) -> c194(FST(z0)) 100.54/26.81 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.54/26.81 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.54/26.81 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.54/26.81 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.54/26.81 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.54/26.81 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.54/26.81 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.54/26.81 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.54/26.81 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.54/26.81 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.54/26.81 U46'(mark(z0)) -> c205(U46'(z0)) 100.54/26.81 U46'(ok(z0)) -> c206(U46'(z0)) 100.54/26.81 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.54/26.81 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.54/26.81 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.54/26.81 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.54/26.81 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.54/26.81 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.54/26.81 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.54/26.81 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.54/26.81 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.54/26.81 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.54/26.81 U56'(mark(z0)) -> c217(U56'(z0)) 100.54/26.81 U56'(ok(z0)) -> c218(U56'(z0)) 100.54/26.81 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.54/26.81 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.54/26.81 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.54/26.81 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.54/26.81 U63'(mark(z0)) -> c223(U63'(z0)) 100.54/26.81 U63'(ok(z0)) -> c224(U63'(z0)) 100.54/26.81 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.54/26.81 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.54/26.81 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.54/26.81 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.54/26.81 U73'(mark(z0)) -> c229(U73'(z0)) 100.54/26.81 U73'(ok(z0)) -> c230(U73'(z0)) 100.54/26.81 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.54/26.81 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.54/26.81 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.54/26.81 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.54/26.81 U83'(mark(z0)) -> c235(U83'(z0)) 100.54/26.81 U83'(ok(z0)) -> c236(U83'(z0)) 100.54/26.81 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.54/26.81 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.54/26.81 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.54/26.81 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.54/26.81 U93'(mark(z0)) -> c241(U93'(z0)) 100.54/26.81 U93'(ok(z0)) -> c242(U93'(z0)) 100.54/26.81 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.54/26.81 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.54/26.81 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.54/26.81 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.54/26.81 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.54/26.81 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.54/26.81 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.54/26.81 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.54/26.81 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.54/26.81 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.54/26.81 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.54/26.81 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.54/26.81 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.54/26.81 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.54/26.81 TOP(mark(z0)) -> c260(TOP(proper(z0)), PROPER(z0)) 100.54/26.81 S tuples: 100.54/26.81 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.54/26.81 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.54/26.81 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.54/26.81 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.54/26.81 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.54/26.81 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.54/26.81 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.54/26.81 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.54/26.81 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.54/26.81 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.54/26.81 U106'(mark(z0)) -> c10(U106'(z0)) 100.54/26.81 U106'(ok(z0)) -> c11(U106'(z0)) 100.54/26.81 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.54/26.81 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.54/26.81 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.54/26.81 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.54/26.81 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.54/26.81 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.54/26.81 U112'(mark(z0)) -> c18(U112'(z0)) 100.54/26.81 U112'(ok(z0)) -> c19(U112'(z0)) 100.54/26.81 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.54/26.81 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.54/26.81 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.54/26.81 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.54/26.81 U122'(mark(z0)) -> c24(U122'(z0)) 100.54/26.81 U122'(ok(z0)) -> c25(U122'(z0)) 100.54/26.81 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.54/26.81 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.54/26.81 U131'(mark(z0)) -> c28(U131'(z0)) 100.54/26.81 U131'(ok(z0)) -> c29(U131'(z0)) 100.54/26.81 SND(mark(z0)) -> c30(SND(z0)) 100.54/26.81 SND(ok(z0)) -> c31(SND(z0)) 100.54/26.81 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.54/26.81 U141'(mark(z0)) -> c35(U141'(z0)) 100.54/26.81 U141'(ok(z0)) -> c36(U141'(z0)) 100.54/26.81 U151'(mark(z0)) -> c37(U151'(z0)) 100.54/26.81 U151'(ok(z0)) -> c38(U151'(z0)) 100.54/26.81 U161'(mark(z0)) -> c39(U161'(z0)) 100.54/26.81 U161'(ok(z0)) -> c40(U161'(z0)) 100.54/26.81 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.54/26.81 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.54/26.81 U172'(mark(z0)) -> c43(U172'(z0)) 100.54/26.81 U172'(ok(z0)) -> c44(U172'(z0)) 100.54/26.81 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.54/26.81 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.54/26.81 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.54/26.81 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.54/26.81 U183'(mark(z0)) -> c49(U183'(z0)) 100.54/26.81 U183'(ok(z0)) -> c50(U183'(z0)) 100.54/26.81 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.54/26.81 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.54/26.81 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.54/26.81 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.54/26.81 U193'(mark(z0)) -> c55(U193'(z0)) 100.54/26.81 U193'(ok(z0)) -> c56(U193'(z0)) 100.54/26.81 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.54/26.81 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.54/26.81 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.54/26.81 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.54/26.81 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.54/26.81 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.54/26.81 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.54/26.81 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.54/26.81 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.54/26.81 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.54/26.81 U206'(mark(z0)) -> c67(U206'(z0)) 100.54/26.81 U206'(ok(z0)) -> c68(U206'(z0)) 100.54/26.81 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.54/26.81 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.54/26.81 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.54/26.81 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.54/26.81 U211'(mark(z0)) -> c73(U211'(z0)) 100.54/26.81 U211'(ok(z0)) -> c74(U211'(z0)) 100.54/26.81 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.54/26.81 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.54/26.81 U221'(mark(z0)) -> c77(U221'(z0)) 100.54/26.81 U221'(ok(z0)) -> c78(U221'(z0)) 100.54/26.81 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.54/26.81 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.54/26.81 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.54/26.81 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.54/26.81 U232'(mark(z0)) -> c83(U232'(z0)) 100.54/26.81 U232'(ok(z0)) -> c84(U232'(z0)) 100.54/26.81 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.54/26.81 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.54/26.81 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.54/26.81 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.54/26.81 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.54/26.81 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.54/26.81 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.54/26.81 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.54/26.81 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.54/26.81 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.54/26.81 U246'(mark(z0)) -> c95(U246'(z0)) 100.54/26.81 U246'(ok(z0)) -> c96(U246'(z0)) 100.54/26.81 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.54/26.81 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.54/26.81 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.54/26.81 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.54/26.81 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.54/26.81 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.54/26.81 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.54/26.81 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.54/26.81 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.54/26.81 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.54/26.81 U256'(mark(z0)) -> c107(U256'(z0)) 100.54/26.81 U256'(ok(z0)) -> c108(U256'(z0)) 100.54/26.81 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.54/26.81 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.54/26.81 U262'(mark(z0)) -> c111(U262'(z0)) 100.54/26.81 U262'(ok(z0)) -> c112(U262'(z0)) 100.54/26.81 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.54/26.81 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.54/26.81 U272'(mark(z0)) -> c115(U272'(z0)) 100.54/26.81 U272'(ok(z0)) -> c116(U272'(z0)) 100.54/26.81 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.54/26.81 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.54/26.81 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.54/26.81 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.54/26.81 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.54/26.81 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.54/26.81 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.54/26.81 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.54/26.81 S(mark(z0)) -> c125(S(z0)) 100.54/26.81 S(ok(z0)) -> c126(S(z0)) 100.54/26.81 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.54/26.81 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.54/26.81 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.54/26.81 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.54/26.81 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.54/26.81 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.54/26.81 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.54/26.81 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.54/26.81 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.54/26.81 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.54/26.81 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.54/26.81 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.54/26.81 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.54/26.81 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.54/26.81 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.54/26.81 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.54/26.81 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.54/26.81 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.54/26.81 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.54/26.81 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.54/26.81 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.54/26.81 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.54/26.81 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.54/26.81 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.54/26.81 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.54/26.81 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.54/26.81 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.54/26.81 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.54/26.81 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.54/26.81 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.54/26.81 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.54/26.81 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.54/26.81 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.54/26.81 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.54/26.81 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.54/26.81 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.54/26.81 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.54/26.81 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.54/26.81 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.54/26.81 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.54/26.81 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.54/26.81 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.54/26.81 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.54/26.81 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.54/26.81 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.54/26.81 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.54/26.81 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.54/26.81 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.54/26.81 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.54/26.81 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.54/26.81 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.54/26.81 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.54/26.81 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.54/26.81 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.54/26.81 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.54/26.81 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.54/26.81 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.54/26.81 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.54/26.81 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.54/26.81 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.54/26.81 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.54/26.81 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.54/26.81 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.54/26.81 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.54/26.81 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.54/26.81 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.54/26.81 FST(mark(z0)) -> c193(FST(z0)) 100.54/26.81 FST(ok(z0)) -> c194(FST(z0)) 100.54/26.81 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.54/26.81 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.54/26.81 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.54/26.81 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.54/26.81 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.54/26.81 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.54/26.81 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.54/26.81 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.54/26.81 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.54/26.81 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.54/26.81 U46'(mark(z0)) -> c205(U46'(z0)) 100.54/26.81 U46'(ok(z0)) -> c206(U46'(z0)) 100.54/26.81 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.54/26.81 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.54/26.81 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.54/26.81 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.54/26.81 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.54/26.81 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.54/26.81 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.54/26.81 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.54/26.81 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.54/26.81 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.54/26.81 U56'(mark(z0)) -> c217(U56'(z0)) 100.54/26.81 U56'(ok(z0)) -> c218(U56'(z0)) 100.54/26.81 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.54/26.81 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.54/26.81 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.54/26.81 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.54/26.81 U63'(mark(z0)) -> c223(U63'(z0)) 100.54/26.81 U63'(ok(z0)) -> c224(U63'(z0)) 100.54/26.81 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.54/26.81 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.54/26.81 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.54/26.81 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.54/26.81 U73'(mark(z0)) -> c229(U73'(z0)) 100.54/26.81 U73'(ok(z0)) -> c230(U73'(z0)) 100.54/26.81 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.54/26.81 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.54/26.81 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.54/26.81 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.54/26.81 U83'(mark(z0)) -> c235(U83'(z0)) 100.54/26.81 U83'(ok(z0)) -> c236(U83'(z0)) 100.54/26.81 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.54/26.81 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.54/26.81 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.54/26.81 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.54/26.81 U93'(mark(z0)) -> c241(U93'(z0)) 100.54/26.81 U93'(ok(z0)) -> c242(U93'(z0)) 100.54/26.81 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.54/26.81 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.54/26.81 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.54/26.81 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.54/26.81 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.54/26.81 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.54/26.81 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.54/26.81 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.54/26.81 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.54/26.81 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.54/26.81 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.54/26.81 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.54/26.81 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.54/26.81 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.54/26.81 TOP(mark(z0)) -> c260(TOP(proper(z0)), PROPER(z0)) 100.54/26.81 K tuples:none 100.54/26.81 Defined Rule Symbols: U101_3, U102_3, U103_3, U104_3, U105_2, U106_1, U11_3, U12_3, U111_2, U112_1, U13_3, U121_2, U122_1, U14_3, U131_1, snd_1, splitAt_2, U141_1, U151_1, U161_1, U171_2, U172_1, U181_2, U182_2, U183_1, U191_2, U192_2, U193_1, U201_3, U202_3, U203_3, U204_3, U205_2, U206_1, U21_3, U22_3, U211_1, U23_3, U221_1, U24_2, U231_2, U232_1, U241_3, U242_3, U243_3, U244_3, U245_2, U246_1, U251_3, U252_3, U253_3, U254_3, U255_2, U256_1, U261_2, U262_1, U271_2, U272_1, U281_2, U282_2, cons_2, natsFrom_1, s_1, U291_3, U292_3, U293_3, U294_3, head_1, afterNth_2, U301_3, U302_2, U303_2, U304_2, U31_3, U32_3, U311_2, U312_2, pair_2, U33_3, U321_4, U322_4, U323_4, U324_4, U325_4, U326_4, U327_2, U34_2, U331_3, U332_2, U333_2, U334_2, U341_3, U342_3, U343_3, U344_3, fst_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_2, U72_2, U73_1, U81_2, U82_2, U83_1, U91_2, U92_2, U93_1, tail_1, take_2, sel_2, proper_1, isNaturalKind_1, isLNatKind_1, isNatural_1, isLNat_1, isPLNatKind_1, isPLNat_1, top_1 100.54/26.81 100.54/26.81 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.54/26.81 100.54/26.81 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_2 100.54/26.81 100.54/26.81 100.54/26.81 ---------------------------------------- 100.54/26.81 100.54/26.81 (9) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) 100.54/26.81 Removed 1 trailing tuple parts 100.54/26.81 ---------------------------------------- 100.54/26.81 100.54/26.81 (10) 100.54/26.81 Obligation: 100.54/26.81 Complexity Dependency Tuples Problem 100.54/26.81 100.54/26.81 Rules: 100.54/26.81 U101(mark(z0), z1, z2) -> mark(U101(z0, z1, z2)) 100.54/26.81 U101(ok(z0), ok(z1), ok(z2)) -> ok(U101(z0, z1, z2)) 100.54/26.81 U102(mark(z0), z1, z2) -> mark(U102(z0, z1, z2)) 100.54/26.81 U102(ok(z0), ok(z1), ok(z2)) -> ok(U102(z0, z1, z2)) 100.54/26.81 U103(mark(z0), z1, z2) -> mark(U103(z0, z1, z2)) 100.54/26.81 U103(ok(z0), ok(z1), ok(z2)) -> ok(U103(z0, z1, z2)) 100.54/26.81 U104(mark(z0), z1, z2) -> mark(U104(z0, z1, z2)) 100.54/26.81 U104(ok(z0), ok(z1), ok(z2)) -> ok(U104(z0, z1, z2)) 100.54/26.81 U105(mark(z0), z1) -> mark(U105(z0, z1)) 100.54/26.81 U105(ok(z0), ok(z1)) -> ok(U105(z0, z1)) 100.54/26.81 U106(mark(z0)) -> mark(U106(z0)) 100.54/26.81 U106(ok(z0)) -> ok(U106(z0)) 100.54/26.81 U11(mark(z0), z1, z2) -> mark(U11(z0, z1, z2)) 100.54/26.81 U11(ok(z0), ok(z1), ok(z2)) -> ok(U11(z0, z1, z2)) 100.54/26.81 U12(mark(z0), z1, z2) -> mark(U12(z0, z1, z2)) 100.54/26.81 U12(ok(z0), ok(z1), ok(z2)) -> ok(U12(z0, z1, z2)) 100.54/26.81 U111(mark(z0), z1) -> mark(U111(z0, z1)) 100.54/26.81 U111(ok(z0), ok(z1)) -> ok(U111(z0, z1)) 100.54/26.81 U112(mark(z0)) -> mark(U112(z0)) 100.54/26.81 U112(ok(z0)) -> ok(U112(z0)) 100.54/26.81 U13(mark(z0), z1, z2) -> mark(U13(z0, z1, z2)) 100.54/26.81 U13(ok(z0), ok(z1), ok(z2)) -> ok(U13(z0, z1, z2)) 100.54/26.81 U121(mark(z0), z1) -> mark(U121(z0, z1)) 100.54/26.81 U121(ok(z0), ok(z1)) -> ok(U121(z0, z1)) 100.54/26.81 U122(mark(z0)) -> mark(U122(z0)) 100.54/26.81 U122(ok(z0)) -> ok(U122(z0)) 100.54/26.81 U14(mark(z0), z1, z2) -> mark(U14(z0, z1, z2)) 100.54/26.81 U14(ok(z0), ok(z1), ok(z2)) -> ok(U14(z0, z1, z2)) 100.54/26.81 U131(mark(z0)) -> mark(U131(z0)) 100.54/26.81 U131(ok(z0)) -> ok(U131(z0)) 100.54/26.81 snd(mark(z0)) -> mark(snd(z0)) 100.54/26.81 snd(ok(z0)) -> ok(snd(z0)) 100.54/26.81 splitAt(mark(z0), z1) -> mark(splitAt(z0, z1)) 100.54/26.81 splitAt(z0, mark(z1)) -> mark(splitAt(z0, z1)) 100.54/26.81 splitAt(ok(z0), ok(z1)) -> ok(splitAt(z0, z1)) 100.54/26.81 U141(mark(z0)) -> mark(U141(z0)) 100.54/26.81 U141(ok(z0)) -> ok(U141(z0)) 100.54/26.81 U151(mark(z0)) -> mark(U151(z0)) 100.54/26.81 U151(ok(z0)) -> ok(U151(z0)) 100.54/26.81 U161(mark(z0)) -> mark(U161(z0)) 100.54/26.81 U161(ok(z0)) -> ok(U161(z0)) 100.54/26.81 U171(mark(z0), z1) -> mark(U171(z0, z1)) 100.54/26.81 U171(ok(z0), ok(z1)) -> ok(U171(z0, z1)) 100.54/26.81 U172(mark(z0)) -> mark(U172(z0)) 100.54/26.81 U172(ok(z0)) -> ok(U172(z0)) 100.54/26.81 U181(mark(z0), z1) -> mark(U181(z0, z1)) 100.54/26.81 U181(ok(z0), ok(z1)) -> ok(U181(z0, z1)) 100.54/26.81 U182(mark(z0), z1) -> mark(U182(z0, z1)) 100.54/26.81 U182(ok(z0), ok(z1)) -> ok(U182(z0, z1)) 100.54/26.81 U183(mark(z0)) -> mark(U183(z0)) 100.54/26.81 U183(ok(z0)) -> ok(U183(z0)) 100.54/26.81 U191(mark(z0), z1) -> mark(U191(z0, z1)) 100.54/26.81 U191(ok(z0), ok(z1)) -> ok(U191(z0, z1)) 100.54/26.81 U192(mark(z0), z1) -> mark(U192(z0, z1)) 100.54/26.81 U192(ok(z0), ok(z1)) -> ok(U192(z0, z1)) 100.54/26.81 U193(mark(z0)) -> mark(U193(z0)) 100.54/26.81 U193(ok(z0)) -> ok(U193(z0)) 100.54/26.81 U201(mark(z0), z1, z2) -> mark(U201(z0, z1, z2)) 100.54/26.81 U201(ok(z0), ok(z1), ok(z2)) -> ok(U201(z0, z1, z2)) 100.54/26.81 U202(mark(z0), z1, z2) -> mark(U202(z0, z1, z2)) 100.54/26.81 U202(ok(z0), ok(z1), ok(z2)) -> ok(U202(z0, z1, z2)) 100.54/26.81 U203(mark(z0), z1, z2) -> mark(U203(z0, z1, z2)) 100.54/26.81 U203(ok(z0), ok(z1), ok(z2)) -> ok(U203(z0, z1, z2)) 100.54/26.81 U204(mark(z0), z1, z2) -> mark(U204(z0, z1, z2)) 100.54/26.81 U204(ok(z0), ok(z1), ok(z2)) -> ok(U204(z0, z1, z2)) 100.54/26.81 U205(mark(z0), z1) -> mark(U205(z0, z1)) 100.54/26.81 U205(ok(z0), ok(z1)) -> ok(U205(z0, z1)) 100.54/26.81 U206(mark(z0)) -> mark(U206(z0)) 100.54/26.81 U206(ok(z0)) -> ok(U206(z0)) 100.54/26.81 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 100.54/26.81 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 100.54/26.81 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 100.54/26.81 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 100.54/26.81 U211(mark(z0)) -> mark(U211(z0)) 100.54/26.81 U211(ok(z0)) -> ok(U211(z0)) 100.54/26.81 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 100.54/26.81 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 100.54/26.81 U221(mark(z0)) -> mark(U221(z0)) 100.54/26.81 U221(ok(z0)) -> ok(U221(z0)) 100.54/26.81 U24(mark(z0), z1) -> mark(U24(z0, z1)) 100.54/26.81 U24(ok(z0), ok(z1)) -> ok(U24(z0, z1)) 100.54/26.81 U231(mark(z0), z1) -> mark(U231(z0, z1)) 100.54/26.81 U231(ok(z0), ok(z1)) -> ok(U231(z0, z1)) 100.54/26.81 U232(mark(z0)) -> mark(U232(z0)) 100.54/26.81 U232(ok(z0)) -> ok(U232(z0)) 100.54/26.81 U241(mark(z0), z1, z2) -> mark(U241(z0, z1, z2)) 100.54/26.81 U241(ok(z0), ok(z1), ok(z2)) -> ok(U241(z0, z1, z2)) 100.54/26.81 U242(mark(z0), z1, z2) -> mark(U242(z0, z1, z2)) 100.54/26.81 U242(ok(z0), ok(z1), ok(z2)) -> ok(U242(z0, z1, z2)) 100.54/26.81 U243(mark(z0), z1, z2) -> mark(U243(z0, z1, z2)) 100.54/26.81 U243(ok(z0), ok(z1), ok(z2)) -> ok(U243(z0, z1, z2)) 100.54/26.81 U244(mark(z0), z1, z2) -> mark(U244(z0, z1, z2)) 100.54/26.81 U244(ok(z0), ok(z1), ok(z2)) -> ok(U244(z0, z1, z2)) 100.54/26.81 U245(mark(z0), z1) -> mark(U245(z0, z1)) 100.54/26.81 U245(ok(z0), ok(z1)) -> ok(U245(z0, z1)) 100.54/26.81 U246(mark(z0)) -> mark(U246(z0)) 100.54/26.81 U246(ok(z0)) -> ok(U246(z0)) 100.54/26.81 U251(mark(z0), z1, z2) -> mark(U251(z0, z1, z2)) 100.54/26.81 U251(ok(z0), ok(z1), ok(z2)) -> ok(U251(z0, z1, z2)) 100.54/26.81 U252(mark(z0), z1, z2) -> mark(U252(z0, z1, z2)) 100.54/26.81 U252(ok(z0), ok(z1), ok(z2)) -> ok(U252(z0, z1, z2)) 100.54/26.81 U253(mark(z0), z1, z2) -> mark(U253(z0, z1, z2)) 100.54/26.81 U253(ok(z0), ok(z1), ok(z2)) -> ok(U253(z0, z1, z2)) 100.54/26.81 U254(mark(z0), z1, z2) -> mark(U254(z0, z1, z2)) 100.54/26.81 U254(ok(z0), ok(z1), ok(z2)) -> ok(U254(z0, z1, z2)) 100.54/26.81 U255(mark(z0), z1) -> mark(U255(z0, z1)) 100.54/26.81 U255(ok(z0), ok(z1)) -> ok(U255(z0, z1)) 100.54/26.81 U256(mark(z0)) -> mark(U256(z0)) 100.54/26.81 U256(ok(z0)) -> ok(U256(z0)) 100.54/26.81 U261(mark(z0), z1) -> mark(U261(z0, z1)) 100.54/26.81 U261(ok(z0), ok(z1)) -> ok(U261(z0, z1)) 100.54/26.81 U262(mark(z0)) -> mark(U262(z0)) 100.54/26.81 U262(ok(z0)) -> ok(U262(z0)) 100.54/26.81 U271(mark(z0), z1) -> mark(U271(z0, z1)) 100.54/26.81 U271(ok(z0), ok(z1)) -> ok(U271(z0, z1)) 100.54/26.81 U272(mark(z0)) -> mark(U272(z0)) 100.54/26.81 U272(ok(z0)) -> ok(U272(z0)) 100.54/26.81 U281(mark(z0), z1) -> mark(U281(z0, z1)) 100.54/26.81 U281(ok(z0), ok(z1)) -> ok(U281(z0, z1)) 100.54/26.81 U282(mark(z0), z1) -> mark(U282(z0, z1)) 100.54/26.81 U282(ok(z0), ok(z1)) -> ok(U282(z0, z1)) 100.54/26.81 cons(mark(z0), z1) -> mark(cons(z0, z1)) 100.54/26.81 cons(ok(z0), ok(z1)) -> ok(cons(z0, z1)) 100.54/26.81 natsFrom(mark(z0)) -> mark(natsFrom(z0)) 100.54/26.81 natsFrom(ok(z0)) -> ok(natsFrom(z0)) 100.54/26.81 s(mark(z0)) -> mark(s(z0)) 100.54/26.81 s(ok(z0)) -> ok(s(z0)) 100.54/26.81 U291(mark(z0), z1, z2) -> mark(U291(z0, z1, z2)) 100.54/26.81 U291(ok(z0), ok(z1), ok(z2)) -> ok(U291(z0, z1, z2)) 100.54/26.81 U292(mark(z0), z1, z2) -> mark(U292(z0, z1, z2)) 100.54/26.81 U292(ok(z0), ok(z1), ok(z2)) -> ok(U292(z0, z1, z2)) 100.54/26.81 U293(mark(z0), z1, z2) -> mark(U293(z0, z1, z2)) 100.54/26.81 U293(ok(z0), ok(z1), ok(z2)) -> ok(U293(z0, z1, z2)) 100.54/26.81 U294(mark(z0), z1, z2) -> mark(U294(z0, z1, z2)) 100.54/26.81 U294(ok(z0), ok(z1), ok(z2)) -> ok(U294(z0, z1, z2)) 100.54/26.81 head(mark(z0)) -> mark(head(z0)) 100.54/26.81 head(ok(z0)) -> ok(head(z0)) 100.54/26.81 afterNth(mark(z0), z1) -> mark(afterNth(z0, z1)) 100.54/26.81 afterNth(z0, mark(z1)) -> mark(afterNth(z0, z1)) 100.54/26.81 afterNth(ok(z0), ok(z1)) -> ok(afterNth(z0, z1)) 100.54/26.81 U301(mark(z0), z1, z2) -> mark(U301(z0, z1, z2)) 100.54/26.81 U301(ok(z0), ok(z1), ok(z2)) -> ok(U301(z0, z1, z2)) 100.54/26.81 U302(mark(z0), z1) -> mark(U302(z0, z1)) 100.54/26.81 U302(ok(z0), ok(z1)) -> ok(U302(z0, z1)) 100.54/26.81 U303(mark(z0), z1) -> mark(U303(z0, z1)) 100.54/26.81 U303(ok(z0), ok(z1)) -> ok(U303(z0, z1)) 100.54/26.81 U304(mark(z0), z1) -> mark(U304(z0, z1)) 100.54/26.81 U304(ok(z0), ok(z1)) -> ok(U304(z0, z1)) 100.54/26.81 U31(mark(z0), z1, z2) -> mark(U31(z0, z1, z2)) 100.54/26.81 U31(ok(z0), ok(z1), ok(z2)) -> ok(U31(z0, z1, z2)) 100.54/26.81 U32(mark(z0), z1, z2) -> mark(U32(z0, z1, z2)) 100.54/26.81 U32(ok(z0), ok(z1), ok(z2)) -> ok(U32(z0, z1, z2)) 100.54/26.81 U311(mark(z0), z1) -> mark(U311(z0, z1)) 100.54/26.81 U311(ok(z0), ok(z1)) -> ok(U311(z0, z1)) 100.54/26.81 U312(mark(z0), z1) -> mark(U312(z0, z1)) 100.54/26.81 U312(ok(z0), ok(z1)) -> ok(U312(z0, z1)) 100.54/26.81 pair(mark(z0), z1) -> mark(pair(z0, z1)) 100.54/26.81 pair(z0, mark(z1)) -> mark(pair(z0, z1)) 100.54/26.81 pair(ok(z0), ok(z1)) -> ok(pair(z0, z1)) 100.54/26.81 U33(mark(z0), z1, z2) -> mark(U33(z0, z1, z2)) 100.54/26.81 U33(ok(z0), ok(z1), ok(z2)) -> ok(U33(z0, z1, z2)) 100.54/26.81 U321(mark(z0), z1, z2, z3) -> mark(U321(z0, z1, z2, z3)) 100.54/26.81 U321(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U321(z0, z1, z2, z3)) 100.54/26.81 U322(mark(z0), z1, z2, z3) -> mark(U322(z0, z1, z2, z3)) 100.54/26.81 U322(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U322(z0, z1, z2, z3)) 100.54/26.81 U323(mark(z0), z1, z2, z3) -> mark(U323(z0, z1, z2, z3)) 100.54/26.81 U323(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U323(z0, z1, z2, z3)) 100.54/26.81 U324(mark(z0), z1, z2, z3) -> mark(U324(z0, z1, z2, z3)) 100.54/26.81 U324(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U324(z0, z1, z2, z3)) 100.54/26.81 U325(mark(z0), z1, z2, z3) -> mark(U325(z0, z1, z2, z3)) 100.54/26.81 U325(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U325(z0, z1, z2, z3)) 100.54/26.81 U326(mark(z0), z1, z2, z3) -> mark(U326(z0, z1, z2, z3)) 100.54/26.81 U326(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U326(z0, z1, z2, z3)) 100.54/26.81 U327(mark(z0), z1) -> mark(U327(z0, z1)) 100.54/26.81 U327(ok(z0), ok(z1)) -> ok(U327(z0, z1)) 100.54/26.81 U34(mark(z0), z1) -> mark(U34(z0, z1)) 100.54/26.81 U34(ok(z0), ok(z1)) -> ok(U34(z0, z1)) 100.54/26.81 U331(mark(z0), z1, z2) -> mark(U331(z0, z1, z2)) 100.54/26.81 U331(ok(z0), ok(z1), ok(z2)) -> ok(U331(z0, z1, z2)) 100.54/26.81 U332(mark(z0), z1) -> mark(U332(z0, z1)) 100.54/26.81 U332(ok(z0), ok(z1)) -> ok(U332(z0, z1)) 100.54/26.81 U333(mark(z0), z1) -> mark(U333(z0, z1)) 100.54/26.81 U333(ok(z0), ok(z1)) -> ok(U333(z0, z1)) 100.54/26.81 U334(mark(z0), z1) -> mark(U334(z0, z1)) 100.54/26.81 U334(ok(z0), ok(z1)) -> ok(U334(z0, z1)) 100.54/26.81 U341(mark(z0), z1, z2) -> mark(U341(z0, z1, z2)) 100.54/26.81 U341(ok(z0), ok(z1), ok(z2)) -> ok(U341(z0, z1, z2)) 100.54/26.81 U342(mark(z0), z1, z2) -> mark(U342(z0, z1, z2)) 100.54/26.81 U342(ok(z0), ok(z1), ok(z2)) -> ok(U342(z0, z1, z2)) 100.54/26.81 U343(mark(z0), z1, z2) -> mark(U343(z0, z1, z2)) 100.54/26.81 U343(ok(z0), ok(z1), ok(z2)) -> ok(U343(z0, z1, z2)) 100.54/26.81 U344(mark(z0), z1, z2) -> mark(U344(z0, z1, z2)) 100.54/26.81 U344(ok(z0), ok(z1), ok(z2)) -> ok(U344(z0, z1, z2)) 100.54/26.81 fst(mark(z0)) -> mark(fst(z0)) 100.54/26.81 fst(ok(z0)) -> ok(fst(z0)) 100.54/26.81 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 100.54/26.81 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 100.54/26.81 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 100.54/26.81 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 100.54/26.81 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 100.54/26.81 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 100.54/26.81 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 100.54/26.81 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 100.54/26.81 U45(mark(z0), z1) -> mark(U45(z0, z1)) 100.54/26.81 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 100.54/26.81 U46(mark(z0)) -> mark(U46(z0)) 100.54/26.81 U46(ok(z0)) -> ok(U46(z0)) 100.54/26.81 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 100.54/26.81 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 100.54/26.81 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 100.54/26.81 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 100.54/26.81 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 100.54/26.81 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 100.54/26.81 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 100.54/26.81 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 100.54/26.81 U55(mark(z0), z1) -> mark(U55(z0, z1)) 100.54/26.81 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 100.54/26.81 U56(mark(z0)) -> mark(U56(z0)) 100.54/26.81 U56(ok(z0)) -> ok(U56(z0)) 100.54/26.81 U61(mark(z0), z1) -> mark(U61(z0, z1)) 100.54/26.81 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 100.54/26.81 U62(mark(z0), z1) -> mark(U62(z0, z1)) 100.54/26.81 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 100.54/26.81 U63(mark(z0)) -> mark(U63(z0)) 100.54/26.81 U63(ok(z0)) -> ok(U63(z0)) 100.54/26.81 U71(mark(z0), z1) -> mark(U71(z0, z1)) 100.54/26.81 U71(ok(z0), ok(z1)) -> ok(U71(z0, z1)) 100.54/26.81 U72(mark(z0), z1) -> mark(U72(z0, z1)) 100.54/26.81 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 100.54/26.81 U73(mark(z0)) -> mark(U73(z0)) 100.54/26.81 U73(ok(z0)) -> ok(U73(z0)) 100.54/26.81 U81(mark(z0), z1) -> mark(U81(z0, z1)) 100.54/26.81 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 100.54/26.81 U82(mark(z0), z1) -> mark(U82(z0, z1)) 100.54/26.81 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 100.54/26.81 U83(mark(z0)) -> mark(U83(z0)) 100.54/26.81 U83(ok(z0)) -> ok(U83(z0)) 100.54/26.81 U91(mark(z0), z1) -> mark(U91(z0, z1)) 100.54/26.81 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 100.54/26.81 U92(mark(z0), z1) -> mark(U92(z0, z1)) 100.54/26.81 U92(ok(z0), ok(z1)) -> ok(U92(z0, z1)) 100.54/26.81 U93(mark(z0)) -> mark(U93(z0)) 100.54/26.81 U93(ok(z0)) -> ok(U93(z0)) 100.54/26.81 tail(mark(z0)) -> mark(tail(z0)) 100.54/26.81 tail(ok(z0)) -> ok(tail(z0)) 100.54/26.81 take(mark(z0), z1) -> mark(take(z0, z1)) 100.54/26.81 take(z0, mark(z1)) -> mark(take(z0, z1)) 100.54/26.81 take(ok(z0), ok(z1)) -> ok(take(z0, z1)) 100.54/26.81 sel(mark(z0), z1) -> mark(sel(z0, z1)) 100.54/26.81 sel(z0, mark(z1)) -> mark(sel(z0, z1)) 100.54/26.81 sel(ok(z0), ok(z1)) -> ok(sel(z0, z1)) 100.54/26.81 proper(tt) -> ok(tt) 100.54/26.81 proper(nil) -> ok(nil) 100.54/26.81 proper(0) -> ok(0) 100.54/26.81 isNaturalKind(ok(z0)) -> ok(isNaturalKind(z0)) 100.54/26.81 isLNatKind(ok(z0)) -> ok(isLNatKind(z0)) 100.54/26.81 isNatural(ok(z0)) -> ok(isNatural(z0)) 100.54/26.81 isLNat(ok(z0)) -> ok(isLNat(z0)) 100.54/26.81 isPLNatKind(ok(z0)) -> ok(isPLNatKind(z0)) 100.54/26.81 isPLNat(ok(z0)) -> ok(isPLNat(z0)) 100.54/26.81 top(mark(z0)) -> top(proper(z0)) 100.54/26.81 top(ok(z0)) -> top(active(z0)) 100.54/26.81 Tuples: 100.54/26.81 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.54/26.81 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.54/26.81 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.54/26.81 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.54/26.81 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.54/26.81 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.54/26.81 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.54/26.81 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.54/26.81 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.54/26.81 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.54/26.81 U106'(mark(z0)) -> c10(U106'(z0)) 100.54/26.81 U106'(ok(z0)) -> c11(U106'(z0)) 100.54/26.81 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.54/26.81 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.54/26.81 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.54/26.81 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.54/26.81 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.54/26.81 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.54/26.81 U112'(mark(z0)) -> c18(U112'(z0)) 100.54/26.81 U112'(ok(z0)) -> c19(U112'(z0)) 100.54/26.81 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.54/26.81 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.54/26.81 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.54/26.81 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.54/26.81 U122'(mark(z0)) -> c24(U122'(z0)) 100.54/26.81 U122'(ok(z0)) -> c25(U122'(z0)) 100.54/26.81 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.54/26.81 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.54/26.81 U131'(mark(z0)) -> c28(U131'(z0)) 100.54/26.81 U131'(ok(z0)) -> c29(U131'(z0)) 100.54/26.81 SND(mark(z0)) -> c30(SND(z0)) 100.54/26.81 SND(ok(z0)) -> c31(SND(z0)) 100.54/26.81 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.54/26.81 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.54/26.81 U141'(mark(z0)) -> c35(U141'(z0)) 100.54/26.81 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.82 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.82 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.82 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.82 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.82 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.82 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.82 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.82 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.82 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.82 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.82 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.82 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.82 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.82 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.82 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.82 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.82 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.82 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.82 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.82 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.82 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.82 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.82 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.82 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.82 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.82 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.82 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.82 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.82 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.82 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.82 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.82 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.82 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.82 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.82 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.82 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.82 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.82 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.82 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.82 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.82 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.82 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.82 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.82 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.82 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.82 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.82 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.82 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.82 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.82 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.82 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.82 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.82 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.82 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.82 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.82 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.82 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.82 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.82 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.82 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.82 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.82 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.82 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.82 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.82 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.82 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.82 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.82 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.82 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.82 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.82 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.82 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.82 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.82 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.82 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.82 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.82 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.82 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.82 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.82 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.82 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.82 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.82 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.82 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.82 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.82 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.82 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.82 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.82 S(mark(z0)) -> c125(S(z0)) 100.84/26.82 S(ok(z0)) -> c126(S(z0)) 100.84/26.82 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.82 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.82 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.82 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.82 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.82 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.82 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.82 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.82 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.82 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.82 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.82 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.82 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.82 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.82 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.82 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.82 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.82 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.82 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.82 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.82 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.82 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.82 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.82 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.82 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.82 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.82 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.82 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.82 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.82 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.82 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.82 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.82 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.82 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.82 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.82 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.82 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.82 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.82 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.82 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.82 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.82 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.82 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.82 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.82 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.82 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.82 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.82 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.82 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.82 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.82 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.82 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.82 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.82 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.82 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.82 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.82 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.82 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.82 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.82 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.82 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.82 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.82 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.82 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.82 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.82 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.82 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.82 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.82 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.82 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.82 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.82 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.82 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.82 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.82 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.82 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.82 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.82 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.82 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.82 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.82 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.82 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.82 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.82 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.82 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.82 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.82 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.82 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.82 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.82 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.82 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.82 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.82 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.82 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.82 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.82 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.82 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.82 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.82 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.82 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.82 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.82 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.82 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.82 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.82 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.82 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.82 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.82 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.82 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.82 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.82 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.82 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.82 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.82 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.82 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.82 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.82 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.82 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.82 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.82 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.82 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.82 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.82 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.82 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.82 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.82 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.82 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.82 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.82 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.82 S tuples: 100.84/26.82 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.82 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.82 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.82 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.82 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.82 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.82 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.82 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.82 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.82 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.82 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.82 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.82 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.82 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.82 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.82 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.82 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.82 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.82 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.82 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.82 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.82 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.82 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.82 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.82 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.82 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.82 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.82 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.82 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.82 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.82 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.82 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.82 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.82 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.82 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.82 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.82 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.82 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.82 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.82 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.82 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.82 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.82 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.82 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.82 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.82 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.82 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.82 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.82 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.82 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.82 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.82 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.82 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.82 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.82 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.82 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.82 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.82 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.82 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.82 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.82 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.82 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.82 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.82 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.82 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.82 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.82 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.82 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.82 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.82 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.82 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.82 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.82 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.82 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.82 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.82 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.82 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.82 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.82 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.82 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.82 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.82 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.82 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.82 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.82 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.82 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.82 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.82 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.82 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.82 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.82 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.82 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.82 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.82 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.82 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.82 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.82 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.82 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.82 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.82 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.82 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.82 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.82 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.82 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.82 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.82 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.82 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.82 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.82 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.82 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.82 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.82 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.82 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.82 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.82 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.82 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.82 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.82 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.82 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.82 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.82 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.82 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.82 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.82 S(mark(z0)) -> c125(S(z0)) 100.84/26.82 S(ok(z0)) -> c126(S(z0)) 100.84/26.82 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.82 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.82 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.82 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.82 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.82 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.82 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.82 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.82 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.82 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.82 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.82 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.82 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.82 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.82 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.82 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.82 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.82 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.82 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.82 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.82 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.82 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.82 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.82 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.82 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.82 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.82 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.82 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.82 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.82 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.82 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.82 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.82 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.82 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.82 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.82 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.82 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.82 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.82 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.82 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.82 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.82 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.82 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.82 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.82 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.82 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.82 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.82 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.82 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.82 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.82 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.82 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.82 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.82 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.82 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.82 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.82 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.82 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.82 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.82 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.82 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.82 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.82 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.82 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.82 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.82 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.82 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.82 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.82 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.82 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.82 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.82 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.82 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.82 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.82 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.82 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.82 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.82 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.82 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.82 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.82 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.82 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.82 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.82 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.82 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.82 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.82 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.82 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.82 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.82 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.82 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.82 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.82 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.82 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.82 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.82 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.82 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.82 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.82 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.82 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.82 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.82 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.82 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.82 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.82 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.82 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.82 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.82 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.82 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.82 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.82 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.82 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.82 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.82 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.82 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.82 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.82 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.82 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.82 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.82 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.82 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.82 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.82 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.82 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.82 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.82 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.82 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.82 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.82 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.82 K tuples:none 100.84/26.82 Defined Rule Symbols: U101_3, U102_3, U103_3, U104_3, U105_2, U106_1, U11_3, U12_3, U111_2, U112_1, U13_3, U121_2, U122_1, U14_3, U131_1, snd_1, splitAt_2, U141_1, U151_1, U161_1, U171_2, U172_1, U181_2, U182_2, U183_1, U191_2, U192_2, U193_1, U201_3, U202_3, U203_3, U204_3, U205_2, U206_1, U21_3, U22_3, U211_1, U23_3, U221_1, U24_2, U231_2, U232_1, U241_3, U242_3, U243_3, U244_3, U245_2, U246_1, U251_3, U252_3, U253_3, U254_3, U255_2, U256_1, U261_2, U262_1, U271_2, U272_1, U281_2, U282_2, cons_2, natsFrom_1, s_1, U291_3, U292_3, U293_3, U294_3, head_1, afterNth_2, U301_3, U302_2, U303_2, U304_2, U31_3, U32_3, U311_2, U312_2, pair_2, U33_3, U321_4, U322_4, U323_4, U324_4, U325_4, U326_4, U327_2, U34_2, U331_3, U332_2, U333_2, U334_2, U341_3, U342_3, U343_3, U344_3, fst_1, U41_3, U42_3, U43_3, U44_3, U45_2, U46_1, U51_3, U52_3, U53_3, U54_3, U55_2, U56_1, U61_2, U62_2, U63_1, U71_2, U72_2, U73_1, U81_2, U82_2, U83_1, U91_2, U92_2, U93_1, tail_1, take_2, sel_2, proper_1, isNaturalKind_1, isLNatKind_1, isNatural_1, isLNat_1, isPLNatKind_1, isPLNat_1, top_1 100.84/26.82 100.84/26.82 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.84/26.82 100.84/26.82 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_1 100.84/26.82 100.84/26.82 100.84/26.82 ---------------------------------------- 100.84/26.82 100.84/26.82 (11) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) 100.84/26.82 The following rules are not usable and were removed: 100.84/26.82 U101(mark(z0), z1, z2) -> mark(U101(z0, z1, z2)) 100.84/26.82 U101(ok(z0), ok(z1), ok(z2)) -> ok(U101(z0, z1, z2)) 100.84/26.82 U102(mark(z0), z1, z2) -> mark(U102(z0, z1, z2)) 100.84/26.82 U102(ok(z0), ok(z1), ok(z2)) -> ok(U102(z0, z1, z2)) 100.84/26.82 U103(mark(z0), z1, z2) -> mark(U103(z0, z1, z2)) 100.84/26.82 U103(ok(z0), ok(z1), ok(z2)) -> ok(U103(z0, z1, z2)) 100.84/26.82 U104(mark(z0), z1, z2) -> mark(U104(z0, z1, z2)) 100.84/26.82 U104(ok(z0), ok(z1), ok(z2)) -> ok(U104(z0, z1, z2)) 100.84/26.82 U105(mark(z0), z1) -> mark(U105(z0, z1)) 100.84/26.82 U105(ok(z0), ok(z1)) -> ok(U105(z0, z1)) 100.84/26.82 U106(mark(z0)) -> mark(U106(z0)) 100.84/26.82 U106(ok(z0)) -> ok(U106(z0)) 100.84/26.82 U11(mark(z0), z1, z2) -> mark(U11(z0, z1, z2)) 100.84/26.82 U11(ok(z0), ok(z1), ok(z2)) -> ok(U11(z0, z1, z2)) 100.84/26.82 U12(mark(z0), z1, z2) -> mark(U12(z0, z1, z2)) 100.84/26.82 U12(ok(z0), ok(z1), ok(z2)) -> ok(U12(z0, z1, z2)) 100.84/26.82 U111(mark(z0), z1) -> mark(U111(z0, z1)) 100.84/26.82 U111(ok(z0), ok(z1)) -> ok(U111(z0, z1)) 100.84/26.82 U112(mark(z0)) -> mark(U112(z0)) 100.84/26.82 U112(ok(z0)) -> ok(U112(z0)) 100.84/26.82 U13(mark(z0), z1, z2) -> mark(U13(z0, z1, z2)) 100.84/26.82 U13(ok(z0), ok(z1), ok(z2)) -> ok(U13(z0, z1, z2)) 100.84/26.82 U121(mark(z0), z1) -> mark(U121(z0, z1)) 100.84/26.82 U121(ok(z0), ok(z1)) -> ok(U121(z0, z1)) 100.84/26.82 U122(mark(z0)) -> mark(U122(z0)) 100.84/26.82 U122(ok(z0)) -> ok(U122(z0)) 100.84/26.82 U14(mark(z0), z1, z2) -> mark(U14(z0, z1, z2)) 100.84/26.82 U14(ok(z0), ok(z1), ok(z2)) -> ok(U14(z0, z1, z2)) 100.84/26.82 U131(mark(z0)) -> mark(U131(z0)) 100.84/26.82 U131(ok(z0)) -> ok(U131(z0)) 100.84/26.82 snd(mark(z0)) -> mark(snd(z0)) 100.84/26.82 snd(ok(z0)) -> ok(snd(z0)) 100.84/26.82 splitAt(mark(z0), z1) -> mark(splitAt(z0, z1)) 100.84/26.82 splitAt(z0, mark(z1)) -> mark(splitAt(z0, z1)) 100.84/26.82 splitAt(ok(z0), ok(z1)) -> ok(splitAt(z0, z1)) 100.84/26.82 U141(mark(z0)) -> mark(U141(z0)) 100.84/26.82 U141(ok(z0)) -> ok(U141(z0)) 100.84/26.82 U151(mark(z0)) -> mark(U151(z0)) 100.84/26.82 U151(ok(z0)) -> ok(U151(z0)) 100.84/26.82 U161(mark(z0)) -> mark(U161(z0)) 100.84/26.82 U161(ok(z0)) -> ok(U161(z0)) 100.84/26.82 U171(mark(z0), z1) -> mark(U171(z0, z1)) 100.84/26.82 U171(ok(z0), ok(z1)) -> ok(U171(z0, z1)) 100.84/26.82 U172(mark(z0)) -> mark(U172(z0)) 100.84/26.82 U172(ok(z0)) -> ok(U172(z0)) 100.84/26.82 U181(mark(z0), z1) -> mark(U181(z0, z1)) 100.84/26.82 U181(ok(z0), ok(z1)) -> ok(U181(z0, z1)) 100.84/26.82 U182(mark(z0), z1) -> mark(U182(z0, z1)) 100.84/26.82 U182(ok(z0), ok(z1)) -> ok(U182(z0, z1)) 100.84/26.82 U183(mark(z0)) -> mark(U183(z0)) 100.84/26.82 U183(ok(z0)) -> ok(U183(z0)) 100.84/26.82 U191(mark(z0), z1) -> mark(U191(z0, z1)) 100.84/26.82 U191(ok(z0), ok(z1)) -> ok(U191(z0, z1)) 100.84/26.82 U192(mark(z0), z1) -> mark(U192(z0, z1)) 100.84/26.82 U192(ok(z0), ok(z1)) -> ok(U192(z0, z1)) 100.84/26.82 U193(mark(z0)) -> mark(U193(z0)) 100.84/26.82 U193(ok(z0)) -> ok(U193(z0)) 100.84/26.82 U201(mark(z0), z1, z2) -> mark(U201(z0, z1, z2)) 100.84/26.82 U201(ok(z0), ok(z1), ok(z2)) -> ok(U201(z0, z1, z2)) 100.84/26.82 U202(mark(z0), z1, z2) -> mark(U202(z0, z1, z2)) 100.84/26.82 U202(ok(z0), ok(z1), ok(z2)) -> ok(U202(z0, z1, z2)) 100.84/26.82 U203(mark(z0), z1, z2) -> mark(U203(z0, z1, z2)) 100.84/26.82 U203(ok(z0), ok(z1), ok(z2)) -> ok(U203(z0, z1, z2)) 100.84/26.82 U204(mark(z0), z1, z2) -> mark(U204(z0, z1, z2)) 100.84/26.82 U204(ok(z0), ok(z1), ok(z2)) -> ok(U204(z0, z1, z2)) 100.84/26.82 U205(mark(z0), z1) -> mark(U205(z0, z1)) 100.84/26.82 U205(ok(z0), ok(z1)) -> ok(U205(z0, z1)) 100.84/26.82 U206(mark(z0)) -> mark(U206(z0)) 100.84/26.82 U206(ok(z0)) -> ok(U206(z0)) 100.84/26.82 U21(mark(z0), z1, z2) -> mark(U21(z0, z1, z2)) 100.84/26.82 U21(ok(z0), ok(z1), ok(z2)) -> ok(U21(z0, z1, z2)) 100.84/26.82 U22(mark(z0), z1, z2) -> mark(U22(z0, z1, z2)) 100.84/26.82 U22(ok(z0), ok(z1), ok(z2)) -> ok(U22(z0, z1, z2)) 100.84/26.82 U211(mark(z0)) -> mark(U211(z0)) 100.84/26.82 U211(ok(z0)) -> ok(U211(z0)) 100.84/26.82 U23(mark(z0), z1, z2) -> mark(U23(z0, z1, z2)) 100.84/26.82 U23(ok(z0), ok(z1), ok(z2)) -> ok(U23(z0, z1, z2)) 100.84/26.82 U221(mark(z0)) -> mark(U221(z0)) 100.84/26.82 U221(ok(z0)) -> ok(U221(z0)) 100.84/26.82 U24(mark(z0), z1) -> mark(U24(z0, z1)) 100.84/26.82 U24(ok(z0), ok(z1)) -> ok(U24(z0, z1)) 100.84/26.82 U231(mark(z0), z1) -> mark(U231(z0, z1)) 100.84/26.82 U231(ok(z0), ok(z1)) -> ok(U231(z0, z1)) 100.84/26.82 U232(mark(z0)) -> mark(U232(z0)) 100.84/26.82 U232(ok(z0)) -> ok(U232(z0)) 100.84/26.82 U241(mark(z0), z1, z2) -> mark(U241(z0, z1, z2)) 100.84/26.82 U241(ok(z0), ok(z1), ok(z2)) -> ok(U241(z0, z1, z2)) 100.84/26.82 U242(mark(z0), z1, z2) -> mark(U242(z0, z1, z2)) 100.84/26.82 U242(ok(z0), ok(z1), ok(z2)) -> ok(U242(z0, z1, z2)) 100.84/26.82 U243(mark(z0), z1, z2) -> mark(U243(z0, z1, z2)) 100.84/26.82 U243(ok(z0), ok(z1), ok(z2)) -> ok(U243(z0, z1, z2)) 100.84/26.82 U244(mark(z0), z1, z2) -> mark(U244(z0, z1, z2)) 100.84/26.82 U244(ok(z0), ok(z1), ok(z2)) -> ok(U244(z0, z1, z2)) 100.84/26.82 U245(mark(z0), z1) -> mark(U245(z0, z1)) 100.84/26.82 U245(ok(z0), ok(z1)) -> ok(U245(z0, z1)) 100.84/26.82 U246(mark(z0)) -> mark(U246(z0)) 100.84/26.82 U246(ok(z0)) -> ok(U246(z0)) 100.84/26.82 U251(mark(z0), z1, z2) -> mark(U251(z0, z1, z2)) 100.84/26.82 U251(ok(z0), ok(z1), ok(z2)) -> ok(U251(z0, z1, z2)) 100.84/26.82 U252(mark(z0), z1, z2) -> mark(U252(z0, z1, z2)) 100.84/26.82 U252(ok(z0), ok(z1), ok(z2)) -> ok(U252(z0, z1, z2)) 100.84/26.82 U253(mark(z0), z1, z2) -> mark(U253(z0, z1, z2)) 100.84/26.82 U253(ok(z0), ok(z1), ok(z2)) -> ok(U253(z0, z1, z2)) 100.84/26.82 U254(mark(z0), z1, z2) -> mark(U254(z0, z1, z2)) 100.84/26.82 U254(ok(z0), ok(z1), ok(z2)) -> ok(U254(z0, z1, z2)) 100.84/26.82 U255(mark(z0), z1) -> mark(U255(z0, z1)) 100.84/26.82 U255(ok(z0), ok(z1)) -> ok(U255(z0, z1)) 100.84/26.82 U256(mark(z0)) -> mark(U256(z0)) 100.84/26.82 U256(ok(z0)) -> ok(U256(z0)) 100.84/26.82 U261(mark(z0), z1) -> mark(U261(z0, z1)) 100.84/26.82 U261(ok(z0), ok(z1)) -> ok(U261(z0, z1)) 100.84/26.82 U262(mark(z0)) -> mark(U262(z0)) 100.84/26.82 U262(ok(z0)) -> ok(U262(z0)) 100.84/26.82 U271(mark(z0), z1) -> mark(U271(z0, z1)) 100.84/26.82 U271(ok(z0), ok(z1)) -> ok(U271(z0, z1)) 100.84/26.82 U272(mark(z0)) -> mark(U272(z0)) 100.84/26.82 U272(ok(z0)) -> ok(U272(z0)) 100.84/26.82 U281(mark(z0), z1) -> mark(U281(z0, z1)) 100.84/26.82 U281(ok(z0), ok(z1)) -> ok(U281(z0, z1)) 100.84/26.82 U282(mark(z0), z1) -> mark(U282(z0, z1)) 100.84/26.82 U282(ok(z0), ok(z1)) -> ok(U282(z0, z1)) 100.84/26.82 cons(mark(z0), z1) -> mark(cons(z0, z1)) 100.84/26.82 cons(ok(z0), ok(z1)) -> ok(cons(z0, z1)) 100.84/26.82 natsFrom(mark(z0)) -> mark(natsFrom(z0)) 100.84/26.82 natsFrom(ok(z0)) -> ok(natsFrom(z0)) 100.84/26.82 s(mark(z0)) -> mark(s(z0)) 100.84/26.82 s(ok(z0)) -> ok(s(z0)) 100.84/26.82 U291(mark(z0), z1, z2) -> mark(U291(z0, z1, z2)) 100.84/26.82 U291(ok(z0), ok(z1), ok(z2)) -> ok(U291(z0, z1, z2)) 100.84/26.82 U292(mark(z0), z1, z2) -> mark(U292(z0, z1, z2)) 100.84/26.82 U292(ok(z0), ok(z1), ok(z2)) -> ok(U292(z0, z1, z2)) 100.84/26.82 U293(mark(z0), z1, z2) -> mark(U293(z0, z1, z2)) 100.84/26.82 U293(ok(z0), ok(z1), ok(z2)) -> ok(U293(z0, z1, z2)) 100.84/26.82 U294(mark(z0), z1, z2) -> mark(U294(z0, z1, z2)) 100.84/26.82 U294(ok(z0), ok(z1), ok(z2)) -> ok(U294(z0, z1, z2)) 100.84/26.82 head(mark(z0)) -> mark(head(z0)) 100.84/26.82 head(ok(z0)) -> ok(head(z0)) 100.84/26.82 afterNth(mark(z0), z1) -> mark(afterNth(z0, z1)) 100.84/26.82 afterNth(z0, mark(z1)) -> mark(afterNth(z0, z1)) 100.84/26.82 afterNth(ok(z0), ok(z1)) -> ok(afterNth(z0, z1)) 100.84/26.82 U301(mark(z0), z1, z2) -> mark(U301(z0, z1, z2)) 100.84/26.82 U301(ok(z0), ok(z1), ok(z2)) -> ok(U301(z0, z1, z2)) 100.84/26.82 U302(mark(z0), z1) -> mark(U302(z0, z1)) 100.84/26.82 U302(ok(z0), ok(z1)) -> ok(U302(z0, z1)) 100.84/26.82 U303(mark(z0), z1) -> mark(U303(z0, z1)) 100.84/26.82 U303(ok(z0), ok(z1)) -> ok(U303(z0, z1)) 100.84/26.82 U304(mark(z0), z1) -> mark(U304(z0, z1)) 100.84/26.82 U304(ok(z0), ok(z1)) -> ok(U304(z0, z1)) 100.84/26.82 U31(mark(z0), z1, z2) -> mark(U31(z0, z1, z2)) 100.84/26.82 U31(ok(z0), ok(z1), ok(z2)) -> ok(U31(z0, z1, z2)) 100.84/26.82 U32(mark(z0), z1, z2) -> mark(U32(z0, z1, z2)) 100.84/26.82 U32(ok(z0), ok(z1), ok(z2)) -> ok(U32(z0, z1, z2)) 100.84/26.82 U311(mark(z0), z1) -> mark(U311(z0, z1)) 100.84/26.82 U311(ok(z0), ok(z1)) -> ok(U311(z0, z1)) 100.84/26.82 U312(mark(z0), z1) -> mark(U312(z0, z1)) 100.84/26.82 U312(ok(z0), ok(z1)) -> ok(U312(z0, z1)) 100.84/26.82 pair(mark(z0), z1) -> mark(pair(z0, z1)) 100.84/26.82 pair(z0, mark(z1)) -> mark(pair(z0, z1)) 100.84/26.82 pair(ok(z0), ok(z1)) -> ok(pair(z0, z1)) 100.84/26.82 U33(mark(z0), z1, z2) -> mark(U33(z0, z1, z2)) 100.84/26.82 U33(ok(z0), ok(z1), ok(z2)) -> ok(U33(z0, z1, z2)) 100.84/26.82 U321(mark(z0), z1, z2, z3) -> mark(U321(z0, z1, z2, z3)) 100.84/26.82 U321(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U321(z0, z1, z2, z3)) 100.84/26.82 U322(mark(z0), z1, z2, z3) -> mark(U322(z0, z1, z2, z3)) 100.84/26.82 U322(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U322(z0, z1, z2, z3)) 100.84/26.82 U323(mark(z0), z1, z2, z3) -> mark(U323(z0, z1, z2, z3)) 100.84/26.82 U323(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U323(z0, z1, z2, z3)) 100.84/26.82 U324(mark(z0), z1, z2, z3) -> mark(U324(z0, z1, z2, z3)) 100.84/26.82 U324(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U324(z0, z1, z2, z3)) 100.84/26.82 U325(mark(z0), z1, z2, z3) -> mark(U325(z0, z1, z2, z3)) 100.84/26.82 U325(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U325(z0, z1, z2, z3)) 100.84/26.82 U326(mark(z0), z1, z2, z3) -> mark(U326(z0, z1, z2, z3)) 100.84/26.82 U326(ok(z0), ok(z1), ok(z2), ok(z3)) -> ok(U326(z0, z1, z2, z3)) 100.84/26.82 U327(mark(z0), z1) -> mark(U327(z0, z1)) 100.84/26.82 U327(ok(z0), ok(z1)) -> ok(U327(z0, z1)) 100.84/26.82 U34(mark(z0), z1) -> mark(U34(z0, z1)) 100.84/26.82 U34(ok(z0), ok(z1)) -> ok(U34(z0, z1)) 100.84/26.82 U331(mark(z0), z1, z2) -> mark(U331(z0, z1, z2)) 100.84/26.82 U331(ok(z0), ok(z1), ok(z2)) -> ok(U331(z0, z1, z2)) 100.84/26.82 U332(mark(z0), z1) -> mark(U332(z0, z1)) 100.84/26.82 U332(ok(z0), ok(z1)) -> ok(U332(z0, z1)) 100.84/26.82 U333(mark(z0), z1) -> mark(U333(z0, z1)) 100.84/26.82 U333(ok(z0), ok(z1)) -> ok(U333(z0, z1)) 100.84/26.82 U334(mark(z0), z1) -> mark(U334(z0, z1)) 100.84/26.82 U334(ok(z0), ok(z1)) -> ok(U334(z0, z1)) 100.84/26.82 U341(mark(z0), z1, z2) -> mark(U341(z0, z1, z2)) 100.84/26.82 U341(ok(z0), ok(z1), ok(z2)) -> ok(U341(z0, z1, z2)) 100.84/26.82 U342(mark(z0), z1, z2) -> mark(U342(z0, z1, z2)) 100.84/26.82 U342(ok(z0), ok(z1), ok(z2)) -> ok(U342(z0, z1, z2)) 100.84/26.82 U343(mark(z0), z1, z2) -> mark(U343(z0, z1, z2)) 100.84/26.82 U343(ok(z0), ok(z1), ok(z2)) -> ok(U343(z0, z1, z2)) 100.84/26.82 U344(mark(z0), z1, z2) -> mark(U344(z0, z1, z2)) 100.84/26.82 U344(ok(z0), ok(z1), ok(z2)) -> ok(U344(z0, z1, z2)) 100.84/26.82 fst(mark(z0)) -> mark(fst(z0)) 100.84/26.82 fst(ok(z0)) -> ok(fst(z0)) 100.84/26.82 U41(mark(z0), z1, z2) -> mark(U41(z0, z1, z2)) 100.84/26.82 U41(ok(z0), ok(z1), ok(z2)) -> ok(U41(z0, z1, z2)) 100.84/26.82 U42(mark(z0), z1, z2) -> mark(U42(z0, z1, z2)) 100.84/26.82 U42(ok(z0), ok(z1), ok(z2)) -> ok(U42(z0, z1, z2)) 100.84/26.82 U43(mark(z0), z1, z2) -> mark(U43(z0, z1, z2)) 100.84/26.82 U43(ok(z0), ok(z1), ok(z2)) -> ok(U43(z0, z1, z2)) 100.84/26.82 U44(mark(z0), z1, z2) -> mark(U44(z0, z1, z2)) 100.84/26.82 U44(ok(z0), ok(z1), ok(z2)) -> ok(U44(z0, z1, z2)) 100.84/26.82 U45(mark(z0), z1) -> mark(U45(z0, z1)) 100.84/26.82 U45(ok(z0), ok(z1)) -> ok(U45(z0, z1)) 100.84/26.82 U46(mark(z0)) -> mark(U46(z0)) 100.84/26.82 U46(ok(z0)) -> ok(U46(z0)) 100.84/26.82 U51(mark(z0), z1, z2) -> mark(U51(z0, z1, z2)) 100.84/26.82 U51(ok(z0), ok(z1), ok(z2)) -> ok(U51(z0, z1, z2)) 100.84/26.82 U52(mark(z0), z1, z2) -> mark(U52(z0, z1, z2)) 100.84/26.82 U52(ok(z0), ok(z1), ok(z2)) -> ok(U52(z0, z1, z2)) 100.84/26.82 U53(mark(z0), z1, z2) -> mark(U53(z0, z1, z2)) 100.84/26.82 U53(ok(z0), ok(z1), ok(z2)) -> ok(U53(z0, z1, z2)) 100.84/26.82 U54(mark(z0), z1, z2) -> mark(U54(z0, z1, z2)) 100.84/26.82 U54(ok(z0), ok(z1), ok(z2)) -> ok(U54(z0, z1, z2)) 100.84/26.82 U55(mark(z0), z1) -> mark(U55(z0, z1)) 100.84/26.82 U55(ok(z0), ok(z1)) -> ok(U55(z0, z1)) 100.84/26.82 U56(mark(z0)) -> mark(U56(z0)) 100.84/26.82 U56(ok(z0)) -> ok(U56(z0)) 100.84/26.82 U61(mark(z0), z1) -> mark(U61(z0, z1)) 100.84/26.82 U61(ok(z0), ok(z1)) -> ok(U61(z0, z1)) 100.84/26.82 U62(mark(z0), z1) -> mark(U62(z0, z1)) 100.84/26.82 U62(ok(z0), ok(z1)) -> ok(U62(z0, z1)) 100.84/26.82 U63(mark(z0)) -> mark(U63(z0)) 100.84/26.82 U63(ok(z0)) -> ok(U63(z0)) 100.84/26.82 U71(mark(z0), z1) -> mark(U71(z0, z1)) 100.84/26.82 U71(ok(z0), ok(z1)) -> ok(U71(z0, z1)) 100.84/26.82 U72(mark(z0), z1) -> mark(U72(z0, z1)) 100.84/26.82 U72(ok(z0), ok(z1)) -> ok(U72(z0, z1)) 100.84/26.82 U73(mark(z0)) -> mark(U73(z0)) 100.84/26.82 U73(ok(z0)) -> ok(U73(z0)) 100.84/26.82 U81(mark(z0), z1) -> mark(U81(z0, z1)) 100.84/26.82 U81(ok(z0), ok(z1)) -> ok(U81(z0, z1)) 100.84/26.82 U82(mark(z0), z1) -> mark(U82(z0, z1)) 100.84/26.82 U82(ok(z0), ok(z1)) -> ok(U82(z0, z1)) 100.84/26.82 U83(mark(z0)) -> mark(U83(z0)) 100.84/26.82 U83(ok(z0)) -> ok(U83(z0)) 100.84/26.82 U91(mark(z0), z1) -> mark(U91(z0, z1)) 100.84/26.82 U91(ok(z0), ok(z1)) -> ok(U91(z0, z1)) 100.84/26.82 U92(mark(z0), z1) -> mark(U92(z0, z1)) 100.84/26.82 U92(ok(z0), ok(z1)) -> ok(U92(z0, z1)) 100.84/26.82 U93(mark(z0)) -> mark(U93(z0)) 100.84/26.82 U93(ok(z0)) -> ok(U93(z0)) 100.84/26.82 tail(mark(z0)) -> mark(tail(z0)) 100.84/26.82 tail(ok(z0)) -> ok(tail(z0)) 100.84/26.82 take(mark(z0), z1) -> mark(take(z0, z1)) 100.84/26.82 take(z0, mark(z1)) -> mark(take(z0, z1)) 100.84/26.82 take(ok(z0), ok(z1)) -> ok(take(z0, z1)) 100.84/26.82 sel(mark(z0), z1) -> mark(sel(z0, z1)) 100.84/26.82 sel(z0, mark(z1)) -> mark(sel(z0, z1)) 100.84/26.82 sel(ok(z0), ok(z1)) -> ok(sel(z0, z1)) 100.84/26.82 isNaturalKind(ok(z0)) -> ok(isNaturalKind(z0)) 100.84/26.82 isLNatKind(ok(z0)) -> ok(isLNatKind(z0)) 100.84/26.82 isNatural(ok(z0)) -> ok(isNatural(z0)) 100.84/26.82 isLNat(ok(z0)) -> ok(isLNat(z0)) 100.84/26.82 isPLNatKind(ok(z0)) -> ok(isPLNatKind(z0)) 100.84/26.82 isPLNat(ok(z0)) -> ok(isPLNat(z0)) 100.84/26.82 top(mark(z0)) -> top(proper(z0)) 100.84/26.82 top(ok(z0)) -> top(active(z0)) 100.84/26.82 100.84/26.82 ---------------------------------------- 100.84/26.82 100.84/26.82 (12) 100.84/26.82 Obligation: 100.84/26.82 Complexity Dependency Tuples Problem 100.84/26.82 100.84/26.82 Rules: 100.84/26.82 proper(tt) -> ok(tt) 100.84/26.82 proper(nil) -> ok(nil) 100.84/26.82 proper(0) -> ok(0) 100.84/26.82 Tuples: 100.84/26.82 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.82 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.82 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.82 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.82 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.82 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.82 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.82 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.82 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.82 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.82 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.82 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.82 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.82 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.82 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.82 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.82 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.82 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.82 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.82 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.82 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.82 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.82 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.82 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.82 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.82 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.82 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.82 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.82 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.82 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.82 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.82 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.82 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.82 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.82 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.82 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.82 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.82 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.82 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.82 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.82 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.82 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.82 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.82 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.82 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.82 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.82 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.82 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.82 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.82 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.82 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.82 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.82 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.82 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.82 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.82 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.82 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.82 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.82 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.82 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.82 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.82 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.82 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.82 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.82 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.82 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.82 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.82 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.82 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.82 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.82 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.82 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.82 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.82 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.82 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.82 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.82 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.82 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.82 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.82 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.82 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.82 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.82 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.82 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.82 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.82 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.82 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.82 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.82 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.82 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.82 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.82 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.82 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.82 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.82 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.82 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.82 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.82 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.82 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.82 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.82 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.82 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.82 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.82 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.82 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.82 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.82 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.82 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.82 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.82 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.82 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.82 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.82 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.82 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.82 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.82 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.82 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.82 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.82 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.82 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.82 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.82 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.82 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.82 S(mark(z0)) -> c125(S(z0)) 100.84/26.82 S(ok(z0)) -> c126(S(z0)) 100.84/26.82 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.82 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.82 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.82 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.82 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.82 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.82 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.82 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.82 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.82 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.82 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.82 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.82 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.82 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.82 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.82 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.82 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.82 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.82 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.82 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.82 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.82 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.82 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.82 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.82 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.82 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.82 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.82 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.82 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.82 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.82 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.82 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.82 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.82 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.82 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.82 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.82 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.82 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.82 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.82 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.82 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.82 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.82 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.82 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.82 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.82 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.82 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.82 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.82 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.82 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.82 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.82 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.82 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.82 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.82 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.82 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.82 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.82 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.82 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.82 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.82 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.82 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.82 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.82 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.82 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.82 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.82 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.82 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.82 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.82 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.82 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.82 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.82 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.82 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.82 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.82 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.82 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.82 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.82 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.82 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.82 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.82 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.82 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.82 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.82 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.82 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.82 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.82 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.82 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.82 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.82 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.82 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.82 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.82 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.82 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.82 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.82 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.82 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.82 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.82 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.82 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.82 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.82 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.82 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.82 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.82 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.82 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.82 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.82 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.82 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.82 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.82 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.82 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.82 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.82 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.82 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.82 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.82 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.82 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.82 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.82 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.82 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.82 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.82 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.82 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.82 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.82 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.82 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.82 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.82 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.82 S tuples: 100.84/26.82 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.82 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.82 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.82 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.82 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.82 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.82 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.82 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.82 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.82 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.82 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.82 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.82 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.82 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.82 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.82 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.82 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.82 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.82 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.82 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.82 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.82 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.82 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.82 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.82 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.82 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.82 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.82 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.82 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.82 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.82 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.82 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.82 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.82 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.82 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.82 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.82 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.82 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.82 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.82 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.82 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.82 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.82 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.82 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.82 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.82 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.82 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.82 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.82 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.82 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.82 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.82 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.82 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.82 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.82 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.82 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.82 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.82 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.82 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.82 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.82 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.82 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.82 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.82 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.82 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.82 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.82 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.82 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.82 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.82 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.82 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.82 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.82 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.82 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.82 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.82 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.82 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.82 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.82 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.82 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.82 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.82 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.82 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.82 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.82 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.82 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.82 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.82 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.82 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.82 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.82 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.82 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.82 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.82 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.82 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.82 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.82 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.82 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.82 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.82 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.82 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.82 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.82 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.82 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.82 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.82 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.82 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.82 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.82 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.82 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.82 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.82 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.82 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.82 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.82 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.82 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.82 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.82 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.82 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.82 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.82 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.86 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.86 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.86 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.86 S(mark(z0)) -> c125(S(z0)) 100.84/26.86 S(ok(z0)) -> c126(S(z0)) 100.84/26.86 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.86 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.86 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.86 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.86 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.86 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.86 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.86 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.86 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.86 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.86 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.86 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.86 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.86 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.86 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.86 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.86 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.86 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.86 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.86 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.86 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.86 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.86 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.86 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.86 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.86 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.86 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.86 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.86 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.86 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.86 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.86 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.86 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.86 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.86 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.86 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.86 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.86 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.86 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.86 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.86 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.86 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.86 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.86 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.86 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.86 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.86 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.86 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.86 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.86 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.86 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.86 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.86 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.86 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.86 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.86 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.86 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.86 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.86 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.86 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.86 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.86 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.86 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.86 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.86 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.86 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.86 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.86 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.86 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.86 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.86 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.86 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.86 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.86 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.86 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.86 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.86 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.86 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.86 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.86 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.86 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.86 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.86 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.86 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.86 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.86 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.86 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.86 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.86 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.86 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.86 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.86 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.86 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.86 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.86 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.86 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.86 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.86 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.86 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.86 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.86 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.86 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.86 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.86 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.86 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.86 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.86 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.86 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.86 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.86 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.86 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.86 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.86 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.86 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.86 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.86 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.86 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.86 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.86 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.86 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.86 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.86 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.86 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.86 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.86 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.86 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.86 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.86 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.86 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.86 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.86 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.86 K tuples:none 100.84/26.86 Defined Rule Symbols: proper_1 100.84/26.86 100.84/26.86 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.84/26.86 100.84/26.86 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_1 100.84/26.86 100.84/26.86 100.84/26.86 ---------------------------------------- 100.84/26.86 100.84/26.86 (13) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 100.84/26.86 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 100.84/26.86 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.86 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.86 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.86 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.86 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.86 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.86 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.86 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.86 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.86 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.86 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.86 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.86 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.86 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.86 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.86 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.86 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.86 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.86 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.86 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.86 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.86 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.86 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.86 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.86 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.86 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.86 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.86 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.86 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.86 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.86 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.86 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.86 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.86 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.86 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.86 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.86 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.86 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.86 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.86 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.86 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.86 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.86 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.86 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.86 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.86 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.86 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.86 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.86 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.86 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.86 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.86 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.86 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.86 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.86 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.86 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.86 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.86 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.86 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.86 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.86 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.86 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.86 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.86 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.86 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.86 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.86 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.86 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.86 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.86 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.86 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.86 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.86 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.86 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.86 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.86 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.86 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.86 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.86 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.86 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.86 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.86 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.86 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.86 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.86 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.86 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.86 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.86 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.86 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.86 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.86 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.86 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.86 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.86 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.86 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.86 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.86 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.86 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.86 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.86 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.86 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.86 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.86 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.86 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.86 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.86 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.86 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.86 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.86 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.86 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.86 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.86 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.86 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.86 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.86 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.86 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.86 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.86 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.86 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.86 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.86 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.86 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.86 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.86 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.86 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.86 S(mark(z0)) -> c125(S(z0)) 100.84/26.86 S(ok(z0)) -> c126(S(z0)) 100.84/26.86 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.86 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.86 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.86 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.86 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.86 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.86 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.86 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.86 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.86 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.86 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.86 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.86 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.86 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.86 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.86 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.86 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.86 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.86 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.86 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.86 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.86 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.86 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.86 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.86 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.86 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.86 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.86 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.86 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.87 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.87 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.87 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.87 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.87 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.87 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.87 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.87 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.87 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.87 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.87 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.87 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.87 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.87 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.87 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.87 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.87 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.87 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.87 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.87 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.87 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.87 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.87 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.87 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.87 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.87 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.87 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.87 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.87 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.87 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.87 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.87 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.87 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.87 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.87 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.87 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.87 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.87 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.87 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.87 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.87 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.87 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.87 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.87 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.87 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.87 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.87 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.87 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.87 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.87 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.87 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.87 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.87 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.87 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.87 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.87 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.87 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.87 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.87 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.87 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.87 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.87 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.87 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.87 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.87 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.87 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.87 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.87 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.87 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.87 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.87 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.87 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.87 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.87 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.87 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.87 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.87 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.87 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.87 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.87 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.87 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.87 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.87 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.87 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.87 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.87 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.87 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.87 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.87 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.87 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.87 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.87 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.87 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.87 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.87 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.87 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.87 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.87 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.87 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.87 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.87 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.87 We considered the (Usable) Rules: 100.84/26.87 proper(tt) -> ok(tt) 100.84/26.87 proper(nil) -> ok(nil) 100.84/26.87 proper(0) -> ok(0) 100.84/26.87 And the Tuples: 100.84/26.87 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.87 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.87 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.87 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.87 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.87 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.87 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.87 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.87 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.87 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.87 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.87 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.87 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.87 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.87 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.87 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.87 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.87 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.87 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.87 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.87 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.87 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.87 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.87 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.87 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.87 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.87 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.87 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.87 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.87 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.87 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.87 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.87 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.87 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.87 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.87 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.87 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.87 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.87 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.87 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.87 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.87 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.87 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.87 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.87 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.87 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.87 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.87 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.87 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.87 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.87 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.87 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.87 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.87 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.87 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.87 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.87 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.87 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.87 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.87 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.87 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.87 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.87 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.87 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.87 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.87 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.87 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.87 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.87 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.87 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.87 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.87 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.87 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.87 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.87 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.87 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.87 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.87 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.87 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.87 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.87 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.87 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.87 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.87 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.87 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.87 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.87 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.87 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.87 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.87 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.87 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.87 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.87 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.87 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.87 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.87 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.87 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.87 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.87 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.87 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.87 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.87 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.87 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.87 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.87 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.87 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.87 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.87 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.87 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.87 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.87 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.87 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.87 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.87 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.87 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.87 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.87 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.87 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.87 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.87 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.87 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.87 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.87 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.87 S(mark(z0)) -> c125(S(z0)) 100.84/26.87 S(ok(z0)) -> c126(S(z0)) 100.84/26.87 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.87 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.87 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.87 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.87 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.87 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.87 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.87 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.87 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.87 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.87 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.87 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.87 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.87 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.87 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.87 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.87 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.87 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.87 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.87 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.87 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.87 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.87 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.87 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.87 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.87 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.87 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.87 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.87 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.87 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.87 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.87 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.87 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.87 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.87 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.87 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.87 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.87 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.87 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.87 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.87 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.87 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.87 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.87 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.87 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.87 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.87 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.87 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.87 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.87 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.87 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.87 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.87 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.87 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.87 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.87 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.87 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.87 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.87 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.87 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.87 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.87 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.87 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.87 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.87 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.87 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.87 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.87 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.87 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.87 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.87 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.87 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.87 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.87 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.87 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.87 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.87 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.87 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.87 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.87 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.87 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.87 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.87 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.87 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.87 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.87 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.87 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.87 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.87 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.87 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.87 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.87 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.87 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.87 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.87 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.87 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.87 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.87 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.87 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.87 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.87 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.87 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.87 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.87 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.87 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.87 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.87 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.87 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.87 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.87 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.87 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.87 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.87 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.87 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.87 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.87 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.87 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.87 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.87 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.87 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.87 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.87 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.87 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.87 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.87 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.87 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.87 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.87 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.87 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.87 The order we found is given by the following interpretation: 100.84/26.87 100.84/26.87 Polynomial interpretation : 100.84/26.87 100.84/26.87 POL(0) = [1] 100.84/26.87 POL(AFTERNTH(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(CONS(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(FST(x_1)) = x_1 100.84/26.87 POL(HEAD(x_1)) = x_1 100.84/26.87 POL(ISLNAT(x_1)) = x_1 100.84/26.87 POL(ISLNATKIND(x_1)) = x_1 100.84/26.87 POL(ISNATURAL(x_1)) = x_1 100.84/26.87 POL(ISNATURALKIND(x_1)) = x_1 100.84/26.87 POL(ISPLNAT(x_1)) = x_1 100.84/26.87 POL(ISPLNATKIND(x_1)) = x_1 100.84/26.87 POL(NATSFROM(x_1)) = x_1 100.84/26.87 POL(PAIR(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(S(x_1)) = x_1 100.84/26.87 POL(SEL(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(SND(x_1)) = x_1 100.84/26.87 POL(SPLITAT(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(TAIL(x_1)) = x_1 100.84/26.87 POL(TAKE(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(TOP(x_1)) = x_1 100.84/26.87 POL(U101'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U102'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U103'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U104'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U105'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U106'(x_1)) = x_1 100.84/26.87 POL(U11'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U111'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U112'(x_1)) = x_1 100.84/26.87 POL(U12'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U121'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U122'(x_1)) = x_1 100.84/26.87 POL(U13'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U131'(x_1)) = x_1 100.84/26.87 POL(U14'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U141'(x_1)) = x_1 100.84/26.87 POL(U151'(x_1)) = x_1 100.84/26.87 POL(U161'(x_1)) = x_1 100.84/26.87 POL(U171'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U172'(x_1)) = x_1 100.84/26.87 POL(U181'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U182'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U183'(x_1)) = x_1 100.84/26.87 POL(U191'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U192'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U193'(x_1)) = x_1 100.84/26.87 POL(U201'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U202'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U203'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U204'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U205'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U206'(x_1)) = x_1 100.84/26.87 POL(U21'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U211'(x_1)) = x_1 100.84/26.87 POL(U22'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U221'(x_1)) = x_1 100.84/26.87 POL(U23'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U231'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U232'(x_1)) = x_1 100.84/26.87 POL(U24'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U241'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U242'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U243'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U244'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U245'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U246'(x_1)) = x_1 100.84/26.87 POL(U251'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U252'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U253'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U254'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U255'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U256'(x_1)) = x_1 100.84/26.87 POL(U261'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U262'(x_1)) = x_1 100.84/26.87 POL(U271'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U272'(x_1)) = x_1 100.84/26.87 POL(U281'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U282'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U291'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U292'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U293'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U294'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U301'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U302'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U303'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U304'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U31'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U311'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U312'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U32'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U321'(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 100.84/26.87 POL(U322'(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 100.84/26.87 POL(U323'(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 100.84/26.87 POL(U324'(x_1, x_2, x_3, x_4)) = x_1 + x_3 + x_4 100.84/26.87 POL(U325'(x_1, x_2, x_3, x_4)) = x_1 + x_3 + x_4 100.84/26.87 POL(U326'(x_1, x_2, x_3, x_4)) = x_1 + x_3 + x_4 100.84/26.87 POL(U327'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U33'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U331'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U332'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U333'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U334'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U34'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U341'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U342'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U343'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U344'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U41'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U42'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U43'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U44'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U45'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U46'(x_1)) = x_1 100.84/26.87 POL(U51'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U52'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U53'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U54'(x_1, x_2, x_3)) = x_1 + x_2 + x_3 100.84/26.87 POL(U55'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U56'(x_1)) = x_1 100.84/26.87 POL(U61'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U62'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U63'(x_1)) = x_1 100.84/26.87 POL(U71'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U72'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U73'(x_1)) = x_1 100.84/26.87 POL(U81'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U82'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U83'(x_1)) = x_1 100.84/26.87 POL(U91'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U92'(x_1, x_2)) = x_1 + x_2 100.84/26.87 POL(U93'(x_1)) = x_1 100.84/26.87 POL(c(x_1)) = x_1 100.84/26.87 POL(c1(x_1)) = x_1 100.84/26.87 POL(c10(x_1)) = x_1 100.84/26.87 POL(c100(x_1)) = x_1 100.84/26.87 POL(c101(x_1)) = x_1 100.84/26.87 POL(c102(x_1)) = x_1 100.84/26.87 POL(c103(x_1)) = x_1 100.84/26.87 POL(c104(x_1)) = x_1 100.84/26.87 POL(c105(x_1)) = x_1 100.84/26.87 POL(c106(x_1)) = x_1 100.84/26.87 POL(c107(x_1)) = x_1 100.84/26.87 POL(c108(x_1)) = x_1 100.84/26.87 POL(c109(x_1)) = x_1 100.84/26.87 POL(c11(x_1)) = x_1 100.84/26.87 POL(c110(x_1)) = x_1 100.84/26.87 POL(c111(x_1)) = x_1 100.84/26.87 POL(c112(x_1)) = x_1 100.84/26.87 POL(c113(x_1)) = x_1 100.84/26.87 POL(c114(x_1)) = x_1 100.84/26.87 POL(c115(x_1)) = x_1 100.84/26.87 POL(c116(x_1)) = x_1 100.84/26.87 POL(c117(x_1)) = x_1 100.84/26.87 POL(c118(x_1)) = x_1 100.84/26.87 POL(c119(x_1)) = x_1 100.84/26.87 POL(c12(x_1)) = x_1 100.84/26.87 POL(c120(x_1)) = x_1 100.84/26.87 POL(c121(x_1)) = x_1 100.84/26.87 POL(c122(x_1)) = x_1 100.84/26.87 POL(c123(x_1)) = x_1 100.84/26.87 POL(c124(x_1)) = x_1 100.84/26.87 POL(c125(x_1)) = x_1 100.84/26.87 POL(c126(x_1)) = x_1 100.84/26.87 POL(c127(x_1)) = x_1 100.84/26.87 POL(c128(x_1)) = x_1 100.84/26.87 POL(c129(x_1)) = x_1 100.84/26.87 POL(c13(x_1)) = x_1 100.84/26.87 POL(c130(x_1)) = x_1 100.84/26.87 POL(c131(x_1)) = x_1 100.84/26.87 POL(c132(x_1)) = x_1 100.84/26.87 POL(c133(x_1)) = x_1 100.84/26.87 POL(c134(x_1)) = x_1 100.84/26.87 POL(c135(x_1)) = x_1 100.84/26.87 POL(c136(x_1)) = x_1 100.84/26.87 POL(c137(x_1)) = x_1 100.84/26.87 POL(c138(x_1)) = x_1 100.84/26.87 POL(c139(x_1)) = x_1 100.84/26.87 POL(c14(x_1)) = x_1 100.84/26.87 POL(c140(x_1)) = x_1 100.84/26.87 POL(c141(x_1)) = x_1 100.84/26.87 POL(c142(x_1)) = x_1 100.84/26.87 POL(c143(x_1)) = x_1 100.84/26.87 POL(c144(x_1)) = x_1 100.84/26.87 POL(c145(x_1)) = x_1 100.84/26.87 POL(c146(x_1)) = x_1 100.84/26.87 POL(c147(x_1)) = x_1 100.84/26.87 POL(c148(x_1)) = x_1 100.84/26.87 POL(c149(x_1)) = x_1 100.84/26.87 POL(c15(x_1)) = x_1 100.84/26.87 POL(c150(x_1)) = x_1 100.84/26.87 POL(c151(x_1)) = x_1 100.84/26.87 POL(c152(x_1)) = x_1 100.84/26.87 POL(c153(x_1)) = x_1 100.84/26.87 POL(c154(x_1)) = x_1 100.84/26.87 POL(c155(x_1)) = x_1 100.84/26.87 POL(c156(x_1)) = x_1 100.84/26.87 POL(c157(x_1)) = x_1 100.84/26.87 POL(c158(x_1)) = x_1 100.84/26.87 POL(c159(x_1)) = x_1 100.84/26.87 POL(c16(x_1)) = x_1 100.84/26.87 POL(c160(x_1)) = x_1 100.84/26.87 POL(c161(x_1)) = x_1 100.84/26.87 POL(c162(x_1)) = x_1 100.84/26.87 POL(c163(x_1)) = x_1 100.84/26.87 POL(c164(x_1)) = x_1 100.84/26.87 POL(c165(x_1)) = x_1 100.84/26.87 POL(c166(x_1)) = x_1 100.84/26.87 POL(c167(x_1)) = x_1 100.84/26.87 POL(c168(x_1)) = x_1 100.84/26.87 POL(c169(x_1)) = x_1 100.84/26.87 POL(c17(x_1)) = x_1 100.84/26.87 POL(c170(x_1)) = x_1 100.84/26.87 POL(c171(x_1)) = x_1 100.84/26.87 POL(c172(x_1)) = x_1 100.84/26.87 POL(c173(x_1)) = x_1 100.84/26.87 POL(c174(x_1)) = x_1 100.84/26.87 POL(c175(x_1)) = x_1 100.84/26.87 POL(c176(x_1)) = x_1 100.84/26.87 POL(c177(x_1)) = x_1 100.84/26.87 POL(c178(x_1)) = x_1 100.84/26.87 POL(c179(x_1)) = x_1 100.84/26.87 POL(c18(x_1)) = x_1 100.84/26.87 POL(c180(x_1)) = x_1 100.84/26.87 POL(c181(x_1)) = x_1 100.84/26.87 POL(c182(x_1)) = x_1 100.84/26.87 POL(c183(x_1)) = x_1 100.84/26.87 POL(c184(x_1)) = x_1 100.84/26.87 POL(c185(x_1)) = x_1 100.84/26.87 POL(c186(x_1)) = x_1 100.84/26.87 POL(c187(x_1)) = x_1 100.84/26.87 POL(c188(x_1)) = x_1 100.84/26.87 POL(c189(x_1)) = x_1 100.84/26.87 POL(c19(x_1)) = x_1 100.84/26.87 POL(c190(x_1)) = x_1 100.84/26.87 POL(c191(x_1)) = x_1 100.84/26.87 POL(c192(x_1)) = x_1 100.84/26.87 POL(c193(x_1)) = x_1 100.84/26.87 POL(c194(x_1)) = x_1 100.84/26.87 POL(c195(x_1)) = x_1 100.84/26.87 POL(c196(x_1)) = x_1 100.84/26.87 POL(c197(x_1)) = x_1 100.84/26.87 POL(c198(x_1)) = x_1 100.84/26.87 POL(c199(x_1)) = x_1 100.84/26.87 POL(c2(x_1)) = x_1 100.84/26.87 POL(c20(x_1)) = x_1 100.84/26.87 POL(c200(x_1)) = x_1 100.84/26.87 POL(c201(x_1)) = x_1 100.84/26.87 POL(c202(x_1)) = x_1 100.84/26.87 POL(c203(x_1)) = x_1 100.84/26.87 POL(c204(x_1)) = x_1 100.84/26.87 POL(c205(x_1)) = x_1 100.84/26.87 POL(c206(x_1)) = x_1 100.84/26.87 POL(c207(x_1)) = x_1 100.84/26.87 POL(c208(x_1)) = x_1 100.84/26.87 POL(c209(x_1)) = x_1 100.84/26.87 POL(c21(x_1)) = x_1 100.84/26.87 POL(c210(x_1)) = x_1 100.84/26.87 POL(c211(x_1)) = x_1 100.84/26.87 POL(c212(x_1)) = x_1 100.84/26.87 POL(c213(x_1)) = x_1 100.84/26.87 POL(c214(x_1)) = x_1 100.84/26.87 POL(c215(x_1)) = x_1 100.84/26.87 POL(c216(x_1)) = x_1 100.84/26.87 POL(c217(x_1)) = x_1 100.84/26.87 POL(c218(x_1)) = x_1 100.84/26.87 POL(c219(x_1)) = x_1 100.84/26.87 POL(c22(x_1)) = x_1 100.84/26.87 POL(c220(x_1)) = x_1 100.84/26.87 POL(c221(x_1)) = x_1 100.84/26.87 POL(c222(x_1)) = x_1 100.84/26.87 POL(c223(x_1)) = x_1 100.84/26.87 POL(c224(x_1)) = x_1 100.84/26.87 POL(c225(x_1)) = x_1 100.84/26.87 POL(c226(x_1)) = x_1 100.84/26.87 POL(c227(x_1)) = x_1 100.84/26.87 POL(c228(x_1)) = x_1 100.84/26.87 POL(c229(x_1)) = x_1 100.84/26.87 POL(c23(x_1)) = x_1 100.84/26.87 POL(c230(x_1)) = x_1 100.84/26.87 POL(c231(x_1)) = x_1 100.84/26.87 POL(c232(x_1)) = x_1 100.84/26.87 POL(c233(x_1)) = x_1 100.84/26.87 POL(c234(x_1)) = x_1 100.84/26.87 POL(c235(x_1)) = x_1 100.84/26.87 POL(c236(x_1)) = x_1 100.84/26.87 POL(c237(x_1)) = x_1 100.84/26.87 POL(c238(x_1)) = x_1 100.84/26.87 POL(c239(x_1)) = x_1 100.84/26.87 POL(c24(x_1)) = x_1 100.84/26.87 POL(c240(x_1)) = x_1 100.84/26.87 POL(c241(x_1)) = x_1 100.84/26.87 POL(c242(x_1)) = x_1 100.84/26.87 POL(c243(x_1)) = x_1 100.84/26.87 POL(c244(x_1)) = x_1 100.84/26.87 POL(c245(x_1)) = x_1 100.84/26.87 POL(c246(x_1)) = x_1 100.84/26.87 POL(c247(x_1)) = x_1 100.84/26.87 POL(c248(x_1)) = x_1 100.84/26.87 POL(c249(x_1)) = x_1 100.84/26.87 POL(c25(x_1)) = x_1 100.84/26.87 POL(c250(x_1)) = x_1 100.84/26.87 POL(c254(x_1)) = x_1 100.84/26.87 POL(c255(x_1)) = x_1 100.84/26.87 POL(c256(x_1)) = x_1 100.84/26.87 POL(c257(x_1)) = x_1 100.84/26.87 POL(c258(x_1)) = x_1 100.84/26.87 POL(c259(x_1)) = x_1 100.84/26.87 POL(c26(x_1)) = x_1 100.84/26.87 POL(c260(x_1)) = x_1 100.84/26.87 POL(c27(x_1)) = x_1 100.84/26.87 POL(c28(x_1)) = x_1 100.84/26.87 POL(c29(x_1)) = x_1 100.84/26.87 POL(c3(x_1)) = x_1 100.84/26.87 POL(c30(x_1)) = x_1 100.84/26.87 POL(c31(x_1)) = x_1 100.84/26.87 POL(c32(x_1)) = x_1 100.84/26.87 POL(c33(x_1)) = x_1 100.84/26.87 POL(c34(x_1)) = x_1 100.84/26.87 POL(c35(x_1)) = x_1 100.84/26.87 POL(c36(x_1)) = x_1 100.84/26.87 POL(c37(x_1)) = x_1 100.84/26.87 POL(c38(x_1)) = x_1 100.84/26.87 POL(c39(x_1)) = x_1 100.84/26.87 POL(c4(x_1)) = x_1 100.84/26.87 POL(c40(x_1)) = x_1 100.84/26.87 POL(c41(x_1)) = x_1 100.84/26.87 POL(c42(x_1)) = x_1 100.84/26.87 POL(c43(x_1)) = x_1 100.84/26.87 POL(c44(x_1)) = x_1 100.84/26.87 POL(c45(x_1)) = x_1 100.84/26.87 POL(c46(x_1)) = x_1 100.84/26.87 POL(c47(x_1)) = x_1 100.84/26.87 POL(c48(x_1)) = x_1 100.84/26.87 POL(c49(x_1)) = x_1 100.84/26.87 POL(c5(x_1)) = x_1 100.84/26.87 POL(c50(x_1)) = x_1 100.84/26.87 POL(c51(x_1)) = x_1 100.84/26.87 POL(c52(x_1)) = x_1 100.84/26.87 POL(c53(x_1)) = x_1 100.84/26.87 POL(c54(x_1)) = x_1 100.84/26.87 POL(c55(x_1)) = x_1 100.84/26.87 POL(c56(x_1)) = x_1 100.84/26.87 POL(c57(x_1)) = x_1 100.84/26.87 POL(c58(x_1)) = x_1 100.84/26.87 POL(c59(x_1)) = x_1 100.84/26.87 POL(c6(x_1)) = x_1 100.84/26.87 POL(c60(x_1)) = x_1 100.84/26.87 POL(c61(x_1)) = x_1 100.84/26.87 POL(c62(x_1)) = x_1 100.84/26.87 POL(c63(x_1)) = x_1 100.84/26.87 POL(c64(x_1)) = x_1 100.84/26.87 POL(c65(x_1)) = x_1 100.84/26.87 POL(c66(x_1)) = x_1 100.84/26.87 POL(c67(x_1)) = x_1 100.84/26.87 POL(c68(x_1)) = x_1 100.84/26.87 POL(c69(x_1)) = x_1 100.84/26.87 POL(c7(x_1)) = x_1 100.84/26.87 POL(c70(x_1)) = x_1 100.84/26.87 POL(c71(x_1)) = x_1 100.84/26.87 POL(c72(x_1)) = x_1 100.84/26.87 POL(c73(x_1)) = x_1 100.84/26.87 POL(c74(x_1)) = x_1 100.84/26.87 POL(c75(x_1)) = x_1 100.84/26.87 POL(c76(x_1)) = x_1 100.84/26.87 POL(c77(x_1)) = x_1 100.84/26.87 POL(c78(x_1)) = x_1 100.84/26.87 POL(c79(x_1)) = x_1 100.84/26.87 POL(c8(x_1)) = x_1 100.84/26.87 POL(c80(x_1)) = x_1 100.84/26.87 POL(c81(x_1)) = x_1 100.84/26.87 POL(c82(x_1)) = x_1 100.84/26.87 POL(c83(x_1)) = x_1 100.84/26.87 POL(c84(x_1)) = x_1 100.84/26.87 POL(c85(x_1)) = x_1 100.84/26.87 POL(c86(x_1)) = x_1 100.84/26.87 POL(c87(x_1)) = x_1 100.84/26.87 POL(c88(x_1)) = x_1 100.84/26.87 POL(c89(x_1)) = x_1 100.84/26.87 POL(c9(x_1)) = x_1 100.84/26.87 POL(c90(x_1)) = x_1 100.84/26.87 POL(c91(x_1)) = x_1 100.84/26.87 POL(c92(x_1)) = x_1 100.84/26.87 POL(c93(x_1)) = x_1 100.84/26.87 POL(c94(x_1)) = x_1 100.84/26.87 POL(c95(x_1)) = x_1 100.84/26.87 POL(c96(x_1)) = x_1 100.84/26.87 POL(c97(x_1)) = x_1 100.84/26.87 POL(c98(x_1)) = x_1 100.84/26.87 POL(c99(x_1)) = x_1 100.84/26.87 POL(mark(x_1)) = [1] + x_1 100.84/26.87 POL(nil) = [1] 100.84/26.87 POL(ok(x_1)) = [1] + x_1 100.84/26.87 POL(proper(x_1)) = [1] + x_1 100.84/26.87 POL(tt) = [1] 100.84/26.87 100.84/26.87 ---------------------------------------- 100.84/26.87 100.84/26.87 (14) 100.84/26.87 Obligation: 100.84/26.87 Complexity Dependency Tuples Problem 100.84/26.87 100.84/26.87 Rules: 100.84/26.87 proper(tt) -> ok(tt) 100.84/26.87 proper(nil) -> ok(nil) 100.84/26.87 proper(0) -> ok(0) 100.84/26.87 Tuples: 100.84/26.87 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.87 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.87 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.87 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.87 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.87 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.87 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.87 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.87 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.87 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.87 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.87 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.87 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.87 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.87 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.87 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.87 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.87 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.87 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.87 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.87 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.87 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.87 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.87 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.87 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.87 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.87 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.87 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.87 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.87 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.87 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.87 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.87 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.87 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.87 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.87 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.87 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.87 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.87 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.87 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.87 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.87 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.87 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.87 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.87 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.87 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.87 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.87 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.87 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.87 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.87 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.87 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.87 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.87 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.87 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.87 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.87 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.87 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.87 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.87 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.87 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.87 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.87 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.87 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.87 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.87 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.87 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.87 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.87 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.87 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.87 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.87 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.87 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.87 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.87 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.87 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.87 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.87 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.87 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.87 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.87 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.87 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.87 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.87 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.87 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.87 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.87 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.87 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.87 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.87 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.87 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.87 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.87 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.87 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.87 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.87 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.87 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.87 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.87 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.87 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.87 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.87 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.87 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.87 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.87 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.87 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.87 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.87 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.87 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.87 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.87 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.87 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.87 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.87 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.87 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.87 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.87 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.87 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.87 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.87 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.87 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.87 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.87 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.87 S(mark(z0)) -> c125(S(z0)) 100.84/26.87 S(ok(z0)) -> c126(S(z0)) 100.84/26.87 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.87 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.87 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.87 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.87 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.87 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.87 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.87 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.87 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.87 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.87 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.87 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.87 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.87 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.87 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.87 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.87 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.87 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.87 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.87 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.87 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.87 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.87 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.87 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.87 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.87 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.87 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.87 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.87 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.87 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.87 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.87 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.87 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.87 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.87 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.87 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.87 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.87 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.87 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.87 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.87 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.87 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.87 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.87 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.87 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.87 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.87 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.87 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.87 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.87 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.87 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.87 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.87 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.87 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.87 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.87 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.87 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.87 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.87 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.87 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.87 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.87 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.87 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.87 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.87 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.87 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.87 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.87 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.87 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.87 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.87 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.87 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.87 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.87 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.87 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.87 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.87 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.87 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.87 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.87 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.87 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.87 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.87 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.87 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.87 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.87 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.87 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.87 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.87 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.87 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.87 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.87 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.87 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.87 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.87 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.87 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.87 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.87 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.87 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.87 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.87 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.87 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.87 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.87 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.87 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.87 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.87 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.87 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.87 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.87 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.87 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.87 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.87 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.87 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.87 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.87 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.87 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.87 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.87 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.87 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.87 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.87 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.87 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.87 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.87 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.87 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.87 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.87 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.87 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.87 S tuples: 100.84/26.87 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.87 K tuples: 100.84/26.87 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.87 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.87 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.87 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.87 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.87 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.87 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.87 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.87 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.87 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.87 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.87 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.87 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.87 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.87 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.87 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.87 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.87 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.87 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.87 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.87 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.87 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.87 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.87 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.87 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.87 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.87 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.87 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.87 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.87 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.87 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.87 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.87 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.87 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.87 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.87 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.87 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.87 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.87 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.87 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.87 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.87 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.87 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.87 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.87 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.87 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.87 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.87 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.87 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.87 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.87 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.87 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.87 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.87 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.87 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.87 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.87 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.87 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.87 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.87 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.87 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.87 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.87 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.87 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.87 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.87 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.87 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.87 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.87 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.87 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.87 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.87 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.87 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.87 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.87 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.87 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.87 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.87 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.87 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.87 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.87 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.87 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.87 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.87 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.87 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.87 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.87 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.87 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.87 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.87 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.87 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.87 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.87 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.87 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.87 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.87 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.87 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.87 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.87 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.87 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.87 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.87 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.87 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.87 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.87 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.87 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.87 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.87 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.87 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.87 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.87 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.87 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.87 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.87 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.87 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.87 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.87 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.87 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.87 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.87 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.87 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.87 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.87 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.87 S(mark(z0)) -> c125(S(z0)) 100.84/26.87 S(ok(z0)) -> c126(S(z0)) 100.84/26.87 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.87 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.87 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.87 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.87 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.87 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.87 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.87 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.87 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.87 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.87 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.87 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.87 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.87 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.87 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.87 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.87 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.87 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.87 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.87 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.87 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.87 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.87 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.87 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.87 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.87 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.87 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.87 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.87 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.87 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.87 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.87 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.87 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.87 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.87 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.87 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.87 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.87 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.87 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.87 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.87 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.87 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.87 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.87 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.87 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.87 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.87 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.87 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.87 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.87 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.87 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.87 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.87 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.87 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.87 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.87 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.87 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.87 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.87 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.87 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.87 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.87 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.87 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.87 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.87 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.87 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.87 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.87 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.87 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.87 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.87 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.87 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.87 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.87 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.87 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.87 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.87 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.87 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.87 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.87 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.87 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.87 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.87 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.87 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.87 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.87 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.87 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.87 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.87 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.87 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.87 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.87 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.87 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.87 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.87 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.87 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.87 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.87 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.87 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.87 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.87 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.87 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.87 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.87 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.87 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.87 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.87 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.87 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.87 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.87 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.87 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.87 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.87 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.87 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.87 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.87 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.87 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.87 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.87 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.87 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.87 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.87 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.87 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.87 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.87 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.87 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.87 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.87 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.87 Defined Rule Symbols: proper_1 100.84/26.87 100.84/26.87 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.84/26.87 100.84/26.87 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_1 100.84/26.87 100.84/26.87 100.84/26.87 ---------------------------------------- 100.84/26.87 100.84/26.87 (15) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 100.84/26.87 Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 100.84/26.87 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.87 We considered the (Usable) Rules: 100.84/26.87 proper(tt) -> ok(tt) 100.84/26.87 proper(nil) -> ok(nil) 100.84/26.87 proper(0) -> ok(0) 100.84/26.87 And the Tuples: 100.84/26.87 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.87 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.87 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.87 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.87 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.87 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.87 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.87 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.87 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.87 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.87 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.87 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.87 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.87 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.87 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.87 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.87 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.87 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.87 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.87 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.87 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.87 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.87 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.87 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.87 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.87 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.87 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.87 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.87 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.87 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.87 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.87 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.87 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.87 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.87 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.87 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.87 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.87 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.87 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.87 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.87 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.87 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.87 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.87 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.87 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.87 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.87 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.87 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.87 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.87 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.87 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.87 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.87 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.87 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.87 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.87 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.87 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.87 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.87 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.87 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.87 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.87 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.87 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.87 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.87 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.87 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.87 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.87 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.87 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.87 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.87 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.87 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.87 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.87 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.87 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.87 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.87 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.87 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.87 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.87 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.87 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.87 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.87 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.87 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.87 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.87 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.87 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.87 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.87 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.87 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.87 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.87 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.87 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.87 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.87 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.87 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.87 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.87 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.87 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.87 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.87 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.87 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.87 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.87 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.87 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.87 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.87 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.87 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.87 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.87 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.87 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.87 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.87 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.87 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.87 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.87 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.87 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.87 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.87 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.87 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.87 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.87 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.87 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.87 S(mark(z0)) -> c125(S(z0)) 100.84/26.87 S(ok(z0)) -> c126(S(z0)) 100.84/26.87 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.87 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.87 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.87 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.87 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.87 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.87 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.87 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.87 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.87 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.87 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.87 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.87 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.87 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.87 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.87 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.87 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.87 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.87 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.87 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.87 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.87 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.87 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.87 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.87 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.87 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.87 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.87 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.87 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.87 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.87 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.87 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.87 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.87 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.87 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.87 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.87 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.87 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.87 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.87 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.87 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.87 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.87 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.87 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.87 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.87 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.87 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.87 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.87 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.87 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.87 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.87 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.87 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.87 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.87 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.87 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.87 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.87 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.87 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.87 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.87 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.87 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.87 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.87 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.87 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.87 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.87 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.87 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.87 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.87 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.87 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.87 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.87 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.87 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.87 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.87 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.87 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.87 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.87 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.87 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.87 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.87 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.87 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.87 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.87 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.87 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.87 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.87 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.87 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.87 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.87 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.87 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.87 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.87 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.87 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.87 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.87 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.87 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.87 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.87 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.87 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.87 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.87 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.87 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.87 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.87 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.87 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.87 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.87 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.87 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.87 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.87 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.87 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.87 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.87 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.87 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.87 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.87 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.87 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.87 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.87 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.87 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.87 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.87 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.87 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.87 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.87 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.87 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.87 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.87 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.87 The order we found is given by the following interpretation: 100.84/26.87 100.84/26.87 Polynomial interpretation : 100.84/26.87 100.84/26.87 POL(0) = [2] 100.84/26.87 POL(AFTERNTH(x_1, x_2)) = 0 100.84/26.87 POL(CONS(x_1, x_2)) = 0 100.84/26.87 POL(FST(x_1)) = 0 100.84/26.87 POL(HEAD(x_1)) = 0 100.84/26.87 POL(ISLNAT(x_1)) = 0 100.84/26.87 POL(ISLNATKIND(x_1)) = 0 100.84/26.87 POL(ISNATURAL(x_1)) = 0 100.84/26.87 POL(ISNATURALKIND(x_1)) = 0 100.84/26.87 POL(ISPLNAT(x_1)) = 0 100.84/26.87 POL(ISPLNATKIND(x_1)) = 0 100.84/26.87 POL(NATSFROM(x_1)) = 0 100.84/26.87 POL(PAIR(x_1, x_2)) = 0 100.84/26.87 POL(S(x_1)) = 0 100.84/26.87 POL(SEL(x_1, x_2)) = 0 100.84/26.87 POL(SND(x_1)) = 0 100.84/26.87 POL(SPLITAT(x_1, x_2)) = 0 100.84/26.87 POL(TAIL(x_1)) = 0 100.84/26.87 POL(TAKE(x_1, x_2)) = 0 100.84/26.87 POL(TOP(x_1)) = [3]x_1 100.84/26.87 POL(U101'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U102'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U103'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U104'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U105'(x_1, x_2)) = 0 100.84/26.87 POL(U106'(x_1)) = 0 100.84/26.87 POL(U11'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U111'(x_1, x_2)) = 0 100.84/26.87 POL(U112'(x_1)) = 0 100.84/26.87 POL(U12'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U121'(x_1, x_2)) = 0 100.84/26.87 POL(U122'(x_1)) = 0 100.84/26.87 POL(U13'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U131'(x_1)) = 0 100.84/26.87 POL(U14'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U141'(x_1)) = 0 100.84/26.87 POL(U151'(x_1)) = 0 100.84/26.87 POL(U161'(x_1)) = 0 100.84/26.87 POL(U171'(x_1, x_2)) = 0 100.84/26.87 POL(U172'(x_1)) = 0 100.84/26.87 POL(U181'(x_1, x_2)) = 0 100.84/26.87 POL(U182'(x_1, x_2)) = 0 100.84/26.87 POL(U183'(x_1)) = 0 100.84/26.87 POL(U191'(x_1, x_2)) = 0 100.84/26.87 POL(U192'(x_1, x_2)) = 0 100.84/26.87 POL(U193'(x_1)) = 0 100.84/26.87 POL(U201'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U202'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U203'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U204'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U205'(x_1, x_2)) = 0 100.84/26.87 POL(U206'(x_1)) = 0 100.84/26.87 POL(U21'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U211'(x_1)) = 0 100.84/26.87 POL(U22'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U221'(x_1)) = 0 100.84/26.87 POL(U23'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U231'(x_1, x_2)) = 0 100.84/26.87 POL(U232'(x_1)) = 0 100.84/26.87 POL(U24'(x_1, x_2)) = 0 100.84/26.87 POL(U241'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U242'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U243'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U244'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U245'(x_1, x_2)) = 0 100.84/26.87 POL(U246'(x_1)) = 0 100.84/26.87 POL(U251'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U252'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U253'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U254'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U255'(x_1, x_2)) = 0 100.84/26.87 POL(U256'(x_1)) = 0 100.84/26.87 POL(U261'(x_1, x_2)) = 0 100.84/26.87 POL(U262'(x_1)) = 0 100.84/26.87 POL(U271'(x_1, x_2)) = 0 100.84/26.87 POL(U272'(x_1)) = 0 100.84/26.87 POL(U281'(x_1, x_2)) = 0 100.84/26.87 POL(U282'(x_1, x_2)) = 0 100.84/26.87 POL(U291'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U292'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U293'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U294'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U301'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U302'(x_1, x_2)) = 0 100.84/26.87 POL(U303'(x_1, x_2)) = 0 100.84/26.87 POL(U304'(x_1, x_2)) = 0 100.84/26.87 POL(U31'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U311'(x_1, x_2)) = 0 100.84/26.87 POL(U312'(x_1, x_2)) = 0 100.84/26.87 POL(U32'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U321'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U322'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U323'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U324'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U325'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U326'(x_1, x_2, x_3, x_4)) = 0 100.84/26.87 POL(U327'(x_1, x_2)) = 0 100.84/26.87 POL(U33'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U331'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U332'(x_1, x_2)) = 0 100.84/26.87 POL(U333'(x_1, x_2)) = 0 100.84/26.87 POL(U334'(x_1, x_2)) = 0 100.84/26.87 POL(U34'(x_1, x_2)) = 0 100.84/26.87 POL(U341'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U342'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U343'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U344'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U41'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U42'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U43'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U44'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U45'(x_1, x_2)) = 0 100.84/26.87 POL(U46'(x_1)) = 0 100.84/26.87 POL(U51'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U52'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U53'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U54'(x_1, x_2, x_3)) = 0 100.84/26.87 POL(U55'(x_1, x_2)) = 0 100.84/26.87 POL(U56'(x_1)) = 0 100.84/26.87 POL(U61'(x_1, x_2)) = 0 100.84/26.87 POL(U62'(x_1, x_2)) = 0 100.84/26.87 POL(U63'(x_1)) = 0 100.84/26.87 POL(U71'(x_1, x_2)) = 0 100.84/26.87 POL(U72'(x_1, x_2)) = 0 100.84/26.87 POL(U73'(x_1)) = 0 100.84/26.87 POL(U81'(x_1, x_2)) = 0 100.84/26.87 POL(U82'(x_1, x_2)) = 0 100.84/26.87 POL(U83'(x_1)) = 0 100.84/26.87 POL(U91'(x_1, x_2)) = 0 100.84/26.87 POL(U92'(x_1, x_2)) = 0 100.84/26.87 POL(U93'(x_1)) = 0 100.84/26.87 POL(c(x_1)) = x_1 100.84/26.87 POL(c1(x_1)) = x_1 100.84/26.87 POL(c10(x_1)) = x_1 100.84/26.87 POL(c100(x_1)) = x_1 100.84/26.87 POL(c101(x_1)) = x_1 100.84/26.87 POL(c102(x_1)) = x_1 100.84/26.87 POL(c103(x_1)) = x_1 100.84/26.87 POL(c104(x_1)) = x_1 100.84/26.87 POL(c105(x_1)) = x_1 100.84/26.87 POL(c106(x_1)) = x_1 100.84/26.87 POL(c107(x_1)) = x_1 100.84/26.87 POL(c108(x_1)) = x_1 100.84/26.87 POL(c109(x_1)) = x_1 100.84/26.87 POL(c11(x_1)) = x_1 100.84/26.87 POL(c110(x_1)) = x_1 100.84/26.87 POL(c111(x_1)) = x_1 100.84/26.87 POL(c112(x_1)) = x_1 100.84/26.87 POL(c113(x_1)) = x_1 100.84/26.87 POL(c114(x_1)) = x_1 100.84/26.87 POL(c115(x_1)) = x_1 100.84/26.87 POL(c116(x_1)) = x_1 100.84/26.87 POL(c117(x_1)) = x_1 100.84/26.87 POL(c118(x_1)) = x_1 100.84/26.87 POL(c119(x_1)) = x_1 100.84/26.87 POL(c12(x_1)) = x_1 100.84/26.87 POL(c120(x_1)) = x_1 100.84/26.87 POL(c121(x_1)) = x_1 100.84/26.87 POL(c122(x_1)) = x_1 100.84/26.87 POL(c123(x_1)) = x_1 100.84/26.87 POL(c124(x_1)) = x_1 100.84/26.87 POL(c125(x_1)) = x_1 100.84/26.87 POL(c126(x_1)) = x_1 100.84/26.87 POL(c127(x_1)) = x_1 100.84/26.87 POL(c128(x_1)) = x_1 100.84/26.87 POL(c129(x_1)) = x_1 100.84/26.87 POL(c13(x_1)) = x_1 100.84/26.87 POL(c130(x_1)) = x_1 100.84/26.87 POL(c131(x_1)) = x_1 100.84/26.87 POL(c132(x_1)) = x_1 100.84/26.87 POL(c133(x_1)) = x_1 100.84/26.87 POL(c134(x_1)) = x_1 100.84/26.87 POL(c135(x_1)) = x_1 100.84/26.87 POL(c136(x_1)) = x_1 100.84/26.87 POL(c137(x_1)) = x_1 100.84/26.87 POL(c138(x_1)) = x_1 100.84/26.87 POL(c139(x_1)) = x_1 100.84/26.87 POL(c14(x_1)) = x_1 100.84/26.87 POL(c140(x_1)) = x_1 100.84/26.87 POL(c141(x_1)) = x_1 100.84/26.87 POL(c142(x_1)) = x_1 100.84/26.87 POL(c143(x_1)) = x_1 100.84/26.87 POL(c144(x_1)) = x_1 100.84/26.87 POL(c145(x_1)) = x_1 100.84/26.87 POL(c146(x_1)) = x_1 100.84/26.87 POL(c147(x_1)) = x_1 100.84/26.87 POL(c148(x_1)) = x_1 100.84/26.87 POL(c149(x_1)) = x_1 100.84/26.87 POL(c15(x_1)) = x_1 100.84/26.87 POL(c150(x_1)) = x_1 100.84/26.87 POL(c151(x_1)) = x_1 100.84/26.87 POL(c152(x_1)) = x_1 100.84/26.87 POL(c153(x_1)) = x_1 100.84/26.87 POL(c154(x_1)) = x_1 100.84/26.87 POL(c155(x_1)) = x_1 100.84/26.87 POL(c156(x_1)) = x_1 100.84/26.87 POL(c157(x_1)) = x_1 100.84/26.87 POL(c158(x_1)) = x_1 100.84/26.87 POL(c159(x_1)) = x_1 100.84/26.87 POL(c16(x_1)) = x_1 100.84/26.87 POL(c160(x_1)) = x_1 100.84/26.87 POL(c161(x_1)) = x_1 100.84/26.87 POL(c162(x_1)) = x_1 100.84/26.87 POL(c163(x_1)) = x_1 100.84/26.87 POL(c164(x_1)) = x_1 100.84/26.87 POL(c165(x_1)) = x_1 100.84/26.87 POL(c166(x_1)) = x_1 100.84/26.87 POL(c167(x_1)) = x_1 100.84/26.87 POL(c168(x_1)) = x_1 100.84/26.87 POL(c169(x_1)) = x_1 100.84/26.87 POL(c17(x_1)) = x_1 100.84/26.87 POL(c170(x_1)) = x_1 100.84/26.87 POL(c171(x_1)) = x_1 100.84/26.87 POL(c172(x_1)) = x_1 100.84/26.87 POL(c173(x_1)) = x_1 100.84/26.87 POL(c174(x_1)) = x_1 100.84/26.87 POL(c175(x_1)) = x_1 100.84/26.87 POL(c176(x_1)) = x_1 100.84/26.87 POL(c177(x_1)) = x_1 100.84/26.87 POL(c178(x_1)) = x_1 100.84/26.87 POL(c179(x_1)) = x_1 100.84/26.87 POL(c18(x_1)) = x_1 100.84/26.87 POL(c180(x_1)) = x_1 100.84/26.87 POL(c181(x_1)) = x_1 100.84/26.87 POL(c182(x_1)) = x_1 100.84/26.87 POL(c183(x_1)) = x_1 100.84/26.87 POL(c184(x_1)) = x_1 100.84/26.87 POL(c185(x_1)) = x_1 100.84/26.87 POL(c186(x_1)) = x_1 100.84/26.87 POL(c187(x_1)) = x_1 100.84/26.87 POL(c188(x_1)) = x_1 100.84/26.87 POL(c189(x_1)) = x_1 100.84/26.87 POL(c19(x_1)) = x_1 100.84/26.87 POL(c190(x_1)) = x_1 100.84/26.87 POL(c191(x_1)) = x_1 100.84/26.87 POL(c192(x_1)) = x_1 100.84/26.87 POL(c193(x_1)) = x_1 100.84/26.87 POL(c194(x_1)) = x_1 100.84/26.87 POL(c195(x_1)) = x_1 100.84/26.87 POL(c196(x_1)) = x_1 100.84/26.87 POL(c197(x_1)) = x_1 100.84/26.87 POL(c198(x_1)) = x_1 100.84/26.87 POL(c199(x_1)) = x_1 100.84/26.87 POL(c2(x_1)) = x_1 100.84/26.87 POL(c20(x_1)) = x_1 100.84/26.87 POL(c200(x_1)) = x_1 100.84/26.87 POL(c201(x_1)) = x_1 100.84/26.87 POL(c202(x_1)) = x_1 100.84/26.87 POL(c203(x_1)) = x_1 100.84/26.87 POL(c204(x_1)) = x_1 100.84/26.87 POL(c205(x_1)) = x_1 100.84/26.87 POL(c206(x_1)) = x_1 100.84/26.87 POL(c207(x_1)) = x_1 100.84/26.87 POL(c208(x_1)) = x_1 100.84/26.87 POL(c209(x_1)) = x_1 100.84/26.87 POL(c21(x_1)) = x_1 100.84/26.87 POL(c210(x_1)) = x_1 100.84/26.87 POL(c211(x_1)) = x_1 100.84/26.87 POL(c212(x_1)) = x_1 100.84/26.87 POL(c213(x_1)) = x_1 100.84/26.87 POL(c214(x_1)) = x_1 100.84/26.87 POL(c215(x_1)) = x_1 100.84/26.87 POL(c216(x_1)) = x_1 100.84/26.87 POL(c217(x_1)) = x_1 100.84/26.87 POL(c218(x_1)) = x_1 100.84/26.87 POL(c219(x_1)) = x_1 100.84/26.87 POL(c22(x_1)) = x_1 100.84/26.87 POL(c220(x_1)) = x_1 100.84/26.87 POL(c221(x_1)) = x_1 100.84/26.87 POL(c222(x_1)) = x_1 100.84/26.87 POL(c223(x_1)) = x_1 100.84/26.87 POL(c224(x_1)) = x_1 100.84/26.87 POL(c225(x_1)) = x_1 100.84/26.87 POL(c226(x_1)) = x_1 100.84/26.87 POL(c227(x_1)) = x_1 100.84/26.87 POL(c228(x_1)) = x_1 100.84/26.87 POL(c229(x_1)) = x_1 100.84/26.87 POL(c23(x_1)) = x_1 100.84/26.87 POL(c230(x_1)) = x_1 100.84/26.87 POL(c231(x_1)) = x_1 100.84/26.87 POL(c232(x_1)) = x_1 100.84/26.87 POL(c233(x_1)) = x_1 100.84/26.87 POL(c234(x_1)) = x_1 100.84/26.87 POL(c235(x_1)) = x_1 100.84/26.87 POL(c236(x_1)) = x_1 100.84/26.87 POL(c237(x_1)) = x_1 100.84/26.87 POL(c238(x_1)) = x_1 100.84/26.87 POL(c239(x_1)) = x_1 100.84/26.87 POL(c24(x_1)) = x_1 100.84/26.87 POL(c240(x_1)) = x_1 100.84/26.87 POL(c241(x_1)) = x_1 100.84/26.87 POL(c242(x_1)) = x_1 100.84/26.87 POL(c243(x_1)) = x_1 100.84/26.87 POL(c244(x_1)) = x_1 100.84/26.87 POL(c245(x_1)) = x_1 100.84/26.87 POL(c246(x_1)) = x_1 100.84/26.87 POL(c247(x_1)) = x_1 100.84/26.87 POL(c248(x_1)) = x_1 100.84/26.87 POL(c249(x_1)) = x_1 100.84/26.87 POL(c25(x_1)) = x_1 100.84/26.87 POL(c250(x_1)) = x_1 100.84/26.87 POL(c254(x_1)) = x_1 100.84/26.87 POL(c255(x_1)) = x_1 100.84/26.87 POL(c256(x_1)) = x_1 100.84/26.87 POL(c257(x_1)) = x_1 100.84/26.87 POL(c258(x_1)) = x_1 100.84/26.87 POL(c259(x_1)) = x_1 100.84/26.87 POL(c26(x_1)) = x_1 100.84/26.87 POL(c260(x_1)) = x_1 100.84/26.87 POL(c27(x_1)) = x_1 100.84/26.87 POL(c28(x_1)) = x_1 100.84/26.87 POL(c29(x_1)) = x_1 100.84/26.87 POL(c3(x_1)) = x_1 100.84/26.87 POL(c30(x_1)) = x_1 100.84/26.87 POL(c31(x_1)) = x_1 100.84/26.87 POL(c32(x_1)) = x_1 100.84/26.87 POL(c33(x_1)) = x_1 100.84/26.87 POL(c34(x_1)) = x_1 100.84/26.87 POL(c35(x_1)) = x_1 100.84/26.87 POL(c36(x_1)) = x_1 100.84/26.87 POL(c37(x_1)) = x_1 100.84/26.87 POL(c38(x_1)) = x_1 100.84/26.87 POL(c39(x_1)) = x_1 100.84/26.87 POL(c4(x_1)) = x_1 100.84/26.87 POL(c40(x_1)) = x_1 100.84/26.87 POL(c41(x_1)) = x_1 100.84/26.87 POL(c42(x_1)) = x_1 100.84/26.87 POL(c43(x_1)) = x_1 100.84/26.87 POL(c44(x_1)) = x_1 100.84/26.87 POL(c45(x_1)) = x_1 100.84/26.87 POL(c46(x_1)) = x_1 100.84/26.87 POL(c47(x_1)) = x_1 100.84/26.87 POL(c48(x_1)) = x_1 100.84/26.87 POL(c49(x_1)) = x_1 100.84/26.87 POL(c5(x_1)) = x_1 100.84/26.87 POL(c50(x_1)) = x_1 100.84/26.87 POL(c51(x_1)) = x_1 100.84/26.87 POL(c52(x_1)) = x_1 100.84/26.87 POL(c53(x_1)) = x_1 100.84/26.87 POL(c54(x_1)) = x_1 100.84/26.87 POL(c55(x_1)) = x_1 100.84/26.87 POL(c56(x_1)) = x_1 100.84/26.87 POL(c57(x_1)) = x_1 100.84/26.87 POL(c58(x_1)) = x_1 100.84/26.87 POL(c59(x_1)) = x_1 100.84/26.87 POL(c6(x_1)) = x_1 100.84/26.87 POL(c60(x_1)) = x_1 100.84/26.87 POL(c61(x_1)) = x_1 100.84/26.87 POL(c62(x_1)) = x_1 100.84/26.87 POL(c63(x_1)) = x_1 100.84/26.87 POL(c64(x_1)) = x_1 100.84/26.87 POL(c65(x_1)) = x_1 100.84/26.87 POL(c66(x_1)) = x_1 100.84/26.87 POL(c67(x_1)) = x_1 100.84/26.87 POL(c68(x_1)) = x_1 100.84/26.87 POL(c69(x_1)) = x_1 100.84/26.87 POL(c7(x_1)) = x_1 100.84/26.87 POL(c70(x_1)) = x_1 100.84/26.87 POL(c71(x_1)) = x_1 100.84/26.87 POL(c72(x_1)) = x_1 100.84/26.87 POL(c73(x_1)) = x_1 100.84/26.87 POL(c74(x_1)) = x_1 100.84/26.87 POL(c75(x_1)) = x_1 100.84/26.87 POL(c76(x_1)) = x_1 100.84/26.87 POL(c77(x_1)) = x_1 100.84/26.87 POL(c78(x_1)) = x_1 100.84/26.87 POL(c79(x_1)) = x_1 100.84/26.87 POL(c8(x_1)) = x_1 100.84/26.87 POL(c80(x_1)) = x_1 100.84/26.87 POL(c81(x_1)) = x_1 100.84/26.87 POL(c82(x_1)) = x_1 100.84/26.87 POL(c83(x_1)) = x_1 100.84/26.87 POL(c84(x_1)) = x_1 100.84/26.87 POL(c85(x_1)) = x_1 100.84/26.87 POL(c86(x_1)) = x_1 100.84/26.87 POL(c87(x_1)) = x_1 100.84/26.87 POL(c88(x_1)) = x_1 100.84/26.87 POL(c89(x_1)) = x_1 100.84/26.87 POL(c9(x_1)) = x_1 100.84/26.87 POL(c90(x_1)) = x_1 100.84/26.87 POL(c91(x_1)) = x_1 100.84/26.87 POL(c92(x_1)) = x_1 100.84/26.87 POL(c93(x_1)) = x_1 100.84/26.87 POL(c94(x_1)) = x_1 100.84/26.87 POL(c95(x_1)) = x_1 100.84/26.87 POL(c96(x_1)) = x_1 100.84/26.87 POL(c97(x_1)) = x_1 100.84/26.87 POL(c98(x_1)) = x_1 100.84/26.87 POL(c99(x_1)) = x_1 100.84/26.87 POL(mark(x_1)) = [3] + x_1 100.84/26.87 POL(nil) = [2] 100.84/26.87 POL(ok(x_1)) = 0 100.84/26.87 POL(proper(x_1)) = x_1 100.84/26.87 POL(tt) = [2] 100.84/26.87 100.84/26.87 ---------------------------------------- 100.84/26.87 100.84/26.87 (16) 100.84/26.87 Obligation: 100.84/26.87 Complexity Dependency Tuples Problem 100.84/26.87 100.84/26.87 Rules: 100.84/26.87 proper(tt) -> ok(tt) 100.84/26.87 proper(nil) -> ok(nil) 100.84/26.87 proper(0) -> ok(0) 100.84/26.87 Tuples: 100.84/26.87 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.87 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.87 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.87 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.87 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.87 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.87 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.87 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.87 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.87 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.87 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.87 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.87 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.87 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.87 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.87 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.87 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.87 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.87 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.87 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.87 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.87 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.87 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.87 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.87 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.87 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.87 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.87 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.87 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.87 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.87 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.87 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.87 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.87 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.87 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.87 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.87 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.87 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.87 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.87 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.87 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.87 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.87 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.87 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.87 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.87 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.87 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.87 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.87 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.87 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.87 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.87 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.88 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.88 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.88 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.88 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.88 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.88 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.88 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.88 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.88 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.88 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.88 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.88 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.88 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.88 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.88 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.88 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.88 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.88 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.88 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.88 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.88 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.88 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.88 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.88 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.88 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.88 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.88 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.88 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.88 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.88 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.88 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.88 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.88 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.88 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.88 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.88 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.88 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.88 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.88 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.88 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.88 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.88 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.88 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.88 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.88 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.88 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.88 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.88 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.88 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.88 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.88 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.88 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.88 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.88 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.88 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.88 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.88 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.88 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.88 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.88 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.88 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.88 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.88 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.88 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.88 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.88 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.88 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.88 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.88 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.88 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.88 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.88 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.88 S(mark(z0)) -> c125(S(z0)) 100.84/26.88 S(ok(z0)) -> c126(S(z0)) 100.84/26.88 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.88 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.88 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.88 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.88 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.88 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.88 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.88 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.88 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.88 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.88 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.88 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.88 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.88 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.88 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.88 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.88 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.88 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.88 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.88 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.88 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.88 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.88 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.88 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.88 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.88 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.88 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.88 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.88 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.88 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.88 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.88 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.88 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.88 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.88 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.88 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.88 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.88 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.88 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.88 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.88 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.88 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.88 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.88 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.88 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.88 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.88 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.88 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.88 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.88 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.88 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.88 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.88 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.88 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.88 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.88 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.88 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.88 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.88 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.88 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.88 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.88 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.88 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.88 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.88 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.88 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.88 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.88 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.88 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.88 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.88 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.88 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.88 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.88 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.88 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.88 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.88 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.88 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.88 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.88 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.88 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.88 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.88 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.88 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.88 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.88 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.88 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.88 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.88 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.88 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.88 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.88 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.88 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.88 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.88 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.88 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.88 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.88 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.88 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.88 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.88 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.88 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.88 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.88 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.88 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.88 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.88 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.88 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.88 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.88 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.88 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.88 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.88 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.88 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.88 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.88 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.88 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.88 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.88 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.88 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.88 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.88 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.88 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.88 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.88 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.88 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.88 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.88 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.88 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.88 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.88 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.88 S tuples:none 100.84/26.88 K tuples: 100.84/26.88 U101'(mark(z0), z1, z2) -> c(U101'(z0, z1, z2)) 100.84/26.88 U101'(ok(z0), ok(z1), ok(z2)) -> c1(U101'(z0, z1, z2)) 100.84/26.88 U102'(mark(z0), z1, z2) -> c2(U102'(z0, z1, z2)) 100.84/26.88 U102'(ok(z0), ok(z1), ok(z2)) -> c3(U102'(z0, z1, z2)) 100.84/26.88 U103'(mark(z0), z1, z2) -> c4(U103'(z0, z1, z2)) 100.84/26.88 U103'(ok(z0), ok(z1), ok(z2)) -> c5(U103'(z0, z1, z2)) 100.84/26.88 U104'(mark(z0), z1, z2) -> c6(U104'(z0, z1, z2)) 100.84/26.88 U104'(ok(z0), ok(z1), ok(z2)) -> c7(U104'(z0, z1, z2)) 100.84/26.88 U105'(mark(z0), z1) -> c8(U105'(z0, z1)) 100.84/26.88 U105'(ok(z0), ok(z1)) -> c9(U105'(z0, z1)) 100.84/26.88 U106'(mark(z0)) -> c10(U106'(z0)) 100.84/26.88 U106'(ok(z0)) -> c11(U106'(z0)) 100.84/26.88 U11'(mark(z0), z1, z2) -> c12(U11'(z0, z1, z2)) 100.84/26.88 U11'(ok(z0), ok(z1), ok(z2)) -> c13(U11'(z0, z1, z2)) 100.84/26.88 U12'(mark(z0), z1, z2) -> c14(U12'(z0, z1, z2)) 100.84/26.88 U12'(ok(z0), ok(z1), ok(z2)) -> c15(U12'(z0, z1, z2)) 100.84/26.88 U111'(mark(z0), z1) -> c16(U111'(z0, z1)) 100.84/26.88 U111'(ok(z0), ok(z1)) -> c17(U111'(z0, z1)) 100.84/26.88 U112'(mark(z0)) -> c18(U112'(z0)) 100.84/26.88 U112'(ok(z0)) -> c19(U112'(z0)) 100.84/26.88 U13'(mark(z0), z1, z2) -> c20(U13'(z0, z1, z2)) 100.84/26.88 U13'(ok(z0), ok(z1), ok(z2)) -> c21(U13'(z0, z1, z2)) 100.84/26.88 U121'(mark(z0), z1) -> c22(U121'(z0, z1)) 100.84/26.88 U121'(ok(z0), ok(z1)) -> c23(U121'(z0, z1)) 100.84/26.88 U122'(mark(z0)) -> c24(U122'(z0)) 100.84/26.88 U122'(ok(z0)) -> c25(U122'(z0)) 100.84/26.88 U14'(mark(z0), z1, z2) -> c26(U14'(z0, z1, z2)) 100.84/26.88 U14'(ok(z0), ok(z1), ok(z2)) -> c27(U14'(z0, z1, z2)) 100.84/26.88 U131'(mark(z0)) -> c28(U131'(z0)) 100.84/26.88 U131'(ok(z0)) -> c29(U131'(z0)) 100.84/26.88 SND(mark(z0)) -> c30(SND(z0)) 100.84/26.88 SND(ok(z0)) -> c31(SND(z0)) 100.84/26.88 SPLITAT(mark(z0), z1) -> c32(SPLITAT(z0, z1)) 100.84/26.88 SPLITAT(z0, mark(z1)) -> c33(SPLITAT(z0, z1)) 100.84/26.88 SPLITAT(ok(z0), ok(z1)) -> c34(SPLITAT(z0, z1)) 100.84/26.88 U141'(mark(z0)) -> c35(U141'(z0)) 100.84/26.88 U141'(ok(z0)) -> c36(U141'(z0)) 100.84/26.88 U151'(mark(z0)) -> c37(U151'(z0)) 100.84/26.88 U151'(ok(z0)) -> c38(U151'(z0)) 100.84/26.88 U161'(mark(z0)) -> c39(U161'(z0)) 100.84/26.88 U161'(ok(z0)) -> c40(U161'(z0)) 100.84/26.88 U171'(mark(z0), z1) -> c41(U171'(z0, z1)) 100.84/26.88 U171'(ok(z0), ok(z1)) -> c42(U171'(z0, z1)) 100.84/26.88 U172'(mark(z0)) -> c43(U172'(z0)) 100.84/26.88 U172'(ok(z0)) -> c44(U172'(z0)) 100.84/26.88 U181'(mark(z0), z1) -> c45(U181'(z0, z1)) 100.84/26.88 U181'(ok(z0), ok(z1)) -> c46(U181'(z0, z1)) 100.84/26.88 U182'(mark(z0), z1) -> c47(U182'(z0, z1)) 100.84/26.88 U182'(ok(z0), ok(z1)) -> c48(U182'(z0, z1)) 100.84/26.88 U183'(mark(z0)) -> c49(U183'(z0)) 100.84/26.88 U183'(ok(z0)) -> c50(U183'(z0)) 100.84/26.88 U191'(mark(z0), z1) -> c51(U191'(z0, z1)) 100.84/26.88 U191'(ok(z0), ok(z1)) -> c52(U191'(z0, z1)) 100.84/26.88 U192'(mark(z0), z1) -> c53(U192'(z0, z1)) 100.84/26.88 U192'(ok(z0), ok(z1)) -> c54(U192'(z0, z1)) 100.84/26.88 U193'(mark(z0)) -> c55(U193'(z0)) 100.84/26.88 U193'(ok(z0)) -> c56(U193'(z0)) 100.84/26.88 U201'(mark(z0), z1, z2) -> c57(U201'(z0, z1, z2)) 100.84/26.88 U201'(ok(z0), ok(z1), ok(z2)) -> c58(U201'(z0, z1, z2)) 100.84/26.88 U202'(mark(z0), z1, z2) -> c59(U202'(z0, z1, z2)) 100.84/26.88 U202'(ok(z0), ok(z1), ok(z2)) -> c60(U202'(z0, z1, z2)) 100.84/26.88 U203'(mark(z0), z1, z2) -> c61(U203'(z0, z1, z2)) 100.84/26.88 U203'(ok(z0), ok(z1), ok(z2)) -> c62(U203'(z0, z1, z2)) 100.84/26.88 U204'(mark(z0), z1, z2) -> c63(U204'(z0, z1, z2)) 100.84/26.88 U204'(ok(z0), ok(z1), ok(z2)) -> c64(U204'(z0, z1, z2)) 100.84/26.88 U205'(mark(z0), z1) -> c65(U205'(z0, z1)) 100.84/26.88 U205'(ok(z0), ok(z1)) -> c66(U205'(z0, z1)) 100.84/26.88 U206'(mark(z0)) -> c67(U206'(z0)) 100.84/26.88 U206'(ok(z0)) -> c68(U206'(z0)) 100.84/26.88 U21'(mark(z0), z1, z2) -> c69(U21'(z0, z1, z2)) 100.84/26.88 U21'(ok(z0), ok(z1), ok(z2)) -> c70(U21'(z0, z1, z2)) 100.84/26.88 U22'(mark(z0), z1, z2) -> c71(U22'(z0, z1, z2)) 100.84/26.88 U22'(ok(z0), ok(z1), ok(z2)) -> c72(U22'(z0, z1, z2)) 100.84/26.88 U211'(mark(z0)) -> c73(U211'(z0)) 100.84/26.88 U211'(ok(z0)) -> c74(U211'(z0)) 100.84/26.88 U23'(mark(z0), z1, z2) -> c75(U23'(z0, z1, z2)) 100.84/26.88 U23'(ok(z0), ok(z1), ok(z2)) -> c76(U23'(z0, z1, z2)) 100.84/26.88 U221'(mark(z0)) -> c77(U221'(z0)) 100.84/26.88 U221'(ok(z0)) -> c78(U221'(z0)) 100.84/26.88 U24'(mark(z0), z1) -> c79(U24'(z0, z1)) 100.84/26.88 U24'(ok(z0), ok(z1)) -> c80(U24'(z0, z1)) 100.84/26.88 U231'(mark(z0), z1) -> c81(U231'(z0, z1)) 100.84/26.88 U231'(ok(z0), ok(z1)) -> c82(U231'(z0, z1)) 100.84/26.88 U232'(mark(z0)) -> c83(U232'(z0)) 100.84/26.88 U232'(ok(z0)) -> c84(U232'(z0)) 100.84/26.88 U241'(mark(z0), z1, z2) -> c85(U241'(z0, z1, z2)) 100.84/26.88 U241'(ok(z0), ok(z1), ok(z2)) -> c86(U241'(z0, z1, z2)) 100.84/26.88 U242'(mark(z0), z1, z2) -> c87(U242'(z0, z1, z2)) 100.84/26.88 U242'(ok(z0), ok(z1), ok(z2)) -> c88(U242'(z0, z1, z2)) 100.84/26.88 U243'(mark(z0), z1, z2) -> c89(U243'(z0, z1, z2)) 100.84/26.88 U243'(ok(z0), ok(z1), ok(z2)) -> c90(U243'(z0, z1, z2)) 100.84/26.88 U244'(mark(z0), z1, z2) -> c91(U244'(z0, z1, z2)) 100.84/26.88 U244'(ok(z0), ok(z1), ok(z2)) -> c92(U244'(z0, z1, z2)) 100.84/26.88 U245'(mark(z0), z1) -> c93(U245'(z0, z1)) 100.84/26.88 U245'(ok(z0), ok(z1)) -> c94(U245'(z0, z1)) 100.84/26.88 U246'(mark(z0)) -> c95(U246'(z0)) 100.84/26.88 U246'(ok(z0)) -> c96(U246'(z0)) 100.84/26.88 U251'(mark(z0), z1, z2) -> c97(U251'(z0, z1, z2)) 100.84/26.88 U251'(ok(z0), ok(z1), ok(z2)) -> c98(U251'(z0, z1, z2)) 100.84/26.88 U252'(mark(z0), z1, z2) -> c99(U252'(z0, z1, z2)) 100.84/26.88 U252'(ok(z0), ok(z1), ok(z2)) -> c100(U252'(z0, z1, z2)) 100.84/26.88 U253'(mark(z0), z1, z2) -> c101(U253'(z0, z1, z2)) 100.84/26.88 U253'(ok(z0), ok(z1), ok(z2)) -> c102(U253'(z0, z1, z2)) 100.84/26.88 U254'(mark(z0), z1, z2) -> c103(U254'(z0, z1, z2)) 100.84/26.88 U254'(ok(z0), ok(z1), ok(z2)) -> c104(U254'(z0, z1, z2)) 100.84/26.88 U255'(mark(z0), z1) -> c105(U255'(z0, z1)) 100.84/26.88 U255'(ok(z0), ok(z1)) -> c106(U255'(z0, z1)) 100.84/26.88 U256'(mark(z0)) -> c107(U256'(z0)) 100.84/26.88 U256'(ok(z0)) -> c108(U256'(z0)) 100.84/26.88 U261'(mark(z0), z1) -> c109(U261'(z0, z1)) 100.84/26.88 U261'(ok(z0), ok(z1)) -> c110(U261'(z0, z1)) 100.84/26.88 U262'(mark(z0)) -> c111(U262'(z0)) 100.84/26.88 U262'(ok(z0)) -> c112(U262'(z0)) 100.84/26.88 U271'(mark(z0), z1) -> c113(U271'(z0, z1)) 100.84/26.88 U271'(ok(z0), ok(z1)) -> c114(U271'(z0, z1)) 100.84/26.88 U272'(mark(z0)) -> c115(U272'(z0)) 100.84/26.88 U272'(ok(z0)) -> c116(U272'(z0)) 100.84/26.88 U281'(mark(z0), z1) -> c117(U281'(z0, z1)) 100.84/26.88 U281'(ok(z0), ok(z1)) -> c118(U281'(z0, z1)) 100.84/26.88 U282'(mark(z0), z1) -> c119(U282'(z0, z1)) 100.84/26.88 U282'(ok(z0), ok(z1)) -> c120(U282'(z0, z1)) 100.84/26.88 CONS(mark(z0), z1) -> c121(CONS(z0, z1)) 100.84/26.88 CONS(ok(z0), ok(z1)) -> c122(CONS(z0, z1)) 100.84/26.88 NATSFROM(mark(z0)) -> c123(NATSFROM(z0)) 100.84/26.88 NATSFROM(ok(z0)) -> c124(NATSFROM(z0)) 100.84/26.88 S(mark(z0)) -> c125(S(z0)) 100.84/26.88 S(ok(z0)) -> c126(S(z0)) 100.84/26.88 U291'(mark(z0), z1, z2) -> c127(U291'(z0, z1, z2)) 100.84/26.88 U291'(ok(z0), ok(z1), ok(z2)) -> c128(U291'(z0, z1, z2)) 100.84/26.88 U292'(mark(z0), z1, z2) -> c129(U292'(z0, z1, z2)) 100.84/26.88 U292'(ok(z0), ok(z1), ok(z2)) -> c130(U292'(z0, z1, z2)) 100.84/26.88 U293'(mark(z0), z1, z2) -> c131(U293'(z0, z1, z2)) 100.84/26.88 U293'(ok(z0), ok(z1), ok(z2)) -> c132(U293'(z0, z1, z2)) 100.84/26.88 U294'(mark(z0), z1, z2) -> c133(U294'(z0, z1, z2)) 100.84/26.88 U294'(ok(z0), ok(z1), ok(z2)) -> c134(U294'(z0, z1, z2)) 100.84/26.88 HEAD(mark(z0)) -> c135(HEAD(z0)) 100.84/26.88 HEAD(ok(z0)) -> c136(HEAD(z0)) 100.84/26.88 AFTERNTH(mark(z0), z1) -> c137(AFTERNTH(z0, z1)) 100.84/26.88 AFTERNTH(z0, mark(z1)) -> c138(AFTERNTH(z0, z1)) 100.84/26.88 AFTERNTH(ok(z0), ok(z1)) -> c139(AFTERNTH(z0, z1)) 100.84/26.88 U301'(mark(z0), z1, z2) -> c140(U301'(z0, z1, z2)) 100.84/26.88 U301'(ok(z0), ok(z1), ok(z2)) -> c141(U301'(z0, z1, z2)) 100.84/26.88 U302'(mark(z0), z1) -> c142(U302'(z0, z1)) 100.84/26.88 U302'(ok(z0), ok(z1)) -> c143(U302'(z0, z1)) 100.84/26.88 U303'(mark(z0), z1) -> c144(U303'(z0, z1)) 100.84/26.88 U303'(ok(z0), ok(z1)) -> c145(U303'(z0, z1)) 100.84/26.88 U304'(mark(z0), z1) -> c146(U304'(z0, z1)) 100.84/26.88 U304'(ok(z0), ok(z1)) -> c147(U304'(z0, z1)) 100.84/26.88 U31'(mark(z0), z1, z2) -> c148(U31'(z0, z1, z2)) 100.84/26.88 U31'(ok(z0), ok(z1), ok(z2)) -> c149(U31'(z0, z1, z2)) 100.84/26.88 U32'(mark(z0), z1, z2) -> c150(U32'(z0, z1, z2)) 100.84/26.88 U32'(ok(z0), ok(z1), ok(z2)) -> c151(U32'(z0, z1, z2)) 100.84/26.88 U311'(mark(z0), z1) -> c152(U311'(z0, z1)) 100.84/26.88 U311'(ok(z0), ok(z1)) -> c153(U311'(z0, z1)) 100.84/26.88 U312'(mark(z0), z1) -> c154(U312'(z0, z1)) 100.84/26.88 U312'(ok(z0), ok(z1)) -> c155(U312'(z0, z1)) 100.84/26.88 PAIR(mark(z0), z1) -> c156(PAIR(z0, z1)) 100.84/26.88 PAIR(z0, mark(z1)) -> c157(PAIR(z0, z1)) 100.84/26.88 PAIR(ok(z0), ok(z1)) -> c158(PAIR(z0, z1)) 100.84/26.88 U33'(mark(z0), z1, z2) -> c159(U33'(z0, z1, z2)) 100.84/26.88 U33'(ok(z0), ok(z1), ok(z2)) -> c160(U33'(z0, z1, z2)) 100.84/26.88 U321'(mark(z0), z1, z2, z3) -> c161(U321'(z0, z1, z2, z3)) 100.84/26.88 U321'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c162(U321'(z0, z1, z2, z3)) 100.84/26.88 U322'(mark(z0), z1, z2, z3) -> c163(U322'(z0, z1, z2, z3)) 100.84/26.88 U322'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c164(U322'(z0, z1, z2, z3)) 100.84/26.88 U323'(mark(z0), z1, z2, z3) -> c165(U323'(z0, z1, z2, z3)) 100.84/26.88 U323'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c166(U323'(z0, z1, z2, z3)) 100.84/26.88 U324'(mark(z0), z1, z2, z3) -> c167(U324'(z0, z1, z2, z3)) 100.84/26.88 U324'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c168(U324'(z0, z1, z2, z3)) 100.84/26.88 U325'(mark(z0), z1, z2, z3) -> c169(U325'(z0, z1, z2, z3)) 100.84/26.88 U325'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c170(U325'(z0, z1, z2, z3)) 100.84/26.88 U326'(mark(z0), z1, z2, z3) -> c171(U326'(z0, z1, z2, z3)) 100.84/26.88 U326'(ok(z0), ok(z1), ok(z2), ok(z3)) -> c172(U326'(z0, z1, z2, z3)) 100.84/26.88 U327'(mark(z0), z1) -> c173(U327'(z0, z1)) 100.84/26.88 U327'(ok(z0), ok(z1)) -> c174(U327'(z0, z1)) 100.84/26.88 U34'(mark(z0), z1) -> c175(U34'(z0, z1)) 100.84/26.88 U34'(ok(z0), ok(z1)) -> c176(U34'(z0, z1)) 100.84/26.88 U331'(mark(z0), z1, z2) -> c177(U331'(z0, z1, z2)) 100.84/26.88 U331'(ok(z0), ok(z1), ok(z2)) -> c178(U331'(z0, z1, z2)) 100.84/26.88 U332'(mark(z0), z1) -> c179(U332'(z0, z1)) 100.84/26.88 U332'(ok(z0), ok(z1)) -> c180(U332'(z0, z1)) 100.84/26.88 U333'(mark(z0), z1) -> c181(U333'(z0, z1)) 100.84/26.88 U333'(ok(z0), ok(z1)) -> c182(U333'(z0, z1)) 100.84/26.88 U334'(mark(z0), z1) -> c183(U334'(z0, z1)) 100.84/26.88 U334'(ok(z0), ok(z1)) -> c184(U334'(z0, z1)) 100.84/26.88 U341'(mark(z0), z1, z2) -> c185(U341'(z0, z1, z2)) 100.84/26.88 U341'(ok(z0), ok(z1), ok(z2)) -> c186(U341'(z0, z1, z2)) 100.84/26.88 U342'(mark(z0), z1, z2) -> c187(U342'(z0, z1, z2)) 100.84/26.88 U342'(ok(z0), ok(z1), ok(z2)) -> c188(U342'(z0, z1, z2)) 100.84/26.88 U343'(mark(z0), z1, z2) -> c189(U343'(z0, z1, z2)) 100.84/26.88 U343'(ok(z0), ok(z1), ok(z2)) -> c190(U343'(z0, z1, z2)) 100.84/26.88 U344'(mark(z0), z1, z2) -> c191(U344'(z0, z1, z2)) 100.84/26.88 U344'(ok(z0), ok(z1), ok(z2)) -> c192(U344'(z0, z1, z2)) 100.84/26.88 FST(mark(z0)) -> c193(FST(z0)) 100.84/26.88 FST(ok(z0)) -> c194(FST(z0)) 100.84/26.88 U41'(mark(z0), z1, z2) -> c195(U41'(z0, z1, z2)) 100.84/26.88 U41'(ok(z0), ok(z1), ok(z2)) -> c196(U41'(z0, z1, z2)) 100.84/26.88 U42'(mark(z0), z1, z2) -> c197(U42'(z0, z1, z2)) 100.84/26.88 U42'(ok(z0), ok(z1), ok(z2)) -> c198(U42'(z0, z1, z2)) 100.84/26.88 U43'(mark(z0), z1, z2) -> c199(U43'(z0, z1, z2)) 100.84/26.88 U43'(ok(z0), ok(z1), ok(z2)) -> c200(U43'(z0, z1, z2)) 100.84/26.88 U44'(mark(z0), z1, z2) -> c201(U44'(z0, z1, z2)) 100.84/26.88 U44'(ok(z0), ok(z1), ok(z2)) -> c202(U44'(z0, z1, z2)) 100.84/26.88 U45'(mark(z0), z1) -> c203(U45'(z0, z1)) 100.84/26.88 U45'(ok(z0), ok(z1)) -> c204(U45'(z0, z1)) 100.84/26.88 U46'(mark(z0)) -> c205(U46'(z0)) 100.84/26.88 U46'(ok(z0)) -> c206(U46'(z0)) 100.84/26.88 U51'(mark(z0), z1, z2) -> c207(U51'(z0, z1, z2)) 100.84/26.88 U51'(ok(z0), ok(z1), ok(z2)) -> c208(U51'(z0, z1, z2)) 100.84/26.88 U52'(mark(z0), z1, z2) -> c209(U52'(z0, z1, z2)) 100.84/26.88 U52'(ok(z0), ok(z1), ok(z2)) -> c210(U52'(z0, z1, z2)) 100.84/26.88 U53'(mark(z0), z1, z2) -> c211(U53'(z0, z1, z2)) 100.84/26.88 U53'(ok(z0), ok(z1), ok(z2)) -> c212(U53'(z0, z1, z2)) 100.84/26.88 U54'(mark(z0), z1, z2) -> c213(U54'(z0, z1, z2)) 100.84/26.88 U54'(ok(z0), ok(z1), ok(z2)) -> c214(U54'(z0, z1, z2)) 100.84/26.88 U55'(mark(z0), z1) -> c215(U55'(z0, z1)) 100.84/26.88 U55'(ok(z0), ok(z1)) -> c216(U55'(z0, z1)) 100.84/26.88 U56'(mark(z0)) -> c217(U56'(z0)) 100.84/26.88 U56'(ok(z0)) -> c218(U56'(z0)) 100.84/26.88 U61'(mark(z0), z1) -> c219(U61'(z0, z1)) 100.84/26.88 U61'(ok(z0), ok(z1)) -> c220(U61'(z0, z1)) 100.84/26.88 U62'(mark(z0), z1) -> c221(U62'(z0, z1)) 100.84/26.88 U62'(ok(z0), ok(z1)) -> c222(U62'(z0, z1)) 100.84/26.88 U63'(mark(z0)) -> c223(U63'(z0)) 100.84/26.88 U63'(ok(z0)) -> c224(U63'(z0)) 100.84/26.88 U71'(mark(z0), z1) -> c225(U71'(z0, z1)) 100.84/26.88 U71'(ok(z0), ok(z1)) -> c226(U71'(z0, z1)) 100.84/26.88 U72'(mark(z0), z1) -> c227(U72'(z0, z1)) 100.84/26.88 U72'(ok(z0), ok(z1)) -> c228(U72'(z0, z1)) 100.84/26.88 U73'(mark(z0)) -> c229(U73'(z0)) 100.84/26.88 U73'(ok(z0)) -> c230(U73'(z0)) 100.84/26.88 U81'(mark(z0), z1) -> c231(U81'(z0, z1)) 100.84/26.88 U81'(ok(z0), ok(z1)) -> c232(U81'(z0, z1)) 100.84/26.88 U82'(mark(z0), z1) -> c233(U82'(z0, z1)) 100.84/26.88 U82'(ok(z0), ok(z1)) -> c234(U82'(z0, z1)) 100.84/26.88 U83'(mark(z0)) -> c235(U83'(z0)) 100.84/26.88 U83'(ok(z0)) -> c236(U83'(z0)) 100.84/26.88 U91'(mark(z0), z1) -> c237(U91'(z0, z1)) 100.84/26.88 U91'(ok(z0), ok(z1)) -> c238(U91'(z0, z1)) 100.84/26.88 U92'(mark(z0), z1) -> c239(U92'(z0, z1)) 100.84/26.88 U92'(ok(z0), ok(z1)) -> c240(U92'(z0, z1)) 100.84/26.88 U93'(mark(z0)) -> c241(U93'(z0)) 100.84/26.88 U93'(ok(z0)) -> c242(U93'(z0)) 100.84/26.88 TAIL(mark(z0)) -> c243(TAIL(z0)) 100.84/26.88 TAIL(ok(z0)) -> c244(TAIL(z0)) 100.84/26.88 TAKE(mark(z0), z1) -> c245(TAKE(z0, z1)) 100.84/26.88 TAKE(z0, mark(z1)) -> c246(TAKE(z0, z1)) 100.84/26.88 TAKE(ok(z0), ok(z1)) -> c247(TAKE(z0, z1)) 100.84/26.88 SEL(mark(z0), z1) -> c248(SEL(z0, z1)) 100.84/26.88 SEL(z0, mark(z1)) -> c249(SEL(z0, z1)) 100.84/26.88 SEL(ok(z0), ok(z1)) -> c250(SEL(z0, z1)) 100.84/26.88 ISNATURALKIND(ok(z0)) -> c254(ISNATURALKIND(z0)) 100.84/26.88 ISLNATKIND(ok(z0)) -> c255(ISLNATKIND(z0)) 100.84/26.88 ISNATURAL(ok(z0)) -> c256(ISNATURAL(z0)) 100.84/26.88 ISLNAT(ok(z0)) -> c257(ISLNAT(z0)) 100.84/26.88 ISPLNATKIND(ok(z0)) -> c258(ISPLNATKIND(z0)) 100.84/26.88 ISPLNAT(ok(z0)) -> c259(ISPLNAT(z0)) 100.84/26.88 TOP(mark(z0)) -> c260(TOP(proper(z0))) 100.84/26.88 Defined Rule Symbols: proper_1 100.84/26.88 100.84/26.88 Defined Pair Symbols: U101'_3, U102'_3, U103'_3, U104'_3, U105'_2, U106'_1, U11'_3, U12'_3, U111'_2, U112'_1, U13'_3, U121'_2, U122'_1, U14'_3, U131'_1, SND_1, SPLITAT_2, U141'_1, U151'_1, U161'_1, U171'_2, U172'_1, U181'_2, U182'_2, U183'_1, U191'_2, U192'_2, U193'_1, U201'_3, U202'_3, U203'_3, U204'_3, U205'_2, U206'_1, U21'_3, U22'_3, U211'_1, U23'_3, U221'_1, U24'_2, U231'_2, U232'_1, U241'_3, U242'_3, U243'_3, U244'_3, U245'_2, U246'_1, U251'_3, U252'_3, U253'_3, U254'_3, U255'_2, U256'_1, U261'_2, U262'_1, U271'_2, U272'_1, U281'_2, U282'_2, CONS_2, NATSFROM_1, S_1, U291'_3, U292'_3, U293'_3, U294'_3, HEAD_1, AFTERNTH_2, U301'_3, U302'_2, U303'_2, U304'_2, U31'_3, U32'_3, U311'_2, U312'_2, PAIR_2, U33'_3, U321'_4, U322'_4, U323'_4, U324'_4, U325'_4, U326'_4, U327'_2, U34'_2, U331'_3, U332'_2, U333'_2, U334'_2, U341'_3, U342'_3, U343'_3, U344'_3, FST_1, U41'_3, U42'_3, U43'_3, U44'_3, U45'_2, U46'_1, U51'_3, U52'_3, U53'_3, U54'_3, U55'_2, U56'_1, U61'_2, U62'_2, U63'_1, U71'_2, U72'_2, U73'_1, U81'_2, U82'_2, U83'_1, U91'_2, U92'_2, U93'_1, TAIL_1, TAKE_2, SEL_2, ISNATURALKIND_1, ISLNATKIND_1, ISNATURAL_1, ISLNAT_1, ISPLNATKIND_1, ISPLNAT_1, TOP_1 100.84/26.88 100.84/26.88 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c80_1, c81_1, c82_1, c83_1, c84_1, c85_1, c86_1, c87_1, c88_1, c89_1, c90_1, c91_1, c92_1, c93_1, c94_1, c95_1, c96_1, c97_1, c98_1, c99_1, c100_1, c101_1, c102_1, c103_1, c104_1, c105_1, c106_1, c107_1, c108_1, c109_1, c110_1, c111_1, c112_1, c113_1, c114_1, c115_1, c116_1, c117_1, c118_1, c119_1, c120_1, c121_1, c122_1, c123_1, c124_1, c125_1, c126_1, c127_1, c128_1, c129_1, c130_1, c131_1, c132_1, c133_1, c134_1, c135_1, c136_1, c137_1, c138_1, c139_1, c140_1, c141_1, c142_1, c143_1, c144_1, c145_1, c146_1, c147_1, c148_1, c149_1, c150_1, c151_1, c152_1, c153_1, c154_1, c155_1, c156_1, c157_1, c158_1, c159_1, c160_1, c161_1, c162_1, c163_1, c164_1, c165_1, c166_1, c167_1, c168_1, c169_1, c170_1, c171_1, c172_1, c173_1, c174_1, c175_1, c176_1, c177_1, c178_1, c179_1, c180_1, c181_1, c182_1, c183_1, c184_1, c185_1, c186_1, c187_1, c188_1, c189_1, c190_1, c191_1, c192_1, c193_1, c194_1, c195_1, c196_1, c197_1, c198_1, c199_1, c200_1, c201_1, c202_1, c203_1, c204_1, c205_1, c206_1, c207_1, c208_1, c209_1, c210_1, c211_1, c212_1, c213_1, c214_1, c215_1, c216_1, c217_1, c218_1, c219_1, c220_1, c221_1, c222_1, c223_1, c224_1, c225_1, c226_1, c227_1, c228_1, c229_1, c230_1, c231_1, c232_1, c233_1, c234_1, c235_1, c236_1, c237_1, c238_1, c239_1, c240_1, c241_1, c242_1, c243_1, c244_1, c245_1, c246_1, c247_1, c248_1, c249_1, c250_1, c254_1, c255_1, c256_1, c257_1, c258_1, c259_1, c260_1 100.84/26.88 100.84/26.88 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (17) SIsEmptyProof (BOTH BOUNDS(ID, ID)) 100.84/26.88 The set S is empty 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (18) 100.84/26.88 BOUNDS(1, 1) 100.84/26.88 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (19) RenamingProof (BOTH BOUNDS(ID, ID)) 100.84/26.88 Renamed function symbols to avoid clashes with predefined symbol. 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (20) 100.84/26.88 Obligation: 100.84/26.88 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 100.84/26.88 100.84/26.88 100.84/26.88 The TRS R consists of the following rules: 100.84/26.88 100.84/26.88 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 100.84/26.88 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 100.84/26.88 active(U106(tt)) -> mark(tt) 100.84/26.88 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 100.84/26.88 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 100.84/26.88 active(U112(tt)) -> mark(tt) 100.84/26.88 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 100.84/26.88 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 100.84/26.88 active(U122(tt)) -> mark(tt) 100.84/26.88 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 100.84/26.88 active(U131(tt)) -> mark(tt) 100.84/26.88 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 100.84/26.88 active(U141(tt)) -> mark(tt) 100.84/26.88 active(U151(tt)) -> mark(tt) 100.84/26.88 active(U161(tt)) -> mark(tt) 100.84/26.88 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 100.84/26.88 active(U172(tt)) -> mark(tt) 100.84/26.88 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 100.84/26.88 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 100.84/26.88 active(U183(tt)) -> mark(tt) 100.84/26.88 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 100.84/26.88 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 100.84/26.88 active(U193(tt)) -> mark(tt) 100.84/26.88 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 100.84/26.88 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 100.84/26.88 active(U206(tt)) -> mark(tt) 100.84/26.88 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 100.84/26.88 active(U211(tt)) -> mark(tt) 100.84/26.88 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 100.84/26.88 active(U221(tt)) -> mark(tt) 100.84/26.88 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 100.84/26.88 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 100.84/26.88 active(U232(tt)) -> mark(tt) 100.84/26.88 active(U24(tt, X)) -> mark(X) 100.84/26.88 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 100.84/26.88 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 100.84/26.88 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 100.84/26.88 active(U246(tt)) -> mark(tt) 100.84/26.88 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 100.84/26.88 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 100.84/26.88 active(U256(tt)) -> mark(tt) 100.84/26.88 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 100.84/26.88 active(U262(tt)) -> mark(tt) 100.84/26.88 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 100.84/26.88 active(U272(tt)) -> mark(tt) 100.84/26.88 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 100.84/26.88 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 100.84/26.88 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 100.84/26.88 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 100.84/26.88 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 100.84/26.88 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 100.84/26.88 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 100.84/26.88 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 100.84/26.88 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 100.84/26.88 active(U304(tt, Y)) -> mark(Y) 100.84/26.88 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 100.84/26.88 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 100.84/26.88 active(U312(tt, XS)) -> mark(pair(nil, XS)) 100.84/26.88 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 100.84/26.88 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 100.84/26.88 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 100.84/26.88 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 100.84/26.88 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 100.84/26.88 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 100.84/26.88 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 100.84/26.88 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 100.84/26.88 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 100.84/26.88 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 100.84/26.88 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 100.84/26.88 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 100.84/26.88 active(U334(tt, XS)) -> mark(XS) 100.84/26.88 active(U34(tt, N)) -> mark(N) 100.84/26.88 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 100.84/26.88 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 100.84/26.88 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 100.84/26.88 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 100.84/26.88 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 100.84/26.88 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 100.84/26.88 active(U46(tt)) -> mark(tt) 100.84/26.88 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 100.84/26.88 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 100.84/26.88 active(U56(tt)) -> mark(tt) 100.84/26.88 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 100.84/26.88 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 100.84/26.88 active(U63(tt)) -> mark(tt) 100.84/26.88 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 100.84/26.88 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 100.84/26.88 active(U73(tt)) -> mark(tt) 100.84/26.88 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 100.84/26.88 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 100.84/26.88 active(U83(tt)) -> mark(tt) 100.84/26.88 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 100.84/26.88 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 100.84/26.88 active(U93(tt)) -> mark(tt) 100.84/26.88 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 100.84/26.88 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 100.84/26.88 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 100.84/26.88 active(isLNat(nil)) -> mark(tt) 100.84/26.88 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 100.84/26.88 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 100.84/26.88 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 100.84/26.88 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 100.84/26.88 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNatKind(nil)) -> mark(tt) 100.84/26.88 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 100.84/26.88 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 100.84/26.88 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 100.84/26.88 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 100.84/26.88 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 100.84/26.88 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 100.84/26.88 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 100.84/26.88 active(isNatural(0')) -> mark(tt) 100.84/26.88 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 100.84/26.88 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 100.84/26.88 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isNaturalKind(0')) -> mark(tt) 100.84/26.88 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 100.84/26.88 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 100.84/26.88 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 100.84/26.88 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 100.84/26.88 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 100.84/26.88 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 100.84/26.88 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 100.84/26.88 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 100.84/26.88 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 100.84/26.88 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 100.84/26.88 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 100.84/26.88 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 100.84/26.88 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 100.84/26.88 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 100.84/26.88 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 100.84/26.88 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 100.84/26.88 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 100.84/26.88 active(U105(X1, X2)) -> U105(active(X1), X2) 100.84/26.88 active(U106(X)) -> U106(active(X)) 100.84/26.88 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 100.84/26.88 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 100.84/26.88 active(U111(X1, X2)) -> U111(active(X1), X2) 100.84/26.88 active(U112(X)) -> U112(active(X)) 100.84/26.88 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 100.84/26.88 active(U121(X1, X2)) -> U121(active(X1), X2) 100.84/26.88 active(U122(X)) -> U122(active(X)) 100.84/26.88 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 100.84/26.88 active(U131(X)) -> U131(active(X)) 100.84/26.88 active(snd(X)) -> snd(active(X)) 100.84/26.88 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 100.84/26.88 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 100.84/26.88 active(U141(X)) -> U141(active(X)) 100.84/26.88 active(U151(X)) -> U151(active(X)) 100.84/26.88 active(U161(X)) -> U161(active(X)) 100.84/26.88 active(U171(X1, X2)) -> U171(active(X1), X2) 100.84/26.88 active(U172(X)) -> U172(active(X)) 100.84/26.88 active(U181(X1, X2)) -> U181(active(X1), X2) 100.84/26.88 active(U182(X1, X2)) -> U182(active(X1), X2) 100.84/26.88 active(U183(X)) -> U183(active(X)) 100.84/26.88 active(U191(X1, X2)) -> U191(active(X1), X2) 100.84/26.88 active(U192(X1, X2)) -> U192(active(X1), X2) 100.84/26.88 active(U193(X)) -> U193(active(X)) 100.84/26.88 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 100.84/26.88 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 100.84/26.88 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 100.84/26.88 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 100.84/26.88 active(U205(X1, X2)) -> U205(active(X1), X2) 100.84/26.88 active(U206(X)) -> U206(active(X)) 100.84/26.88 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 100.84/26.88 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 100.84/26.88 active(U211(X)) -> U211(active(X)) 100.84/26.88 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 100.84/26.88 active(U221(X)) -> U221(active(X)) 100.84/26.88 active(U24(X1, X2)) -> U24(active(X1), X2) 100.84/26.88 active(U231(X1, X2)) -> U231(active(X1), X2) 100.84/26.88 active(U232(X)) -> U232(active(X)) 100.84/26.88 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 100.84/26.88 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 100.84/26.88 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 100.84/26.88 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 100.84/26.88 active(U245(X1, X2)) -> U245(active(X1), X2) 100.84/26.88 active(U246(X)) -> U246(active(X)) 100.84/26.88 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 100.84/26.88 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 100.84/26.88 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 100.84/26.88 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 100.84/26.88 active(U255(X1, X2)) -> U255(active(X1), X2) 100.84/26.88 active(U256(X)) -> U256(active(X)) 100.84/26.88 active(U261(X1, X2)) -> U261(active(X1), X2) 100.84/26.88 active(U262(X)) -> U262(active(X)) 100.84/26.88 active(U271(X1, X2)) -> U271(active(X1), X2) 100.84/26.88 active(U272(X)) -> U272(active(X)) 100.84/26.88 active(U281(X1, X2)) -> U281(active(X1), X2) 100.84/26.88 active(U282(X1, X2)) -> U282(active(X1), X2) 100.84/26.88 active(cons(X1, X2)) -> cons(active(X1), X2) 100.84/26.88 active(natsFrom(X)) -> natsFrom(active(X)) 100.84/26.88 active(s(X)) -> s(active(X)) 100.84/26.88 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 100.84/26.88 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 100.84/26.88 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 100.84/26.88 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 100.84/26.88 active(head(X)) -> head(active(X)) 100.84/26.88 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 100.84/26.88 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 100.84/26.88 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 100.84/26.88 active(U302(X1, X2)) -> U302(active(X1), X2) 100.84/26.88 active(U303(X1, X2)) -> U303(active(X1), X2) 100.84/26.88 active(U304(X1, X2)) -> U304(active(X1), X2) 100.84/26.88 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 100.84/26.88 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 100.84/26.88 active(U311(X1, X2)) -> U311(active(X1), X2) 100.84/26.88 active(U312(X1, X2)) -> U312(active(X1), X2) 100.84/26.88 active(pair(X1, X2)) -> pair(active(X1), X2) 100.84/26.88 active(pair(X1, X2)) -> pair(X1, active(X2)) 100.84/26.88 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 100.84/26.88 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 100.84/26.88 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 100.84/26.88 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 100.84/26.88 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 100.84/26.88 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 100.84/26.88 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 100.84/26.88 active(U327(X1, X2)) -> U327(active(X1), X2) 100.84/26.88 active(U34(X1, X2)) -> U34(active(X1), X2) 100.84/26.88 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 100.84/26.88 active(U332(X1, X2)) -> U332(active(X1), X2) 100.84/26.88 active(U333(X1, X2)) -> U333(active(X1), X2) 100.84/26.88 active(U334(X1, X2)) -> U334(active(X1), X2) 100.84/26.88 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 100.84/26.88 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 100.84/26.88 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 100.84/26.88 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 100.84/26.88 active(fst(X)) -> fst(active(X)) 100.84/26.88 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 100.84/26.88 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 100.84/26.88 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 100.84/26.88 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 100.84/26.88 active(U45(X1, X2)) -> U45(active(X1), X2) 100.84/26.88 active(U46(X)) -> U46(active(X)) 100.84/26.88 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 100.84/26.88 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 100.84/26.88 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 100.84/26.88 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 100.84/26.88 active(U55(X1, X2)) -> U55(active(X1), X2) 100.84/26.88 active(U56(X)) -> U56(active(X)) 100.84/26.88 active(U61(X1, X2)) -> U61(active(X1), X2) 100.84/26.88 active(U62(X1, X2)) -> U62(active(X1), X2) 100.84/26.88 active(U63(X)) -> U63(active(X)) 100.84/26.88 active(U71(X1, X2)) -> U71(active(X1), X2) 100.84/26.88 active(U72(X1, X2)) -> U72(active(X1), X2) 100.84/26.88 active(U73(X)) -> U73(active(X)) 100.84/26.88 active(U81(X1, X2)) -> U81(active(X1), X2) 100.84/26.88 active(U82(X1, X2)) -> U82(active(X1), X2) 100.84/26.88 active(U83(X)) -> U83(active(X)) 100.84/26.88 active(U91(X1, X2)) -> U91(active(X1), X2) 100.84/26.88 active(U92(X1, X2)) -> U92(active(X1), X2) 100.84/26.88 active(U93(X)) -> U93(active(X)) 100.84/26.88 active(tail(X)) -> tail(active(X)) 100.84/26.88 active(take(X1, X2)) -> take(active(X1), X2) 100.84/26.88 active(take(X1, X2)) -> take(X1, active(X2)) 100.84/26.88 active(sel(X1, X2)) -> sel(active(X1), X2) 100.84/26.88 active(sel(X1, X2)) -> sel(X1, active(X2)) 100.84/26.88 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 100.84/26.88 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 100.84/26.88 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 100.84/26.88 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 100.84/26.88 U105(mark(X1), X2) -> mark(U105(X1, X2)) 100.84/26.88 U106(mark(X)) -> mark(U106(X)) 100.84/26.88 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 100.84/26.88 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 100.84/26.88 U111(mark(X1), X2) -> mark(U111(X1, X2)) 100.84/26.88 U112(mark(X)) -> mark(U112(X)) 100.84/26.88 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 100.84/26.88 U121(mark(X1), X2) -> mark(U121(X1, X2)) 100.84/26.88 U122(mark(X)) -> mark(U122(X)) 100.84/26.88 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 100.84/26.88 U131(mark(X)) -> mark(U131(X)) 100.84/26.88 snd(mark(X)) -> mark(snd(X)) 100.84/26.88 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 100.84/26.88 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 100.84/26.88 U141(mark(X)) -> mark(U141(X)) 100.84/26.88 U151(mark(X)) -> mark(U151(X)) 100.84/26.88 U161(mark(X)) -> mark(U161(X)) 100.84/26.88 U171(mark(X1), X2) -> mark(U171(X1, X2)) 100.84/26.88 U172(mark(X)) -> mark(U172(X)) 100.84/26.88 U181(mark(X1), X2) -> mark(U181(X1, X2)) 100.84/26.88 U182(mark(X1), X2) -> mark(U182(X1, X2)) 100.84/26.88 U183(mark(X)) -> mark(U183(X)) 100.84/26.88 U191(mark(X1), X2) -> mark(U191(X1, X2)) 100.84/26.88 U192(mark(X1), X2) -> mark(U192(X1, X2)) 100.84/26.88 U193(mark(X)) -> mark(U193(X)) 100.84/26.88 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 100.84/26.88 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 100.84/26.88 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 100.84/26.88 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 100.84/26.88 U205(mark(X1), X2) -> mark(U205(X1, X2)) 100.84/26.88 U206(mark(X)) -> mark(U206(X)) 100.84/26.88 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 100.84/26.88 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 100.84/26.88 U211(mark(X)) -> mark(U211(X)) 100.84/26.88 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 100.84/26.88 U221(mark(X)) -> mark(U221(X)) 100.84/26.88 U24(mark(X1), X2) -> mark(U24(X1, X2)) 100.84/26.88 U231(mark(X1), X2) -> mark(U231(X1, X2)) 100.84/26.88 U232(mark(X)) -> mark(U232(X)) 100.84/26.88 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 100.84/26.88 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 100.84/26.88 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 100.84/26.88 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 100.84/26.88 U245(mark(X1), X2) -> mark(U245(X1, X2)) 100.84/26.88 U246(mark(X)) -> mark(U246(X)) 100.84/26.88 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 100.84/26.88 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 100.84/26.88 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 100.84/26.88 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 100.84/26.88 U255(mark(X1), X2) -> mark(U255(X1, X2)) 100.84/26.88 U256(mark(X)) -> mark(U256(X)) 100.84/26.88 U261(mark(X1), X2) -> mark(U261(X1, X2)) 100.84/26.88 U262(mark(X)) -> mark(U262(X)) 100.84/26.88 U271(mark(X1), X2) -> mark(U271(X1, X2)) 100.84/26.88 U272(mark(X)) -> mark(U272(X)) 100.84/26.88 U281(mark(X1), X2) -> mark(U281(X1, X2)) 100.84/26.88 U282(mark(X1), X2) -> mark(U282(X1, X2)) 100.84/26.88 cons(mark(X1), X2) -> mark(cons(X1, X2)) 100.84/26.88 natsFrom(mark(X)) -> mark(natsFrom(X)) 100.84/26.88 s(mark(X)) -> mark(s(X)) 100.84/26.88 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 100.84/26.88 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 100.84/26.88 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 100.84/26.88 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 100.84/26.88 head(mark(X)) -> mark(head(X)) 100.84/26.88 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 100.84/26.88 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 100.84/26.88 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 100.84/26.88 U302(mark(X1), X2) -> mark(U302(X1, X2)) 100.84/26.88 U303(mark(X1), X2) -> mark(U303(X1, X2)) 100.84/26.88 U304(mark(X1), X2) -> mark(U304(X1, X2)) 100.84/26.88 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 100.84/26.88 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 100.84/26.88 U311(mark(X1), X2) -> mark(U311(X1, X2)) 100.84/26.88 U312(mark(X1), X2) -> mark(U312(X1, X2)) 100.84/26.88 pair(mark(X1), X2) -> mark(pair(X1, X2)) 100.84/26.88 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 100.84/26.88 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 100.84/26.88 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 100.84/26.88 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 100.84/26.88 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 100.84/26.88 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 100.84/26.88 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 100.84/26.88 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 100.84/26.88 U327(mark(X1), X2) -> mark(U327(X1, X2)) 100.84/26.88 U34(mark(X1), X2) -> mark(U34(X1, X2)) 100.84/26.88 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 100.84/26.88 U332(mark(X1), X2) -> mark(U332(X1, X2)) 100.84/26.88 U333(mark(X1), X2) -> mark(U333(X1, X2)) 100.84/26.88 U334(mark(X1), X2) -> mark(U334(X1, X2)) 100.84/26.88 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 100.84/26.88 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 100.84/26.88 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 100.84/26.88 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 100.84/26.88 fst(mark(X)) -> mark(fst(X)) 100.84/26.88 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 100.84/26.88 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 100.84/26.88 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 100.84/26.88 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 100.84/26.88 U45(mark(X1), X2) -> mark(U45(X1, X2)) 100.84/26.88 U46(mark(X)) -> mark(U46(X)) 100.84/26.88 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 100.84/26.88 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 100.84/26.88 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 100.84/26.88 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 100.84/26.88 U55(mark(X1), X2) -> mark(U55(X1, X2)) 100.84/26.88 U56(mark(X)) -> mark(U56(X)) 100.84/26.88 U61(mark(X1), X2) -> mark(U61(X1, X2)) 100.84/26.88 U62(mark(X1), X2) -> mark(U62(X1, X2)) 100.84/26.88 U63(mark(X)) -> mark(U63(X)) 100.84/26.88 U71(mark(X1), X2) -> mark(U71(X1, X2)) 100.84/26.88 U72(mark(X1), X2) -> mark(U72(X1, X2)) 100.84/26.88 U73(mark(X)) -> mark(U73(X)) 100.84/26.88 U81(mark(X1), X2) -> mark(U81(X1, X2)) 100.84/26.88 U82(mark(X1), X2) -> mark(U82(X1, X2)) 100.84/26.88 U83(mark(X)) -> mark(U83(X)) 100.84/26.88 U91(mark(X1), X2) -> mark(U91(X1, X2)) 100.84/26.88 U92(mark(X1), X2) -> mark(U92(X1, X2)) 100.84/26.88 U93(mark(X)) -> mark(U93(X)) 100.84/26.88 tail(mark(X)) -> mark(tail(X)) 100.84/26.88 take(mark(X1), X2) -> mark(take(X1, X2)) 100.84/26.88 take(X1, mark(X2)) -> mark(take(X1, X2)) 100.84/26.88 sel(mark(X1), X2) -> mark(sel(X1, X2)) 100.84/26.88 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 100.84/26.88 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(tt) -> ok(tt) 100.84/26.88 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 100.84/26.88 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 100.84/26.88 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 100.84/26.88 proper(isNatural(X)) -> isNatural(proper(X)) 100.84/26.88 proper(U106(X)) -> U106(proper(X)) 100.84/26.88 proper(isLNat(X)) -> isLNat(proper(X)) 100.84/26.88 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 100.84/26.88 proper(U112(X)) -> U112(proper(X)) 100.84/26.88 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 100.84/26.88 proper(U122(X)) -> U122(proper(X)) 100.84/26.88 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U131(X)) -> U131(proper(X)) 100.84/26.88 proper(snd(X)) -> snd(proper(X)) 100.84/26.88 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 100.84/26.88 proper(U141(X)) -> U141(proper(X)) 100.84/26.88 proper(U151(X)) -> U151(proper(X)) 100.84/26.88 proper(U161(X)) -> U161(proper(X)) 100.84/26.88 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 100.84/26.88 proper(U172(X)) -> U172(proper(X)) 100.84/26.88 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 100.84/26.88 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 100.84/26.88 proper(U183(X)) -> U183(proper(X)) 100.84/26.88 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 100.84/26.88 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 100.84/26.88 proper(U193(X)) -> U193(proper(X)) 100.84/26.88 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 100.84/26.88 proper(U206(X)) -> U206(proper(X)) 100.84/26.88 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U211(X)) -> U211(proper(X)) 100.84/26.88 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U221(X)) -> U221(proper(X)) 100.84/26.88 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 100.84/26.88 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 100.84/26.88 proper(U232(X)) -> U232(proper(X)) 100.84/26.88 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 100.84/26.88 proper(U246(X)) -> U246(proper(X)) 100.84/26.88 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 100.84/26.88 proper(U256(X)) -> U256(proper(X)) 100.84/26.88 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 100.84/26.88 proper(U262(X)) -> U262(proper(X)) 100.84/26.88 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 100.84/26.88 proper(U272(X)) -> U272(proper(X)) 100.84/26.88 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 100.84/26.88 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 100.84/26.88 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 100.84/26.88 proper(natsFrom(X)) -> natsFrom(proper(X)) 100.84/26.88 proper(s(X)) -> s(proper(X)) 100.84/26.88 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(head(X)) -> head(proper(X)) 100.84/26.88 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 100.84/26.88 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 100.84/26.88 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 100.84/26.88 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 100.84/26.88 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 100.84/26.88 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 100.84/26.88 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 100.84/26.88 proper(nil) -> ok(nil) 100.84/26.88 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 100.84/26.88 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 100.84/26.88 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 100.84/26.88 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 100.84/26.88 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 100.84/26.88 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 100.84/26.88 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(fst(X)) -> fst(proper(X)) 100.84/26.88 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 100.84/26.88 proper(U46(X)) -> U46(proper(X)) 100.84/26.88 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 100.84/26.88 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 100.84/26.88 proper(U56(X)) -> U56(proper(X)) 100.84/26.88 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 100.84/26.88 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 100.84/26.88 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 100.84/26.88 proper(U63(X)) -> U63(proper(X)) 100.84/26.88 proper(isPLNat(X)) -> isPLNat(proper(X)) 100.84/26.88 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 100.84/26.88 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 100.84/26.88 proper(U73(X)) -> U73(proper(X)) 100.84/26.88 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 100.84/26.88 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 100.84/26.88 proper(U83(X)) -> U83(proper(X)) 100.84/26.88 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 100.84/26.88 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 100.84/26.88 proper(U93(X)) -> U93(proper(X)) 100.84/26.88 proper(tail(X)) -> tail(proper(X)) 100.84/26.88 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 100.84/26.88 proper(0') -> ok(0') 100.84/26.88 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 100.84/26.88 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 100.84/26.88 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 100.84/26.88 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 100.84/26.88 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 100.84/26.88 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 100.84/26.88 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 100.84/26.88 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 100.84/26.88 isNatural(ok(X)) -> ok(isNatural(X)) 100.84/26.88 U106(ok(X)) -> ok(U106(X)) 100.84/26.88 isLNat(ok(X)) -> ok(isLNat(X)) 100.84/26.88 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 100.84/26.88 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 100.84/26.88 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 100.84/26.88 U112(ok(X)) -> ok(U112(X)) 100.84/26.88 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 100.84/26.88 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 100.84/26.88 U122(ok(X)) -> ok(U122(X)) 100.84/26.88 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 100.84/26.88 U131(ok(X)) -> ok(U131(X)) 100.84/26.88 snd(ok(X)) -> ok(snd(X)) 100.84/26.88 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 100.84/26.88 U141(ok(X)) -> ok(U141(X)) 100.84/26.88 U151(ok(X)) -> ok(U151(X)) 100.84/26.88 U161(ok(X)) -> ok(U161(X)) 100.84/26.88 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 100.84/26.88 U172(ok(X)) -> ok(U172(X)) 100.84/26.88 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 100.84/26.88 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 100.84/26.88 U183(ok(X)) -> ok(U183(X)) 100.84/26.88 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 100.84/26.88 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 100.84/26.88 U193(ok(X)) -> ok(U193(X)) 100.84/26.88 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 100.84/26.88 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 100.84/26.88 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 100.84/26.88 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 100.84/26.88 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 100.84/26.88 U206(ok(X)) -> ok(U206(X)) 100.84/26.88 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 100.84/26.88 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 100.84/26.88 U211(ok(X)) -> ok(U211(X)) 100.84/26.88 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 100.84/26.88 U221(ok(X)) -> ok(U221(X)) 100.84/26.88 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 100.84/26.88 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 100.84/26.88 U232(ok(X)) -> ok(U232(X)) 100.84/26.88 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 100.84/26.88 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 100.84/26.88 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 100.84/26.88 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 100.84/26.88 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 100.84/26.88 U246(ok(X)) -> ok(U246(X)) 100.84/26.88 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 100.84/26.88 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 100.84/26.88 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 100.84/26.88 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 100.84/26.88 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 100.84/26.88 U256(ok(X)) -> ok(U256(X)) 100.84/26.88 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 100.84/26.88 U262(ok(X)) -> ok(U262(X)) 100.84/26.88 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 100.84/26.88 U272(ok(X)) -> ok(U272(X)) 100.84/26.88 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 100.84/26.88 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 100.84/26.88 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 100.84/26.88 natsFrom(ok(X)) -> ok(natsFrom(X)) 100.84/26.88 s(ok(X)) -> ok(s(X)) 100.84/26.88 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 100.84/26.88 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 100.84/26.88 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 100.84/26.88 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 100.84/26.88 head(ok(X)) -> ok(head(X)) 100.84/26.88 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 100.84/26.88 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 100.84/26.88 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 100.84/26.88 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 100.84/26.88 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 100.84/26.88 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 100.84/26.88 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 100.84/26.88 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 100.84/26.88 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 100.84/26.88 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 100.84/26.88 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 100.84/26.88 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 100.84/26.88 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 100.84/26.88 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 100.84/26.88 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 100.84/26.88 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 100.84/26.88 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 100.84/26.88 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 100.84/26.88 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 100.84/26.88 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 100.84/26.88 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 100.84/26.88 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 100.84/26.88 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 100.84/26.88 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 100.84/26.88 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 100.84/26.88 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 100.84/26.88 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 100.84/26.88 fst(ok(X)) -> ok(fst(X)) 100.84/26.88 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 100.84/26.88 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 100.84/26.88 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 100.84/26.88 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 100.84/26.88 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 100.84/26.88 U46(ok(X)) -> ok(U46(X)) 100.84/26.88 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 100.84/26.88 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 100.84/26.88 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 100.84/26.88 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 100.84/26.88 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 100.84/26.88 U56(ok(X)) -> ok(U56(X)) 100.84/26.88 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 100.84/26.88 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 100.84/26.88 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 100.84/26.88 U63(ok(X)) -> ok(U63(X)) 100.84/26.88 isPLNat(ok(X)) -> ok(isPLNat(X)) 100.84/26.88 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 100.84/26.88 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 100.84/26.88 U73(ok(X)) -> ok(U73(X)) 100.84/26.88 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 100.84/26.88 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 100.84/26.88 U83(ok(X)) -> ok(U83(X)) 100.84/26.88 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 100.84/26.88 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 100.84/26.88 U93(ok(X)) -> ok(U93(X)) 100.84/26.88 tail(ok(X)) -> ok(tail(X)) 100.84/26.88 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 100.84/26.88 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 100.84/26.88 top(mark(X)) -> top(proper(X)) 100.84/26.88 top(ok(X)) -> top(active(X)) 100.84/26.88 100.84/26.88 S is empty. 100.84/26.88 Rewrite Strategy: FULL 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 100.84/26.88 Infered types. 100.84/26.88 ---------------------------------------- 100.84/26.88 100.84/26.88 (22) 100.84/26.88 Obligation: 100.84/26.88 TRS: 100.84/26.88 Rules: 100.84/26.88 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 100.84/26.88 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 100.84/26.88 active(U106(tt)) -> mark(tt) 100.84/26.88 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 100.84/26.88 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 100.84/26.88 active(U112(tt)) -> mark(tt) 100.84/26.88 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 100.84/26.88 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 100.84/26.88 active(U122(tt)) -> mark(tt) 100.84/26.88 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 100.84/26.88 active(U131(tt)) -> mark(tt) 100.84/26.88 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 100.84/26.88 active(U141(tt)) -> mark(tt) 100.84/26.88 active(U151(tt)) -> mark(tt) 100.84/26.88 active(U161(tt)) -> mark(tt) 100.84/26.88 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 100.84/26.88 active(U172(tt)) -> mark(tt) 100.84/26.88 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 100.84/26.88 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 100.84/26.88 active(U183(tt)) -> mark(tt) 100.84/26.88 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 100.84/26.88 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 100.84/26.88 active(U193(tt)) -> mark(tt) 100.84/26.88 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 100.84/26.88 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 100.84/26.88 active(U206(tt)) -> mark(tt) 100.84/26.88 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 100.84/26.88 active(U211(tt)) -> mark(tt) 100.84/26.88 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 100.84/26.88 active(U221(tt)) -> mark(tt) 100.84/26.88 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 100.84/26.88 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 100.84/26.88 active(U232(tt)) -> mark(tt) 100.84/26.88 active(U24(tt, X)) -> mark(X) 100.84/26.88 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 100.84/26.88 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 100.84/26.88 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 100.84/26.88 active(U246(tt)) -> mark(tt) 100.84/26.88 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 100.84/26.88 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 100.84/26.88 active(U256(tt)) -> mark(tt) 100.84/26.88 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 100.84/26.88 active(U262(tt)) -> mark(tt) 100.84/26.88 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 100.84/26.88 active(U272(tt)) -> mark(tt) 100.84/26.88 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 100.84/26.88 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 100.84/26.88 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 100.84/26.88 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 100.84/26.88 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 100.84/26.88 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 100.84/26.88 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 100.84/26.88 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 100.84/26.88 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 100.84/26.88 active(U304(tt, Y)) -> mark(Y) 100.84/26.88 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 100.84/26.88 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 100.84/26.88 active(U312(tt, XS)) -> mark(pair(nil, XS)) 100.84/26.88 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 100.84/26.88 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 100.84/26.88 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 100.84/26.88 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 100.84/26.88 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 100.84/26.88 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 100.84/26.88 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 100.84/26.88 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 100.84/26.88 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 100.84/26.88 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 100.84/26.88 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 100.84/26.88 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 100.84/26.88 active(U334(tt, XS)) -> mark(XS) 100.84/26.88 active(U34(tt, N)) -> mark(N) 100.84/26.88 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 100.84/26.88 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 100.84/26.88 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 100.84/26.88 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 100.84/26.88 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 100.84/26.88 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 100.84/26.88 active(U46(tt)) -> mark(tt) 100.84/26.88 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 100.84/26.88 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 100.84/26.88 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 100.84/26.88 active(U56(tt)) -> mark(tt) 100.84/26.88 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 100.84/26.88 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 100.84/26.88 active(U63(tt)) -> mark(tt) 100.84/26.88 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 100.84/26.88 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 100.84/26.88 active(U73(tt)) -> mark(tt) 100.84/26.88 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 100.84/26.88 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 100.84/26.88 active(U83(tt)) -> mark(tt) 100.84/26.88 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 100.84/26.88 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 100.84/26.88 active(U93(tt)) -> mark(tt) 100.84/26.88 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 100.84/26.88 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 100.84/26.88 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 100.84/26.88 active(isLNat(nil)) -> mark(tt) 100.84/26.88 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 100.84/26.88 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 100.84/26.88 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 100.84/26.88 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 100.84/26.88 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isLNatKind(nil)) -> mark(tt) 100.84/26.88 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 100.84/26.88 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 100.84/26.88 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 100.84/26.88 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 100.84/26.88 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 100.84/26.88 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 100.84/26.88 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 100.84/26.88 active(isNatural(0')) -> mark(tt) 100.84/26.88 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 100.84/26.88 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 100.84/26.88 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isNaturalKind(0')) -> mark(tt) 100.84/26.88 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 100.84/26.88 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 100.84/26.88 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 100.84/26.88 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 100.84/26.88 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 100.84/26.88 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 100.84/26.88 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 100.84/26.88 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 100.84/26.88 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 100.84/26.88 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 100.84/26.88 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 100.84/26.88 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 100.84/26.88 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 100.84/26.88 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 100.84/26.88 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 100.84/26.88 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 100.84/26.88 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 100.84/26.88 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 100.84/26.88 active(U105(X1, X2)) -> U105(active(X1), X2) 100.84/26.88 active(U106(X)) -> U106(active(X)) 100.84/26.88 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 100.84/26.88 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 100.84/26.88 active(U111(X1, X2)) -> U111(active(X1), X2) 100.84/26.88 active(U112(X)) -> U112(active(X)) 100.84/26.88 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 100.84/26.88 active(U121(X1, X2)) -> U121(active(X1), X2) 100.84/26.88 active(U122(X)) -> U122(active(X)) 100.84/26.88 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 100.84/26.88 active(U131(X)) -> U131(active(X)) 100.84/26.88 active(snd(X)) -> snd(active(X)) 100.84/26.88 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 100.84/26.88 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 100.84/26.88 active(U141(X)) -> U141(active(X)) 100.84/26.88 active(U151(X)) -> U151(active(X)) 100.84/26.88 active(U161(X)) -> U161(active(X)) 100.84/26.88 active(U171(X1, X2)) -> U171(active(X1), X2) 100.84/26.88 active(U172(X)) -> U172(active(X)) 100.84/26.88 active(U181(X1, X2)) -> U181(active(X1), X2) 100.84/26.88 active(U182(X1, X2)) -> U182(active(X1), X2) 100.84/26.88 active(U183(X)) -> U183(active(X)) 100.84/26.88 active(U191(X1, X2)) -> U191(active(X1), X2) 100.84/26.88 active(U192(X1, X2)) -> U192(active(X1), X2) 100.84/26.88 active(U193(X)) -> U193(active(X)) 100.84/26.88 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 100.84/26.88 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 100.84/26.88 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 100.84/26.88 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 100.84/26.88 active(U205(X1, X2)) -> U205(active(X1), X2) 100.84/26.88 active(U206(X)) -> U206(active(X)) 100.84/26.88 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 100.84/26.88 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 100.84/26.88 active(U211(X)) -> U211(active(X)) 100.84/26.88 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 100.84/26.88 active(U221(X)) -> U221(active(X)) 100.84/26.88 active(U24(X1, X2)) -> U24(active(X1), X2) 100.84/26.88 active(U231(X1, X2)) -> U231(active(X1), X2) 100.84/26.88 active(U232(X)) -> U232(active(X)) 100.84/26.88 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.11/26.88 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.11/26.88 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.11/26.88 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.11/26.88 active(U245(X1, X2)) -> U245(active(X1), X2) 101.11/26.88 active(U246(X)) -> U246(active(X)) 101.11/26.88 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.11/26.88 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.11/26.88 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.11/26.88 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.11/26.88 active(U255(X1, X2)) -> U255(active(X1), X2) 101.11/26.88 active(U256(X)) -> U256(active(X)) 101.11/26.88 active(U261(X1, X2)) -> U261(active(X1), X2) 101.11/26.88 active(U262(X)) -> U262(active(X)) 101.11/26.88 active(U271(X1, X2)) -> U271(active(X1), X2) 101.11/26.88 active(U272(X)) -> U272(active(X)) 101.11/26.88 active(U281(X1, X2)) -> U281(active(X1), X2) 101.11/26.88 active(U282(X1, X2)) -> U282(active(X1), X2) 101.11/26.88 active(cons(X1, X2)) -> cons(active(X1), X2) 101.11/26.88 active(natsFrom(X)) -> natsFrom(active(X)) 101.11/26.88 active(s(X)) -> s(active(X)) 101.11/26.88 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.11/26.88 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.11/26.89 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.11/26.89 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.11/26.89 active(head(X)) -> head(active(X)) 101.11/26.89 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.11/26.89 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.11/26.89 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.11/26.89 active(U302(X1, X2)) -> U302(active(X1), X2) 101.11/26.89 active(U303(X1, X2)) -> U303(active(X1), X2) 101.11/26.89 active(U304(X1, X2)) -> U304(active(X1), X2) 101.11/26.89 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.11/26.89 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.11/26.89 active(U311(X1, X2)) -> U311(active(X1), X2) 101.11/26.89 active(U312(X1, X2)) -> U312(active(X1), X2) 101.11/26.89 active(pair(X1, X2)) -> pair(active(X1), X2) 101.11/26.89 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.11/26.89 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.11/26.89 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.11/26.89 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.11/26.89 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.11/26.89 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.11/26.89 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.11/26.89 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.11/26.89 active(U327(X1, X2)) -> U327(active(X1), X2) 101.11/26.89 active(U34(X1, X2)) -> U34(active(X1), X2) 101.11/26.89 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.11/26.89 active(U332(X1, X2)) -> U332(active(X1), X2) 101.11/26.89 active(U333(X1, X2)) -> U333(active(X1), X2) 101.11/26.89 active(U334(X1, X2)) -> U334(active(X1), X2) 101.11/26.89 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.11/26.89 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.11/26.89 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.11/26.89 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.11/26.89 active(fst(X)) -> fst(active(X)) 101.11/26.89 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.11/26.89 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.11/26.89 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.11/26.89 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.11/26.89 active(U45(X1, X2)) -> U45(active(X1), X2) 101.11/26.89 active(U46(X)) -> U46(active(X)) 101.11/26.89 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.11/26.89 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.11/26.89 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.11/26.89 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.11/26.89 active(U55(X1, X2)) -> U55(active(X1), X2) 101.11/26.89 active(U56(X)) -> U56(active(X)) 101.11/26.89 active(U61(X1, X2)) -> U61(active(X1), X2) 101.11/26.89 active(U62(X1, X2)) -> U62(active(X1), X2) 101.11/26.89 active(U63(X)) -> U63(active(X)) 101.11/26.89 active(U71(X1, X2)) -> U71(active(X1), X2) 101.11/26.89 active(U72(X1, X2)) -> U72(active(X1), X2) 101.11/26.89 active(U73(X)) -> U73(active(X)) 101.11/26.89 active(U81(X1, X2)) -> U81(active(X1), X2) 101.11/26.89 active(U82(X1, X2)) -> U82(active(X1), X2) 101.11/26.89 active(U83(X)) -> U83(active(X)) 101.11/26.89 active(U91(X1, X2)) -> U91(active(X1), X2) 101.11/26.89 active(U92(X1, X2)) -> U92(active(X1), X2) 101.11/26.89 active(U93(X)) -> U93(active(X)) 101.11/26.89 active(tail(X)) -> tail(active(X)) 101.11/26.89 active(take(X1, X2)) -> take(active(X1), X2) 101.11/26.89 active(take(X1, X2)) -> take(X1, active(X2)) 101.11/26.89 active(sel(X1, X2)) -> sel(active(X1), X2) 101.11/26.89 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.11/26.89 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.11/26.89 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.11/26.89 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.11/26.89 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.11/26.89 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.11/26.89 U106(mark(X)) -> mark(U106(X)) 101.11/26.89 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.11/26.89 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.11/26.89 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.11/26.89 U112(mark(X)) -> mark(U112(X)) 101.11/26.89 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.11/26.89 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.11/26.89 U122(mark(X)) -> mark(U122(X)) 101.11/26.89 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.11/26.89 U131(mark(X)) -> mark(U131(X)) 101.11/26.89 snd(mark(X)) -> mark(snd(X)) 101.11/26.89 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.11/26.89 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.11/26.89 U141(mark(X)) -> mark(U141(X)) 101.11/26.89 U151(mark(X)) -> mark(U151(X)) 101.11/26.89 U161(mark(X)) -> mark(U161(X)) 101.11/26.89 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.11/26.89 U172(mark(X)) -> mark(U172(X)) 101.11/26.89 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.11/26.89 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.11/26.89 U183(mark(X)) -> mark(U183(X)) 101.11/26.89 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.11/26.89 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.11/26.89 U193(mark(X)) -> mark(U193(X)) 101.11/26.89 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.11/26.89 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.11/26.89 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.11/26.89 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.11/26.89 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.11/26.89 U206(mark(X)) -> mark(U206(X)) 101.11/26.89 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.11/26.89 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.11/26.89 U211(mark(X)) -> mark(U211(X)) 101.11/26.89 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.11/26.89 U221(mark(X)) -> mark(U221(X)) 101.11/26.89 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.11/26.89 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.11/26.89 U232(mark(X)) -> mark(U232(X)) 101.11/26.89 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.11/26.89 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.11/26.89 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.11/26.89 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.11/26.89 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.11/26.89 U246(mark(X)) -> mark(U246(X)) 101.11/26.89 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.11/26.89 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.11/26.89 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.11/26.89 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.11/26.89 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.11/26.89 U256(mark(X)) -> mark(U256(X)) 101.11/26.89 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.11/26.89 U262(mark(X)) -> mark(U262(X)) 101.11/26.89 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.11/26.89 U272(mark(X)) -> mark(U272(X)) 101.11/26.89 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.11/26.89 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.11/26.89 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.11/26.89 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.11/26.89 s(mark(X)) -> mark(s(X)) 101.11/26.89 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.11/26.89 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.11/26.89 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.11/26.89 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.11/26.89 head(mark(X)) -> mark(head(X)) 101.11/26.89 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.11/26.89 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.11/26.89 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.11/26.89 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.11/26.89 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.11/26.89 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.11/26.89 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.11/26.89 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.11/26.89 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.11/26.89 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.11/26.89 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.11/26.89 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.11/26.89 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.11/26.89 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.11/26.89 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.11/26.89 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.11/26.89 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.11/26.89 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.11/26.89 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.11/26.89 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.11/26.89 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.11/26.89 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.11/26.89 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.11/26.89 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.11/26.89 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.11/26.89 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.11/26.89 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.11/26.89 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.11/26.89 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.11/26.89 fst(mark(X)) -> mark(fst(X)) 101.11/26.89 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.11/26.89 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.11/26.89 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.11/26.89 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.11/26.89 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.11/26.89 U46(mark(X)) -> mark(U46(X)) 101.11/26.89 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.11/26.89 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.11/26.89 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.11/26.89 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.11/26.89 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.11/26.89 U56(mark(X)) -> mark(U56(X)) 101.11/26.89 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.11/26.89 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.11/26.89 U63(mark(X)) -> mark(U63(X)) 101.11/26.89 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.11/26.89 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.11/26.89 U73(mark(X)) -> mark(U73(X)) 101.11/26.89 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.11/26.89 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.11/26.89 U83(mark(X)) -> mark(U83(X)) 101.11/26.89 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.11/26.89 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.11/26.89 U93(mark(X)) -> mark(U93(X)) 101.11/26.89 tail(mark(X)) -> mark(tail(X)) 101.11/26.89 take(mark(X1), X2) -> mark(take(X1, X2)) 101.11/26.89 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.11/26.89 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.11/26.89 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.11/26.89 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(tt) -> ok(tt) 101.11/26.89 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.11/26.89 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.11/26.89 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.11/26.89 proper(isNatural(X)) -> isNatural(proper(X)) 101.11/26.89 proper(U106(X)) -> U106(proper(X)) 101.11/26.89 proper(isLNat(X)) -> isLNat(proper(X)) 101.11/26.89 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.11/26.89 proper(U112(X)) -> U112(proper(X)) 101.11/26.89 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.11/26.89 proper(U122(X)) -> U122(proper(X)) 101.11/26.89 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U131(X)) -> U131(proper(X)) 101.11/26.89 proper(snd(X)) -> snd(proper(X)) 101.11/26.89 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.11/26.89 proper(U141(X)) -> U141(proper(X)) 101.11/26.89 proper(U151(X)) -> U151(proper(X)) 101.11/26.89 proper(U161(X)) -> U161(proper(X)) 101.11/26.89 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.11/26.89 proper(U172(X)) -> U172(proper(X)) 101.11/26.89 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.11/26.89 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.11/26.89 proper(U183(X)) -> U183(proper(X)) 101.11/26.89 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.11/26.89 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.11/26.89 proper(U193(X)) -> U193(proper(X)) 101.11/26.89 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.11/26.89 proper(U206(X)) -> U206(proper(X)) 101.11/26.89 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U211(X)) -> U211(proper(X)) 101.11/26.89 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U221(X)) -> U221(proper(X)) 101.11/26.89 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.11/26.89 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.11/26.89 proper(U232(X)) -> U232(proper(X)) 101.11/26.89 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.11/26.89 proper(U246(X)) -> U246(proper(X)) 101.11/26.89 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.11/26.89 proper(U256(X)) -> U256(proper(X)) 101.11/26.89 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.11/26.89 proper(U262(X)) -> U262(proper(X)) 101.11/26.89 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.11/26.89 proper(U272(X)) -> U272(proper(X)) 101.11/26.89 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.11/26.89 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.11/26.89 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.11/26.89 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.11/26.89 proper(s(X)) -> s(proper(X)) 101.11/26.89 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(head(X)) -> head(proper(X)) 101.11/26.89 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.11/26.89 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.11/26.89 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.11/26.89 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.11/26.89 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.11/26.89 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.11/26.89 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.11/26.89 proper(nil) -> ok(nil) 101.11/26.89 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.11/26.89 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.11/26.89 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.11/26.89 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.11/26.89 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.11/26.89 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(fst(X)) -> fst(proper(X)) 101.11/26.89 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.11/26.89 proper(U46(X)) -> U46(proper(X)) 101.11/26.89 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.11/26.89 proper(U56(X)) -> U56(proper(X)) 101.11/26.89 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.11/26.89 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.11/26.89 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.11/26.89 proper(U63(X)) -> U63(proper(X)) 101.11/26.89 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.11/26.89 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.11/26.89 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.11/26.89 proper(U73(X)) -> U73(proper(X)) 101.11/26.89 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.11/26.89 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.11/26.89 proper(U83(X)) -> U83(proper(X)) 101.11/26.89 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.11/26.89 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.11/26.89 proper(U93(X)) -> U93(proper(X)) 101.11/26.89 proper(tail(X)) -> tail(proper(X)) 101.11/26.89 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.11/26.89 proper(0') -> ok(0') 101.11/26.89 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.11/26.89 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.11/26.89 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.11/26.89 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.11/26.89 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.11/26.89 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.11/26.89 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.11/26.89 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.11/26.89 isNatural(ok(X)) -> ok(isNatural(X)) 101.11/26.89 U106(ok(X)) -> ok(U106(X)) 101.11/26.89 isLNat(ok(X)) -> ok(isLNat(X)) 101.11/26.89 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.11/26.89 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.11/26.89 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.11/26.89 U112(ok(X)) -> ok(U112(X)) 101.11/26.89 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.11/26.89 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.11/26.89 U122(ok(X)) -> ok(U122(X)) 101.11/26.89 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.11/26.89 U131(ok(X)) -> ok(U131(X)) 101.11/26.89 snd(ok(X)) -> ok(snd(X)) 101.11/26.89 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.11/26.89 U141(ok(X)) -> ok(U141(X)) 101.11/26.89 U151(ok(X)) -> ok(U151(X)) 101.11/26.89 U161(ok(X)) -> ok(U161(X)) 101.11/26.89 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.11/26.89 U172(ok(X)) -> ok(U172(X)) 101.11/26.89 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.11/26.89 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.11/26.89 U183(ok(X)) -> ok(U183(X)) 101.11/26.89 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.11/26.89 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.11/26.89 U193(ok(X)) -> ok(U193(X)) 101.11/26.89 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.11/26.89 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.11/26.89 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.11/26.89 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.11/26.89 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.11/26.89 U206(ok(X)) -> ok(U206(X)) 101.11/26.89 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.11/26.89 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.11/26.89 U211(ok(X)) -> ok(U211(X)) 101.11/26.89 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.11/26.89 U221(ok(X)) -> ok(U221(X)) 101.11/26.89 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.11/26.89 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.11/26.89 U232(ok(X)) -> ok(U232(X)) 101.11/26.89 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.11/26.89 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.11/26.89 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.11/26.89 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.11/26.89 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.11/26.89 U246(ok(X)) -> ok(U246(X)) 101.11/26.89 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.11/26.89 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.11/26.89 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.11/26.89 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.11/26.89 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.11/26.89 U256(ok(X)) -> ok(U256(X)) 101.11/26.89 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.11/26.89 U262(ok(X)) -> ok(U262(X)) 101.11/26.89 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.11/26.89 U272(ok(X)) -> ok(U272(X)) 101.11/26.89 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.11/26.89 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.11/26.89 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.11/26.89 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.11/26.89 s(ok(X)) -> ok(s(X)) 101.11/26.89 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.11/26.89 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.11/26.89 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.11/26.89 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.11/26.89 head(ok(X)) -> ok(head(X)) 101.11/26.89 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.11/26.89 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.11/26.89 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.11/26.89 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.11/26.89 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.11/26.89 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.11/26.89 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.11/26.89 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.11/26.89 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.11/26.89 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.11/26.89 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.11/26.89 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.11/26.89 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.11/26.89 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.11/26.89 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.11/26.89 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.11/26.89 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.11/26.89 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.11/26.89 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.11/26.89 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.11/26.89 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.11/26.89 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.11/26.89 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.11/26.89 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.11/26.89 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.11/26.89 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.11/26.89 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.11/26.89 fst(ok(X)) -> ok(fst(X)) 101.11/26.89 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.11/26.89 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.11/26.89 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.11/26.89 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.11/26.89 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.11/26.89 U46(ok(X)) -> ok(U46(X)) 101.11/26.89 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.11/26.89 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.11/26.89 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.11/26.89 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.11/26.89 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.11/26.89 U56(ok(X)) -> ok(U56(X)) 101.11/26.89 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.11/26.89 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.11/26.89 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.11/26.89 U63(ok(X)) -> ok(U63(X)) 101.11/26.89 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.11/26.89 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.11/26.89 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.11/26.89 U73(ok(X)) -> ok(U73(X)) 101.11/26.89 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.11/26.89 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.11/26.89 U83(ok(X)) -> ok(U83(X)) 101.11/26.89 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.11/26.89 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.11/26.89 U93(ok(X)) -> ok(U93(X)) 101.11/26.89 tail(ok(X)) -> ok(tail(X)) 101.11/26.89 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.11/26.89 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.11/26.89 top(mark(X)) -> top(proper(X)) 101.11/26.89 top(ok(X)) -> top(active(X)) 101.11/26.89 101.11/26.89 Types: 101.11/26.89 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 tt :: tt:mark:nil:0':ok 101.11/26.89 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 nil :: tt:mark:nil:0':ok 101.11/26.89 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 0' :: tt:mark:nil:0':ok 101.11/26.89 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 top :: tt:mark:nil:0':ok -> top 101.11/26.89 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.11/26.89 hole_top2_0 :: top 101.11/26.89 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.11/26.89 101.11/26.89 ---------------------------------------- 101.11/26.89 101.11/26.89 (23) OrderProof (LOWER BOUND(ID)) 101.11/26.89 Heuristically decided to analyse the following defined symbols: 101.11/26.89 active, U102, isNaturalKind, U103, isLNatKind, U104, U105, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.11/26.89 101.11/26.89 They will be analysed ascendingly in the following order: 101.11/26.89 U102 < active 101.11/26.89 isNaturalKind < active 101.11/26.89 U103 < active 101.11/26.89 isLNatKind < active 101.11/26.89 U104 < active 101.11/26.89 U105 < active 101.11/26.89 isNatural < active 101.11/26.89 U106 < active 101.11/26.89 isLNat < active 101.11/26.89 U12 < active 101.11/26.89 U112 < active 101.11/26.89 U13 < active 101.11/26.89 U122 < active 101.11/26.89 U14 < active 101.11/26.89 snd < active 101.11/26.89 splitAt < active 101.11/26.89 U172 < active 101.11/26.89 U182 < active 101.11/26.89 U183 < active 101.11/26.89 U192 < active 101.11/26.89 U193 < active 101.11/26.89 U202 < active 101.11/26.89 U203 < active 101.11/26.89 U204 < active 101.11/26.89 U205 < active 101.11/26.89 U206 < active 101.11/26.89 U22 < active 101.11/26.89 U23 < active 101.11/26.89 U24 < active 101.11/26.89 U232 < active 101.11/26.89 U242 < active 101.11/26.89 U243 < active 101.11/26.89 U244 < active 101.11/26.89 U245 < active 101.11/26.89 U246 < active 101.11/26.89 U252 < active 101.11/26.89 U253 < active 101.11/26.89 U254 < active 101.11/26.89 U255 < active 101.11/26.89 U256 < active 101.11/26.89 U262 < active 101.11/26.89 U272 < active 101.11/26.89 U282 < active 101.11/26.89 cons < active 101.11/26.89 natsFrom < active 101.11/26.89 s < active 101.11/26.89 U292 < active 101.11/26.89 U293 < active 101.11/26.89 U294 < active 101.11/26.89 head < active 101.11/26.89 afterNth < active 101.11/26.89 U302 < active 101.11/26.89 U303 < active 101.11/26.89 U304 < active 101.11/26.89 U32 < active 101.11/26.89 U312 < active 101.11/26.89 pair < active 101.11/26.89 U33 < active 101.11/26.89 U322 < active 101.11/26.89 U323 < active 101.11/26.89 U324 < active 101.11/26.89 U325 < active 101.11/26.89 U326 < active 101.11/26.89 U327 < active 101.11/26.89 U34 < active 101.11/26.89 U332 < active 101.11/26.89 U333 < active 101.11/26.89 U334 < active 101.11/26.89 U342 < active 101.11/26.89 U343 < active 101.11/26.89 U344 < active 101.11/26.89 fst < active 101.11/26.89 U42 < active 101.11/26.89 U43 < active 101.11/26.89 U44 < active 101.11/26.89 U45 < active 101.11/26.89 U46 < active 101.11/26.89 U52 < active 101.11/26.89 U53 < active 101.11/26.89 U54 < active 101.11/26.89 U55 < active 101.11/26.89 U56 < active 101.11/26.89 U62 < active 101.11/26.89 isPLNatKind < active 101.11/26.89 U63 < active 101.11/26.89 isPLNat < active 101.11/26.89 U72 < active 101.11/26.89 U73 < active 101.11/26.89 U82 < active 101.11/26.89 U83 < active 101.11/26.89 U92 < active 101.11/26.89 U93 < active 101.11/26.89 U11 < active 101.11/26.89 U21 < active 101.11/26.89 U31 < active 101.11/26.89 U41 < active 101.11/26.89 U51 < active 101.11/26.89 U61 < active 101.11/26.89 U71 < active 101.11/26.89 U81 < active 101.11/26.89 U91 < active 101.11/26.89 U101 < active 101.11/26.89 U111 < active 101.11/26.89 U121 < active 101.11/26.89 U131 < active 101.11/26.89 U141 < active 101.11/26.89 U151 < active 101.11/26.89 U161 < active 101.11/26.89 U171 < active 101.11/26.89 U181 < active 101.11/26.89 U191 < active 101.11/26.89 U201 < active 101.11/26.89 U211 < active 101.11/26.89 U221 < active 101.11/26.89 U231 < active 101.11/26.89 U241 < active 101.11/26.89 U251 < active 101.11/26.89 U261 < active 101.11/26.89 U271 < active 101.11/26.89 U281 < active 101.11/26.89 U291 < active 101.11/26.89 U301 < active 101.11/26.89 U311 < active 101.11/26.89 U321 < active 101.11/26.89 U331 < active 101.11/26.89 U341 < active 101.11/26.89 tail < active 101.11/26.89 take < active 101.11/26.89 sel < active 101.11/26.89 active < top 101.11/26.89 U102 < proper 101.11/26.89 isNaturalKind < proper 101.11/26.89 U103 < proper 101.11/26.89 isLNatKind < proper 101.11/26.89 U104 < proper 101.11/26.89 U105 < proper 101.11/26.89 isNatural < proper 101.11/26.89 U106 < proper 101.11/26.89 isLNat < proper 101.11/26.89 U12 < proper 101.11/26.89 U112 < proper 101.11/26.89 U13 < proper 101.11/26.89 U122 < proper 101.11/26.89 U14 < proper 101.11/26.89 snd < proper 101.11/26.89 splitAt < proper 101.11/26.89 U172 < proper 101.11/26.89 U182 < proper 101.11/26.89 U183 < proper 101.11/26.89 U192 < proper 101.11/26.89 U193 < proper 101.11/26.89 U202 < proper 101.11/26.89 U203 < proper 101.11/26.89 U204 < proper 101.11/26.89 U205 < proper 101.11/26.89 U206 < proper 101.11/26.89 U22 < proper 101.11/26.89 U23 < proper 101.11/26.89 U24 < proper 101.11/26.89 U232 < proper 101.11/26.89 U242 < proper 101.11/26.89 U243 < proper 101.11/26.89 U244 < proper 101.11/26.89 U245 < proper 101.11/26.89 U246 < proper 101.11/26.89 U252 < proper 101.11/26.89 U253 < proper 101.11/26.89 U254 < proper 101.11/26.89 U255 < proper 101.11/26.89 U256 < proper 101.11/26.89 U262 < proper 101.11/26.89 U272 < proper 101.11/26.89 U282 < proper 101.11/26.89 cons < proper 101.11/26.89 natsFrom < proper 101.11/26.89 s < proper 101.11/26.89 U292 < proper 101.11/26.89 U293 < proper 101.11/26.89 U294 < proper 101.11/26.89 head < proper 101.11/26.89 afterNth < proper 101.11/26.89 U302 < proper 101.11/26.89 U303 < proper 101.11/26.89 U304 < proper 101.11/26.89 U32 < proper 101.11/26.89 U312 < proper 101.11/26.89 pair < proper 101.11/26.89 U33 < proper 101.11/26.89 U322 < proper 101.11/26.89 U323 < proper 101.11/26.89 U324 < proper 101.11/26.89 U325 < proper 101.11/26.89 U326 < proper 101.11/26.89 U327 < proper 101.11/26.89 U34 < proper 101.11/26.89 U332 < proper 101.11/26.89 U333 < proper 101.11/26.89 U334 < proper 101.11/26.89 U342 < proper 101.11/26.89 U343 < proper 101.11/26.89 U344 < proper 101.11/26.89 fst < proper 101.11/26.89 U42 < proper 101.11/26.89 U43 < proper 101.11/26.89 U44 < proper 101.11/26.89 U45 < proper 101.11/26.89 U46 < proper 101.11/26.89 U52 < proper 101.11/26.89 U53 < proper 101.11/26.89 U54 < proper 101.11/26.89 U55 < proper 101.11/26.89 U56 < proper 101.11/26.89 U62 < proper 101.11/26.89 isPLNatKind < proper 101.11/26.89 U63 < proper 101.11/26.89 isPLNat < proper 101.11/26.89 U72 < proper 101.11/26.89 U73 < proper 101.11/26.89 U82 < proper 101.11/26.89 U83 < proper 101.11/26.89 U92 < proper 101.11/26.89 U93 < proper 101.11/26.89 U11 < proper 101.11/26.89 U21 < proper 101.11/26.89 U31 < proper 101.11/26.89 U41 < proper 101.11/26.89 U51 < proper 101.11/26.89 U61 < proper 101.11/26.89 U71 < proper 101.11/26.89 U81 < proper 101.11/26.89 U91 < proper 101.11/26.89 U101 < proper 101.11/26.89 U111 < proper 101.11/26.89 U121 < proper 101.11/26.89 U131 < proper 101.11/26.89 U141 < proper 101.11/26.89 U151 < proper 101.11/26.89 U161 < proper 101.11/26.89 U171 < proper 101.11/26.89 U181 < proper 101.11/26.89 U191 < proper 101.11/26.89 U201 < proper 101.11/26.89 U211 < proper 101.11/26.89 U221 < proper 101.11/26.89 U231 < proper 101.11/26.89 U241 < proper 101.11/26.89 U251 < proper 101.11/26.89 U261 < proper 101.11/26.89 U271 < proper 101.11/26.89 U281 < proper 101.11/26.89 U291 < proper 101.11/26.89 U301 < proper 101.11/26.89 U311 < proper 101.11/26.89 U321 < proper 101.11/26.89 U331 < proper 101.11/26.89 U341 < proper 101.11/26.89 tail < proper 101.11/26.89 take < proper 101.11/26.89 sel < proper 101.11/26.89 proper < top 101.11/26.89 101.11/26.89 ---------------------------------------- 101.11/26.89 101.11/26.89 (24) 101.11/26.89 Obligation: 101.11/26.89 TRS: 101.11/26.89 Rules: 101.11/26.89 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.11/26.89 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.11/26.89 active(U106(tt)) -> mark(tt) 101.11/26.89 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.11/26.89 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.11/26.89 active(U112(tt)) -> mark(tt) 101.11/26.89 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.11/26.89 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.11/26.89 active(U122(tt)) -> mark(tt) 101.11/26.89 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.11/26.89 active(U131(tt)) -> mark(tt) 101.11/26.89 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.11/26.89 active(U141(tt)) -> mark(tt) 101.11/26.89 active(U151(tt)) -> mark(tt) 101.11/26.89 active(U161(tt)) -> mark(tt) 101.11/26.89 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.11/26.89 active(U172(tt)) -> mark(tt) 101.11/26.89 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.11/26.89 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.11/26.89 active(U183(tt)) -> mark(tt) 101.11/26.89 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.11/26.89 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.11/26.89 active(U193(tt)) -> mark(tt) 101.11/26.89 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.11/26.89 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.11/26.89 active(U206(tt)) -> mark(tt) 101.11/26.89 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.11/26.89 active(U211(tt)) -> mark(tt) 101.11/26.89 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.11/26.89 active(U221(tt)) -> mark(tt) 101.11/26.89 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.11/26.89 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.11/26.89 active(U232(tt)) -> mark(tt) 101.11/26.89 active(U24(tt, X)) -> mark(X) 101.11/26.89 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.11/26.89 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.11/26.89 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.11/26.89 active(U246(tt)) -> mark(tt) 101.11/26.89 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.11/26.89 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.11/26.89 active(U256(tt)) -> mark(tt) 101.11/26.89 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.11/26.89 active(U262(tt)) -> mark(tt) 101.11/26.89 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.11/26.89 active(U272(tt)) -> mark(tt) 101.11/26.89 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.11/26.89 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.11/26.89 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.11/26.89 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.11/26.89 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.11/26.89 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.11/26.89 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.11/26.89 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.11/26.89 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.11/26.89 active(U304(tt, Y)) -> mark(Y) 101.11/26.89 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.11/26.89 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.11/26.89 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.11/26.89 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.11/26.89 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.11/26.89 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.11/26.89 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.11/26.89 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.11/26.89 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.11/26.89 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.11/26.89 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.11/26.89 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.11/26.89 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.11/26.89 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.11/26.89 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.11/26.89 active(U334(tt, XS)) -> mark(XS) 101.11/26.89 active(U34(tt, N)) -> mark(N) 101.11/26.89 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.11/26.89 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.11/26.89 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.11/26.89 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.11/26.89 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.11/26.89 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.11/26.89 active(U46(tt)) -> mark(tt) 101.11/26.89 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.11/26.89 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.11/26.89 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.11/26.89 active(U56(tt)) -> mark(tt) 101.11/26.89 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.11/26.89 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.11/26.89 active(U63(tt)) -> mark(tt) 101.11/26.89 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.11/26.89 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.11/26.89 active(U73(tt)) -> mark(tt) 101.11/26.89 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.11/26.89 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.11/26.89 active(U83(tt)) -> mark(tt) 101.11/26.89 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.11/26.89 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.11/26.89 active(U93(tt)) -> mark(tt) 101.11/26.89 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.11/26.89 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.11/26.89 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.11/26.89 active(isLNat(nil)) -> mark(tt) 101.11/26.89 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.11/26.89 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.11/26.89 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.11/26.89 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.11/26.89 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(isLNatKind(nil)) -> mark(tt) 101.11/26.89 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.11/26.89 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.11/26.89 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.11/26.89 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.11/26.89 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.11/26.89 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.11/26.89 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.11/26.89 active(isNatural(0')) -> mark(tt) 101.11/26.89 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.11/26.89 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.11/26.89 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(isNaturalKind(0')) -> mark(tt) 101.11/26.89 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.11/26.89 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.11/26.89 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.11/26.89 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.11/26.89 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.11/26.89 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.11/26.89 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.11/26.89 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.11/26.89 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.11/26.89 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.11/26.89 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.11/26.89 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.11/26.89 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.11/26.89 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.11/26.89 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.11/26.89 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.11/26.89 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.11/26.89 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.11/26.89 active(U105(X1, X2)) -> U105(active(X1), X2) 101.11/26.89 active(U106(X)) -> U106(active(X)) 101.11/26.89 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.11/26.89 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.11/26.89 active(U111(X1, X2)) -> U111(active(X1), X2) 101.11/26.89 active(U112(X)) -> U112(active(X)) 101.11/26.89 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.11/26.89 active(U121(X1, X2)) -> U121(active(X1), X2) 101.11/26.89 active(U122(X)) -> U122(active(X)) 101.11/26.89 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.11/26.89 active(U131(X)) -> U131(active(X)) 101.11/26.89 active(snd(X)) -> snd(active(X)) 101.11/26.89 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.11/26.89 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.11/26.89 active(U141(X)) -> U141(active(X)) 101.11/26.89 active(U151(X)) -> U151(active(X)) 101.11/26.89 active(U161(X)) -> U161(active(X)) 101.11/26.89 active(U171(X1, X2)) -> U171(active(X1), X2) 101.11/26.89 active(U172(X)) -> U172(active(X)) 101.11/26.89 active(U181(X1, X2)) -> U181(active(X1), X2) 101.11/26.89 active(U182(X1, X2)) -> U182(active(X1), X2) 101.11/26.89 active(U183(X)) -> U183(active(X)) 101.11/26.89 active(U191(X1, X2)) -> U191(active(X1), X2) 101.11/26.89 active(U192(X1, X2)) -> U192(active(X1), X2) 101.11/26.89 active(U193(X)) -> U193(active(X)) 101.11/26.89 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.11/26.89 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.11/26.89 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.11/26.89 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.11/26.89 active(U205(X1, X2)) -> U205(active(X1), X2) 101.11/26.89 active(U206(X)) -> U206(active(X)) 101.11/26.89 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.11/26.89 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.11/26.89 active(U211(X)) -> U211(active(X)) 101.11/26.89 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.11/26.89 active(U221(X)) -> U221(active(X)) 101.11/26.89 active(U24(X1, X2)) -> U24(active(X1), X2) 101.11/26.89 active(U231(X1, X2)) -> U231(active(X1), X2) 101.11/26.89 active(U232(X)) -> U232(active(X)) 101.11/26.89 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.11/26.89 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.11/26.89 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.11/26.89 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.11/26.89 active(U245(X1, X2)) -> U245(active(X1), X2) 101.11/26.89 active(U246(X)) -> U246(active(X)) 101.11/26.89 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.11/26.89 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.11/26.89 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.11/26.89 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.11/26.89 active(U255(X1, X2)) -> U255(active(X1), X2) 101.11/26.89 active(U256(X)) -> U256(active(X)) 101.11/26.89 active(U261(X1, X2)) -> U261(active(X1), X2) 101.11/26.89 active(U262(X)) -> U262(active(X)) 101.11/26.89 active(U271(X1, X2)) -> U271(active(X1), X2) 101.11/26.89 active(U272(X)) -> U272(active(X)) 101.11/26.89 active(U281(X1, X2)) -> U281(active(X1), X2) 101.11/26.89 active(U282(X1, X2)) -> U282(active(X1), X2) 101.11/26.89 active(cons(X1, X2)) -> cons(active(X1), X2) 101.11/26.89 active(natsFrom(X)) -> natsFrom(active(X)) 101.11/26.89 active(s(X)) -> s(active(X)) 101.11/26.89 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.11/26.89 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.11/26.89 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.11/26.89 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.11/26.89 active(head(X)) -> head(active(X)) 101.11/26.89 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.11/26.89 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.11/26.89 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.11/26.89 active(U302(X1, X2)) -> U302(active(X1), X2) 101.11/26.89 active(U303(X1, X2)) -> U303(active(X1), X2) 101.11/26.89 active(U304(X1, X2)) -> U304(active(X1), X2) 101.11/26.89 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.11/26.89 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.11/26.89 active(U311(X1, X2)) -> U311(active(X1), X2) 101.11/26.89 active(U312(X1, X2)) -> U312(active(X1), X2) 101.11/26.89 active(pair(X1, X2)) -> pair(active(X1), X2) 101.11/26.89 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.11/26.89 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.11/26.89 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.11/26.89 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.11/26.89 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.11/26.89 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.11/26.89 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.11/26.89 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.11/26.89 active(U327(X1, X2)) -> U327(active(X1), X2) 101.11/26.89 active(U34(X1, X2)) -> U34(active(X1), X2) 101.11/26.89 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.11/26.89 active(U332(X1, X2)) -> U332(active(X1), X2) 101.11/26.89 active(U333(X1, X2)) -> U333(active(X1), X2) 101.11/26.89 active(U334(X1, X2)) -> U334(active(X1), X2) 101.11/26.89 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.11/26.89 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.11/26.89 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.11/26.89 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.11/26.89 active(fst(X)) -> fst(active(X)) 101.11/26.89 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.11/26.89 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.11/26.89 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.11/26.89 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.11/26.89 active(U45(X1, X2)) -> U45(active(X1), X2) 101.11/26.89 active(U46(X)) -> U46(active(X)) 101.11/26.89 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.11/26.89 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.11/26.89 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.11/26.89 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.11/26.89 active(U55(X1, X2)) -> U55(active(X1), X2) 101.11/26.89 active(U56(X)) -> U56(active(X)) 101.11/26.89 active(U61(X1, X2)) -> U61(active(X1), X2) 101.11/26.89 active(U62(X1, X2)) -> U62(active(X1), X2) 101.11/26.89 active(U63(X)) -> U63(active(X)) 101.11/26.89 active(U71(X1, X2)) -> U71(active(X1), X2) 101.11/26.89 active(U72(X1, X2)) -> U72(active(X1), X2) 101.11/26.89 active(U73(X)) -> U73(active(X)) 101.11/26.89 active(U81(X1, X2)) -> U81(active(X1), X2) 101.11/26.89 active(U82(X1, X2)) -> U82(active(X1), X2) 101.11/26.89 active(U83(X)) -> U83(active(X)) 101.11/26.89 active(U91(X1, X2)) -> U91(active(X1), X2) 101.11/26.89 active(U92(X1, X2)) -> U92(active(X1), X2) 101.11/26.89 active(U93(X)) -> U93(active(X)) 101.11/26.89 active(tail(X)) -> tail(active(X)) 101.11/26.89 active(take(X1, X2)) -> take(active(X1), X2) 101.11/26.89 active(take(X1, X2)) -> take(X1, active(X2)) 101.11/26.89 active(sel(X1, X2)) -> sel(active(X1), X2) 101.11/26.89 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.11/26.89 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.11/26.89 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.11/26.89 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.11/26.89 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.11/26.89 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.11/26.89 U106(mark(X)) -> mark(U106(X)) 101.11/26.89 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.11/26.89 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.11/26.89 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.11/26.89 U112(mark(X)) -> mark(U112(X)) 101.11/26.89 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.11/26.89 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.11/26.89 U122(mark(X)) -> mark(U122(X)) 101.11/26.89 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.11/26.89 U131(mark(X)) -> mark(U131(X)) 101.11/26.89 snd(mark(X)) -> mark(snd(X)) 101.11/26.89 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.11/26.89 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.11/26.89 U141(mark(X)) -> mark(U141(X)) 101.11/26.89 U151(mark(X)) -> mark(U151(X)) 101.11/26.89 U161(mark(X)) -> mark(U161(X)) 101.11/26.89 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.11/26.89 U172(mark(X)) -> mark(U172(X)) 101.11/26.89 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.11/26.89 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.11/26.89 U183(mark(X)) -> mark(U183(X)) 101.11/26.89 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.11/26.89 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.11/26.89 U193(mark(X)) -> mark(U193(X)) 101.11/26.89 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.11/26.89 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.11/26.89 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.11/26.89 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.11/26.89 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.11/26.89 U206(mark(X)) -> mark(U206(X)) 101.11/26.89 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.11/26.89 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.11/26.89 U211(mark(X)) -> mark(U211(X)) 101.11/26.89 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.11/26.89 U221(mark(X)) -> mark(U221(X)) 101.11/26.89 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.11/26.89 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.11/26.89 U232(mark(X)) -> mark(U232(X)) 101.11/26.89 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.11/26.89 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.11/26.89 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.11/26.89 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.11/26.89 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.11/26.89 U246(mark(X)) -> mark(U246(X)) 101.11/26.89 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.11/26.89 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.11/26.89 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.11/26.89 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.11/26.89 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.11/26.89 U256(mark(X)) -> mark(U256(X)) 101.11/26.89 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.11/26.89 U262(mark(X)) -> mark(U262(X)) 101.11/26.89 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.11/26.89 U272(mark(X)) -> mark(U272(X)) 101.11/26.89 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.11/26.89 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.11/26.89 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.11/26.89 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.11/26.89 s(mark(X)) -> mark(s(X)) 101.11/26.89 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.11/26.89 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.11/26.89 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.11/26.89 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.11/26.89 head(mark(X)) -> mark(head(X)) 101.11/26.89 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.11/26.89 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.11/26.89 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.11/26.89 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.11/26.89 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.11/26.89 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.11/26.89 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.11/26.89 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.11/26.89 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.11/26.89 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.11/26.89 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.11/26.89 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.11/26.89 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.11/26.89 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.11/26.89 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.11/26.89 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.11/26.89 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.11/26.89 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.11/26.89 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.11/26.89 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.11/26.89 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.11/26.89 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.11/26.89 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.11/26.89 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.11/26.89 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.11/26.89 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.11/26.89 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.11/26.89 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.11/26.89 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.11/26.89 fst(mark(X)) -> mark(fst(X)) 101.11/26.89 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.11/26.89 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.11/26.89 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.11/26.89 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.11/26.89 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.11/26.89 U46(mark(X)) -> mark(U46(X)) 101.11/26.89 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.11/26.89 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.11/26.89 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.11/26.89 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.11/26.89 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.11/26.89 U56(mark(X)) -> mark(U56(X)) 101.11/26.89 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.11/26.89 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.11/26.89 U63(mark(X)) -> mark(U63(X)) 101.11/26.89 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.11/26.89 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.11/26.89 U73(mark(X)) -> mark(U73(X)) 101.11/26.89 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.11/26.89 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.11/26.89 U83(mark(X)) -> mark(U83(X)) 101.11/26.89 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.11/26.89 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.11/26.89 U93(mark(X)) -> mark(U93(X)) 101.11/26.89 tail(mark(X)) -> mark(tail(X)) 101.11/26.89 take(mark(X1), X2) -> mark(take(X1, X2)) 101.11/26.89 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.11/26.89 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.11/26.89 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.11/26.89 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(tt) -> ok(tt) 101.11/26.89 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.11/26.89 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.11/26.89 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.11/26.89 proper(isNatural(X)) -> isNatural(proper(X)) 101.11/26.89 proper(U106(X)) -> U106(proper(X)) 101.11/26.89 proper(isLNat(X)) -> isLNat(proper(X)) 101.11/26.89 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.11/26.89 proper(U112(X)) -> U112(proper(X)) 101.11/26.89 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.11/26.89 proper(U122(X)) -> U122(proper(X)) 101.11/26.89 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U131(X)) -> U131(proper(X)) 101.11/26.89 proper(snd(X)) -> snd(proper(X)) 101.11/26.89 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.11/26.89 proper(U141(X)) -> U141(proper(X)) 101.11/26.89 proper(U151(X)) -> U151(proper(X)) 101.11/26.89 proper(U161(X)) -> U161(proper(X)) 101.11/26.89 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.11/26.89 proper(U172(X)) -> U172(proper(X)) 101.11/26.89 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.11/26.89 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.11/26.89 proper(U183(X)) -> U183(proper(X)) 101.11/26.89 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.11/26.89 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.11/26.89 proper(U193(X)) -> U193(proper(X)) 101.11/26.89 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.11/26.89 proper(U206(X)) -> U206(proper(X)) 101.11/26.89 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U211(X)) -> U211(proper(X)) 101.11/26.89 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U221(X)) -> U221(proper(X)) 101.11/26.89 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.11/26.89 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.11/26.89 proper(U232(X)) -> U232(proper(X)) 101.11/26.89 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.11/26.89 proper(U246(X)) -> U246(proper(X)) 101.11/26.89 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.11/26.89 proper(U256(X)) -> U256(proper(X)) 101.11/26.89 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.11/26.89 proper(U262(X)) -> U262(proper(X)) 101.11/26.89 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.11/26.89 proper(U272(X)) -> U272(proper(X)) 101.11/26.89 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.11/26.89 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.11/26.89 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.11/26.89 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.11/26.89 proper(s(X)) -> s(proper(X)) 101.11/26.89 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(head(X)) -> head(proper(X)) 101.11/26.89 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.11/26.89 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.11/26.89 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.11/26.89 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.11/26.89 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.11/26.89 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.11/26.89 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.11/26.89 proper(nil) -> ok(nil) 101.11/26.89 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.89 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.11/26.89 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.11/26.89 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.11/26.89 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.11/26.89 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.11/26.89 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(fst(X)) -> fst(proper(X)) 101.11/26.89 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.11/26.89 proper(U46(X)) -> U46(proper(X)) 101.11/26.89 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.11/26.89 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.11/26.89 proper(U56(X)) -> U56(proper(X)) 101.11/26.89 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.11/26.89 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.11/26.89 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.11/26.89 proper(U63(X)) -> U63(proper(X)) 101.11/26.89 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.11/26.89 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.11/26.89 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.11/26.89 proper(U73(X)) -> U73(proper(X)) 101.11/26.89 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.11/26.89 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.11/26.89 proper(U83(X)) -> U83(proper(X)) 101.11/26.89 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.11/26.89 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.11/26.89 proper(U93(X)) -> U93(proper(X)) 101.11/26.89 proper(tail(X)) -> tail(proper(X)) 101.11/26.89 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.11/26.89 proper(0') -> ok(0') 101.11/26.89 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.11/26.89 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.11/26.89 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.11/26.89 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.11/26.89 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.11/26.89 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.11/26.89 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.11/26.89 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.11/26.89 isNatural(ok(X)) -> ok(isNatural(X)) 101.11/26.89 U106(ok(X)) -> ok(U106(X)) 101.11/26.89 isLNat(ok(X)) -> ok(isLNat(X)) 101.11/26.89 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.11/26.89 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.11/26.89 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.11/26.89 U112(ok(X)) -> ok(U112(X)) 101.11/26.89 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.11/26.89 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.11/26.89 U122(ok(X)) -> ok(U122(X)) 101.11/26.89 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.11/26.89 U131(ok(X)) -> ok(U131(X)) 101.11/26.89 snd(ok(X)) -> ok(snd(X)) 101.11/26.89 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.11/26.89 U141(ok(X)) -> ok(U141(X)) 101.11/26.89 U151(ok(X)) -> ok(U151(X)) 101.11/26.89 U161(ok(X)) -> ok(U161(X)) 101.11/26.89 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.11/26.89 U172(ok(X)) -> ok(U172(X)) 101.11/26.89 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.11/26.89 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.11/26.89 U183(ok(X)) -> ok(U183(X)) 101.11/26.89 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.11/26.89 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.11/26.89 U193(ok(X)) -> ok(U193(X)) 101.11/26.89 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.11/26.89 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.11/26.89 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.11/26.89 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.11/26.89 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.11/26.89 U206(ok(X)) -> ok(U206(X)) 101.11/26.89 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.11/26.89 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.11/26.89 U211(ok(X)) -> ok(U211(X)) 101.11/26.89 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.11/26.89 U221(ok(X)) -> ok(U221(X)) 101.11/26.89 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.11/26.89 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.11/26.89 U232(ok(X)) -> ok(U232(X)) 101.11/26.89 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.11/26.89 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.11/26.89 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.11/26.89 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.11/26.89 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.11/26.89 U246(ok(X)) -> ok(U246(X)) 101.11/26.89 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.11/26.89 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.11/26.89 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.11/26.89 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.11/26.89 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.11/26.89 U256(ok(X)) -> ok(U256(X)) 101.11/26.89 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.11/26.89 U262(ok(X)) -> ok(U262(X)) 101.11/26.89 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.11/26.89 U272(ok(X)) -> ok(U272(X)) 101.11/26.89 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.11/26.89 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.11/26.89 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.11/26.89 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.11/26.89 s(ok(X)) -> ok(s(X)) 101.11/26.89 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.11/26.89 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.11/26.89 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.11/26.89 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.11/26.89 head(ok(X)) -> ok(head(X)) 101.11/26.89 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.11/26.89 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.11/26.89 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.11/26.89 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.11/26.89 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.11/26.89 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.11/26.89 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.11/26.89 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.11/26.89 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.11/26.89 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.11/26.89 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.11/26.89 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.11/26.89 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.11/26.89 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.11/26.89 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.11/26.89 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.11/26.89 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.11/26.89 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.11/26.89 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.11/26.89 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.11/26.89 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.11/26.89 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.11/26.89 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.11/26.89 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.11/26.89 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.11/26.89 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.11/26.89 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.11/26.89 fst(ok(X)) -> ok(fst(X)) 101.11/26.89 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.11/26.89 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.11/26.89 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.11/26.89 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.11/26.89 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.11/26.89 U46(ok(X)) -> ok(U46(X)) 101.11/26.89 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.11/26.89 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.11/26.89 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.11/26.89 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.11/26.89 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.11/26.89 U56(ok(X)) -> ok(U56(X)) 101.11/26.89 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.11/26.89 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.11/26.89 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.11/26.89 U63(ok(X)) -> ok(U63(X)) 101.11/26.89 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.11/26.89 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.11/26.89 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.11/26.89 U73(ok(X)) -> ok(U73(X)) 101.11/26.89 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.11/26.89 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.11/26.89 U83(ok(X)) -> ok(U83(X)) 101.11/26.89 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.11/26.89 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.11/26.89 U93(ok(X)) -> ok(U93(X)) 101.11/26.89 tail(ok(X)) -> ok(tail(X)) 101.11/26.89 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.11/26.89 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.11/26.89 top(mark(X)) -> top(proper(X)) 101.11/26.89 top(ok(X)) -> top(active(X)) 101.11/26.89 101.11/26.89 Types: 101.11/26.89 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 tt :: tt:mark:nil:0':ok 101.11/26.89 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 nil :: tt:mark:nil:0':ok 101.11/26.89 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 0' :: tt:mark:nil:0':ok 101.11/26.89 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.89 top :: tt:mark:nil:0':ok -> top 101.11/26.89 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.11/26.89 hole_top2_0 :: top 101.11/26.89 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.11/26.89 101.11/26.89 101.11/26.89 Generator Equations: 101.11/26.89 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.11/26.89 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.11/26.89 101.11/26.89 101.11/26.89 The following defined symbols remain to be analysed: 101.11/26.89 U102, active, isNaturalKind, U103, isLNatKind, U104, U105, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.11/26.89 101.11/26.89 They will be analysed ascendingly in the following order: 101.11/26.89 U102 < active 101.11/26.89 isNaturalKind < active 101.11/26.89 U103 < active 101.11/26.89 isLNatKind < active 101.11/26.89 U104 < active 101.11/26.89 U105 < active 101.11/26.89 isNatural < active 101.11/26.89 U106 < active 101.11/26.89 isLNat < active 101.11/26.89 U12 < active 101.11/26.89 U112 < active 101.11/26.89 U13 < active 101.11/26.89 U122 < active 101.11/26.89 U14 < active 101.11/26.89 snd < active 101.11/26.89 splitAt < active 101.11/26.89 U172 < active 101.11/26.89 U182 < active 101.11/26.89 U183 < active 101.11/26.89 U192 < active 101.11/26.89 U193 < active 101.11/26.89 U202 < active 101.11/26.89 U203 < active 101.11/26.89 U204 < active 101.11/26.89 U205 < active 101.11/26.89 U206 < active 101.11/26.89 U22 < active 101.11/26.89 U23 < active 101.11/26.89 U24 < active 101.11/26.89 U232 < active 101.11/26.89 U242 < active 101.11/26.89 U243 < active 101.11/26.89 U244 < active 101.11/26.89 U245 < active 101.11/26.89 U246 < active 101.11/26.89 U252 < active 101.11/26.89 U253 < active 101.11/26.89 U254 < active 101.11/26.89 U255 < active 101.11/26.89 U256 < active 101.11/26.89 U262 < active 101.11/26.89 U272 < active 101.11/26.89 U282 < active 101.11/26.89 cons < active 101.11/26.89 natsFrom < active 101.11/26.89 s < active 101.11/26.89 U292 < active 101.11/26.89 U293 < active 101.11/26.89 U294 < active 101.11/26.89 head < active 101.11/26.89 afterNth < active 101.11/26.89 U302 < active 101.11/26.89 U303 < active 101.11/26.89 U304 < active 101.11/26.89 U32 < active 101.11/26.89 U312 < active 101.11/26.89 pair < active 101.11/26.89 U33 < active 101.11/26.89 U322 < active 101.11/26.89 U323 < active 101.11/26.89 U324 < active 101.11/26.89 U325 < active 101.11/26.89 U326 < active 101.11/26.89 U327 < active 101.11/26.89 U34 < active 101.11/26.89 U332 < active 101.11/26.89 U333 < active 101.11/26.89 U334 < active 101.11/26.89 U342 < active 101.11/26.89 U343 < active 101.11/26.89 U344 < active 101.11/26.89 fst < active 101.11/26.89 U42 < active 101.11/26.89 U43 < active 101.11/26.89 U44 < active 101.11/26.89 U45 < active 101.11/26.89 U46 < active 101.11/26.89 U52 < active 101.11/26.89 U53 < active 101.11/26.89 U54 < active 101.11/26.89 U55 < active 101.11/26.89 U56 < active 101.11/26.89 U62 < active 101.11/26.89 isPLNatKind < active 101.11/26.89 U63 < active 101.11/26.89 isPLNat < active 101.11/26.89 U72 < active 101.11/26.89 U73 < active 101.11/26.89 U82 < active 101.11/26.89 U83 < active 101.11/26.89 U92 < active 101.11/26.89 U93 < active 101.11/26.89 U11 < active 101.11/26.89 U21 < active 101.11/26.89 U31 < active 101.11/26.89 U41 < active 101.11/26.89 U51 < active 101.11/26.89 U61 < active 101.11/26.89 U71 < active 101.11/26.89 U81 < active 101.11/26.89 U91 < active 101.11/26.89 U101 < active 101.11/26.89 U111 < active 101.11/26.89 U121 < active 101.11/26.89 U131 < active 101.11/26.89 U141 < active 101.11/26.89 U151 < active 101.11/26.89 U161 < active 101.11/26.89 U171 < active 101.11/26.89 U181 < active 101.11/26.89 U191 < active 101.11/26.89 U201 < active 101.11/26.89 U211 < active 101.11/26.89 U221 < active 101.11/26.89 U231 < active 101.11/26.89 U241 < active 101.11/26.89 U251 < active 101.11/26.89 U261 < active 101.11/26.89 U271 < active 101.11/26.89 U281 < active 101.11/26.89 U291 < active 101.11/26.89 U301 < active 101.11/26.89 U311 < active 101.11/26.89 U321 < active 101.11/26.89 U331 < active 101.11/26.89 U341 < active 101.11/26.89 tail < active 101.11/26.89 take < active 101.11/26.89 sel < active 101.11/26.89 active < top 101.11/26.89 U102 < proper 101.11/26.89 isNaturalKind < proper 101.11/26.89 U103 < proper 101.11/26.89 isLNatKind < proper 101.11/26.89 U104 < proper 101.11/26.89 U105 < proper 101.11/26.89 isNatural < proper 101.11/26.89 U106 < proper 101.11/26.89 isLNat < proper 101.11/26.89 U12 < proper 101.11/26.89 U112 < proper 101.11/26.89 U13 < proper 101.11/26.89 U122 < proper 101.11/26.89 U14 < proper 101.11/26.89 snd < proper 101.11/26.89 splitAt < proper 101.11/26.89 U172 < proper 101.11/26.89 U182 < proper 101.11/26.89 U183 < proper 101.11/26.89 U192 < proper 101.11/26.89 U193 < proper 101.11/26.89 U202 < proper 101.11/26.89 U203 < proper 101.11/26.89 U204 < proper 101.11/26.89 U205 < proper 101.11/26.89 U206 < proper 101.11/26.89 U22 < proper 101.11/26.89 U23 < proper 101.11/26.89 U24 < proper 101.11/26.89 U232 < proper 101.11/26.89 U242 < proper 101.11/26.89 U243 < proper 101.11/26.89 U244 < proper 101.11/26.90 U245 < proper 101.11/26.90 U246 < proper 101.11/26.90 U252 < proper 101.11/26.90 U253 < proper 101.11/26.90 U254 < proper 101.11/26.90 U255 < proper 101.11/26.90 U256 < proper 101.11/26.90 U262 < proper 101.11/26.90 U272 < proper 101.11/26.90 U282 < proper 101.11/26.90 cons < proper 101.11/26.90 natsFrom < proper 101.11/26.90 s < proper 101.11/26.90 U292 < proper 101.11/26.90 U293 < proper 101.11/26.90 U294 < proper 101.11/26.90 head < proper 101.11/26.90 afterNth < proper 101.11/26.90 U302 < proper 101.11/26.90 U303 < proper 101.11/26.90 U304 < proper 101.11/26.90 U32 < proper 101.11/26.90 U312 < proper 101.11/26.90 pair < proper 101.11/26.90 U33 < proper 101.11/26.90 U322 < proper 101.11/26.90 U323 < proper 101.11/26.90 U324 < proper 101.11/26.90 U325 < proper 101.11/26.90 U326 < proper 101.11/26.90 U327 < proper 101.11/26.90 U34 < proper 101.11/26.90 U332 < proper 101.11/26.90 U333 < proper 101.11/26.90 U334 < proper 101.11/26.90 U342 < proper 101.11/26.90 U343 < proper 101.11/26.90 U344 < proper 101.11/26.90 fst < proper 101.11/26.90 U42 < proper 101.11/26.90 U43 < proper 101.11/26.90 U44 < proper 101.11/26.90 U45 < proper 101.11/26.90 U46 < proper 101.11/26.90 U52 < proper 101.11/26.90 U53 < proper 101.11/26.90 U54 < proper 101.11/26.90 U55 < proper 101.11/26.90 U56 < proper 101.11/26.90 U62 < proper 101.11/26.90 isPLNatKind < proper 101.11/26.90 U63 < proper 101.11/26.90 isPLNat < proper 101.11/26.90 U72 < proper 101.11/26.90 U73 < proper 101.11/26.90 U82 < proper 101.11/26.90 U83 < proper 101.11/26.90 U92 < proper 101.11/26.90 U93 < proper 101.11/26.90 U11 < proper 101.11/26.90 U21 < proper 101.11/26.90 U31 < proper 101.11/26.90 U41 < proper 101.11/26.90 U51 < proper 101.11/26.90 U61 < proper 101.11/26.90 U71 < proper 101.11/26.90 U81 < proper 101.11/26.90 U91 < proper 101.11/26.90 U101 < proper 101.11/26.90 U111 < proper 101.11/26.90 U121 < proper 101.11/26.90 U131 < proper 101.11/26.90 U141 < proper 101.11/26.90 U151 < proper 101.11/26.90 U161 < proper 101.11/26.90 U171 < proper 101.11/26.90 U181 < proper 101.11/26.90 U191 < proper 101.11/26.90 U201 < proper 101.11/26.90 U211 < proper 101.11/26.90 U221 < proper 101.11/26.90 U231 < proper 101.11/26.90 U241 < proper 101.11/26.90 U251 < proper 101.11/26.90 U261 < proper 101.11/26.90 U271 < proper 101.11/26.90 U281 < proper 101.11/26.90 U291 < proper 101.11/26.90 U301 < proper 101.11/26.90 U311 < proper 101.11/26.90 U321 < proper 101.11/26.90 U331 < proper 101.11/26.90 U341 < proper 101.11/26.90 tail < proper 101.11/26.90 take < proper 101.11/26.90 sel < proper 101.11/26.90 proper < top 101.11/26.90 101.11/26.90 ---------------------------------------- 101.11/26.90 101.11/26.90 (25) RewriteLemmaProof (LOWER BOUND(ID)) 101.11/26.90 Proved the following rewrite lemma: 101.11/26.90 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.11/26.90 101.11/26.90 Induction Base: 101.11/26.90 U102(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.11/26.90 101.11/26.90 Induction Step: 101.11/26.90 U102(gen_tt:mark:nil:0':ok3_0(+(1, +(n5_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.11/26.90 mark(U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.11/26.90 mark(*4_0) 101.11/26.90 101.11/26.90 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.11/26.90 ---------------------------------------- 101.11/26.90 101.11/26.90 (26) 101.11/26.90 Complex Obligation (BEST) 101.11/26.90 101.11/26.90 ---------------------------------------- 101.11/26.90 101.11/26.90 (27) 101.11/26.90 Obligation: 101.11/26.90 Proved the lower bound n^1 for the following obligation: 101.11/26.90 101.11/26.90 TRS: 101.11/26.90 Rules: 101.11/26.90 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.11/26.90 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.11/26.90 active(U106(tt)) -> mark(tt) 101.11/26.90 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.11/26.90 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.11/26.90 active(U112(tt)) -> mark(tt) 101.11/26.90 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.11/26.90 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.11/26.90 active(U122(tt)) -> mark(tt) 101.11/26.90 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.11/26.90 active(U131(tt)) -> mark(tt) 101.11/26.90 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.11/26.90 active(U141(tt)) -> mark(tt) 101.11/26.90 active(U151(tt)) -> mark(tt) 101.11/26.90 active(U161(tt)) -> mark(tt) 101.11/26.90 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.11/26.90 active(U172(tt)) -> mark(tt) 101.11/26.90 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.11/26.90 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.11/26.90 active(U183(tt)) -> mark(tt) 101.11/26.90 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.11/26.90 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.11/26.90 active(U193(tt)) -> mark(tt) 101.11/26.90 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.11/26.90 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.11/26.90 active(U206(tt)) -> mark(tt) 101.11/26.90 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.11/26.90 active(U211(tt)) -> mark(tt) 101.11/26.90 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.11/26.90 active(U221(tt)) -> mark(tt) 101.11/26.90 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.11/26.90 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.11/26.90 active(U232(tt)) -> mark(tt) 101.11/26.90 active(U24(tt, X)) -> mark(X) 101.11/26.90 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.11/26.90 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.11/26.90 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.11/26.90 active(U246(tt)) -> mark(tt) 101.11/26.90 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.11/26.90 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.11/26.90 active(U256(tt)) -> mark(tt) 101.11/26.90 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.11/26.90 active(U262(tt)) -> mark(tt) 101.11/26.90 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.11/26.90 active(U272(tt)) -> mark(tt) 101.11/26.90 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.11/26.90 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.11/26.90 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.11/26.90 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.11/26.90 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.11/26.90 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.11/26.90 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.11/26.90 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.11/26.90 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.11/26.90 active(U304(tt, Y)) -> mark(Y) 101.11/26.90 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.11/26.90 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.11/26.90 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.11/26.90 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.11/26.90 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.11/26.90 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.11/26.90 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.11/26.90 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.11/26.90 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.11/26.90 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.11/26.90 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.11/26.90 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.11/26.90 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.11/26.90 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.11/26.90 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.11/26.90 active(U334(tt, XS)) -> mark(XS) 101.11/26.90 active(U34(tt, N)) -> mark(N) 101.11/26.90 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.11/26.90 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.11/26.90 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.11/26.90 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.11/26.90 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.11/26.90 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.11/26.90 active(U46(tt)) -> mark(tt) 101.11/26.90 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.11/26.90 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.11/26.90 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.11/26.90 active(U56(tt)) -> mark(tt) 101.11/26.90 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.11/26.90 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.11/26.90 active(U63(tt)) -> mark(tt) 101.11/26.90 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.11/26.90 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.11/26.90 active(U73(tt)) -> mark(tt) 101.11/26.90 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.11/26.90 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.11/26.90 active(U83(tt)) -> mark(tt) 101.11/26.90 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.11/26.90 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.11/26.90 active(U93(tt)) -> mark(tt) 101.11/26.90 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.11/26.90 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.11/26.90 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.11/26.90 active(isLNat(nil)) -> mark(tt) 101.11/26.90 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.11/26.90 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.11/26.90 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.11/26.90 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.11/26.90 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(isLNatKind(nil)) -> mark(tt) 101.11/26.90 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.11/26.90 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.11/26.90 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.11/26.90 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.11/26.90 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.11/26.90 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.11/26.90 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.11/26.90 active(isNatural(0')) -> mark(tt) 101.11/26.90 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.11/26.90 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.11/26.90 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(isNaturalKind(0')) -> mark(tt) 101.11/26.90 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.11/26.90 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.11/26.90 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.11/26.90 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.11/26.90 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.11/26.90 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.11/26.90 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.11/26.90 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.11/26.90 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.11/26.90 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.11/26.90 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.11/26.90 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.11/26.90 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.11/26.90 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.11/26.90 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.11/26.90 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.11/26.90 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.11/26.90 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.11/26.90 active(U105(X1, X2)) -> U105(active(X1), X2) 101.11/26.90 active(U106(X)) -> U106(active(X)) 101.11/26.90 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.11/26.90 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.11/26.90 active(U111(X1, X2)) -> U111(active(X1), X2) 101.11/26.90 active(U112(X)) -> U112(active(X)) 101.11/26.90 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.11/26.90 active(U121(X1, X2)) -> U121(active(X1), X2) 101.11/26.90 active(U122(X)) -> U122(active(X)) 101.11/26.90 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.11/26.90 active(U131(X)) -> U131(active(X)) 101.11/26.90 active(snd(X)) -> snd(active(X)) 101.11/26.90 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.11/26.90 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.11/26.90 active(U141(X)) -> U141(active(X)) 101.11/26.90 active(U151(X)) -> U151(active(X)) 101.11/26.90 active(U161(X)) -> U161(active(X)) 101.11/26.90 active(U171(X1, X2)) -> U171(active(X1), X2) 101.11/26.90 active(U172(X)) -> U172(active(X)) 101.11/26.90 active(U181(X1, X2)) -> U181(active(X1), X2) 101.11/26.90 active(U182(X1, X2)) -> U182(active(X1), X2) 101.11/26.90 active(U183(X)) -> U183(active(X)) 101.11/26.90 active(U191(X1, X2)) -> U191(active(X1), X2) 101.11/26.90 active(U192(X1, X2)) -> U192(active(X1), X2) 101.11/26.90 active(U193(X)) -> U193(active(X)) 101.11/26.90 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.11/26.90 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.11/26.90 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.11/26.90 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.11/26.90 active(U205(X1, X2)) -> U205(active(X1), X2) 101.11/26.90 active(U206(X)) -> U206(active(X)) 101.11/26.90 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.11/26.90 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.11/26.90 active(U211(X)) -> U211(active(X)) 101.11/26.90 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.11/26.90 active(U221(X)) -> U221(active(X)) 101.11/26.90 active(U24(X1, X2)) -> U24(active(X1), X2) 101.11/26.90 active(U231(X1, X2)) -> U231(active(X1), X2) 101.11/26.90 active(U232(X)) -> U232(active(X)) 101.11/26.90 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.11/26.90 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.11/26.90 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.11/26.90 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.11/26.90 active(U245(X1, X2)) -> U245(active(X1), X2) 101.11/26.90 active(U246(X)) -> U246(active(X)) 101.11/26.90 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.11/26.90 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.11/26.90 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.11/26.90 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.11/26.90 active(U255(X1, X2)) -> U255(active(X1), X2) 101.11/26.90 active(U256(X)) -> U256(active(X)) 101.11/26.90 active(U261(X1, X2)) -> U261(active(X1), X2) 101.11/26.90 active(U262(X)) -> U262(active(X)) 101.11/26.90 active(U271(X1, X2)) -> U271(active(X1), X2) 101.11/26.90 active(U272(X)) -> U272(active(X)) 101.11/26.90 active(U281(X1, X2)) -> U281(active(X1), X2) 101.11/26.90 active(U282(X1, X2)) -> U282(active(X1), X2) 101.11/26.90 active(cons(X1, X2)) -> cons(active(X1), X2) 101.11/26.90 active(natsFrom(X)) -> natsFrom(active(X)) 101.11/26.90 active(s(X)) -> s(active(X)) 101.11/26.90 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.11/26.90 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.11/26.90 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.11/26.90 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.11/26.90 active(head(X)) -> head(active(X)) 101.11/26.90 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.11/26.90 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.11/26.90 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.11/26.90 active(U302(X1, X2)) -> U302(active(X1), X2) 101.11/26.90 active(U303(X1, X2)) -> U303(active(X1), X2) 101.11/26.90 active(U304(X1, X2)) -> U304(active(X1), X2) 101.11/26.90 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.11/26.90 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.11/26.90 active(U311(X1, X2)) -> U311(active(X1), X2) 101.11/26.90 active(U312(X1, X2)) -> U312(active(X1), X2) 101.11/26.90 active(pair(X1, X2)) -> pair(active(X1), X2) 101.11/26.90 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.11/26.90 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.11/26.90 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.11/26.90 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.11/26.90 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.11/26.90 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.11/26.90 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.11/26.90 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.11/26.90 active(U327(X1, X2)) -> U327(active(X1), X2) 101.11/26.90 active(U34(X1, X2)) -> U34(active(X1), X2) 101.11/26.90 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.11/26.90 active(U332(X1, X2)) -> U332(active(X1), X2) 101.11/26.90 active(U333(X1, X2)) -> U333(active(X1), X2) 101.11/26.90 active(U334(X1, X2)) -> U334(active(X1), X2) 101.11/26.90 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.11/26.90 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.11/26.90 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.11/26.90 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.11/26.90 active(fst(X)) -> fst(active(X)) 101.11/26.90 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.11/26.90 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.11/26.90 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.11/26.90 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.11/26.90 active(U45(X1, X2)) -> U45(active(X1), X2) 101.11/26.90 active(U46(X)) -> U46(active(X)) 101.11/26.90 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.11/26.90 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.11/26.90 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.11/26.90 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.11/26.90 active(U55(X1, X2)) -> U55(active(X1), X2) 101.11/26.90 active(U56(X)) -> U56(active(X)) 101.11/26.90 active(U61(X1, X2)) -> U61(active(X1), X2) 101.11/26.90 active(U62(X1, X2)) -> U62(active(X1), X2) 101.11/26.90 active(U63(X)) -> U63(active(X)) 101.11/26.90 active(U71(X1, X2)) -> U71(active(X1), X2) 101.11/26.90 active(U72(X1, X2)) -> U72(active(X1), X2) 101.11/26.90 active(U73(X)) -> U73(active(X)) 101.11/26.90 active(U81(X1, X2)) -> U81(active(X1), X2) 101.11/26.90 active(U82(X1, X2)) -> U82(active(X1), X2) 101.11/26.90 active(U83(X)) -> U83(active(X)) 101.11/26.90 active(U91(X1, X2)) -> U91(active(X1), X2) 101.11/26.90 active(U92(X1, X2)) -> U92(active(X1), X2) 101.11/26.90 active(U93(X)) -> U93(active(X)) 101.11/26.90 active(tail(X)) -> tail(active(X)) 101.11/26.90 active(take(X1, X2)) -> take(active(X1), X2) 101.11/26.90 active(take(X1, X2)) -> take(X1, active(X2)) 101.11/26.90 active(sel(X1, X2)) -> sel(active(X1), X2) 101.11/26.90 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.11/26.90 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.11/26.90 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.11/26.90 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.11/26.90 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.11/26.90 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.11/26.90 U106(mark(X)) -> mark(U106(X)) 101.11/26.90 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.11/26.90 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.11/26.90 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.11/26.90 U112(mark(X)) -> mark(U112(X)) 101.11/26.90 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.11/26.90 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.11/26.90 U122(mark(X)) -> mark(U122(X)) 101.11/26.90 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.11/26.90 U131(mark(X)) -> mark(U131(X)) 101.11/26.90 snd(mark(X)) -> mark(snd(X)) 101.11/26.90 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.11/26.90 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.11/26.90 U141(mark(X)) -> mark(U141(X)) 101.11/26.90 U151(mark(X)) -> mark(U151(X)) 101.11/26.90 U161(mark(X)) -> mark(U161(X)) 101.11/26.90 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.11/26.90 U172(mark(X)) -> mark(U172(X)) 101.11/26.90 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.11/26.90 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.11/26.90 U183(mark(X)) -> mark(U183(X)) 101.11/26.90 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.11/26.90 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.11/26.90 U193(mark(X)) -> mark(U193(X)) 101.11/26.90 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.11/26.90 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.11/26.90 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.11/26.90 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.11/26.90 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.11/26.90 U206(mark(X)) -> mark(U206(X)) 101.11/26.90 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.11/26.90 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.11/26.90 U211(mark(X)) -> mark(U211(X)) 101.11/26.90 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.11/26.90 U221(mark(X)) -> mark(U221(X)) 101.11/26.90 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.11/26.90 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.11/26.90 U232(mark(X)) -> mark(U232(X)) 101.11/26.90 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.11/26.90 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.11/26.90 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.11/26.90 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.11/26.90 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.11/26.90 U246(mark(X)) -> mark(U246(X)) 101.11/26.90 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.11/26.90 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.11/26.90 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.11/26.90 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.11/26.90 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.11/26.90 U256(mark(X)) -> mark(U256(X)) 101.11/26.90 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.11/26.90 U262(mark(X)) -> mark(U262(X)) 101.11/26.90 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.11/26.90 U272(mark(X)) -> mark(U272(X)) 101.11/26.90 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.11/26.90 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.11/26.90 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.11/26.90 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.11/26.90 s(mark(X)) -> mark(s(X)) 101.11/26.90 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.11/26.90 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.11/26.90 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.11/26.90 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.11/26.90 head(mark(X)) -> mark(head(X)) 101.11/26.90 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.11/26.90 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.11/26.90 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.11/26.90 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.11/26.90 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.11/26.90 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.11/26.90 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.11/26.90 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.11/26.90 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.11/26.90 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.11/26.90 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.11/26.90 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.11/26.90 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.11/26.90 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.11/26.90 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.11/26.90 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.11/26.90 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.11/26.90 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.11/26.90 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.11/26.90 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.11/26.90 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.11/26.90 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.11/26.90 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.11/26.90 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.11/26.90 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.11/26.90 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.11/26.90 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.11/26.90 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.11/26.90 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.11/26.90 fst(mark(X)) -> mark(fst(X)) 101.11/26.90 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.11/26.90 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.11/26.90 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.11/26.90 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.11/26.90 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.11/26.90 U46(mark(X)) -> mark(U46(X)) 101.11/26.90 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.11/26.90 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.11/26.90 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.11/26.90 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.11/26.90 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.11/26.90 U56(mark(X)) -> mark(U56(X)) 101.11/26.90 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.11/26.90 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.11/26.90 U63(mark(X)) -> mark(U63(X)) 101.11/26.90 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.11/26.90 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.11/26.90 U73(mark(X)) -> mark(U73(X)) 101.11/26.90 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.11/26.90 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.11/26.90 U83(mark(X)) -> mark(U83(X)) 101.11/26.90 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.11/26.90 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.11/26.90 U93(mark(X)) -> mark(U93(X)) 101.11/26.90 tail(mark(X)) -> mark(tail(X)) 101.11/26.90 take(mark(X1), X2) -> mark(take(X1, X2)) 101.11/26.90 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.11/26.90 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.11/26.90 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.11/26.90 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(tt) -> ok(tt) 101.11/26.90 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.11/26.90 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.11/26.90 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.11/26.90 proper(isNatural(X)) -> isNatural(proper(X)) 101.11/26.90 proper(U106(X)) -> U106(proper(X)) 101.11/26.90 proper(isLNat(X)) -> isLNat(proper(X)) 101.11/26.90 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.11/26.90 proper(U112(X)) -> U112(proper(X)) 101.11/26.90 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.11/26.90 proper(U122(X)) -> U122(proper(X)) 101.11/26.90 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U131(X)) -> U131(proper(X)) 101.11/26.90 proper(snd(X)) -> snd(proper(X)) 101.11/26.90 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.11/26.90 proper(U141(X)) -> U141(proper(X)) 101.11/26.90 proper(U151(X)) -> U151(proper(X)) 101.11/26.90 proper(U161(X)) -> U161(proper(X)) 101.11/26.90 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.11/26.90 proper(U172(X)) -> U172(proper(X)) 101.11/26.90 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.11/26.90 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.11/26.90 proper(U183(X)) -> U183(proper(X)) 101.11/26.90 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.11/26.90 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.11/26.90 proper(U193(X)) -> U193(proper(X)) 101.11/26.90 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.11/26.90 proper(U206(X)) -> U206(proper(X)) 101.11/26.90 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U211(X)) -> U211(proper(X)) 101.11/26.90 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U221(X)) -> U221(proper(X)) 101.11/26.90 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.11/26.90 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.11/26.90 proper(U232(X)) -> U232(proper(X)) 101.11/26.90 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.11/26.90 proper(U246(X)) -> U246(proper(X)) 101.11/26.90 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.11/26.90 proper(U256(X)) -> U256(proper(X)) 101.11/26.90 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.11/26.90 proper(U262(X)) -> U262(proper(X)) 101.11/26.90 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.11/26.90 proper(U272(X)) -> U272(proper(X)) 101.11/26.90 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.11/26.90 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.11/26.90 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.11/26.90 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.11/26.90 proper(s(X)) -> s(proper(X)) 101.11/26.90 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(head(X)) -> head(proper(X)) 101.11/26.90 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.11/26.90 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.11/26.90 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.11/26.90 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.11/26.90 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.11/26.90 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.11/26.90 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.11/26.90 proper(nil) -> ok(nil) 101.11/26.90 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.90 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.11/26.90 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.11/26.90 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.11/26.90 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.11/26.90 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.11/26.90 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(fst(X)) -> fst(proper(X)) 101.11/26.90 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.11/26.90 proper(U46(X)) -> U46(proper(X)) 101.11/26.90 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.11/26.90 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.11/26.90 proper(U56(X)) -> U56(proper(X)) 101.11/26.90 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.11/26.90 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.11/26.90 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.11/26.90 proper(U63(X)) -> U63(proper(X)) 101.11/26.90 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.11/26.90 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.11/26.90 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.11/26.90 proper(U73(X)) -> U73(proper(X)) 101.11/26.90 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.11/26.90 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.11/26.90 proper(U83(X)) -> U83(proper(X)) 101.11/26.90 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.11/26.90 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.11/26.90 proper(U93(X)) -> U93(proper(X)) 101.11/26.90 proper(tail(X)) -> tail(proper(X)) 101.11/26.90 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.11/26.90 proper(0') -> ok(0') 101.11/26.90 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.11/26.90 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.11/26.90 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.11/26.90 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.11/26.90 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.11/26.90 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.11/26.90 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.11/26.93 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.11/26.93 isNatural(ok(X)) -> ok(isNatural(X)) 101.11/26.93 U106(ok(X)) -> ok(U106(X)) 101.11/26.93 isLNat(ok(X)) -> ok(isLNat(X)) 101.11/26.93 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.11/26.93 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.11/26.93 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.11/26.93 U112(ok(X)) -> ok(U112(X)) 101.11/26.93 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.11/26.93 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.11/26.93 U122(ok(X)) -> ok(U122(X)) 101.11/26.93 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.11/26.93 U131(ok(X)) -> ok(U131(X)) 101.11/26.93 snd(ok(X)) -> ok(snd(X)) 101.11/26.93 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.11/26.93 U141(ok(X)) -> ok(U141(X)) 101.11/26.93 U151(ok(X)) -> ok(U151(X)) 101.11/26.93 U161(ok(X)) -> ok(U161(X)) 101.11/26.93 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.11/26.93 U172(ok(X)) -> ok(U172(X)) 101.11/26.93 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.11/26.93 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.11/26.93 U183(ok(X)) -> ok(U183(X)) 101.11/26.93 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.11/26.93 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.11/26.93 U193(ok(X)) -> ok(U193(X)) 101.11/26.93 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.11/26.93 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.11/26.93 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.11/26.93 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.11/26.93 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.11/26.93 U206(ok(X)) -> ok(U206(X)) 101.11/26.93 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.11/26.93 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.11/26.93 U211(ok(X)) -> ok(U211(X)) 101.11/26.93 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.11/26.93 U221(ok(X)) -> ok(U221(X)) 101.11/26.93 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.11/26.93 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.11/26.93 U232(ok(X)) -> ok(U232(X)) 101.11/26.93 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.11/26.93 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.11/26.93 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.11/26.93 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.11/26.93 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.11/26.93 U246(ok(X)) -> ok(U246(X)) 101.11/26.93 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.11/26.93 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.11/26.93 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.11/26.93 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.11/26.93 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.11/26.93 U256(ok(X)) -> ok(U256(X)) 101.11/26.93 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.11/26.93 U262(ok(X)) -> ok(U262(X)) 101.11/26.93 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.11/26.93 U272(ok(X)) -> ok(U272(X)) 101.11/26.93 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.11/26.93 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.11/26.93 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.11/26.93 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.11/26.93 s(ok(X)) -> ok(s(X)) 101.11/26.93 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.11/26.93 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.11/26.93 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.11/26.93 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.11/26.93 head(ok(X)) -> ok(head(X)) 101.11/26.93 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.11/26.93 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.11/26.93 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.11/26.93 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.11/26.93 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.11/26.93 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.11/26.93 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.11/26.93 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.11/26.93 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.11/26.93 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.11/26.93 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.11/26.93 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.11/26.93 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.11/26.93 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.11/26.93 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.11/26.93 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.11/26.93 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.11/26.93 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.11/26.93 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.11/26.93 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.11/26.93 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.11/26.93 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.11/26.93 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.11/26.93 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.11/26.93 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.11/26.93 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.11/26.93 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.11/26.93 fst(ok(X)) -> ok(fst(X)) 101.11/26.93 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.11/26.93 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.11/26.93 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.11/26.93 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.11/26.93 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.11/26.93 U46(ok(X)) -> ok(U46(X)) 101.11/26.93 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.11/26.93 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.11/26.93 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.11/26.93 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.11/26.93 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.11/26.93 U56(ok(X)) -> ok(U56(X)) 101.11/26.93 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.11/26.93 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.11/26.93 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.11/26.93 U63(ok(X)) -> ok(U63(X)) 101.11/26.93 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.11/26.93 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.11/26.93 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.11/26.93 U73(ok(X)) -> ok(U73(X)) 101.11/26.93 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.11/26.93 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.11/26.93 U83(ok(X)) -> ok(U83(X)) 101.11/26.93 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.11/26.93 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.11/26.93 U93(ok(X)) -> ok(U93(X)) 101.11/26.93 tail(ok(X)) -> ok(tail(X)) 101.11/26.93 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.11/26.93 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.11/26.93 top(mark(X)) -> top(proper(X)) 101.11/26.93 top(ok(X)) -> top(active(X)) 101.11/26.93 101.11/26.93 Types: 101.11/26.93 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 tt :: tt:mark:nil:0':ok 101.11/26.93 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 nil :: tt:mark:nil:0':ok 101.11/26.93 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 0' :: tt:mark:nil:0':ok 101.11/26.93 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 top :: tt:mark:nil:0':ok -> top 101.11/26.93 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.11/26.93 hole_top2_0 :: top 101.11/26.93 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.11/26.93 101.11/26.93 101.11/26.93 Generator Equations: 101.11/26.93 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.11/26.93 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.11/26.93 101.11/26.93 101.11/26.93 The following defined symbols remain to be analysed: 101.11/26.93 U102, active, isNaturalKind, U103, isLNatKind, U104, U105, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.11/26.93 101.11/26.93 They will be analysed ascendingly in the following order: 101.11/26.93 U102 < active 101.11/26.93 isNaturalKind < active 101.11/26.93 U103 < active 101.11/26.93 isLNatKind < active 101.11/26.93 U104 < active 101.11/26.93 U105 < active 101.11/26.93 isNatural < active 101.11/26.93 U106 < active 101.11/26.93 isLNat < active 101.11/26.93 U12 < active 101.11/26.93 U112 < active 101.11/26.93 U13 < active 101.11/26.93 U122 < active 101.11/26.93 U14 < active 101.11/26.93 snd < active 101.11/26.93 splitAt < active 101.11/26.93 U172 < active 101.11/26.93 U182 < active 101.11/26.93 U183 < active 101.11/26.93 U192 < active 101.11/26.93 U193 < active 101.11/26.93 U202 < active 101.11/26.93 U203 < active 101.11/26.93 U204 < active 101.11/26.93 U205 < active 101.11/26.93 U206 < active 101.11/26.93 U22 < active 101.11/26.93 U23 < active 101.11/26.93 U24 < active 101.11/26.93 U232 < active 101.11/26.93 U242 < active 101.11/26.93 U243 < active 101.11/26.93 U244 < active 101.11/26.93 U245 < active 101.11/26.93 U246 < active 101.11/26.93 U252 < active 101.11/26.93 U253 < active 101.11/26.93 U254 < active 101.11/26.93 U255 < active 101.11/26.93 U256 < active 101.11/26.93 U262 < active 101.11/26.93 U272 < active 101.11/26.93 U282 < active 101.11/26.93 cons < active 101.11/26.93 natsFrom < active 101.11/26.93 s < active 101.11/26.93 U292 < active 101.11/26.93 U293 < active 101.11/26.93 U294 < active 101.11/26.93 head < active 101.11/26.93 afterNth < active 101.11/26.93 U302 < active 101.11/26.93 U303 < active 101.11/26.93 U304 < active 101.11/26.93 U32 < active 101.11/26.93 U312 < active 101.11/26.93 pair < active 101.11/26.93 U33 < active 101.11/26.93 U322 < active 101.11/26.93 U323 < active 101.11/26.93 U324 < active 101.11/26.93 U325 < active 101.11/26.93 U326 < active 101.11/26.93 U327 < active 101.11/26.93 U34 < active 101.11/26.93 U332 < active 101.11/26.93 U333 < active 101.11/26.93 U334 < active 101.11/26.93 U342 < active 101.11/26.93 U343 < active 101.11/26.93 U344 < active 101.11/26.93 fst < active 101.11/26.93 U42 < active 101.11/26.93 U43 < active 101.11/26.93 U44 < active 101.11/26.93 U45 < active 101.11/26.93 U46 < active 101.11/26.93 U52 < active 101.11/26.93 U53 < active 101.11/26.93 U54 < active 101.11/26.93 U55 < active 101.11/26.93 U56 < active 101.11/26.93 U62 < active 101.11/26.93 isPLNatKind < active 101.11/26.93 U63 < active 101.11/26.93 isPLNat < active 101.11/26.93 U72 < active 101.11/26.93 U73 < active 101.11/26.93 U82 < active 101.11/26.93 U83 < active 101.11/26.93 U92 < active 101.11/26.93 U93 < active 101.11/26.93 U11 < active 101.11/26.93 U21 < active 101.11/26.93 U31 < active 101.11/26.93 U41 < active 101.11/26.93 U51 < active 101.11/26.93 U61 < active 101.11/26.93 U71 < active 101.11/26.93 U81 < active 101.11/26.93 U91 < active 101.11/26.93 U101 < active 101.11/26.93 U111 < active 101.11/26.93 U121 < active 101.11/26.93 U131 < active 101.11/26.93 U141 < active 101.11/26.93 U151 < active 101.11/26.93 U161 < active 101.11/26.93 U171 < active 101.11/26.93 U181 < active 101.11/26.93 U191 < active 101.11/26.93 U201 < active 101.11/26.93 U211 < active 101.11/26.93 U221 < active 101.11/26.93 U231 < active 101.11/26.93 U241 < active 101.11/26.93 U251 < active 101.11/26.93 U261 < active 101.11/26.93 U271 < active 101.11/26.93 U281 < active 101.11/26.93 U291 < active 101.11/26.93 U301 < active 101.11/26.93 U311 < active 101.11/26.93 U321 < active 101.11/26.93 U331 < active 101.11/26.93 U341 < active 101.11/26.93 tail < active 101.11/26.93 take < active 101.11/26.93 sel < active 101.11/26.93 active < top 101.11/26.93 U102 < proper 101.11/26.93 isNaturalKind < proper 101.11/26.93 U103 < proper 101.11/26.93 isLNatKind < proper 101.11/26.93 U104 < proper 101.11/26.93 U105 < proper 101.11/26.93 isNatural < proper 101.11/26.93 U106 < proper 101.11/26.93 isLNat < proper 101.11/26.93 U12 < proper 101.11/26.93 U112 < proper 101.11/26.93 U13 < proper 101.11/26.93 U122 < proper 101.11/26.93 U14 < proper 101.11/26.93 snd < proper 101.11/26.93 splitAt < proper 101.11/26.93 U172 < proper 101.11/26.93 U182 < proper 101.11/26.93 U183 < proper 101.11/26.93 U192 < proper 101.11/26.93 U193 < proper 101.11/26.93 U202 < proper 101.11/26.93 U203 < proper 101.11/26.93 U204 < proper 101.11/26.93 U205 < proper 101.11/26.93 U206 < proper 101.11/26.93 U22 < proper 101.11/26.93 U23 < proper 101.11/26.93 U24 < proper 101.11/26.93 U232 < proper 101.11/26.93 U242 < proper 101.11/26.93 U243 < proper 101.11/26.93 U244 < proper 101.11/26.93 U245 < proper 101.11/26.93 U246 < proper 101.11/26.93 U252 < proper 101.11/26.93 U253 < proper 101.11/26.93 U254 < proper 101.11/26.93 U255 < proper 101.11/26.93 U256 < proper 101.11/26.93 U262 < proper 101.11/26.93 U272 < proper 101.11/26.93 U282 < proper 101.11/26.93 cons < proper 101.11/26.93 natsFrom < proper 101.11/26.93 s < proper 101.11/26.93 U292 < proper 101.11/26.93 U293 < proper 101.11/26.93 U294 < proper 101.11/26.93 head < proper 101.11/26.93 afterNth < proper 101.11/26.93 U302 < proper 101.11/26.93 U303 < proper 101.11/26.93 U304 < proper 101.11/26.93 U32 < proper 101.11/26.93 U312 < proper 101.11/26.93 pair < proper 101.11/26.93 U33 < proper 101.11/26.93 U322 < proper 101.11/26.93 U323 < proper 101.11/26.93 U324 < proper 101.11/26.93 U325 < proper 101.11/26.93 U326 < proper 101.11/26.93 U327 < proper 101.11/26.93 U34 < proper 101.11/26.93 U332 < proper 101.11/26.93 U333 < proper 101.11/26.93 U334 < proper 101.11/26.93 U342 < proper 101.11/26.93 U343 < proper 101.11/26.93 U344 < proper 101.11/26.93 fst < proper 101.11/26.93 U42 < proper 101.11/26.93 U43 < proper 101.11/26.93 U44 < proper 101.11/26.93 U45 < proper 101.11/26.93 U46 < proper 101.11/26.93 U52 < proper 101.11/26.93 U53 < proper 101.11/26.93 U54 < proper 101.11/26.93 U55 < proper 101.11/26.93 U56 < proper 101.11/26.93 U62 < proper 101.11/26.93 isPLNatKind < proper 101.11/26.93 U63 < proper 101.11/26.93 isPLNat < proper 101.11/26.93 U72 < proper 101.11/26.93 U73 < proper 101.11/26.93 U82 < proper 101.11/26.93 U83 < proper 101.11/26.93 U92 < proper 101.11/26.93 U93 < proper 101.11/26.93 U11 < proper 101.11/26.93 U21 < proper 101.11/26.93 U31 < proper 101.11/26.93 U41 < proper 101.11/26.93 U51 < proper 101.11/26.93 U61 < proper 101.11/26.93 U71 < proper 101.11/26.93 U81 < proper 101.11/26.93 U91 < proper 101.11/26.93 U101 < proper 101.11/26.93 U111 < proper 101.11/26.93 U121 < proper 101.11/26.93 U131 < proper 101.11/26.93 U141 < proper 101.11/26.93 U151 < proper 101.11/26.93 U161 < proper 101.11/26.93 U171 < proper 101.11/26.93 U181 < proper 101.11/26.93 U191 < proper 101.11/26.93 U201 < proper 101.11/26.93 U211 < proper 101.11/26.93 U221 < proper 101.11/26.93 U231 < proper 101.11/26.93 U241 < proper 101.11/26.93 U251 < proper 101.11/26.93 U261 < proper 101.11/26.93 U271 < proper 101.11/26.93 U281 < proper 101.11/26.93 U291 < proper 101.11/26.93 U301 < proper 101.11/26.93 U311 < proper 101.11/26.93 U321 < proper 101.11/26.93 U331 < proper 101.11/26.93 U341 < proper 101.11/26.93 tail < proper 101.11/26.93 take < proper 101.11/26.93 sel < proper 101.11/26.93 proper < top 101.11/26.93 101.11/26.93 ---------------------------------------- 101.11/26.93 101.11/26.93 (28) LowerBoundPropagationProof (FINISHED) 101.11/26.93 Propagated lower bound. 101.11/26.93 ---------------------------------------- 101.11/26.93 101.11/26.93 (29) 101.11/26.93 BOUNDS(n^1, INF) 101.11/26.93 101.11/26.93 ---------------------------------------- 101.11/26.93 101.11/26.93 (30) 101.11/26.93 Obligation: 101.11/26.93 TRS: 101.11/26.93 Rules: 101.11/26.93 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.11/26.93 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.11/26.93 active(U106(tt)) -> mark(tt) 101.11/26.93 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.11/26.93 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.11/26.93 active(U112(tt)) -> mark(tt) 101.11/26.93 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.11/26.93 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.11/26.93 active(U122(tt)) -> mark(tt) 101.11/26.93 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.11/26.93 active(U131(tt)) -> mark(tt) 101.11/26.93 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.11/26.93 active(U141(tt)) -> mark(tt) 101.11/26.93 active(U151(tt)) -> mark(tt) 101.11/26.93 active(U161(tt)) -> mark(tt) 101.11/26.93 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.11/26.93 active(U172(tt)) -> mark(tt) 101.11/26.93 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.11/26.93 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.11/26.93 active(U183(tt)) -> mark(tt) 101.11/26.93 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.11/26.93 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.11/26.93 active(U193(tt)) -> mark(tt) 101.11/26.93 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.11/26.93 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.11/26.93 active(U206(tt)) -> mark(tt) 101.11/26.93 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.11/26.93 active(U211(tt)) -> mark(tt) 101.11/26.93 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.11/26.93 active(U221(tt)) -> mark(tt) 101.11/26.93 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.11/26.93 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.11/26.93 active(U232(tt)) -> mark(tt) 101.11/26.93 active(U24(tt, X)) -> mark(X) 101.11/26.93 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.11/26.93 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.11/26.93 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.11/26.93 active(U246(tt)) -> mark(tt) 101.11/26.93 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.11/26.93 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.11/26.93 active(U256(tt)) -> mark(tt) 101.11/26.93 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.11/26.93 active(U262(tt)) -> mark(tt) 101.11/26.93 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.11/26.93 active(U272(tt)) -> mark(tt) 101.11/26.93 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.11/26.93 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.11/26.93 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.11/26.93 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.11/26.93 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.11/26.93 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.11/26.93 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.11/26.93 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.11/26.93 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.11/26.93 active(U304(tt, Y)) -> mark(Y) 101.11/26.93 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.11/26.93 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.11/26.93 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.11/26.93 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.11/26.93 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.11/26.93 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.11/26.93 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.11/26.93 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.11/26.93 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.11/26.93 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.11/26.93 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.11/26.93 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.11/26.93 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.11/26.93 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.11/26.93 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.11/26.93 active(U334(tt, XS)) -> mark(XS) 101.11/26.93 active(U34(tt, N)) -> mark(N) 101.11/26.93 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.11/26.93 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.11/26.93 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.11/26.93 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.11/26.93 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.11/26.93 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.11/26.93 active(U46(tt)) -> mark(tt) 101.11/26.93 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.11/26.93 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.11/26.93 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.11/26.93 active(U56(tt)) -> mark(tt) 101.11/26.93 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.11/26.93 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.11/26.93 active(U63(tt)) -> mark(tt) 101.11/26.93 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.11/26.93 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.11/26.93 active(U73(tt)) -> mark(tt) 101.11/26.93 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.11/26.93 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.11/26.93 active(U83(tt)) -> mark(tt) 101.11/26.93 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.11/26.93 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.11/26.93 active(U93(tt)) -> mark(tt) 101.11/26.93 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.11/26.93 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.11/26.93 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.11/26.93 active(isLNat(nil)) -> mark(tt) 101.11/26.93 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.11/26.93 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.11/26.93 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.11/26.93 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.11/26.93 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(isLNatKind(nil)) -> mark(tt) 101.11/26.93 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.11/26.93 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.11/26.93 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.11/26.93 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.11/26.93 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.11/26.93 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.11/26.93 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.11/26.93 active(isNatural(0')) -> mark(tt) 101.11/26.93 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.11/26.93 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.11/26.93 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(isNaturalKind(0')) -> mark(tt) 101.11/26.93 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.11/26.93 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.11/26.93 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.11/26.93 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.11/26.93 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.11/26.93 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.11/26.93 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.11/26.93 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.11/26.93 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.11/26.93 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.11/26.93 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.11/26.93 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.11/26.93 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.11/26.93 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.11/26.93 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.11/26.93 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.11/26.93 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.11/26.93 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.11/26.93 active(U105(X1, X2)) -> U105(active(X1), X2) 101.11/26.93 active(U106(X)) -> U106(active(X)) 101.11/26.93 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.11/26.93 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.11/26.93 active(U111(X1, X2)) -> U111(active(X1), X2) 101.11/26.93 active(U112(X)) -> U112(active(X)) 101.11/26.93 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.11/26.93 active(U121(X1, X2)) -> U121(active(X1), X2) 101.11/26.93 active(U122(X)) -> U122(active(X)) 101.11/26.93 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.11/26.93 active(U131(X)) -> U131(active(X)) 101.11/26.93 active(snd(X)) -> snd(active(X)) 101.11/26.93 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.11/26.93 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.11/26.93 active(U141(X)) -> U141(active(X)) 101.11/26.93 active(U151(X)) -> U151(active(X)) 101.11/26.93 active(U161(X)) -> U161(active(X)) 101.11/26.93 active(U171(X1, X2)) -> U171(active(X1), X2) 101.11/26.93 active(U172(X)) -> U172(active(X)) 101.11/26.93 active(U181(X1, X2)) -> U181(active(X1), X2) 101.11/26.93 active(U182(X1, X2)) -> U182(active(X1), X2) 101.11/26.93 active(U183(X)) -> U183(active(X)) 101.11/26.93 active(U191(X1, X2)) -> U191(active(X1), X2) 101.11/26.93 active(U192(X1, X2)) -> U192(active(X1), X2) 101.11/26.93 active(U193(X)) -> U193(active(X)) 101.11/26.93 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.11/26.93 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.11/26.93 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.11/26.93 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.11/26.93 active(U205(X1, X2)) -> U205(active(X1), X2) 101.11/26.93 active(U206(X)) -> U206(active(X)) 101.11/26.93 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.11/26.93 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.11/26.93 active(U211(X)) -> U211(active(X)) 101.11/26.93 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.11/26.93 active(U221(X)) -> U221(active(X)) 101.11/26.93 active(U24(X1, X2)) -> U24(active(X1), X2) 101.11/26.93 active(U231(X1, X2)) -> U231(active(X1), X2) 101.11/26.93 active(U232(X)) -> U232(active(X)) 101.11/26.93 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.11/26.93 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.11/26.93 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.11/26.93 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.11/26.93 active(U245(X1, X2)) -> U245(active(X1), X2) 101.11/26.93 active(U246(X)) -> U246(active(X)) 101.11/26.93 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.11/26.93 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.11/26.93 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.11/26.93 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.11/26.93 active(U255(X1, X2)) -> U255(active(X1), X2) 101.11/26.93 active(U256(X)) -> U256(active(X)) 101.11/26.93 active(U261(X1, X2)) -> U261(active(X1), X2) 101.11/26.93 active(U262(X)) -> U262(active(X)) 101.11/26.93 active(U271(X1, X2)) -> U271(active(X1), X2) 101.11/26.93 active(U272(X)) -> U272(active(X)) 101.11/26.93 active(U281(X1, X2)) -> U281(active(X1), X2) 101.11/26.93 active(U282(X1, X2)) -> U282(active(X1), X2) 101.11/26.93 active(cons(X1, X2)) -> cons(active(X1), X2) 101.11/26.93 active(natsFrom(X)) -> natsFrom(active(X)) 101.11/26.93 active(s(X)) -> s(active(X)) 101.11/26.93 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.11/26.93 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.11/26.93 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.11/26.93 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.11/26.93 active(head(X)) -> head(active(X)) 101.11/26.93 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.11/26.93 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.11/26.93 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.11/26.93 active(U302(X1, X2)) -> U302(active(X1), X2) 101.11/26.93 active(U303(X1, X2)) -> U303(active(X1), X2) 101.11/26.93 active(U304(X1, X2)) -> U304(active(X1), X2) 101.11/26.93 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.11/26.93 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.11/26.93 active(U311(X1, X2)) -> U311(active(X1), X2) 101.11/26.93 active(U312(X1, X2)) -> U312(active(X1), X2) 101.11/26.93 active(pair(X1, X2)) -> pair(active(X1), X2) 101.11/26.93 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.11/26.93 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.11/26.93 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.11/26.93 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.11/26.93 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.11/26.93 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.11/26.93 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.11/26.93 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.11/26.93 active(U327(X1, X2)) -> U327(active(X1), X2) 101.11/26.93 active(U34(X1, X2)) -> U34(active(X1), X2) 101.11/26.93 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.11/26.93 active(U332(X1, X2)) -> U332(active(X1), X2) 101.11/26.93 active(U333(X1, X2)) -> U333(active(X1), X2) 101.11/26.93 active(U334(X1, X2)) -> U334(active(X1), X2) 101.11/26.93 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.11/26.93 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.11/26.93 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.11/26.93 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.11/26.93 active(fst(X)) -> fst(active(X)) 101.11/26.93 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.11/26.93 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.11/26.93 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.11/26.93 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.11/26.93 active(U45(X1, X2)) -> U45(active(X1), X2) 101.11/26.93 active(U46(X)) -> U46(active(X)) 101.11/26.93 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.11/26.93 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.11/26.93 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.11/26.93 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.11/26.93 active(U55(X1, X2)) -> U55(active(X1), X2) 101.11/26.93 active(U56(X)) -> U56(active(X)) 101.11/26.93 active(U61(X1, X2)) -> U61(active(X1), X2) 101.11/26.93 active(U62(X1, X2)) -> U62(active(X1), X2) 101.11/26.93 active(U63(X)) -> U63(active(X)) 101.11/26.93 active(U71(X1, X2)) -> U71(active(X1), X2) 101.11/26.93 active(U72(X1, X2)) -> U72(active(X1), X2) 101.11/26.93 active(U73(X)) -> U73(active(X)) 101.11/26.93 active(U81(X1, X2)) -> U81(active(X1), X2) 101.11/26.93 active(U82(X1, X2)) -> U82(active(X1), X2) 101.11/26.93 active(U83(X)) -> U83(active(X)) 101.11/26.93 active(U91(X1, X2)) -> U91(active(X1), X2) 101.11/26.93 active(U92(X1, X2)) -> U92(active(X1), X2) 101.11/26.93 active(U93(X)) -> U93(active(X)) 101.11/26.93 active(tail(X)) -> tail(active(X)) 101.11/26.93 active(take(X1, X2)) -> take(active(X1), X2) 101.11/26.93 active(take(X1, X2)) -> take(X1, active(X2)) 101.11/26.93 active(sel(X1, X2)) -> sel(active(X1), X2) 101.11/26.93 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.11/26.93 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.11/26.93 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.11/26.93 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.11/26.93 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.11/26.93 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.11/26.93 U106(mark(X)) -> mark(U106(X)) 101.11/26.93 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.11/26.93 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.11/26.93 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.11/26.93 U112(mark(X)) -> mark(U112(X)) 101.11/26.93 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.11/26.93 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.11/26.93 U122(mark(X)) -> mark(U122(X)) 101.11/26.93 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.11/26.93 U131(mark(X)) -> mark(U131(X)) 101.11/26.93 snd(mark(X)) -> mark(snd(X)) 101.11/26.93 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.11/26.93 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.11/26.93 U141(mark(X)) -> mark(U141(X)) 101.11/26.93 U151(mark(X)) -> mark(U151(X)) 101.11/26.93 U161(mark(X)) -> mark(U161(X)) 101.11/26.93 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.11/26.93 U172(mark(X)) -> mark(U172(X)) 101.11/26.93 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.11/26.93 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.11/26.93 U183(mark(X)) -> mark(U183(X)) 101.11/26.93 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.11/26.93 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.11/26.93 U193(mark(X)) -> mark(U193(X)) 101.11/26.93 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.11/26.93 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.11/26.93 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.11/26.93 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.11/26.93 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.11/26.93 U206(mark(X)) -> mark(U206(X)) 101.11/26.93 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.11/26.93 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.11/26.93 U211(mark(X)) -> mark(U211(X)) 101.11/26.93 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.11/26.93 U221(mark(X)) -> mark(U221(X)) 101.11/26.93 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.11/26.93 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.11/26.93 U232(mark(X)) -> mark(U232(X)) 101.11/26.93 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.11/26.93 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.11/26.93 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.11/26.93 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.11/26.93 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.11/26.93 U246(mark(X)) -> mark(U246(X)) 101.11/26.93 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.11/26.93 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.11/26.93 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.11/26.93 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.11/26.93 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.11/26.93 U256(mark(X)) -> mark(U256(X)) 101.11/26.93 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.11/26.93 U262(mark(X)) -> mark(U262(X)) 101.11/26.93 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.11/26.93 U272(mark(X)) -> mark(U272(X)) 101.11/26.93 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.11/26.93 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.11/26.93 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.11/26.93 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.11/26.93 s(mark(X)) -> mark(s(X)) 101.11/26.93 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.11/26.93 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.11/26.93 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.11/26.93 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.11/26.93 head(mark(X)) -> mark(head(X)) 101.11/26.93 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.11/26.93 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.11/26.93 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.11/26.93 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.11/26.93 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.11/26.93 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.11/26.93 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.11/26.93 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.11/26.93 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.11/26.93 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.11/26.93 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.11/26.93 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.11/26.93 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.11/26.93 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.11/26.93 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.11/26.93 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.11/26.93 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.11/26.93 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.11/26.93 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.11/26.93 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.11/26.93 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.11/26.93 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.11/26.93 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.11/26.93 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.11/26.93 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.11/26.93 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.11/26.93 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.11/26.93 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.11/26.93 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.11/26.93 fst(mark(X)) -> mark(fst(X)) 101.11/26.93 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.11/26.93 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.11/26.93 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.11/26.93 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.11/26.93 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.11/26.93 U46(mark(X)) -> mark(U46(X)) 101.11/26.93 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.11/26.93 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.11/26.93 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.11/26.93 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.11/26.93 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.11/26.93 U56(mark(X)) -> mark(U56(X)) 101.11/26.93 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.11/26.93 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.11/26.93 U63(mark(X)) -> mark(U63(X)) 101.11/26.93 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.11/26.93 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.11/26.93 U73(mark(X)) -> mark(U73(X)) 101.11/26.93 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.11/26.93 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.11/26.93 U83(mark(X)) -> mark(U83(X)) 101.11/26.93 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.11/26.93 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.11/26.93 U93(mark(X)) -> mark(U93(X)) 101.11/26.93 tail(mark(X)) -> mark(tail(X)) 101.11/26.93 take(mark(X1), X2) -> mark(take(X1, X2)) 101.11/26.93 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.11/26.93 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.11/26.93 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.11/26.93 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(tt) -> ok(tt) 101.11/26.93 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.11/26.93 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.11/26.93 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.11/26.93 proper(isNatural(X)) -> isNatural(proper(X)) 101.11/26.93 proper(U106(X)) -> U106(proper(X)) 101.11/26.93 proper(isLNat(X)) -> isLNat(proper(X)) 101.11/26.93 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.11/26.93 proper(U112(X)) -> U112(proper(X)) 101.11/26.93 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.11/26.93 proper(U122(X)) -> U122(proper(X)) 101.11/26.93 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U131(X)) -> U131(proper(X)) 101.11/26.93 proper(snd(X)) -> snd(proper(X)) 101.11/26.93 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.11/26.93 proper(U141(X)) -> U141(proper(X)) 101.11/26.93 proper(U151(X)) -> U151(proper(X)) 101.11/26.93 proper(U161(X)) -> U161(proper(X)) 101.11/26.93 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.11/26.93 proper(U172(X)) -> U172(proper(X)) 101.11/26.93 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.11/26.93 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.11/26.93 proper(U183(X)) -> U183(proper(X)) 101.11/26.93 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.11/26.93 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.11/26.93 proper(U193(X)) -> U193(proper(X)) 101.11/26.93 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.11/26.93 proper(U206(X)) -> U206(proper(X)) 101.11/26.93 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U211(X)) -> U211(proper(X)) 101.11/26.93 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U221(X)) -> U221(proper(X)) 101.11/26.93 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.11/26.93 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.11/26.93 proper(U232(X)) -> U232(proper(X)) 101.11/26.93 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.11/26.93 proper(U246(X)) -> U246(proper(X)) 101.11/26.93 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.11/26.93 proper(U256(X)) -> U256(proper(X)) 101.11/26.93 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.11/26.93 proper(U262(X)) -> U262(proper(X)) 101.11/26.93 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.11/26.93 proper(U272(X)) -> U272(proper(X)) 101.11/26.93 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.11/26.93 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.11/26.93 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.11/26.93 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.11/26.93 proper(s(X)) -> s(proper(X)) 101.11/26.93 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(head(X)) -> head(proper(X)) 101.11/26.93 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.11/26.93 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.11/26.93 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.11/26.93 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.11/26.93 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.11/26.93 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.11/26.93 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.11/26.93 proper(nil) -> ok(nil) 101.11/26.93 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.11/26.93 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.11/26.93 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.11/26.93 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.11/26.93 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.11/26.93 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.11/26.93 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(fst(X)) -> fst(proper(X)) 101.11/26.93 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.11/26.93 proper(U46(X)) -> U46(proper(X)) 101.11/26.93 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.11/26.93 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.11/26.93 proper(U56(X)) -> U56(proper(X)) 101.11/26.93 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.11/26.93 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.11/26.93 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.11/26.93 proper(U63(X)) -> U63(proper(X)) 101.11/26.93 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.11/26.93 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.11/26.93 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.11/26.93 proper(U73(X)) -> U73(proper(X)) 101.11/26.93 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.11/26.93 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.11/26.93 proper(U83(X)) -> U83(proper(X)) 101.11/26.93 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.11/26.93 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.11/26.93 proper(U93(X)) -> U93(proper(X)) 101.11/26.93 proper(tail(X)) -> tail(proper(X)) 101.11/26.93 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.11/26.93 proper(0') -> ok(0') 101.11/26.93 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.11/26.93 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.11/26.93 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.11/26.93 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.11/26.93 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.11/26.93 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.11/26.93 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.11/26.93 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.11/26.93 isNatural(ok(X)) -> ok(isNatural(X)) 101.11/26.93 U106(ok(X)) -> ok(U106(X)) 101.11/26.93 isLNat(ok(X)) -> ok(isLNat(X)) 101.11/26.93 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.11/26.93 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.11/26.93 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.11/26.93 U112(ok(X)) -> ok(U112(X)) 101.11/26.93 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.11/26.93 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.11/26.93 U122(ok(X)) -> ok(U122(X)) 101.11/26.93 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.11/26.93 U131(ok(X)) -> ok(U131(X)) 101.11/26.93 snd(ok(X)) -> ok(snd(X)) 101.11/26.93 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.11/26.93 U141(ok(X)) -> ok(U141(X)) 101.11/26.93 U151(ok(X)) -> ok(U151(X)) 101.11/26.93 U161(ok(X)) -> ok(U161(X)) 101.11/26.93 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.11/26.93 U172(ok(X)) -> ok(U172(X)) 101.11/26.93 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.11/26.93 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.11/26.93 U183(ok(X)) -> ok(U183(X)) 101.11/26.93 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.11/26.93 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.11/26.93 U193(ok(X)) -> ok(U193(X)) 101.11/26.93 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.11/26.93 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.11/26.93 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.11/26.93 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.11/26.93 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.11/26.93 U206(ok(X)) -> ok(U206(X)) 101.11/26.93 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.11/26.93 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.11/26.93 U211(ok(X)) -> ok(U211(X)) 101.11/26.93 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.11/26.93 U221(ok(X)) -> ok(U221(X)) 101.11/26.93 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.11/26.93 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.11/26.93 U232(ok(X)) -> ok(U232(X)) 101.11/26.93 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.11/26.93 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.11/26.93 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.11/26.93 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.11/26.93 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.11/26.93 U246(ok(X)) -> ok(U246(X)) 101.11/26.93 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.11/26.93 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.11/26.93 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.11/26.93 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.11/26.93 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.11/26.93 U256(ok(X)) -> ok(U256(X)) 101.11/26.93 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.11/26.93 U262(ok(X)) -> ok(U262(X)) 101.11/26.93 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.11/26.93 U272(ok(X)) -> ok(U272(X)) 101.11/26.93 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.11/26.93 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.11/26.93 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.11/26.93 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.11/26.93 s(ok(X)) -> ok(s(X)) 101.11/26.93 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.11/26.93 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.11/26.93 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.11/26.93 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.11/26.93 head(ok(X)) -> ok(head(X)) 101.11/26.93 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.11/26.93 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.11/26.93 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.11/26.93 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.11/26.93 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.11/26.93 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.11/26.93 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.11/26.93 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.11/26.93 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.11/26.93 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.11/26.93 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.11/26.93 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.11/26.93 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.11/26.93 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.11/26.93 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.11/26.93 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.11/26.93 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.11/26.93 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.11/26.93 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.11/26.93 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.11/26.93 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.11/26.93 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.11/26.93 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.11/26.93 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.11/26.93 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.11/26.93 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.11/26.93 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.11/26.93 fst(ok(X)) -> ok(fst(X)) 101.11/26.93 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.11/26.93 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.11/26.93 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.11/26.93 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.11/26.93 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.11/26.93 U46(ok(X)) -> ok(U46(X)) 101.11/26.93 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.11/26.93 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.11/26.93 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.11/26.93 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.11/26.93 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.11/26.93 U56(ok(X)) -> ok(U56(X)) 101.11/26.93 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.11/26.93 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.11/26.93 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.11/26.93 U63(ok(X)) -> ok(U63(X)) 101.11/26.93 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.11/26.93 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.11/26.93 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.11/26.93 U73(ok(X)) -> ok(U73(X)) 101.11/26.93 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.11/26.93 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.11/26.93 U83(ok(X)) -> ok(U83(X)) 101.11/26.93 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.11/26.93 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.11/26.93 U93(ok(X)) -> ok(U93(X)) 101.11/26.93 tail(ok(X)) -> ok(tail(X)) 101.11/26.93 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.11/26.93 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.11/26.93 top(mark(X)) -> top(proper(X)) 101.11/26.93 top(ok(X)) -> top(active(X)) 101.11/26.93 101.11/26.93 Types: 101.11/26.93 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 tt :: tt:mark:nil:0':ok 101.11/26.93 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.93 nil :: tt:mark:nil:0':ok 101.11/26.93 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 0' :: tt:mark:nil:0':ok 101.11/26.97 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.11/26.97 top :: tt:mark:nil:0':ok -> top 101.11/26.97 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.11/26.97 hole_top2_0 :: top 101.11/26.97 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.11/26.97 101.11/26.97 101.11/26.97 Lemmas: 101.11/26.97 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.11/26.97 101.11/26.97 101.11/26.97 Generator Equations: 101.11/26.97 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.11/26.97 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.11/26.97 101.11/26.97 101.11/26.97 The following defined symbols remain to be analysed: 101.11/26.97 isNaturalKind, active, U103, isLNatKind, U104, U105, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.11/26.97 101.11/26.97 They will be analysed ascendingly in the following order: 101.11/26.97 isNaturalKind < active 101.11/26.97 U103 < active 101.11/26.97 isLNatKind < active 101.11/26.97 U104 < active 101.11/26.97 U105 < active 101.11/26.97 isNatural < active 101.11/26.97 U106 < active 101.11/26.97 isLNat < active 101.11/26.97 U12 < active 101.11/26.97 U112 < active 101.11/26.97 U13 < active 101.11/26.97 U122 < active 101.11/26.97 U14 < active 101.11/26.97 snd < active 101.11/26.97 splitAt < active 101.11/26.97 U172 < active 101.11/26.97 U182 < active 101.11/26.97 U183 < active 101.11/26.97 U192 < active 101.11/26.97 U193 < active 101.11/26.97 U202 < active 101.11/26.97 U203 < active 101.11/26.97 U204 < active 101.11/26.97 U205 < active 101.11/26.97 U206 < active 101.11/26.97 U22 < active 101.11/26.97 U23 < active 101.11/26.97 U24 < active 101.11/26.97 U232 < active 101.11/26.97 U242 < active 101.11/26.97 U243 < active 101.11/26.97 U244 < active 101.11/26.97 U245 < active 101.11/26.97 U246 < active 101.11/26.97 U252 < active 101.11/26.97 U253 < active 101.11/26.97 U254 < active 101.11/26.97 U255 < active 101.11/26.97 U256 < active 101.11/26.97 U262 < active 101.11/26.97 U272 < active 101.11/26.97 U282 < active 101.11/26.97 cons < active 101.11/26.97 natsFrom < active 101.11/26.97 s < active 101.11/26.97 U292 < active 101.11/26.97 U293 < active 101.11/26.97 U294 < active 101.11/26.97 head < active 101.11/26.97 afterNth < active 101.11/26.97 U302 < active 101.11/26.97 U303 < active 101.11/26.97 U304 < active 101.11/26.97 U32 < active 101.11/26.97 U312 < active 101.11/26.97 pair < active 101.11/26.97 U33 < active 101.11/26.97 U322 < active 101.11/26.97 U323 < active 101.11/26.97 U324 < active 101.11/26.97 U325 < active 101.11/26.97 U326 < active 101.11/26.97 U327 < active 101.11/26.97 U34 < active 101.11/26.97 U332 < active 101.11/26.97 U333 < active 101.11/26.97 U334 < active 101.11/26.97 U342 < active 101.11/26.97 U343 < active 101.11/26.97 U344 < active 101.11/26.97 fst < active 101.11/26.97 U42 < active 101.11/26.97 U43 < active 101.11/26.97 U44 < active 101.11/26.97 U45 < active 101.11/26.97 U46 < active 101.11/26.97 U52 < active 101.11/26.97 U53 < active 101.11/26.97 U54 < active 101.11/26.97 U55 < active 101.11/26.97 U56 < active 101.11/26.97 U62 < active 101.11/26.97 isPLNatKind < active 101.11/26.97 U63 < active 101.11/26.97 isPLNat < active 101.11/26.97 U72 < active 101.11/26.97 U73 < active 101.11/26.97 U82 < active 101.11/26.97 U83 < active 101.11/26.97 U92 < active 101.11/26.97 U93 < active 101.11/26.97 U11 < active 101.11/26.97 U21 < active 101.11/26.97 U31 < active 101.11/26.97 U41 < active 101.11/26.97 U51 < active 101.11/26.97 U61 < active 101.11/26.97 U71 < active 101.11/26.97 U81 < active 101.11/26.97 U91 < active 101.11/26.97 U101 < active 101.11/26.97 U111 < active 101.11/26.97 U121 < active 101.11/26.97 U131 < active 101.11/26.97 U141 < active 101.11/26.97 U151 < active 101.11/26.97 U161 < active 101.11/26.97 U171 < active 101.11/26.97 U181 < active 101.11/26.97 U191 < active 101.11/26.97 U201 < active 101.11/26.97 U211 < active 101.11/26.97 U221 < active 101.11/26.97 U231 < active 101.11/26.97 U241 < active 101.11/26.97 U251 < active 101.11/26.97 U261 < active 101.11/26.97 U271 < active 101.11/26.97 U281 < active 101.11/26.97 U291 < active 101.11/26.97 U301 < active 101.11/26.97 U311 < active 101.11/26.97 U321 < active 101.11/26.97 U331 < active 101.11/26.97 U341 < active 101.11/26.97 tail < active 101.11/26.97 take < active 101.11/26.97 sel < active 101.11/26.97 active < top 101.11/26.97 isNaturalKind < proper 101.11/26.97 U103 < proper 101.11/26.97 isLNatKind < proper 101.11/26.97 U104 < proper 101.11/26.97 U105 < proper 101.11/26.97 isNatural < proper 101.11/26.97 U106 < proper 101.11/26.97 isLNat < proper 101.11/26.97 U12 < proper 101.11/26.97 U112 < proper 101.11/26.97 U13 < proper 101.11/26.97 U122 < proper 101.11/26.97 U14 < proper 101.11/26.97 snd < proper 101.11/26.97 splitAt < proper 101.11/26.97 U172 < proper 101.11/26.97 U182 < proper 101.11/26.97 U183 < proper 101.11/26.97 U192 < proper 101.11/26.97 U193 < proper 101.11/26.97 U202 < proper 101.11/26.97 U203 < proper 101.11/26.97 U204 < proper 101.11/26.97 U205 < proper 101.11/26.97 U206 < proper 101.11/26.97 U22 < proper 101.11/26.97 U23 < proper 101.11/26.97 U24 < proper 101.11/26.97 U232 < proper 101.11/26.97 U242 < proper 101.11/26.97 U243 < proper 101.11/26.97 U244 < proper 101.11/26.97 U245 < proper 101.11/26.97 U246 < proper 101.11/26.97 U252 < proper 101.11/26.97 U253 < proper 101.11/26.97 U254 < proper 101.11/26.97 U255 < proper 101.11/26.97 U256 < proper 101.11/26.97 U262 < proper 101.11/26.97 U272 < proper 101.11/26.97 U282 < proper 101.11/26.97 cons < proper 101.11/26.97 natsFrom < proper 101.11/26.97 s < proper 101.11/26.97 U292 < proper 101.11/26.97 U293 < proper 101.11/26.97 U294 < proper 101.11/26.97 head < proper 101.11/26.97 afterNth < proper 101.11/26.97 U302 < proper 101.11/26.97 U303 < proper 101.11/26.97 U304 < proper 101.11/26.97 U32 < proper 101.11/26.97 U312 < proper 101.11/26.97 pair < proper 101.11/26.97 U33 < proper 101.11/26.97 U322 < proper 101.11/26.97 U323 < proper 101.11/26.97 U324 < proper 101.11/26.97 U325 < proper 101.11/26.97 U326 < proper 101.11/26.97 U327 < proper 101.11/26.97 U34 < proper 101.11/26.97 U332 < proper 101.11/26.97 U333 < proper 101.11/26.97 U334 < proper 101.11/26.97 U342 < proper 101.11/26.97 U343 < proper 101.11/26.97 U344 < proper 101.11/26.97 fst < proper 101.11/26.97 U42 < proper 101.11/26.97 U43 < proper 101.11/26.97 U44 < proper 101.11/26.97 U45 < proper 101.11/26.97 U46 < proper 101.11/26.97 U52 < proper 101.11/26.97 U53 < proper 101.11/26.97 U54 < proper 101.11/26.97 U55 < proper 101.11/26.97 U56 < proper 101.11/26.97 U62 < proper 101.11/26.97 isPLNatKind < proper 101.11/26.97 U63 < proper 101.11/26.97 isPLNat < proper 101.11/26.97 U72 < proper 101.11/26.97 U73 < proper 101.11/26.97 U82 < proper 101.11/26.97 U83 < proper 101.11/26.97 U92 < proper 101.11/26.97 U93 < proper 101.11/26.97 U11 < proper 101.11/26.97 U21 < proper 101.11/26.97 U31 < proper 101.11/26.97 U41 < proper 101.11/26.97 U51 < proper 101.11/26.97 U61 < proper 101.11/26.97 U71 < proper 101.11/26.97 U81 < proper 101.11/26.97 U91 < proper 101.11/26.97 U101 < proper 101.11/26.97 U111 < proper 101.11/26.97 U121 < proper 101.11/26.97 U131 < proper 101.11/26.97 U141 < proper 101.11/26.97 U151 < proper 101.11/26.97 U161 < proper 101.11/26.97 U171 < proper 101.11/26.97 U181 < proper 101.11/26.97 U191 < proper 101.11/26.97 U201 < proper 101.11/26.97 U211 < proper 101.11/26.97 U221 < proper 101.11/26.97 U231 < proper 101.11/26.97 U241 < proper 101.11/26.97 U251 < proper 101.11/26.97 U261 < proper 101.11/26.97 U271 < proper 101.11/26.97 U281 < proper 101.11/26.97 U291 < proper 101.11/26.97 U301 < proper 101.11/26.97 U311 < proper 101.11/26.97 U321 < proper 101.11/26.97 U331 < proper 101.11/26.97 U341 < proper 101.11/26.97 tail < proper 101.11/26.97 take < proper 101.11/26.97 sel < proper 101.11/26.97 proper < top 101.11/26.97 101.11/26.97 ---------------------------------------- 101.11/26.97 101.11/26.97 (31) RewriteLemmaProof (LOWER BOUND(ID)) 101.11/26.97 Proved the following rewrite lemma: 101.11/26.97 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.11/26.97 101.11/26.97 Induction Base: 101.11/26.97 U103(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.11/26.97 101.11/26.97 Induction Step: 101.11/26.97 U103(gen_tt:mark:nil:0':ok3_0(+(1, +(n17319_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.11/26.97 mark(U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.11/26.97 mark(*4_0) 101.11/26.97 101.11/26.97 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.11/26.97 ---------------------------------------- 101.11/26.97 101.11/26.97 (32) 101.11/26.97 Obligation: 101.11/26.97 TRS: 101.11/26.97 Rules: 101.11/26.97 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.11/26.97 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.11/26.97 active(U106(tt)) -> mark(tt) 101.11/26.97 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.11/26.97 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.11/26.97 active(U112(tt)) -> mark(tt) 101.11/26.97 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.11/26.97 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.11/26.97 active(U122(tt)) -> mark(tt) 101.11/26.97 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.11/26.97 active(U131(tt)) -> mark(tt) 101.11/26.97 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.11/26.97 active(U141(tt)) -> mark(tt) 101.11/26.97 active(U151(tt)) -> mark(tt) 101.11/26.97 active(U161(tt)) -> mark(tt) 101.11/26.97 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.11/26.97 active(U172(tt)) -> mark(tt) 101.11/26.97 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.11/26.97 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.11/26.97 active(U183(tt)) -> mark(tt) 101.11/26.97 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.11/26.97 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.11/26.97 active(U193(tt)) -> mark(tt) 101.11/26.97 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.11/26.97 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.11/26.97 active(U206(tt)) -> mark(tt) 101.11/26.97 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.11/26.97 active(U211(tt)) -> mark(tt) 101.11/26.97 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.11/26.97 active(U221(tt)) -> mark(tt) 101.11/26.97 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.11/26.97 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.11/26.97 active(U232(tt)) -> mark(tt) 101.11/26.97 active(U24(tt, X)) -> mark(X) 101.11/26.97 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.11/26.97 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.11/26.97 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.11/26.97 active(U246(tt)) -> mark(tt) 101.11/26.97 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.11/26.97 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.11/26.97 active(U256(tt)) -> mark(tt) 101.11/26.97 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.11/26.97 active(U262(tt)) -> mark(tt) 101.11/26.97 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.11/26.97 active(U272(tt)) -> mark(tt) 101.11/26.97 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.11/26.97 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.11/26.97 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.11/26.97 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.11/26.97 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.11/26.97 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.11/26.97 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.11/26.97 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.11/26.97 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.11/26.97 active(U304(tt, Y)) -> mark(Y) 101.11/26.97 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.11/26.97 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.11/26.97 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.11/26.97 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.11/26.97 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.11/26.97 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.11/26.97 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.11/26.97 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.11/26.97 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.11/26.97 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.11/26.97 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.11/26.97 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.11/26.97 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.11/26.97 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.11/26.97 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.11/26.97 active(U334(tt, XS)) -> mark(XS) 101.11/26.97 active(U34(tt, N)) -> mark(N) 101.11/26.97 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.11/26.97 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.11/26.97 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.11/26.97 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.11/26.97 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.11/26.97 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.11/26.97 active(U46(tt)) -> mark(tt) 101.11/26.97 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.11/26.97 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.11/26.97 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.11/26.97 active(U56(tt)) -> mark(tt) 101.11/26.97 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.11/26.97 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.11/26.97 active(U63(tt)) -> mark(tt) 101.11/26.97 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.11/26.97 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.11/26.97 active(U73(tt)) -> mark(tt) 101.11/26.97 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.11/26.97 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.11/26.97 active(U83(tt)) -> mark(tt) 101.11/26.97 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.11/26.97 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.11/26.97 active(U93(tt)) -> mark(tt) 101.11/26.97 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.11/26.97 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.11/26.97 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.11/26.97 active(isLNat(nil)) -> mark(tt) 101.11/26.97 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.11/26.97 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.11/26.97 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.11/26.97 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.11/26.97 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(isLNatKind(nil)) -> mark(tt) 101.11/26.97 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.11/26.97 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.11/26.97 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.11/26.97 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.11/26.97 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.11/26.97 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.11/26.97 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.11/26.97 active(isNatural(0')) -> mark(tt) 101.11/26.97 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.11/26.97 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.11/26.97 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(isNaturalKind(0')) -> mark(tt) 101.11/26.97 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.11/26.97 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.11/26.97 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.11/26.97 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.11/26.97 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.11/26.97 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.11/26.97 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.11/26.97 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.11/26.97 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.11/26.97 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.11/26.97 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.11/26.97 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.11/26.97 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.11/26.97 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.11/26.97 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.11/26.97 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.11/26.97 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.11/26.97 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.11/26.97 active(U105(X1, X2)) -> U105(active(X1), X2) 101.11/26.97 active(U106(X)) -> U106(active(X)) 101.11/26.97 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.11/26.97 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.11/26.97 active(U111(X1, X2)) -> U111(active(X1), X2) 101.11/26.97 active(U112(X)) -> U112(active(X)) 101.11/26.97 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.11/26.97 active(U121(X1, X2)) -> U121(active(X1), X2) 101.11/26.97 active(U122(X)) -> U122(active(X)) 101.11/26.97 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.11/26.97 active(U131(X)) -> U131(active(X)) 101.11/26.97 active(snd(X)) -> snd(active(X)) 101.11/26.97 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.11/26.97 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.11/26.97 active(U141(X)) -> U141(active(X)) 101.11/26.97 active(U151(X)) -> U151(active(X)) 101.11/26.97 active(U161(X)) -> U161(active(X)) 101.11/26.97 active(U171(X1, X2)) -> U171(active(X1), X2) 101.11/26.97 active(U172(X)) -> U172(active(X)) 101.11/26.97 active(U181(X1, X2)) -> U181(active(X1), X2) 101.11/26.97 active(U182(X1, X2)) -> U182(active(X1), X2) 101.11/26.97 active(U183(X)) -> U183(active(X)) 101.11/26.97 active(U191(X1, X2)) -> U191(active(X1), X2) 101.11/26.97 active(U192(X1, X2)) -> U192(active(X1), X2) 101.11/26.97 active(U193(X)) -> U193(active(X)) 101.11/26.97 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.11/26.97 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.11/26.97 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.11/26.97 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.11/26.97 active(U205(X1, X2)) -> U205(active(X1), X2) 101.11/26.97 active(U206(X)) -> U206(active(X)) 101.11/26.97 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.11/26.97 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.11/26.97 active(U211(X)) -> U211(active(X)) 101.11/26.97 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.11/26.97 active(U221(X)) -> U221(active(X)) 101.11/26.97 active(U24(X1, X2)) -> U24(active(X1), X2) 101.11/26.97 active(U231(X1, X2)) -> U231(active(X1), X2) 101.11/26.97 active(U232(X)) -> U232(active(X)) 101.11/26.97 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.11/26.97 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.11/26.97 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.11/26.97 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.11/26.97 active(U245(X1, X2)) -> U245(active(X1), X2) 101.11/26.97 active(U246(X)) -> U246(active(X)) 101.11/26.97 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.11/26.97 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.11/26.97 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.11/26.97 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.11/26.97 active(U255(X1, X2)) -> U255(active(X1), X2) 101.11/26.97 active(U256(X)) -> U256(active(X)) 101.11/26.97 active(U261(X1, X2)) -> U261(active(X1), X2) 101.11/26.97 active(U262(X)) -> U262(active(X)) 101.11/26.97 active(U271(X1, X2)) -> U271(active(X1), X2) 101.11/26.97 active(U272(X)) -> U272(active(X)) 101.11/26.97 active(U281(X1, X2)) -> U281(active(X1), X2) 101.11/26.97 active(U282(X1, X2)) -> U282(active(X1), X2) 101.11/26.97 active(cons(X1, X2)) -> cons(active(X1), X2) 101.11/26.97 active(natsFrom(X)) -> natsFrom(active(X)) 101.11/26.97 active(s(X)) -> s(active(X)) 101.11/26.97 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.11/26.97 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.11/26.97 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.11/26.97 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.11/26.97 active(head(X)) -> head(active(X)) 101.11/26.97 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.11/26.97 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.11/26.97 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.11/26.97 active(U302(X1, X2)) -> U302(active(X1), X2) 101.11/26.97 active(U303(X1, X2)) -> U303(active(X1), X2) 101.11/26.97 active(U304(X1, X2)) -> U304(active(X1), X2) 101.11/26.97 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.11/26.97 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.11/26.97 active(U311(X1, X2)) -> U311(active(X1), X2) 101.11/26.97 active(U312(X1, X2)) -> U312(active(X1), X2) 101.11/26.97 active(pair(X1, X2)) -> pair(active(X1), X2) 101.11/26.97 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.11/26.97 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.11/26.97 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.11/26.97 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.11/26.97 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.11/26.97 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.11/26.97 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.11/26.97 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.11/26.97 active(U327(X1, X2)) -> U327(active(X1), X2) 101.11/26.97 active(U34(X1, X2)) -> U34(active(X1), X2) 101.11/26.97 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.11/26.97 active(U332(X1, X2)) -> U332(active(X1), X2) 101.11/26.97 active(U333(X1, X2)) -> U333(active(X1), X2) 101.11/26.97 active(U334(X1, X2)) -> U334(active(X1), X2) 101.11/26.97 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.11/26.97 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.11/26.97 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.11/26.97 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.11/26.97 active(fst(X)) -> fst(active(X)) 101.11/26.97 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.11/26.97 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.11/26.97 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.11/26.97 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.11/26.97 active(U45(X1, X2)) -> U45(active(X1), X2) 101.11/26.97 active(U46(X)) -> U46(active(X)) 101.11/26.97 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.11/26.97 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.11/26.97 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.11/26.97 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.11/26.97 active(U55(X1, X2)) -> U55(active(X1), X2) 101.11/26.97 active(U56(X)) -> U56(active(X)) 101.11/26.97 active(U61(X1, X2)) -> U61(active(X1), X2) 101.11/26.97 active(U62(X1, X2)) -> U62(active(X1), X2) 101.11/26.97 active(U63(X)) -> U63(active(X)) 101.11/26.97 active(U71(X1, X2)) -> U71(active(X1), X2) 101.11/26.97 active(U72(X1, X2)) -> U72(active(X1), X2) 101.11/26.97 active(U73(X)) -> U73(active(X)) 101.11/26.97 active(U81(X1, X2)) -> U81(active(X1), X2) 101.11/26.97 active(U82(X1, X2)) -> U82(active(X1), X2) 101.11/26.97 active(U83(X)) -> U83(active(X)) 101.11/26.97 active(U91(X1, X2)) -> U91(active(X1), X2) 101.11/26.97 active(U92(X1, X2)) -> U92(active(X1), X2) 101.11/26.97 active(U93(X)) -> U93(active(X)) 101.11/26.97 active(tail(X)) -> tail(active(X)) 101.11/26.97 active(take(X1, X2)) -> take(active(X1), X2) 101.11/26.97 active(take(X1, X2)) -> take(X1, active(X2)) 101.11/26.97 active(sel(X1, X2)) -> sel(active(X1), X2) 101.11/26.97 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.11/26.97 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.11/26.97 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.11/26.97 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.11/26.97 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.11/26.97 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.11/26.97 U106(mark(X)) -> mark(U106(X)) 101.11/26.97 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.11/26.97 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.11/26.97 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.11/26.97 U112(mark(X)) -> mark(U112(X)) 101.11/26.97 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.11/26.97 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.11/26.97 U122(mark(X)) -> mark(U122(X)) 101.11/26.97 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.11/26.97 U131(mark(X)) -> mark(U131(X)) 101.11/26.97 snd(mark(X)) -> mark(snd(X)) 101.11/26.97 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.11/26.97 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.11/26.97 U141(mark(X)) -> mark(U141(X)) 101.11/26.97 U151(mark(X)) -> mark(U151(X)) 101.11/26.97 U161(mark(X)) -> mark(U161(X)) 101.11/26.97 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.11/26.97 U172(mark(X)) -> mark(U172(X)) 101.11/26.97 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.11/26.97 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.11/26.97 U183(mark(X)) -> mark(U183(X)) 101.11/26.97 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.11/26.97 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.11/26.97 U193(mark(X)) -> mark(U193(X)) 101.11/26.97 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.11/26.97 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.11/26.97 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.11/26.97 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.11/26.97 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.11/26.97 U206(mark(X)) -> mark(U206(X)) 101.11/26.97 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.11/26.97 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.11/26.97 U211(mark(X)) -> mark(U211(X)) 101.11/26.97 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.11/26.97 U221(mark(X)) -> mark(U221(X)) 101.11/26.97 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.11/26.97 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.11/26.97 U232(mark(X)) -> mark(U232(X)) 101.11/26.97 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.11/26.97 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.11/26.97 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.11/26.97 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.11/26.97 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.11/26.97 U246(mark(X)) -> mark(U246(X)) 101.11/26.97 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.11/26.97 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.11/26.97 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.11/26.97 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.11/26.97 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.11/26.97 U256(mark(X)) -> mark(U256(X)) 101.11/26.97 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.11/26.97 U262(mark(X)) -> mark(U262(X)) 101.11/26.97 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.11/26.97 U272(mark(X)) -> mark(U272(X)) 101.11/26.97 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.11/26.97 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.11/26.97 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.11/26.97 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.11/26.97 s(mark(X)) -> mark(s(X)) 101.11/26.97 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.11/26.97 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.11/26.97 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.11/26.97 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.11/26.97 head(mark(X)) -> mark(head(X)) 101.11/26.97 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.11/26.97 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.11/26.97 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.11/26.97 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.11/26.97 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.11/26.97 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.11/26.97 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.11/26.97 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.11/26.97 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.11/26.97 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.11/26.97 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.11/26.97 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.11/26.97 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.11/26.97 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.11/26.97 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.11/26.97 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.11/26.97 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.11/26.97 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.11/26.97 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.11/26.97 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.11/26.97 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.11/26.97 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.11/26.97 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.11/26.97 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.11/26.97 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.11/26.97 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.11/26.97 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.11/26.97 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.11/26.97 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.11/26.97 fst(mark(X)) -> mark(fst(X)) 101.11/26.97 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.11/26.97 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.11/26.97 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.11/26.97 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.11/26.97 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.11/26.97 U46(mark(X)) -> mark(U46(X)) 101.11/26.97 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.11/26.97 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.11/26.97 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.11/26.97 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.11/26.97 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.11/26.97 U56(mark(X)) -> mark(U56(X)) 101.11/26.97 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.11/26.97 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.11/26.97 U63(mark(X)) -> mark(U63(X)) 101.11/26.97 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.11/26.97 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.11/26.97 U73(mark(X)) -> mark(U73(X)) 101.11/26.97 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.11/26.97 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.11/26.97 U83(mark(X)) -> mark(U83(X)) 101.11/26.97 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.11/26.97 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.11/26.97 U93(mark(X)) -> mark(U93(X)) 101.11/26.97 tail(mark(X)) -> mark(tail(X)) 101.11/26.97 take(mark(X1), X2) -> mark(take(X1, X2)) 101.11/26.97 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.11/26.97 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.11/26.97 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.11/26.97 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.11/26.97 proper(tt) -> ok(tt) 101.11/26.97 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.11/26.97 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.11/26.97 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.11/26.97 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.11/26.97 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.44/26.97 proper(isNatural(X)) -> isNatural(proper(X)) 101.44/26.97 proper(U106(X)) -> U106(proper(X)) 101.44/26.97 proper(isLNat(X)) -> isLNat(proper(X)) 101.44/26.97 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.44/26.97 proper(U112(X)) -> U112(proper(X)) 101.44/26.97 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.44/26.97 proper(U122(X)) -> U122(proper(X)) 101.44/26.97 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U131(X)) -> U131(proper(X)) 101.44/26.97 proper(snd(X)) -> snd(proper(X)) 101.44/26.97 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.44/26.97 proper(U141(X)) -> U141(proper(X)) 101.44/26.97 proper(U151(X)) -> U151(proper(X)) 101.44/26.97 proper(U161(X)) -> U161(proper(X)) 101.44/26.97 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.44/26.97 proper(U172(X)) -> U172(proper(X)) 101.44/26.97 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.44/26.97 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.44/26.97 proper(U183(X)) -> U183(proper(X)) 101.44/26.97 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.44/26.97 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.44/26.97 proper(U193(X)) -> U193(proper(X)) 101.44/26.97 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.44/26.97 proper(U206(X)) -> U206(proper(X)) 101.44/26.97 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U211(X)) -> U211(proper(X)) 101.44/26.97 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U221(X)) -> U221(proper(X)) 101.44/26.97 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.44/26.97 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.44/26.97 proper(U232(X)) -> U232(proper(X)) 101.44/26.97 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.44/26.97 proper(U246(X)) -> U246(proper(X)) 101.44/26.97 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.44/26.97 proper(U256(X)) -> U256(proper(X)) 101.44/26.97 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.44/26.97 proper(U262(X)) -> U262(proper(X)) 101.44/26.97 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.44/26.97 proper(U272(X)) -> U272(proper(X)) 101.44/26.97 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.44/26.97 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.44/26.97 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.44/26.97 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.44/26.97 proper(s(X)) -> s(proper(X)) 101.44/26.97 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(head(X)) -> head(proper(X)) 101.44/26.97 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.44/26.97 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.44/26.97 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.44/26.97 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.44/26.97 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.44/26.97 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.44/26.97 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.44/26.97 proper(nil) -> ok(nil) 101.44/26.97 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.97 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.44/26.97 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.44/26.97 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.44/26.97 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.44/26.97 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.44/26.97 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(fst(X)) -> fst(proper(X)) 101.44/26.97 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.44/26.97 proper(U46(X)) -> U46(proper(X)) 101.44/26.97 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.44/26.97 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.44/26.97 proper(U56(X)) -> U56(proper(X)) 101.44/26.97 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.44/26.97 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.44/26.97 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.44/26.97 proper(U63(X)) -> U63(proper(X)) 101.44/26.97 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.44/26.97 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.44/26.97 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.44/26.97 proper(U73(X)) -> U73(proper(X)) 101.44/26.97 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.44/26.97 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.44/26.97 proper(U83(X)) -> U83(proper(X)) 101.44/26.97 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.44/26.97 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.44/26.97 proper(U93(X)) -> U93(proper(X)) 101.44/26.97 proper(tail(X)) -> tail(proper(X)) 101.44/26.97 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.44/26.97 proper(0') -> ok(0') 101.44/26.97 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.44/26.97 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.44/26.97 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.44/26.97 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.44/26.97 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.44/26.97 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.44/26.97 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.44/26.97 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.44/26.97 isNatural(ok(X)) -> ok(isNatural(X)) 101.44/26.97 U106(ok(X)) -> ok(U106(X)) 101.44/26.97 isLNat(ok(X)) -> ok(isLNat(X)) 101.44/26.97 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.44/26.97 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.44/26.97 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.44/26.97 U112(ok(X)) -> ok(U112(X)) 101.44/26.97 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.44/26.97 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.44/26.97 U122(ok(X)) -> ok(U122(X)) 101.44/26.97 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.44/26.97 U131(ok(X)) -> ok(U131(X)) 101.44/26.97 snd(ok(X)) -> ok(snd(X)) 101.44/26.97 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.44/26.97 U141(ok(X)) -> ok(U141(X)) 101.44/26.97 U151(ok(X)) -> ok(U151(X)) 101.44/26.97 U161(ok(X)) -> ok(U161(X)) 101.44/26.97 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.44/26.97 U172(ok(X)) -> ok(U172(X)) 101.44/26.97 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.44/26.97 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.44/26.97 U183(ok(X)) -> ok(U183(X)) 101.44/26.97 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.44/26.97 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.44/26.97 U193(ok(X)) -> ok(U193(X)) 101.44/26.97 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.44/26.97 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.44/26.97 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.44/26.97 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.44/26.97 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.44/26.97 U206(ok(X)) -> ok(U206(X)) 101.44/26.97 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.44/26.97 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.44/26.97 U211(ok(X)) -> ok(U211(X)) 101.44/26.97 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.44/26.97 U221(ok(X)) -> ok(U221(X)) 101.44/26.97 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.44/26.97 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.44/26.97 U232(ok(X)) -> ok(U232(X)) 101.44/26.97 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.44/26.97 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.44/26.97 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.44/26.97 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.44/26.97 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.44/26.97 U246(ok(X)) -> ok(U246(X)) 101.44/26.97 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.44/26.97 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.44/26.97 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.44/26.97 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.44/26.97 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.44/26.97 U256(ok(X)) -> ok(U256(X)) 101.44/26.97 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.44/26.97 U262(ok(X)) -> ok(U262(X)) 101.44/26.97 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.44/26.97 U272(ok(X)) -> ok(U272(X)) 101.44/26.97 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.44/26.97 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.44/26.97 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.44/26.97 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.44/26.97 s(ok(X)) -> ok(s(X)) 101.44/26.97 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.44/26.97 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.44/26.97 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.44/26.97 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.44/26.97 head(ok(X)) -> ok(head(X)) 101.44/26.97 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.44/26.97 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.44/26.97 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.44/26.97 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.44/26.97 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.44/26.97 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.44/26.97 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.44/26.97 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.44/26.97 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.44/26.97 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.44/26.97 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.44/26.98 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.44/26.98 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.44/26.98 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.44/26.98 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.44/26.98 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.44/26.98 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.44/26.98 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.44/26.98 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.44/26.98 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.44/26.98 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.44/26.98 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.44/26.98 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.44/26.98 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.44/26.98 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.44/26.98 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.44/26.98 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.44/26.98 fst(ok(X)) -> ok(fst(X)) 101.44/26.98 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.44/26.98 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.44/26.98 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.44/26.98 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.44/26.98 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.44/26.98 U46(ok(X)) -> ok(U46(X)) 101.44/26.98 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.44/26.98 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.44/26.98 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.44/26.98 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.44/26.98 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.44/26.98 U56(ok(X)) -> ok(U56(X)) 101.44/26.98 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.44/26.98 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.44/26.98 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.44/26.98 U63(ok(X)) -> ok(U63(X)) 101.44/26.98 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.44/26.98 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.44/26.98 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.44/26.98 U73(ok(X)) -> ok(U73(X)) 101.44/26.98 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.44/26.98 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.44/26.98 U83(ok(X)) -> ok(U83(X)) 101.44/26.98 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.44/26.98 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.44/26.98 U93(ok(X)) -> ok(U93(X)) 101.44/26.98 tail(ok(X)) -> ok(tail(X)) 101.44/26.98 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.44/26.98 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.44/26.98 top(mark(X)) -> top(proper(X)) 101.44/26.98 top(ok(X)) -> top(active(X)) 101.44/26.98 101.44/26.98 Types: 101.44/26.98 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 tt :: tt:mark:nil:0':ok 101.44/26.98 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 nil :: tt:mark:nil:0':ok 101.44/26.98 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 0' :: tt:mark:nil:0':ok 101.44/26.98 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.98 top :: tt:mark:nil:0':ok -> top 101.44/26.98 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.44/26.98 hole_top2_0 :: top 101.44/26.98 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.44/26.98 101.44/26.98 101.44/26.98 Lemmas: 101.44/26.98 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.44/26.98 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.44/26.98 101.44/26.98 101.44/26.98 Generator Equations: 101.44/26.98 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.44/26.98 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.44/26.98 101.44/26.98 101.44/26.98 The following defined symbols remain to be analysed: 101.44/26.98 isLNatKind, active, U104, U105, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.44/26.98 101.44/26.98 They will be analysed ascendingly in the following order: 101.44/26.98 isLNatKind < active 101.44/26.98 U104 < active 101.44/26.98 U105 < active 101.44/26.98 isNatural < active 101.44/26.98 U106 < active 101.44/26.98 isLNat < active 101.44/26.98 U12 < active 101.44/26.98 U112 < active 101.44/26.98 U13 < active 101.44/26.98 U122 < active 101.44/26.98 U14 < active 101.44/26.98 snd < active 101.44/26.98 splitAt < active 101.44/26.98 U172 < active 101.44/26.98 U182 < active 101.44/26.98 U183 < active 101.44/26.98 U192 < active 101.44/26.98 U193 < active 101.44/26.98 U202 < active 101.44/26.98 U203 < active 101.44/26.98 U204 < active 101.44/26.98 U205 < active 101.44/26.98 U206 < active 101.44/26.98 U22 < active 101.44/26.98 U23 < active 101.44/26.98 U24 < active 101.44/26.98 U232 < active 101.44/26.98 U242 < active 101.44/26.98 U243 < active 101.44/26.98 U244 < active 101.44/26.98 U245 < active 101.44/26.98 U246 < active 101.44/26.98 U252 < active 101.44/26.98 U253 < active 101.44/26.98 U254 < active 101.44/26.98 U255 < active 101.44/26.98 U256 < active 101.44/26.98 U262 < active 101.44/26.98 U272 < active 101.44/26.98 U282 < active 101.44/26.98 cons < active 101.44/26.98 natsFrom < active 101.44/26.98 s < active 101.44/26.98 U292 < active 101.44/26.98 U293 < active 101.44/26.98 U294 < active 101.44/26.98 head < active 101.44/26.98 afterNth < active 101.44/26.98 U302 < active 101.44/26.98 U303 < active 101.44/26.98 U304 < active 101.44/26.98 U32 < active 101.44/26.98 U312 < active 101.44/26.98 pair < active 101.44/26.98 U33 < active 101.44/26.98 U322 < active 101.44/26.98 U323 < active 101.44/26.98 U324 < active 101.44/26.98 U325 < active 101.44/26.98 U326 < active 101.44/26.98 U327 < active 101.44/26.98 U34 < active 101.44/26.98 U332 < active 101.44/26.98 U333 < active 101.44/26.98 U334 < active 101.44/26.98 U342 < active 101.44/26.98 U343 < active 101.44/26.98 U344 < active 101.44/26.98 fst < active 101.44/26.98 U42 < active 101.44/26.98 U43 < active 101.44/26.98 U44 < active 101.44/26.98 U45 < active 101.44/26.98 U46 < active 101.44/26.98 U52 < active 101.44/26.98 U53 < active 101.44/26.98 U54 < active 101.44/26.98 U55 < active 101.44/26.98 U56 < active 101.44/26.98 U62 < active 101.44/26.98 isPLNatKind < active 101.44/26.98 U63 < active 101.44/26.98 isPLNat < active 101.44/26.98 U72 < active 101.44/26.98 U73 < active 101.44/26.98 U82 < active 101.44/26.98 U83 < active 101.44/26.98 U92 < active 101.44/26.98 U93 < active 101.44/26.98 U11 < active 101.44/26.98 U21 < active 101.44/26.98 U31 < active 101.44/26.98 U41 < active 101.44/26.98 U51 < active 101.44/26.98 U61 < active 101.44/26.98 U71 < active 101.44/26.98 U81 < active 101.44/26.98 U91 < active 101.44/26.98 U101 < active 101.44/26.98 U111 < active 101.44/26.98 U121 < active 101.44/26.98 U131 < active 101.44/26.98 U141 < active 101.44/26.98 U151 < active 101.44/26.98 U161 < active 101.44/26.98 U171 < active 101.44/26.98 U181 < active 101.44/26.98 U191 < active 101.44/26.98 U201 < active 101.44/26.98 U211 < active 101.44/26.98 U221 < active 101.44/26.98 U231 < active 101.44/26.98 U241 < active 101.44/26.98 U251 < active 101.44/26.98 U261 < active 101.44/26.98 U271 < active 101.44/26.98 U281 < active 101.44/26.98 U291 < active 101.44/26.98 U301 < active 101.44/26.98 U311 < active 101.44/26.98 U321 < active 101.44/26.98 U331 < active 101.44/26.98 U341 < active 101.44/26.98 tail < active 101.44/26.98 take < active 101.44/26.98 sel < active 101.44/26.98 active < top 101.44/26.98 isLNatKind < proper 101.44/26.98 U104 < proper 101.44/26.98 U105 < proper 101.44/26.98 isNatural < proper 101.44/26.98 U106 < proper 101.44/26.98 isLNat < proper 101.44/26.98 U12 < proper 101.44/26.98 U112 < proper 101.44/26.98 U13 < proper 101.44/26.98 U122 < proper 101.44/26.98 U14 < proper 101.44/26.98 snd < proper 101.44/26.98 splitAt < proper 101.44/26.98 U172 < proper 101.44/26.98 U182 < proper 101.44/26.98 U183 < proper 101.44/26.98 U192 < proper 101.44/26.98 U193 < proper 101.44/26.98 U202 < proper 101.44/26.98 U203 < proper 101.44/26.98 U204 < proper 101.44/26.98 U205 < proper 101.44/26.98 U206 < proper 101.44/26.98 U22 < proper 101.44/26.98 U23 < proper 101.44/26.98 U24 < proper 101.44/26.98 U232 < proper 101.44/26.98 U242 < proper 101.44/26.98 U243 < proper 101.44/26.98 U244 < proper 101.44/26.98 U245 < proper 101.44/26.98 U246 < proper 101.44/26.98 U252 < proper 101.44/26.98 U253 < proper 101.44/26.98 U254 < proper 101.44/26.98 U255 < proper 101.44/26.98 U256 < proper 101.44/26.98 U262 < proper 101.44/26.98 U272 < proper 101.44/26.98 U282 < proper 101.44/26.98 cons < proper 101.44/26.98 natsFrom < proper 101.44/26.98 s < proper 101.44/26.98 U292 < proper 101.44/26.98 U293 < proper 101.44/26.98 U294 < proper 101.44/26.98 head < proper 101.44/26.98 afterNth < proper 101.44/26.98 U302 < proper 101.44/26.98 U303 < proper 101.44/26.98 U304 < proper 101.44/26.98 U32 < proper 101.44/26.98 U312 < proper 101.44/26.98 pair < proper 101.44/26.98 U33 < proper 101.44/26.98 U322 < proper 101.44/26.98 U323 < proper 101.44/26.98 U324 < proper 101.44/26.98 U325 < proper 101.44/26.98 U326 < proper 101.44/26.98 U327 < proper 101.44/26.98 U34 < proper 101.44/26.98 U332 < proper 101.44/26.98 U333 < proper 101.44/26.98 U334 < proper 101.44/26.98 U342 < proper 101.44/26.98 U343 < proper 101.44/26.98 U344 < proper 101.44/26.98 fst < proper 101.44/26.98 U42 < proper 101.44/26.98 U43 < proper 101.44/26.98 U44 < proper 101.44/26.98 U45 < proper 101.44/26.98 U46 < proper 101.44/26.98 U52 < proper 101.44/26.98 U53 < proper 101.44/26.98 U54 < proper 101.44/26.98 U55 < proper 101.44/26.98 U56 < proper 101.44/26.98 U62 < proper 101.44/26.98 isPLNatKind < proper 101.44/26.98 U63 < proper 101.44/26.98 isPLNat < proper 101.44/26.98 U72 < proper 101.44/26.98 U73 < proper 101.44/26.98 U82 < proper 101.44/26.98 U83 < proper 101.44/26.98 U92 < proper 101.44/26.98 U93 < proper 101.44/26.98 U11 < proper 101.44/26.98 U21 < proper 101.44/26.98 U31 < proper 101.44/26.98 U41 < proper 101.44/26.98 U51 < proper 101.44/26.98 U61 < proper 101.44/26.98 U71 < proper 101.44/26.98 U81 < proper 101.44/26.98 U91 < proper 101.44/26.98 U101 < proper 101.44/26.98 U111 < proper 101.44/26.98 U121 < proper 101.44/26.98 U131 < proper 101.44/26.98 U141 < proper 101.44/26.98 U151 < proper 101.44/26.98 U161 < proper 101.44/26.98 U171 < proper 101.44/26.98 U181 < proper 101.44/26.98 U191 < proper 101.44/26.98 U201 < proper 101.44/26.98 U211 < proper 101.44/26.98 U221 < proper 101.44/26.98 U231 < proper 101.44/26.98 U241 < proper 101.44/26.98 U251 < proper 101.44/26.98 U261 < proper 101.44/26.98 U271 < proper 101.44/26.98 U281 < proper 101.44/26.98 U291 < proper 101.44/26.98 U301 < proper 101.44/26.98 U311 < proper 101.44/26.98 U321 < proper 101.44/26.98 U331 < proper 101.44/26.98 U341 < proper 101.44/26.98 tail < proper 101.44/26.98 take < proper 101.44/26.98 sel < proper 101.44/26.98 proper < top 101.44/26.98 101.44/26.98 ---------------------------------------- 101.44/26.98 101.44/26.98 (33) RewriteLemmaProof (LOWER BOUND(ID)) 101.44/26.98 Proved the following rewrite lemma: 101.44/26.98 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.44/26.98 101.44/26.98 Induction Base: 101.44/26.98 U104(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.44/26.98 101.44/26.98 Induction Step: 101.44/26.98 U104(gen_tt:mark:nil:0':ok3_0(+(1, +(n35249_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.44/26.98 mark(U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.44/26.98 mark(*4_0) 101.44/26.98 101.44/26.98 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.44/26.98 ---------------------------------------- 101.44/26.98 101.44/26.98 (34) 101.44/26.98 Obligation: 101.44/26.98 TRS: 101.44/26.98 Rules: 101.44/26.98 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.44/26.98 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.44/26.98 active(U106(tt)) -> mark(tt) 101.44/26.98 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.44/26.98 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.44/26.98 active(U112(tt)) -> mark(tt) 101.44/26.98 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.44/26.98 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.44/26.98 active(U122(tt)) -> mark(tt) 101.44/26.98 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.44/26.98 active(U131(tt)) -> mark(tt) 101.44/26.98 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.44/26.98 active(U141(tt)) -> mark(tt) 101.44/26.98 active(U151(tt)) -> mark(tt) 101.44/26.98 active(U161(tt)) -> mark(tt) 101.44/26.98 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.44/26.98 active(U172(tt)) -> mark(tt) 101.44/26.98 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.44/26.98 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.44/26.98 active(U183(tt)) -> mark(tt) 101.44/26.98 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.44/26.98 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.44/26.98 active(U193(tt)) -> mark(tt) 101.44/26.98 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.44/26.98 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.44/26.98 active(U206(tt)) -> mark(tt) 101.44/26.98 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.44/26.98 active(U211(tt)) -> mark(tt) 101.44/26.98 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.44/26.98 active(U221(tt)) -> mark(tt) 101.44/26.98 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.44/26.98 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.44/26.98 active(U232(tt)) -> mark(tt) 101.44/26.98 active(U24(tt, X)) -> mark(X) 101.44/26.98 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.44/26.98 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.44/26.98 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.44/26.98 active(U246(tt)) -> mark(tt) 101.44/26.98 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.44/26.98 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.44/26.98 active(U256(tt)) -> mark(tt) 101.44/26.98 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.44/26.98 active(U262(tt)) -> mark(tt) 101.44/26.98 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.44/26.98 active(U272(tt)) -> mark(tt) 101.44/26.98 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.44/26.98 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.44/26.98 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.44/26.98 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.44/26.98 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.44/26.98 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.44/26.98 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.44/26.98 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.44/26.98 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.44/26.98 active(U304(tt, Y)) -> mark(Y) 101.44/26.98 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.44/26.98 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.44/26.98 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.44/26.98 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.44/26.98 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.44/26.98 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.44/26.98 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.44/26.98 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.44/26.98 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.44/26.98 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.44/26.98 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.44/26.98 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.44/26.98 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.44/26.98 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.44/26.98 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.44/26.98 active(U334(tt, XS)) -> mark(XS) 101.44/26.98 active(U34(tt, N)) -> mark(N) 101.44/26.98 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.44/26.98 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.44/26.98 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.44/26.98 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.44/26.98 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.44/26.98 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.44/26.98 active(U46(tt)) -> mark(tt) 101.44/26.98 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.44/26.98 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.44/26.98 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.44/26.98 active(U56(tt)) -> mark(tt) 101.44/26.98 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.44/26.98 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.44/26.98 active(U63(tt)) -> mark(tt) 101.44/26.98 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.44/26.98 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.44/26.98 active(U73(tt)) -> mark(tt) 101.44/26.98 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.44/26.98 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.44/26.98 active(U83(tt)) -> mark(tt) 101.44/26.98 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.44/26.98 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.44/26.98 active(U93(tt)) -> mark(tt) 101.44/26.98 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.44/26.98 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.44/26.98 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.44/26.98 active(isLNat(nil)) -> mark(tt) 101.44/26.98 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.44/26.98 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.44/26.98 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.44/26.98 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.44/26.98 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(isLNatKind(nil)) -> mark(tt) 101.44/26.98 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.44/26.98 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.44/26.98 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.44/26.98 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.44/26.98 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.44/26.98 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.44/26.98 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.44/26.98 active(isNatural(0')) -> mark(tt) 101.44/26.98 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.44/26.98 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.44/26.98 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(isNaturalKind(0')) -> mark(tt) 101.44/26.98 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.44/26.98 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.44/26.98 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.44/26.98 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.44/26.98 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.44/26.98 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.44/26.99 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.44/26.99 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.44/26.99 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.44/26.99 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.44/26.99 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.44/26.99 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.44/26.99 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.44/26.99 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.44/26.99 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.44/26.99 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.44/26.99 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.44/26.99 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.44/26.99 active(U105(X1, X2)) -> U105(active(X1), X2) 101.44/26.99 active(U106(X)) -> U106(active(X)) 101.44/26.99 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.44/26.99 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.44/26.99 active(U111(X1, X2)) -> U111(active(X1), X2) 101.44/26.99 active(U112(X)) -> U112(active(X)) 101.44/26.99 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.44/26.99 active(U121(X1, X2)) -> U121(active(X1), X2) 101.44/26.99 active(U122(X)) -> U122(active(X)) 101.44/26.99 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.44/26.99 active(U131(X)) -> U131(active(X)) 101.44/26.99 active(snd(X)) -> snd(active(X)) 101.44/26.99 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.44/26.99 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.44/26.99 active(U141(X)) -> U141(active(X)) 101.44/26.99 active(U151(X)) -> U151(active(X)) 101.44/26.99 active(U161(X)) -> U161(active(X)) 101.44/26.99 active(U171(X1, X2)) -> U171(active(X1), X2) 101.44/26.99 active(U172(X)) -> U172(active(X)) 101.44/26.99 active(U181(X1, X2)) -> U181(active(X1), X2) 101.44/26.99 active(U182(X1, X2)) -> U182(active(X1), X2) 101.44/26.99 active(U183(X)) -> U183(active(X)) 101.44/26.99 active(U191(X1, X2)) -> U191(active(X1), X2) 101.44/26.99 active(U192(X1, X2)) -> U192(active(X1), X2) 101.44/26.99 active(U193(X)) -> U193(active(X)) 101.44/26.99 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.44/26.99 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.44/26.99 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.44/26.99 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.44/26.99 active(U205(X1, X2)) -> U205(active(X1), X2) 101.44/26.99 active(U206(X)) -> U206(active(X)) 101.44/26.99 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.44/26.99 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.44/26.99 active(U211(X)) -> U211(active(X)) 101.44/26.99 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.44/26.99 active(U221(X)) -> U221(active(X)) 101.44/26.99 active(U24(X1, X2)) -> U24(active(X1), X2) 101.44/26.99 active(U231(X1, X2)) -> U231(active(X1), X2) 101.44/26.99 active(U232(X)) -> U232(active(X)) 101.44/26.99 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.44/26.99 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.44/26.99 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.44/26.99 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.44/26.99 active(U245(X1, X2)) -> U245(active(X1), X2) 101.44/26.99 active(U246(X)) -> U246(active(X)) 101.44/26.99 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.44/26.99 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.44/26.99 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.44/26.99 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.44/26.99 active(U255(X1, X2)) -> U255(active(X1), X2) 101.44/26.99 active(U256(X)) -> U256(active(X)) 101.44/26.99 active(U261(X1, X2)) -> U261(active(X1), X2) 101.44/26.99 active(U262(X)) -> U262(active(X)) 101.44/26.99 active(U271(X1, X2)) -> U271(active(X1), X2) 101.44/26.99 active(U272(X)) -> U272(active(X)) 101.44/26.99 active(U281(X1, X2)) -> U281(active(X1), X2) 101.44/26.99 active(U282(X1, X2)) -> U282(active(X1), X2) 101.44/26.99 active(cons(X1, X2)) -> cons(active(X1), X2) 101.44/26.99 active(natsFrom(X)) -> natsFrom(active(X)) 101.44/26.99 active(s(X)) -> s(active(X)) 101.44/26.99 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.44/26.99 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.44/26.99 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.44/26.99 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.44/26.99 active(head(X)) -> head(active(X)) 101.44/26.99 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.44/26.99 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.44/26.99 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.44/26.99 active(U302(X1, X2)) -> U302(active(X1), X2) 101.44/26.99 active(U303(X1, X2)) -> U303(active(X1), X2) 101.44/26.99 active(U304(X1, X2)) -> U304(active(X1), X2) 101.44/26.99 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.44/26.99 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.44/26.99 active(U311(X1, X2)) -> U311(active(X1), X2) 101.44/26.99 active(U312(X1, X2)) -> U312(active(X1), X2) 101.44/26.99 active(pair(X1, X2)) -> pair(active(X1), X2) 101.44/26.99 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.44/26.99 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.44/26.99 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.44/26.99 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.44/26.99 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.44/26.99 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.44/26.99 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.44/26.99 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.44/26.99 active(U327(X1, X2)) -> U327(active(X1), X2) 101.44/26.99 active(U34(X1, X2)) -> U34(active(X1), X2) 101.44/26.99 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.44/26.99 active(U332(X1, X2)) -> U332(active(X1), X2) 101.44/26.99 active(U333(X1, X2)) -> U333(active(X1), X2) 101.44/26.99 active(U334(X1, X2)) -> U334(active(X1), X2) 101.44/26.99 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.44/26.99 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.44/26.99 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.44/26.99 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.44/26.99 active(fst(X)) -> fst(active(X)) 101.44/26.99 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.44/26.99 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.44/26.99 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.44/26.99 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.44/26.99 active(U45(X1, X2)) -> U45(active(X1), X2) 101.44/26.99 active(U46(X)) -> U46(active(X)) 101.44/26.99 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.44/26.99 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.44/26.99 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.44/26.99 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.44/26.99 active(U55(X1, X2)) -> U55(active(X1), X2) 101.44/26.99 active(U56(X)) -> U56(active(X)) 101.44/26.99 active(U61(X1, X2)) -> U61(active(X1), X2) 101.44/26.99 active(U62(X1, X2)) -> U62(active(X1), X2) 101.44/26.99 active(U63(X)) -> U63(active(X)) 101.44/26.99 active(U71(X1, X2)) -> U71(active(X1), X2) 101.44/26.99 active(U72(X1, X2)) -> U72(active(X1), X2) 101.44/26.99 active(U73(X)) -> U73(active(X)) 101.44/26.99 active(U81(X1, X2)) -> U81(active(X1), X2) 101.44/26.99 active(U82(X1, X2)) -> U82(active(X1), X2) 101.44/26.99 active(U83(X)) -> U83(active(X)) 101.44/26.99 active(U91(X1, X2)) -> U91(active(X1), X2) 101.44/26.99 active(U92(X1, X2)) -> U92(active(X1), X2) 101.44/26.99 active(U93(X)) -> U93(active(X)) 101.44/26.99 active(tail(X)) -> tail(active(X)) 101.44/26.99 active(take(X1, X2)) -> take(active(X1), X2) 101.44/26.99 active(take(X1, X2)) -> take(X1, active(X2)) 101.44/26.99 active(sel(X1, X2)) -> sel(active(X1), X2) 101.44/26.99 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.44/26.99 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.44/26.99 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.44/26.99 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.44/26.99 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.44/26.99 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.44/26.99 U106(mark(X)) -> mark(U106(X)) 101.44/26.99 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.44/26.99 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.44/26.99 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.44/26.99 U112(mark(X)) -> mark(U112(X)) 101.44/26.99 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.44/26.99 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.44/26.99 U122(mark(X)) -> mark(U122(X)) 101.44/26.99 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.44/26.99 U131(mark(X)) -> mark(U131(X)) 101.44/26.99 snd(mark(X)) -> mark(snd(X)) 101.44/26.99 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.44/26.99 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.44/26.99 U141(mark(X)) -> mark(U141(X)) 101.44/26.99 U151(mark(X)) -> mark(U151(X)) 101.44/26.99 U161(mark(X)) -> mark(U161(X)) 101.44/26.99 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.44/26.99 U172(mark(X)) -> mark(U172(X)) 101.44/26.99 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.44/26.99 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.44/26.99 U183(mark(X)) -> mark(U183(X)) 101.44/26.99 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.44/26.99 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.44/26.99 U193(mark(X)) -> mark(U193(X)) 101.44/26.99 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.44/26.99 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.44/26.99 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.44/26.99 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.44/26.99 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.44/26.99 U206(mark(X)) -> mark(U206(X)) 101.44/26.99 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.44/26.99 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.44/26.99 U211(mark(X)) -> mark(U211(X)) 101.44/26.99 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.44/26.99 U221(mark(X)) -> mark(U221(X)) 101.44/26.99 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.44/26.99 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.44/26.99 U232(mark(X)) -> mark(U232(X)) 101.44/26.99 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.44/26.99 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.44/26.99 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.44/26.99 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.44/26.99 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.44/26.99 U246(mark(X)) -> mark(U246(X)) 101.44/26.99 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.44/26.99 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.44/26.99 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.44/26.99 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.44/26.99 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.44/26.99 U256(mark(X)) -> mark(U256(X)) 101.44/26.99 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.44/26.99 U262(mark(X)) -> mark(U262(X)) 101.44/26.99 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.44/26.99 U272(mark(X)) -> mark(U272(X)) 101.44/26.99 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.44/26.99 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.44/26.99 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.44/26.99 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.44/26.99 s(mark(X)) -> mark(s(X)) 101.44/26.99 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.44/26.99 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.44/26.99 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.44/26.99 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.44/26.99 head(mark(X)) -> mark(head(X)) 101.44/26.99 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.44/26.99 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.44/26.99 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.44/26.99 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.44/26.99 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.44/26.99 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.44/26.99 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.44/26.99 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.44/26.99 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.44/26.99 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.44/26.99 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.44/26.99 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.44/26.99 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.44/26.99 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.44/26.99 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.44/26.99 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.44/26.99 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.44/26.99 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.44/26.99 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.44/26.99 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.44/26.99 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.44/26.99 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.44/26.99 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.44/26.99 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.44/26.99 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.44/26.99 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.44/26.99 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.44/26.99 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.44/26.99 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.44/26.99 fst(mark(X)) -> mark(fst(X)) 101.44/26.99 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.44/26.99 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.44/26.99 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.44/26.99 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.44/26.99 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.44/26.99 U46(mark(X)) -> mark(U46(X)) 101.44/26.99 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.44/26.99 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.44/26.99 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.44/26.99 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.44/26.99 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.44/26.99 U56(mark(X)) -> mark(U56(X)) 101.44/26.99 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.44/26.99 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.44/26.99 U63(mark(X)) -> mark(U63(X)) 101.44/26.99 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.44/26.99 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.44/26.99 U73(mark(X)) -> mark(U73(X)) 101.44/26.99 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.44/26.99 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.44/26.99 U83(mark(X)) -> mark(U83(X)) 101.44/26.99 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.44/26.99 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.44/26.99 U93(mark(X)) -> mark(U93(X)) 101.44/26.99 tail(mark(X)) -> mark(tail(X)) 101.44/26.99 take(mark(X1), X2) -> mark(take(X1, X2)) 101.44/26.99 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.44/26.99 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.44/26.99 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.44/26.99 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(tt) -> ok(tt) 101.44/26.99 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.44/26.99 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.44/26.99 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.44/26.99 proper(isNatural(X)) -> isNatural(proper(X)) 101.44/26.99 proper(U106(X)) -> U106(proper(X)) 101.44/26.99 proper(isLNat(X)) -> isLNat(proper(X)) 101.44/26.99 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.44/26.99 proper(U112(X)) -> U112(proper(X)) 101.44/26.99 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.44/26.99 proper(U122(X)) -> U122(proper(X)) 101.44/26.99 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U131(X)) -> U131(proper(X)) 101.44/26.99 proper(snd(X)) -> snd(proper(X)) 101.44/26.99 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.44/26.99 proper(U141(X)) -> U141(proper(X)) 101.44/26.99 proper(U151(X)) -> U151(proper(X)) 101.44/26.99 proper(U161(X)) -> U161(proper(X)) 101.44/26.99 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.44/26.99 proper(U172(X)) -> U172(proper(X)) 101.44/26.99 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.44/26.99 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.44/26.99 proper(U183(X)) -> U183(proper(X)) 101.44/26.99 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.44/26.99 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.44/26.99 proper(U193(X)) -> U193(proper(X)) 101.44/26.99 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.44/26.99 proper(U206(X)) -> U206(proper(X)) 101.44/26.99 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U211(X)) -> U211(proper(X)) 101.44/26.99 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U221(X)) -> U221(proper(X)) 101.44/26.99 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.44/26.99 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.44/26.99 proper(U232(X)) -> U232(proper(X)) 101.44/26.99 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.44/26.99 proper(U246(X)) -> U246(proper(X)) 101.44/26.99 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.44/26.99 proper(U256(X)) -> U256(proper(X)) 101.44/26.99 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.44/26.99 proper(U262(X)) -> U262(proper(X)) 101.44/26.99 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.44/26.99 proper(U272(X)) -> U272(proper(X)) 101.44/26.99 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.44/26.99 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.44/26.99 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.44/26.99 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.44/26.99 proper(s(X)) -> s(proper(X)) 101.44/26.99 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(head(X)) -> head(proper(X)) 101.44/26.99 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.44/26.99 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.44/26.99 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.44/26.99 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.44/26.99 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.44/26.99 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.44/26.99 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.44/26.99 proper(nil) -> ok(nil) 101.44/26.99 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.44/26.99 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.44/26.99 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.44/26.99 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.44/26.99 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.44/26.99 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.44/26.99 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(fst(X)) -> fst(proper(X)) 101.44/26.99 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.44/26.99 proper(U46(X)) -> U46(proper(X)) 101.44/26.99 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.44/26.99 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.44/26.99 proper(U56(X)) -> U56(proper(X)) 101.44/26.99 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.44/26.99 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.44/26.99 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.44/26.99 proper(U63(X)) -> U63(proper(X)) 101.44/26.99 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.44/26.99 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.44/26.99 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.44/26.99 proper(U73(X)) -> U73(proper(X)) 101.44/26.99 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.44/26.99 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.44/26.99 proper(U83(X)) -> U83(proper(X)) 101.44/26.99 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.44/26.99 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.44/26.99 proper(U93(X)) -> U93(proper(X)) 101.44/26.99 proper(tail(X)) -> tail(proper(X)) 101.44/26.99 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.44/26.99 proper(0') -> ok(0') 101.44/26.99 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.44/26.99 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.44/26.99 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.44/26.99 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.44/26.99 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.44/26.99 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.44/26.99 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.44/26.99 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.44/26.99 isNatural(ok(X)) -> ok(isNatural(X)) 101.44/26.99 U106(ok(X)) -> ok(U106(X)) 101.44/26.99 isLNat(ok(X)) -> ok(isLNat(X)) 101.44/26.99 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.44/26.99 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.44/26.99 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.44/26.99 U112(ok(X)) -> ok(U112(X)) 101.44/26.99 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.44/26.99 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.44/26.99 U122(ok(X)) -> ok(U122(X)) 101.44/26.99 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.44/26.99 U131(ok(X)) -> ok(U131(X)) 101.44/26.99 snd(ok(X)) -> ok(snd(X)) 101.44/26.99 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.44/26.99 U141(ok(X)) -> ok(U141(X)) 101.44/26.99 U151(ok(X)) -> ok(U151(X)) 101.44/26.99 U161(ok(X)) -> ok(U161(X)) 101.44/26.99 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.44/26.99 U172(ok(X)) -> ok(U172(X)) 101.44/26.99 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.44/26.99 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.44/26.99 U183(ok(X)) -> ok(U183(X)) 101.44/26.99 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.44/26.99 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.44/26.99 U193(ok(X)) -> ok(U193(X)) 101.44/26.99 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.44/26.99 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.44/26.99 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.44/26.99 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.44/26.99 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.44/26.99 U206(ok(X)) -> ok(U206(X)) 101.44/26.99 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.44/26.99 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.44/26.99 U211(ok(X)) -> ok(U211(X)) 101.44/26.99 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.44/26.99 U221(ok(X)) -> ok(U221(X)) 101.44/26.99 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.44/26.99 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.44/26.99 U232(ok(X)) -> ok(U232(X)) 101.44/26.99 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.44/26.99 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.44/26.99 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.44/26.99 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.44/26.99 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.44/26.99 U246(ok(X)) -> ok(U246(X)) 101.44/26.99 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.44/26.99 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.44/26.99 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.44/26.99 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.44/26.99 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.44/26.99 U256(ok(X)) -> ok(U256(X)) 101.44/26.99 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.44/26.99 U262(ok(X)) -> ok(U262(X)) 101.44/26.99 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.44/26.99 U272(ok(X)) -> ok(U272(X)) 101.44/26.99 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.44/26.99 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.44/26.99 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.44/26.99 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.44/26.99 s(ok(X)) -> ok(s(X)) 101.44/26.99 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.44/26.99 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.44/26.99 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.44/26.99 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.44/26.99 head(ok(X)) -> ok(head(X)) 101.44/26.99 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.44/26.99 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.44/26.99 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.44/26.99 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.44/26.99 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.44/26.99 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.44/26.99 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.44/26.99 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.44/26.99 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.44/26.99 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.44/26.99 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.44/26.99 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.44/26.99 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.44/26.99 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.44/26.99 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.44/26.99 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.44/26.99 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.44/26.99 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.44/26.99 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.44/26.99 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.44/26.99 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.44/26.99 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.44/26.99 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.44/26.99 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.44/26.99 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.44/26.99 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.44/26.99 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.44/26.99 fst(ok(X)) -> ok(fst(X)) 101.44/26.99 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.44/26.99 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.44/26.99 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.44/26.99 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.44/26.99 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.44/26.99 U46(ok(X)) -> ok(U46(X)) 101.44/26.99 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.44/26.99 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.44/26.99 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.44/26.99 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.44/26.99 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.44/26.99 U56(ok(X)) -> ok(U56(X)) 101.44/26.99 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.44/26.99 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.44/26.99 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.44/26.99 U63(ok(X)) -> ok(U63(X)) 101.44/26.99 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.44/26.99 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.44/26.99 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.44/26.99 U73(ok(X)) -> ok(U73(X)) 101.44/26.99 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.44/26.99 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.44/26.99 U83(ok(X)) -> ok(U83(X)) 101.44/26.99 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.44/26.99 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.44/26.99 U93(ok(X)) -> ok(U93(X)) 101.44/26.99 tail(ok(X)) -> ok(tail(X)) 101.44/26.99 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.44/26.99 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.44/26.99 top(mark(X)) -> top(proper(X)) 101.44/26.99 top(ok(X)) -> top(active(X)) 101.44/26.99 101.44/26.99 Types: 101.44/26.99 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 tt :: tt:mark:nil:0':ok 101.44/26.99 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 nil :: tt:mark:nil:0':ok 101.44/26.99 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 0' :: tt:mark:nil:0':ok 101.44/26.99 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.44/26.99 top :: tt:mark:nil:0':ok -> top 101.44/26.99 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.44/26.99 hole_top2_0 :: top 101.44/26.99 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.44/26.99 101.44/26.99 101.44/26.99 Lemmas: 101.44/26.99 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.44/26.99 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.44/26.99 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.44/26.99 101.44/26.99 101.44/26.99 Generator Equations: 101.44/26.99 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.44/26.99 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.44/26.99 101.44/26.99 101.44/26.99 The following defined symbols remain to be analysed: 101.44/26.99 U105, active, isNatural, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.44/26.99 101.44/26.99 They will be analysed ascendingly in the following order: 101.44/26.99 U105 < active 101.44/26.99 isNatural < active 101.44/26.99 U106 < active 101.44/26.99 isLNat < active 101.44/26.99 U12 < active 101.44/26.99 U112 < active 101.44/26.99 U13 < active 101.44/26.99 U122 < active 101.44/26.99 U14 < active 101.44/26.99 snd < active 101.44/26.99 splitAt < active 101.44/26.99 U172 < active 101.44/26.99 U182 < active 101.44/26.99 U183 < active 101.44/26.99 U192 < active 101.44/26.99 U193 < active 101.44/26.99 U202 < active 101.44/26.99 U203 < active 101.44/26.99 U204 < active 101.44/26.99 U205 < active 101.44/26.99 U206 < active 101.44/26.99 U22 < active 101.44/26.99 U23 < active 101.44/26.99 U24 < active 101.44/26.99 U232 < active 101.44/26.99 U242 < active 101.44/26.99 U243 < active 101.44/26.99 U244 < active 101.44/26.99 U245 < active 101.44/26.99 U246 < active 101.44/26.99 U252 < active 101.44/26.99 U253 < active 101.44/26.99 U254 < active 101.44/26.99 U255 < active 101.44/26.99 U256 < active 101.44/26.99 U262 < active 101.44/26.99 U272 < active 101.44/26.99 U282 < active 101.44/26.99 cons < active 101.44/26.99 natsFrom < active 101.44/26.99 s < active 101.44/26.99 U292 < active 101.44/26.99 U293 < active 101.44/26.99 U294 < active 101.44/26.99 head < active 101.44/26.99 afterNth < active 101.44/26.99 U302 < active 101.44/26.99 U303 < active 101.44/26.99 U304 < active 101.44/26.99 U32 < active 101.44/26.99 U312 < active 101.44/26.99 pair < active 101.44/26.99 U33 < active 101.44/26.99 U322 < active 101.44/26.99 U323 < active 101.44/26.99 U324 < active 101.44/26.99 U325 < active 101.44/26.99 U326 < active 101.44/26.99 U327 < active 101.44/26.99 U34 < active 101.44/26.99 U332 < active 101.44/26.99 U333 < active 101.44/26.99 U334 < active 101.44/26.99 U342 < active 101.44/26.99 U343 < active 101.44/26.99 U344 < active 101.44/26.99 fst < active 101.44/26.99 U42 < active 101.44/26.99 U43 < active 101.44/26.99 U44 < active 101.44/26.99 U45 < active 101.44/26.99 U46 < active 101.44/26.99 U52 < active 101.44/26.99 U53 < active 101.44/26.99 U54 < active 101.44/26.99 U55 < active 101.44/26.99 U56 < active 101.44/26.99 U62 < active 101.44/26.99 isPLNatKind < active 101.44/26.99 U63 < active 101.44/26.99 isPLNat < active 101.44/26.99 U72 < active 101.44/26.99 U73 < active 101.44/26.99 U82 < active 101.44/26.99 U83 < active 101.44/26.99 U92 < active 101.44/26.99 U93 < active 101.44/26.99 U11 < active 101.44/26.99 U21 < active 101.44/26.99 U31 < active 101.44/26.99 U41 < active 101.44/26.99 U51 < active 101.44/26.99 U61 < active 101.44/26.99 U71 < active 101.44/26.99 U81 < active 101.44/26.99 U91 < active 101.44/26.99 U101 < active 101.44/26.99 U111 < active 101.44/26.99 U121 < active 101.44/26.99 U131 < active 101.44/26.99 U141 < active 101.44/26.99 U151 < active 101.44/26.99 U161 < active 101.44/26.99 U171 < active 101.44/26.99 U181 < active 101.44/26.99 U191 < active 101.44/26.99 U201 < active 101.44/26.99 U211 < active 101.44/26.99 U221 < active 101.44/26.99 U231 < active 101.44/26.99 U241 < active 101.44/26.99 U251 < active 101.44/26.99 U261 < active 101.44/26.99 U271 < active 101.44/26.99 U281 < active 101.44/26.99 U291 < active 101.44/26.99 U301 < active 101.44/26.99 U311 < active 101.44/26.99 U321 < active 101.44/26.99 U331 < active 101.44/26.99 U341 < active 101.44/26.99 tail < active 101.44/26.99 take < active 101.44/26.99 sel < active 101.44/26.99 active < top 101.44/26.99 U105 < proper 101.44/26.99 isNatural < proper 101.44/26.99 U106 < proper 101.44/26.99 isLNat < proper 101.44/26.99 U12 < proper 101.44/26.99 U112 < proper 101.44/26.99 U13 < proper 101.44/26.99 U122 < proper 101.44/26.99 U14 < proper 101.44/26.99 snd < proper 101.44/26.99 splitAt < proper 101.44/26.99 U172 < proper 101.44/26.99 U182 < proper 101.44/26.99 U183 < proper 101.44/26.99 U192 < proper 101.44/26.99 U193 < proper 101.44/26.99 U202 < proper 101.44/26.99 U203 < proper 101.44/26.99 U204 < proper 101.44/26.99 U205 < proper 101.44/26.99 U206 < proper 101.44/26.99 U22 < proper 101.44/26.99 U23 < proper 101.44/26.99 U24 < proper 101.44/26.99 U232 < proper 101.44/26.99 U242 < proper 101.44/26.99 U243 < proper 101.44/26.99 U244 < proper 101.44/26.99 U245 < proper 101.44/26.99 U246 < proper 101.44/26.99 U252 < proper 101.44/26.99 U253 < proper 101.44/26.99 U254 < proper 101.44/26.99 U255 < proper 101.44/26.99 U256 < proper 101.44/26.99 U262 < proper 101.44/26.99 U272 < proper 101.44/26.99 U282 < proper 101.44/26.99 cons < proper 101.44/26.99 natsFrom < proper 101.44/26.99 s < proper 101.44/26.99 U292 < proper 101.44/26.99 U293 < proper 101.44/26.99 U294 < proper 101.44/26.99 head < proper 101.44/26.99 afterNth < proper 101.44/26.99 U302 < proper 101.44/26.99 U303 < proper 101.44/26.99 U304 < proper 101.44/26.99 U32 < proper 101.44/26.99 U312 < proper 101.44/26.99 pair < proper 101.44/26.99 U33 < proper 101.44/26.99 U322 < proper 101.44/26.99 U323 < proper 101.44/26.99 U324 < proper 101.44/26.99 U325 < proper 101.44/26.99 U326 < proper 101.44/26.99 U327 < proper 101.44/26.99 U34 < proper 101.44/26.99 U332 < proper 101.44/26.99 U333 < proper 101.44/26.99 U334 < proper 101.44/26.99 U342 < proper 101.44/26.99 U343 < proper 101.44/26.99 U344 < proper 101.44/26.99 fst < proper 101.44/26.99 U42 < proper 101.44/26.99 U43 < proper 101.44/26.99 U44 < proper 101.44/26.99 U45 < proper 101.44/26.99 U46 < proper 101.44/26.99 U52 < proper 101.44/26.99 U53 < proper 101.44/26.99 U54 < proper 101.44/26.99 U55 < proper 101.44/26.99 U56 < proper 101.44/26.99 U62 < proper 101.44/26.99 isPLNatKind < proper 101.44/26.99 U63 < proper 101.44/26.99 isPLNat < proper 101.44/26.99 U72 < proper 101.44/26.99 U73 < proper 101.44/26.99 U82 < proper 101.44/26.99 U83 < proper 101.44/26.99 U92 < proper 101.44/26.99 U93 < proper 101.44/26.99 U11 < proper 101.44/26.99 U21 < proper 101.44/26.99 U31 < proper 101.44/26.99 U41 < proper 101.44/26.99 U51 < proper 101.44/26.99 U61 < proper 101.44/26.99 U71 < proper 101.44/26.99 U81 < proper 101.44/26.99 U91 < proper 101.44/26.99 U101 < proper 101.44/26.99 U111 < proper 101.44/26.99 U121 < proper 101.44/26.99 U131 < proper 101.44/26.99 U141 < proper 101.44/26.99 U151 < proper 101.44/26.99 U161 < proper 101.44/26.99 U171 < proper 101.44/26.99 U181 < proper 101.44/26.99 U191 < proper 101.44/26.99 U201 < proper 101.44/26.99 U211 < proper 101.44/26.99 U221 < proper 101.44/26.99 U231 < proper 101.44/26.99 U241 < proper 101.44/26.99 U251 < proper 101.44/26.99 U261 < proper 101.44/26.99 U271 < proper 101.44/26.99 U281 < proper 101.44/26.99 U291 < proper 101.44/26.99 U301 < proper 101.44/26.99 U311 < proper 101.44/26.99 U321 < proper 101.44/26.99 U331 < proper 101.44/26.99 U341 < proper 101.44/26.99 tail < proper 101.44/26.99 take < proper 101.44/26.99 sel < proper 101.44/26.99 proper < top 101.44/26.99 101.44/26.99 ---------------------------------------- 101.51/27.00 101.51/27.00 (35) RewriteLemmaProof (LOWER BOUND(ID)) 101.51/27.00 Proved the following rewrite lemma: 101.51/27.00 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.51/27.00 101.51/27.00 Induction Base: 101.51/27.00 U105(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.51/27.00 101.51/27.00 Induction Step: 101.51/27.00 U105(gen_tt:mark:nil:0':ok3_0(+(1, +(n53770_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.51/27.00 mark(U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.51/27.00 mark(*4_0) 101.51/27.00 101.51/27.00 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.51/27.00 ---------------------------------------- 101.51/27.00 101.51/27.00 (36) 101.51/27.00 Obligation: 101.51/27.00 TRS: 101.51/27.00 Rules: 101.51/27.00 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.51/27.00 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.51/27.00 active(U106(tt)) -> mark(tt) 101.51/27.00 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.51/27.00 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.51/27.00 active(U112(tt)) -> mark(tt) 101.51/27.00 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.51/27.00 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.51/27.00 active(U122(tt)) -> mark(tt) 101.51/27.00 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.51/27.00 active(U131(tt)) -> mark(tt) 101.51/27.00 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.51/27.00 active(U141(tt)) -> mark(tt) 101.51/27.00 active(U151(tt)) -> mark(tt) 101.51/27.00 active(U161(tt)) -> mark(tt) 101.51/27.00 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.51/27.00 active(U172(tt)) -> mark(tt) 101.51/27.00 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.51/27.00 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.51/27.00 active(U183(tt)) -> mark(tt) 101.51/27.00 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.51/27.00 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.51/27.00 active(U193(tt)) -> mark(tt) 101.51/27.00 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.51/27.00 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.51/27.00 active(U206(tt)) -> mark(tt) 101.51/27.00 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.51/27.00 active(U211(tt)) -> mark(tt) 101.51/27.00 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.51/27.00 active(U221(tt)) -> mark(tt) 101.51/27.00 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.51/27.00 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.51/27.00 active(U232(tt)) -> mark(tt) 101.51/27.00 active(U24(tt, X)) -> mark(X) 101.51/27.00 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.51/27.00 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.51/27.00 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.51/27.00 active(U246(tt)) -> mark(tt) 101.51/27.00 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.51/27.00 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.51/27.00 active(U256(tt)) -> mark(tt) 101.51/27.00 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.51/27.00 active(U262(tt)) -> mark(tt) 101.51/27.00 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.51/27.00 active(U272(tt)) -> mark(tt) 101.51/27.00 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.51/27.00 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.51/27.00 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.51/27.00 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.51/27.00 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.51/27.00 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.51/27.00 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.51/27.00 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.51/27.00 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.51/27.00 active(U304(tt, Y)) -> mark(Y) 101.51/27.00 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.51/27.00 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.51/27.00 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.51/27.00 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.51/27.00 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.51/27.00 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.51/27.00 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.51/27.00 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.51/27.00 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.51/27.00 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.51/27.00 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.51/27.00 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.51/27.00 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.51/27.00 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.51/27.00 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.51/27.00 active(U334(tt, XS)) -> mark(XS) 101.51/27.00 active(U34(tt, N)) -> mark(N) 101.51/27.00 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.51/27.00 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.51/27.00 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.51/27.00 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.51/27.00 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.51/27.00 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.51/27.00 active(U46(tt)) -> mark(tt) 101.51/27.00 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.51/27.00 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.51/27.00 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.51/27.00 active(U56(tt)) -> mark(tt) 101.51/27.00 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.51/27.00 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.51/27.00 active(U63(tt)) -> mark(tt) 101.51/27.00 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.51/27.00 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.51/27.00 active(U73(tt)) -> mark(tt) 101.51/27.00 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.51/27.00 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.51/27.00 active(U83(tt)) -> mark(tt) 101.51/27.00 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.51/27.00 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.51/27.00 active(U93(tt)) -> mark(tt) 101.51/27.00 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.51/27.00 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.51/27.00 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.51/27.00 active(isLNat(nil)) -> mark(tt) 101.51/27.00 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.51/27.00 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.51/27.00 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.51/27.00 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.51/27.00 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(isLNatKind(nil)) -> mark(tt) 101.51/27.00 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.51/27.00 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.51/27.00 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.51/27.00 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.51/27.00 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.51/27.00 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.51/27.00 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.51/27.00 active(isNatural(0')) -> mark(tt) 101.51/27.00 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.51/27.00 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.51/27.00 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(isNaturalKind(0')) -> mark(tt) 101.51/27.00 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.51/27.00 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.51/27.00 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.51/27.00 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.51/27.00 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.51/27.00 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.51/27.00 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.51/27.00 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.51/27.00 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.51/27.00 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.51/27.00 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.51/27.00 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.51/27.00 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.51/27.00 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.51/27.00 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.51/27.00 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.51/27.00 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.51/27.00 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.51/27.00 active(U105(X1, X2)) -> U105(active(X1), X2) 101.51/27.00 active(U106(X)) -> U106(active(X)) 101.51/27.00 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.51/27.00 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.51/27.00 active(U111(X1, X2)) -> U111(active(X1), X2) 101.51/27.00 active(U112(X)) -> U112(active(X)) 101.51/27.00 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.51/27.00 active(U121(X1, X2)) -> U121(active(X1), X2) 101.51/27.00 active(U122(X)) -> U122(active(X)) 101.51/27.00 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.51/27.00 active(U131(X)) -> U131(active(X)) 101.51/27.00 active(snd(X)) -> snd(active(X)) 101.51/27.00 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.51/27.00 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.51/27.00 active(U141(X)) -> U141(active(X)) 101.51/27.00 active(U151(X)) -> U151(active(X)) 101.51/27.00 active(U161(X)) -> U161(active(X)) 101.51/27.00 active(U171(X1, X2)) -> U171(active(X1), X2) 101.51/27.00 active(U172(X)) -> U172(active(X)) 101.51/27.00 active(U181(X1, X2)) -> U181(active(X1), X2) 101.51/27.00 active(U182(X1, X2)) -> U182(active(X1), X2) 101.51/27.00 active(U183(X)) -> U183(active(X)) 101.51/27.00 active(U191(X1, X2)) -> U191(active(X1), X2) 101.51/27.00 active(U192(X1, X2)) -> U192(active(X1), X2) 101.51/27.00 active(U193(X)) -> U193(active(X)) 101.51/27.00 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.51/27.00 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.51/27.00 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.51/27.00 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.51/27.00 active(U205(X1, X2)) -> U205(active(X1), X2) 101.51/27.00 active(U206(X)) -> U206(active(X)) 101.51/27.00 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.51/27.00 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.51/27.00 active(U211(X)) -> U211(active(X)) 101.51/27.00 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.51/27.00 active(U221(X)) -> U221(active(X)) 101.51/27.00 active(U24(X1, X2)) -> U24(active(X1), X2) 101.51/27.00 active(U231(X1, X2)) -> U231(active(X1), X2) 101.51/27.00 active(U232(X)) -> U232(active(X)) 101.51/27.00 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.51/27.00 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.51/27.00 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.51/27.00 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.51/27.00 active(U245(X1, X2)) -> U245(active(X1), X2) 101.51/27.00 active(U246(X)) -> U246(active(X)) 101.51/27.00 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.51/27.00 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.51/27.00 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.51/27.00 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.51/27.00 active(U255(X1, X2)) -> U255(active(X1), X2) 101.51/27.00 active(U256(X)) -> U256(active(X)) 101.51/27.00 active(U261(X1, X2)) -> U261(active(X1), X2) 101.51/27.00 active(U262(X)) -> U262(active(X)) 101.51/27.00 active(U271(X1, X2)) -> U271(active(X1), X2) 101.51/27.00 active(U272(X)) -> U272(active(X)) 101.51/27.00 active(U281(X1, X2)) -> U281(active(X1), X2) 101.51/27.00 active(U282(X1, X2)) -> U282(active(X1), X2) 101.51/27.00 active(cons(X1, X2)) -> cons(active(X1), X2) 101.51/27.00 active(natsFrom(X)) -> natsFrom(active(X)) 101.51/27.00 active(s(X)) -> s(active(X)) 101.51/27.00 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.51/27.00 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.51/27.00 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.51/27.00 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.51/27.00 active(head(X)) -> head(active(X)) 101.51/27.00 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.51/27.00 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.51/27.00 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.51/27.00 active(U302(X1, X2)) -> U302(active(X1), X2) 101.51/27.00 active(U303(X1, X2)) -> U303(active(X1), X2) 101.51/27.00 active(U304(X1, X2)) -> U304(active(X1), X2) 101.51/27.00 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.51/27.00 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.51/27.00 active(U311(X1, X2)) -> U311(active(X1), X2) 101.51/27.00 active(U312(X1, X2)) -> U312(active(X1), X2) 101.51/27.00 active(pair(X1, X2)) -> pair(active(X1), X2) 101.51/27.00 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.51/27.00 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.51/27.00 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.51/27.00 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.51/27.00 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.51/27.00 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.51/27.00 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.51/27.00 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.51/27.00 active(U327(X1, X2)) -> U327(active(X1), X2) 101.51/27.00 active(U34(X1, X2)) -> U34(active(X1), X2) 101.51/27.00 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.51/27.00 active(U332(X1, X2)) -> U332(active(X1), X2) 101.51/27.00 active(U333(X1, X2)) -> U333(active(X1), X2) 101.51/27.00 active(U334(X1, X2)) -> U334(active(X1), X2) 101.51/27.00 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.51/27.00 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.51/27.00 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.51/27.00 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.51/27.00 active(fst(X)) -> fst(active(X)) 101.51/27.00 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.51/27.00 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.51/27.00 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.51/27.00 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.51/27.00 active(U45(X1, X2)) -> U45(active(X1), X2) 101.51/27.00 active(U46(X)) -> U46(active(X)) 101.51/27.00 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.51/27.00 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.51/27.00 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.51/27.00 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.51/27.00 active(U55(X1, X2)) -> U55(active(X1), X2) 101.51/27.00 active(U56(X)) -> U56(active(X)) 101.51/27.00 active(U61(X1, X2)) -> U61(active(X1), X2) 101.51/27.00 active(U62(X1, X2)) -> U62(active(X1), X2) 101.51/27.00 active(U63(X)) -> U63(active(X)) 101.51/27.00 active(U71(X1, X2)) -> U71(active(X1), X2) 101.51/27.00 active(U72(X1, X2)) -> U72(active(X1), X2) 101.51/27.00 active(U73(X)) -> U73(active(X)) 101.51/27.00 active(U81(X1, X2)) -> U81(active(X1), X2) 101.51/27.00 active(U82(X1, X2)) -> U82(active(X1), X2) 101.51/27.00 active(U83(X)) -> U83(active(X)) 101.51/27.00 active(U91(X1, X2)) -> U91(active(X1), X2) 101.51/27.00 active(U92(X1, X2)) -> U92(active(X1), X2) 101.51/27.00 active(U93(X)) -> U93(active(X)) 101.51/27.00 active(tail(X)) -> tail(active(X)) 101.51/27.00 active(take(X1, X2)) -> take(active(X1), X2) 101.51/27.00 active(take(X1, X2)) -> take(X1, active(X2)) 101.51/27.00 active(sel(X1, X2)) -> sel(active(X1), X2) 101.51/27.00 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.51/27.00 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.51/27.00 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.51/27.00 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.51/27.00 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.51/27.00 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.51/27.00 U106(mark(X)) -> mark(U106(X)) 101.51/27.00 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.51/27.00 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.51/27.00 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.51/27.00 U112(mark(X)) -> mark(U112(X)) 101.51/27.00 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.51/27.00 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.51/27.00 U122(mark(X)) -> mark(U122(X)) 101.51/27.00 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.51/27.00 U131(mark(X)) -> mark(U131(X)) 101.51/27.00 snd(mark(X)) -> mark(snd(X)) 101.51/27.00 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.51/27.00 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.51/27.00 U141(mark(X)) -> mark(U141(X)) 101.51/27.00 U151(mark(X)) -> mark(U151(X)) 101.51/27.00 U161(mark(X)) -> mark(U161(X)) 101.51/27.00 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.51/27.00 U172(mark(X)) -> mark(U172(X)) 101.51/27.00 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.51/27.00 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.51/27.00 U183(mark(X)) -> mark(U183(X)) 101.51/27.00 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.51/27.00 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.51/27.00 U193(mark(X)) -> mark(U193(X)) 101.51/27.00 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.51/27.00 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.51/27.00 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.51/27.00 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.51/27.00 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.51/27.00 U206(mark(X)) -> mark(U206(X)) 101.51/27.00 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.51/27.00 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.51/27.00 U211(mark(X)) -> mark(U211(X)) 101.51/27.00 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.51/27.00 U221(mark(X)) -> mark(U221(X)) 101.51/27.00 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.51/27.00 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.51/27.00 U232(mark(X)) -> mark(U232(X)) 101.51/27.00 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.51/27.00 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.51/27.00 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.51/27.00 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.51/27.00 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.51/27.00 U246(mark(X)) -> mark(U246(X)) 101.51/27.00 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.51/27.00 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.51/27.00 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.51/27.00 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.51/27.00 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.51/27.00 U256(mark(X)) -> mark(U256(X)) 101.51/27.00 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.51/27.00 U262(mark(X)) -> mark(U262(X)) 101.51/27.00 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.51/27.00 U272(mark(X)) -> mark(U272(X)) 101.51/27.00 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.51/27.00 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.51/27.00 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.51/27.00 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.51/27.00 s(mark(X)) -> mark(s(X)) 101.51/27.00 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.51/27.00 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.51/27.00 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.51/27.00 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.51/27.00 head(mark(X)) -> mark(head(X)) 101.51/27.00 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.51/27.00 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.51/27.00 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.51/27.00 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.51/27.00 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.51/27.00 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.51/27.00 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.51/27.00 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.51/27.00 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.51/27.00 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.51/27.00 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.51/27.00 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.51/27.00 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.51/27.00 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.51/27.00 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.51/27.00 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.51/27.00 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.51/27.00 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.51/27.00 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.51/27.00 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.51/27.00 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.51/27.00 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.51/27.00 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.51/27.00 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.51/27.00 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.51/27.00 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.51/27.00 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.51/27.00 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.51/27.00 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.51/27.00 fst(mark(X)) -> mark(fst(X)) 101.51/27.00 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.51/27.00 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.51/27.00 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.51/27.00 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.51/27.00 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.51/27.00 U46(mark(X)) -> mark(U46(X)) 101.51/27.00 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.51/27.00 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.51/27.00 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.51/27.00 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.51/27.00 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.51/27.00 U56(mark(X)) -> mark(U56(X)) 101.51/27.00 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.51/27.00 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.51/27.00 U63(mark(X)) -> mark(U63(X)) 101.51/27.00 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.51/27.00 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.51/27.00 U73(mark(X)) -> mark(U73(X)) 101.51/27.00 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.51/27.00 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.51/27.00 U83(mark(X)) -> mark(U83(X)) 101.51/27.00 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.51/27.00 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.51/27.00 U93(mark(X)) -> mark(U93(X)) 101.51/27.00 tail(mark(X)) -> mark(tail(X)) 101.51/27.00 take(mark(X1), X2) -> mark(take(X1, X2)) 101.51/27.00 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.51/27.00 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.51/27.00 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.51/27.00 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(tt) -> ok(tt) 101.51/27.00 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.51/27.00 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.51/27.00 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.51/27.00 proper(isNatural(X)) -> isNatural(proper(X)) 101.51/27.00 proper(U106(X)) -> U106(proper(X)) 101.51/27.00 proper(isLNat(X)) -> isLNat(proper(X)) 101.51/27.00 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.51/27.00 proper(U112(X)) -> U112(proper(X)) 101.51/27.00 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.51/27.00 proper(U122(X)) -> U122(proper(X)) 101.51/27.00 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U131(X)) -> U131(proper(X)) 101.51/27.00 proper(snd(X)) -> snd(proper(X)) 101.51/27.00 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.51/27.00 proper(U141(X)) -> U141(proper(X)) 101.51/27.00 proper(U151(X)) -> U151(proper(X)) 101.51/27.00 proper(U161(X)) -> U161(proper(X)) 101.51/27.00 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.51/27.00 proper(U172(X)) -> U172(proper(X)) 101.51/27.00 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.51/27.00 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.51/27.00 proper(U183(X)) -> U183(proper(X)) 101.51/27.00 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.51/27.00 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.51/27.00 proper(U193(X)) -> U193(proper(X)) 101.51/27.00 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.51/27.00 proper(U206(X)) -> U206(proper(X)) 101.51/27.00 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U211(X)) -> U211(proper(X)) 101.51/27.00 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U221(X)) -> U221(proper(X)) 101.51/27.00 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.51/27.00 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.51/27.00 proper(U232(X)) -> U232(proper(X)) 101.51/27.00 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.51/27.00 proper(U246(X)) -> U246(proper(X)) 101.51/27.00 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.51/27.00 proper(U256(X)) -> U256(proper(X)) 101.51/27.00 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.51/27.00 proper(U262(X)) -> U262(proper(X)) 101.51/27.00 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.51/27.00 proper(U272(X)) -> U272(proper(X)) 101.51/27.00 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.51/27.00 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.51/27.00 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.51/27.00 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.51/27.00 proper(s(X)) -> s(proper(X)) 101.51/27.00 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(head(X)) -> head(proper(X)) 101.51/27.00 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.51/27.00 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.51/27.00 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.51/27.00 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.51/27.00 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.51/27.00 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.51/27.00 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.51/27.00 proper(nil) -> ok(nil) 101.51/27.00 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.51/27.00 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.51/27.00 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.51/27.00 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.51/27.00 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.51/27.00 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.51/27.00 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(fst(X)) -> fst(proper(X)) 101.51/27.00 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.51/27.00 proper(U46(X)) -> U46(proper(X)) 101.51/27.00 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.51/27.00 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.51/27.00 proper(U56(X)) -> U56(proper(X)) 101.51/27.00 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.51/27.00 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.51/27.00 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.51/27.00 proper(U63(X)) -> U63(proper(X)) 101.51/27.00 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.51/27.00 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.51/27.00 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.51/27.00 proper(U73(X)) -> U73(proper(X)) 101.51/27.00 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.51/27.00 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.51/27.00 proper(U83(X)) -> U83(proper(X)) 101.51/27.00 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.51/27.00 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.51/27.00 proper(U93(X)) -> U93(proper(X)) 101.51/27.00 proper(tail(X)) -> tail(proper(X)) 101.51/27.00 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.51/27.00 proper(0') -> ok(0') 101.51/27.00 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.51/27.00 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.51/27.00 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.51/27.00 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.51/27.00 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.51/27.00 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.51/27.00 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.51/27.00 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.51/27.00 isNatural(ok(X)) -> ok(isNatural(X)) 101.51/27.00 U106(ok(X)) -> ok(U106(X)) 101.51/27.00 isLNat(ok(X)) -> ok(isLNat(X)) 101.51/27.00 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.51/27.00 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.51/27.00 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.51/27.00 U112(ok(X)) -> ok(U112(X)) 101.51/27.00 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.51/27.00 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.51/27.00 U122(ok(X)) -> ok(U122(X)) 101.51/27.00 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.51/27.00 U131(ok(X)) -> ok(U131(X)) 101.51/27.00 snd(ok(X)) -> ok(snd(X)) 101.51/27.00 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.51/27.00 U141(ok(X)) -> ok(U141(X)) 101.51/27.00 U151(ok(X)) -> ok(U151(X)) 101.51/27.00 U161(ok(X)) -> ok(U161(X)) 101.51/27.00 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.51/27.00 U172(ok(X)) -> ok(U172(X)) 101.51/27.00 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.51/27.00 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.51/27.00 U183(ok(X)) -> ok(U183(X)) 101.51/27.00 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.51/27.00 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.51/27.00 U193(ok(X)) -> ok(U193(X)) 101.51/27.00 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.51/27.00 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.51/27.00 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.51/27.00 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.51/27.00 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.51/27.00 U206(ok(X)) -> ok(U206(X)) 101.51/27.00 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.51/27.00 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.51/27.00 U211(ok(X)) -> ok(U211(X)) 101.51/27.00 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.51/27.00 U221(ok(X)) -> ok(U221(X)) 101.51/27.00 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.51/27.00 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.51/27.00 U232(ok(X)) -> ok(U232(X)) 101.51/27.00 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.51/27.00 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.51/27.00 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.51/27.00 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.51/27.00 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.51/27.00 U246(ok(X)) -> ok(U246(X)) 101.51/27.00 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.51/27.00 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.51/27.00 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.51/27.00 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.51/27.00 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.51/27.00 U256(ok(X)) -> ok(U256(X)) 101.51/27.00 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.51/27.00 U262(ok(X)) -> ok(U262(X)) 101.51/27.00 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.51/27.00 U272(ok(X)) -> ok(U272(X)) 101.51/27.00 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.51/27.00 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.51/27.00 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.51/27.00 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.51/27.00 s(ok(X)) -> ok(s(X)) 101.51/27.00 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.51/27.00 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.51/27.00 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.51/27.00 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.51/27.00 head(ok(X)) -> ok(head(X)) 101.51/27.00 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.51/27.00 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.51/27.00 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.51/27.00 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.51/27.00 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.51/27.00 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.51/27.00 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.51/27.00 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.51/27.00 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.51/27.00 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.51/27.00 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.51/27.00 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.51/27.00 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.51/27.00 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.51/27.00 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.51/27.00 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.51/27.00 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.51/27.00 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.51/27.00 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.51/27.00 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.51/27.01 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.51/27.01 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.51/27.01 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.51/27.01 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.51/27.01 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.51/27.01 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.51/27.01 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.51/27.01 fst(ok(X)) -> ok(fst(X)) 101.51/27.01 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.51/27.01 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.51/27.01 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.51/27.01 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.51/27.01 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.51/27.01 U46(ok(X)) -> ok(U46(X)) 101.51/27.01 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.51/27.01 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.51/27.01 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.51/27.01 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.51/27.01 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.51/27.01 U56(ok(X)) -> ok(U56(X)) 101.51/27.01 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.51/27.01 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.51/27.01 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.51/27.01 U63(ok(X)) -> ok(U63(X)) 101.51/27.01 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.51/27.01 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.51/27.01 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.51/27.01 U73(ok(X)) -> ok(U73(X)) 101.51/27.01 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.51/27.01 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.51/27.01 U83(ok(X)) -> ok(U83(X)) 101.51/27.01 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.51/27.01 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.51/27.01 U93(ok(X)) -> ok(U93(X)) 101.51/27.01 tail(ok(X)) -> ok(tail(X)) 101.51/27.01 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.51/27.01 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.51/27.01 top(mark(X)) -> top(proper(X)) 101.51/27.01 top(ok(X)) -> top(active(X)) 101.51/27.01 101.51/27.01 Types: 101.51/27.01 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 tt :: tt:mark:nil:0':ok 101.51/27.01 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 nil :: tt:mark:nil:0':ok 101.51/27.01 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 0' :: tt:mark:nil:0':ok 101.51/27.01 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.51/27.01 top :: tt:mark:nil:0':ok -> top 101.51/27.01 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.51/27.01 hole_top2_0 :: top 101.51/27.01 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.51/27.01 101.51/27.01 101.51/27.01 Lemmas: 101.51/27.01 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.51/27.01 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.51/27.01 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.51/27.01 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.51/27.01 101.51/27.01 101.51/27.01 Generator Equations: 101.51/27.01 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.51/27.01 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.51/27.01 101.51/27.01 101.51/27.01 The following defined symbols remain to be analysed: 101.51/27.01 isNatural, active, U106, isLNat, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.51/27.01 101.51/27.01 They will be analysed ascendingly in the following order: 101.51/27.01 isNatural < active 101.51/27.01 U106 < active 101.51/27.01 isLNat < active 101.51/27.01 U12 < active 101.51/27.01 U112 < active 101.51/27.01 U13 < active 101.51/27.01 U122 < active 101.51/27.01 U14 < active 101.51/27.01 snd < active 101.51/27.01 splitAt < active 101.51/27.01 U172 < active 101.51/27.01 U182 < active 101.51/27.01 U183 < active 101.51/27.01 U192 < active 101.51/27.01 U193 < active 101.51/27.01 U202 < active 101.51/27.01 U203 < active 101.51/27.01 U204 < active 101.51/27.01 U205 < active 101.51/27.01 U206 < active 101.51/27.01 U22 < active 101.51/27.01 U23 < active 101.51/27.01 U24 < active 101.51/27.01 U232 < active 101.51/27.01 U242 < active 101.51/27.01 U243 < active 101.51/27.01 U244 < active 101.51/27.01 U245 < active 101.51/27.01 U246 < active 101.51/27.01 U252 < active 101.51/27.01 U253 < active 101.51/27.01 U254 < active 101.51/27.01 U255 < active 101.51/27.01 U256 < active 101.51/27.01 U262 < active 101.51/27.01 U272 < active 101.51/27.01 U282 < active 101.51/27.01 cons < active 101.51/27.01 natsFrom < active 101.51/27.01 s < active 101.51/27.01 U292 < active 101.51/27.01 U293 < active 101.51/27.01 U294 < active 101.51/27.01 head < active 101.51/27.01 afterNth < active 101.51/27.01 U302 < active 101.51/27.01 U303 < active 101.51/27.01 U304 < active 101.51/27.01 U32 < active 101.51/27.01 U312 < active 101.51/27.01 pair < active 101.51/27.01 U33 < active 101.51/27.01 U322 < active 101.51/27.01 U323 < active 101.51/27.01 U324 < active 101.51/27.01 U325 < active 101.51/27.01 U326 < active 101.51/27.01 U327 < active 101.51/27.01 U34 < active 101.51/27.01 U332 < active 101.51/27.01 U333 < active 101.51/27.01 U334 < active 101.51/27.01 U342 < active 101.51/27.01 U343 < active 101.51/27.01 U344 < active 101.51/27.01 fst < active 101.51/27.01 U42 < active 101.51/27.01 U43 < active 101.51/27.01 U44 < active 101.51/27.01 U45 < active 101.51/27.01 U46 < active 101.51/27.01 U52 < active 101.51/27.01 U53 < active 101.51/27.01 U54 < active 101.51/27.01 U55 < active 101.51/27.01 U56 < active 101.51/27.01 U62 < active 101.51/27.01 isPLNatKind < active 101.51/27.01 U63 < active 101.51/27.01 isPLNat < active 101.51/27.01 U72 < active 101.51/27.01 U73 < active 101.51/27.01 U82 < active 101.51/27.01 U83 < active 101.51/27.01 U92 < active 101.51/27.01 U93 < active 101.51/27.01 U11 < active 101.51/27.01 U21 < active 101.51/27.01 U31 < active 101.51/27.01 U41 < active 101.51/27.01 U51 < active 101.51/27.01 U61 < active 101.51/27.01 U71 < active 101.51/27.01 U81 < active 101.51/27.01 U91 < active 101.51/27.01 U101 < active 101.51/27.01 U111 < active 101.51/27.01 U121 < active 101.51/27.01 U131 < active 101.51/27.01 U141 < active 101.51/27.01 U151 < active 101.51/27.01 U161 < active 101.51/27.01 U171 < active 101.51/27.01 U181 < active 101.51/27.01 U191 < active 101.51/27.01 U201 < active 101.51/27.01 U211 < active 101.51/27.01 U221 < active 101.51/27.01 U231 < active 101.51/27.01 U241 < active 101.51/27.01 U251 < active 101.51/27.01 U261 < active 101.51/27.01 U271 < active 101.51/27.01 U281 < active 101.51/27.01 U291 < active 101.51/27.01 U301 < active 101.51/27.01 U311 < active 101.51/27.01 U321 < active 101.51/27.01 U331 < active 101.51/27.01 U341 < active 101.51/27.01 tail < active 101.51/27.01 take < active 101.51/27.01 sel < active 101.51/27.01 active < top 101.51/27.01 isNatural < proper 101.51/27.01 U106 < proper 101.51/27.01 isLNat < proper 101.51/27.01 U12 < proper 101.51/27.01 U112 < proper 101.51/27.01 U13 < proper 101.51/27.01 U122 < proper 101.51/27.01 U14 < proper 101.51/27.01 snd < proper 101.51/27.01 splitAt < proper 101.51/27.01 U172 < proper 101.51/27.01 U182 < proper 101.51/27.01 U183 < proper 101.51/27.01 U192 < proper 101.51/27.01 U193 < proper 101.51/27.01 U202 < proper 101.51/27.01 U203 < proper 101.51/27.01 U204 < proper 101.51/27.01 U205 < proper 101.51/27.01 U206 < proper 101.51/27.01 U22 < proper 101.51/27.01 U23 < proper 101.51/27.01 U24 < proper 101.51/27.01 U232 < proper 101.51/27.01 U242 < proper 101.51/27.01 U243 < proper 101.51/27.01 U244 < proper 101.51/27.01 U245 < proper 101.51/27.01 U246 < proper 101.51/27.01 U252 < proper 101.51/27.01 U253 < proper 101.51/27.01 U254 < proper 101.51/27.01 U255 < proper 101.51/27.01 U256 < proper 101.51/27.01 U262 < proper 101.51/27.01 U272 < proper 101.51/27.01 U282 < proper 101.51/27.01 cons < proper 101.51/27.01 natsFrom < proper 101.51/27.01 s < proper 101.51/27.01 U292 < proper 101.51/27.01 U293 < proper 101.51/27.01 U294 < proper 101.51/27.01 head < proper 101.51/27.01 afterNth < proper 101.51/27.01 U302 < proper 101.51/27.01 U303 < proper 101.51/27.01 U304 < proper 101.51/27.01 U32 < proper 101.51/27.01 U312 < proper 101.51/27.01 pair < proper 101.51/27.01 U33 < proper 101.51/27.01 U322 < proper 101.51/27.01 U323 < proper 101.51/27.01 U324 < proper 101.51/27.01 U325 < proper 101.51/27.01 U326 < proper 101.51/27.01 U327 < proper 101.51/27.01 U34 < proper 101.51/27.01 U332 < proper 101.51/27.01 U333 < proper 101.51/27.01 U334 < proper 101.51/27.01 U342 < proper 101.51/27.01 U343 < proper 101.51/27.01 U344 < proper 101.51/27.01 fst < proper 101.51/27.01 U42 < proper 101.51/27.01 U43 < proper 101.51/27.01 U44 < proper 101.51/27.01 U45 < proper 101.51/27.01 U46 < proper 101.51/27.01 U52 < proper 101.51/27.01 U53 < proper 101.51/27.01 U54 < proper 101.51/27.01 U55 < proper 101.51/27.01 U56 < proper 101.51/27.01 U62 < proper 101.51/27.01 isPLNatKind < proper 101.51/27.01 U63 < proper 101.51/27.01 isPLNat < proper 101.51/27.01 U72 < proper 101.51/27.01 U73 < proper 101.51/27.01 U82 < proper 101.51/27.01 U83 < proper 101.51/27.01 U92 < proper 101.51/27.01 U93 < proper 101.51/27.01 U11 < proper 101.51/27.01 U21 < proper 101.51/27.01 U31 < proper 101.51/27.01 U41 < proper 101.51/27.01 U51 < proper 101.51/27.01 U61 < proper 101.51/27.01 U71 < proper 101.51/27.01 U81 < proper 101.51/27.01 U91 < proper 101.51/27.01 U101 < proper 101.51/27.01 U111 < proper 101.51/27.01 U121 < proper 101.51/27.01 U131 < proper 101.51/27.01 U141 < proper 101.51/27.01 U151 < proper 101.51/27.01 U161 < proper 101.51/27.01 U171 < proper 101.51/27.01 U181 < proper 101.51/27.01 U191 < proper 101.51/27.01 U201 < proper 101.51/27.01 U211 < proper 101.51/27.01 U221 < proper 101.51/27.01 U231 < proper 101.51/27.01 U241 < proper 101.51/27.01 U251 < proper 101.51/27.01 U261 < proper 101.51/27.01 U271 < proper 101.51/27.01 U281 < proper 101.51/27.01 U291 < proper 101.51/27.01 U301 < proper 101.51/27.01 U311 < proper 101.51/27.01 U321 < proper 101.51/27.01 U331 < proper 101.51/27.01 U341 < proper 101.51/27.01 tail < proper 101.51/27.01 take < proper 101.51/27.01 sel < proper 101.51/27.01 proper < top 101.51/27.01 101.51/27.01 ---------------------------------------- 101.51/27.01 101.51/27.01 (37) RewriteLemmaProof (LOWER BOUND(ID)) 101.51/27.01 Proved the following rewrite lemma: 101.51/27.01 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.51/27.01 101.51/27.01 Induction Base: 101.51/27.01 U106(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.51/27.01 101.51/27.01 Induction Step: 101.51/27.01 U106(gen_tt:mark:nil:0':ok3_0(+(1, +(n64799_0, 1)))) ->_R^Omega(1) 101.51/27.01 mark(U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0)))) ->_IH 101.51/27.01 mark(*4_0) 101.51/27.01 101.51/27.01 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.51/27.01 ---------------------------------------- 101.51/27.01 101.51/27.01 (38) 101.51/27.01 Obligation: 101.51/27.01 TRS: 101.51/27.01 Rules: 101.51/27.01 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.51/27.01 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.51/27.01 active(U106(tt)) -> mark(tt) 101.51/27.01 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.51/27.01 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.51/27.01 active(U112(tt)) -> mark(tt) 101.51/27.01 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.51/27.01 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.51/27.01 active(U122(tt)) -> mark(tt) 101.51/27.01 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.51/27.01 active(U131(tt)) -> mark(tt) 101.51/27.01 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.51/27.01 active(U141(tt)) -> mark(tt) 101.51/27.01 active(U151(tt)) -> mark(tt) 101.51/27.01 active(U161(tt)) -> mark(tt) 101.51/27.01 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.51/27.01 active(U172(tt)) -> mark(tt) 101.51/27.01 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.51/27.01 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.51/27.01 active(U183(tt)) -> mark(tt) 101.51/27.01 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.51/27.01 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.51/27.01 active(U193(tt)) -> mark(tt) 101.51/27.01 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.51/27.01 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.51/27.01 active(U206(tt)) -> mark(tt) 101.51/27.01 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.51/27.01 active(U211(tt)) -> mark(tt) 101.51/27.01 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.51/27.01 active(U221(tt)) -> mark(tt) 101.51/27.01 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.51/27.01 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.51/27.01 active(U232(tt)) -> mark(tt) 101.51/27.01 active(U24(tt, X)) -> mark(X) 101.51/27.01 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.51/27.01 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.51/27.01 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.51/27.01 active(U246(tt)) -> mark(tt) 101.51/27.01 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.51/27.01 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.51/27.01 active(U256(tt)) -> mark(tt) 101.51/27.01 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.51/27.01 active(U262(tt)) -> mark(tt) 101.51/27.01 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.51/27.01 active(U272(tt)) -> mark(tt) 101.51/27.01 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.51/27.01 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.51/27.01 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.51/27.01 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.51/27.01 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.51/27.01 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.51/27.01 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.51/27.01 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.51/27.01 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.51/27.01 active(U304(tt, Y)) -> mark(Y) 101.51/27.01 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.51/27.01 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.51/27.01 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.51/27.01 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.51/27.01 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.51/27.01 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.51/27.01 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.51/27.01 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.51/27.01 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.51/27.01 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.51/27.01 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.51/27.01 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.51/27.01 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.51/27.01 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.51/27.01 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.51/27.01 active(U334(tt, XS)) -> mark(XS) 101.51/27.01 active(U34(tt, N)) -> mark(N) 101.51/27.01 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.51/27.01 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.51/27.01 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.51/27.01 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.51/27.01 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.51/27.01 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.51/27.01 active(U46(tt)) -> mark(tt) 101.51/27.01 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.51/27.01 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.51/27.01 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.51/27.01 active(U56(tt)) -> mark(tt) 101.51/27.01 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.51/27.01 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.51/27.01 active(U63(tt)) -> mark(tt) 101.51/27.01 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.51/27.01 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.51/27.01 active(U73(tt)) -> mark(tt) 101.51/27.01 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.51/27.01 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.51/27.01 active(U83(tt)) -> mark(tt) 101.51/27.01 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.51/27.01 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.51/27.01 active(U93(tt)) -> mark(tt) 101.51/27.01 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.51/27.01 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.51/27.01 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.51/27.01 active(isLNat(nil)) -> mark(tt) 101.51/27.01 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.51/27.01 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.51/27.01 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.51/27.01 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.51/27.01 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(isLNatKind(nil)) -> mark(tt) 101.51/27.01 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.51/27.01 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.51/27.01 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.51/27.01 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.51/27.01 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.51/27.01 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.51/27.01 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.51/27.01 active(isNatural(0')) -> mark(tt) 101.51/27.01 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.51/27.01 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.51/27.01 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(isNaturalKind(0')) -> mark(tt) 101.51/27.01 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.51/27.01 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.51/27.01 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.51/27.01 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.51/27.01 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.51/27.01 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.51/27.01 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.51/27.01 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.51/27.01 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.51/27.01 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.51/27.01 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.51/27.01 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.51/27.01 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.51/27.01 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.51/27.01 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.51/27.01 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.51/27.01 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.51/27.01 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.51/27.01 active(U105(X1, X2)) -> U105(active(X1), X2) 101.51/27.01 active(U106(X)) -> U106(active(X)) 101.51/27.01 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.51/27.01 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.51/27.01 active(U111(X1, X2)) -> U111(active(X1), X2) 101.51/27.01 active(U112(X)) -> U112(active(X)) 101.51/27.01 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.51/27.01 active(U121(X1, X2)) -> U121(active(X1), X2) 101.51/27.01 active(U122(X)) -> U122(active(X)) 101.51/27.01 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.51/27.01 active(U131(X)) -> U131(active(X)) 101.51/27.01 active(snd(X)) -> snd(active(X)) 101.51/27.01 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.51/27.01 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.51/27.01 active(U141(X)) -> U141(active(X)) 101.51/27.01 active(U151(X)) -> U151(active(X)) 101.51/27.01 active(U161(X)) -> U161(active(X)) 101.51/27.01 active(U171(X1, X2)) -> U171(active(X1), X2) 101.51/27.01 active(U172(X)) -> U172(active(X)) 101.51/27.01 active(U181(X1, X2)) -> U181(active(X1), X2) 101.51/27.01 active(U182(X1, X2)) -> U182(active(X1), X2) 101.51/27.01 active(U183(X)) -> U183(active(X)) 101.51/27.01 active(U191(X1, X2)) -> U191(active(X1), X2) 101.51/27.01 active(U192(X1, X2)) -> U192(active(X1), X2) 101.51/27.01 active(U193(X)) -> U193(active(X)) 101.51/27.01 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.51/27.01 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.51/27.01 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.51/27.01 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.51/27.01 active(U205(X1, X2)) -> U205(active(X1), X2) 101.51/27.01 active(U206(X)) -> U206(active(X)) 101.51/27.01 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.51/27.01 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.51/27.01 active(U211(X)) -> U211(active(X)) 101.51/27.01 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.51/27.01 active(U221(X)) -> U221(active(X)) 101.51/27.01 active(U24(X1, X2)) -> U24(active(X1), X2) 101.51/27.01 active(U231(X1, X2)) -> U231(active(X1), X2) 101.51/27.01 active(U232(X)) -> U232(active(X)) 101.51/27.01 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.51/27.01 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.51/27.01 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.51/27.01 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.51/27.01 active(U245(X1, X2)) -> U245(active(X1), X2) 101.51/27.01 active(U246(X)) -> U246(active(X)) 101.51/27.01 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.51/27.01 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.51/27.01 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.51/27.01 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.51/27.01 active(U255(X1, X2)) -> U255(active(X1), X2) 101.51/27.01 active(U256(X)) -> U256(active(X)) 101.51/27.01 active(U261(X1, X2)) -> U261(active(X1), X2) 101.51/27.01 active(U262(X)) -> U262(active(X)) 101.51/27.01 active(U271(X1, X2)) -> U271(active(X1), X2) 101.51/27.01 active(U272(X)) -> U272(active(X)) 101.51/27.01 active(U281(X1, X2)) -> U281(active(X1), X2) 101.51/27.01 active(U282(X1, X2)) -> U282(active(X1), X2) 101.51/27.01 active(cons(X1, X2)) -> cons(active(X1), X2) 101.51/27.01 active(natsFrom(X)) -> natsFrom(active(X)) 101.51/27.01 active(s(X)) -> s(active(X)) 101.51/27.01 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.51/27.01 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.51/27.01 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.51/27.01 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.51/27.01 active(head(X)) -> head(active(X)) 101.51/27.01 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.51/27.01 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.51/27.01 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.51/27.01 active(U302(X1, X2)) -> U302(active(X1), X2) 101.51/27.01 active(U303(X1, X2)) -> U303(active(X1), X2) 101.51/27.01 active(U304(X1, X2)) -> U304(active(X1), X2) 101.51/27.01 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.51/27.01 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.51/27.01 active(U311(X1, X2)) -> U311(active(X1), X2) 101.51/27.01 active(U312(X1, X2)) -> U312(active(X1), X2) 101.51/27.01 active(pair(X1, X2)) -> pair(active(X1), X2) 101.51/27.01 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.51/27.01 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.51/27.01 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.51/27.01 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.51/27.01 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.51/27.01 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.51/27.01 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.51/27.01 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.51/27.01 active(U327(X1, X2)) -> U327(active(X1), X2) 101.51/27.01 active(U34(X1, X2)) -> U34(active(X1), X2) 101.51/27.01 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.51/27.01 active(U332(X1, X2)) -> U332(active(X1), X2) 101.51/27.01 active(U333(X1, X2)) -> U333(active(X1), X2) 101.51/27.01 active(U334(X1, X2)) -> U334(active(X1), X2) 101.51/27.01 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.51/27.01 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.51/27.01 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.51/27.01 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.51/27.01 active(fst(X)) -> fst(active(X)) 101.51/27.01 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.51/27.01 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.51/27.01 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.51/27.01 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.51/27.01 active(U45(X1, X2)) -> U45(active(X1), X2) 101.51/27.01 active(U46(X)) -> U46(active(X)) 101.51/27.01 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.51/27.01 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.51/27.01 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.51/27.01 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.51/27.01 active(U55(X1, X2)) -> U55(active(X1), X2) 101.51/27.01 active(U56(X)) -> U56(active(X)) 101.51/27.01 active(U61(X1, X2)) -> U61(active(X1), X2) 101.51/27.01 active(U62(X1, X2)) -> U62(active(X1), X2) 101.51/27.01 active(U63(X)) -> U63(active(X)) 101.51/27.01 active(U71(X1, X2)) -> U71(active(X1), X2) 101.51/27.01 active(U72(X1, X2)) -> U72(active(X1), X2) 101.51/27.01 active(U73(X)) -> U73(active(X)) 101.51/27.01 active(U81(X1, X2)) -> U81(active(X1), X2) 101.51/27.01 active(U82(X1, X2)) -> U82(active(X1), X2) 101.51/27.01 active(U83(X)) -> U83(active(X)) 101.51/27.01 active(U91(X1, X2)) -> U91(active(X1), X2) 101.51/27.01 active(U92(X1, X2)) -> U92(active(X1), X2) 101.51/27.01 active(U93(X)) -> U93(active(X)) 101.51/27.01 active(tail(X)) -> tail(active(X)) 101.51/27.01 active(take(X1, X2)) -> take(active(X1), X2) 101.51/27.01 active(take(X1, X2)) -> take(X1, active(X2)) 101.51/27.01 active(sel(X1, X2)) -> sel(active(X1), X2) 101.51/27.01 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.51/27.01 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.51/27.01 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.51/27.01 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.51/27.01 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.51/27.01 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.51/27.01 U106(mark(X)) -> mark(U106(X)) 101.51/27.01 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.51/27.01 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.51/27.01 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.51/27.01 U112(mark(X)) -> mark(U112(X)) 101.51/27.01 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.51/27.01 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.51/27.01 U122(mark(X)) -> mark(U122(X)) 101.51/27.01 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.51/27.01 U131(mark(X)) -> mark(U131(X)) 101.51/27.01 snd(mark(X)) -> mark(snd(X)) 101.51/27.01 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.51/27.01 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.51/27.01 U141(mark(X)) -> mark(U141(X)) 101.51/27.01 U151(mark(X)) -> mark(U151(X)) 101.51/27.01 U161(mark(X)) -> mark(U161(X)) 101.51/27.01 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.51/27.01 U172(mark(X)) -> mark(U172(X)) 101.51/27.01 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.51/27.01 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.51/27.01 U183(mark(X)) -> mark(U183(X)) 101.51/27.01 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.51/27.01 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.51/27.01 U193(mark(X)) -> mark(U193(X)) 101.51/27.01 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.51/27.01 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.51/27.01 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.51/27.01 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.51/27.01 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.51/27.01 U206(mark(X)) -> mark(U206(X)) 101.51/27.01 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.51/27.01 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.51/27.01 U211(mark(X)) -> mark(U211(X)) 101.51/27.01 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.51/27.01 U221(mark(X)) -> mark(U221(X)) 101.51/27.01 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.51/27.01 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.51/27.01 U232(mark(X)) -> mark(U232(X)) 101.51/27.01 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.51/27.01 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.51/27.01 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.51/27.01 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.51/27.01 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.51/27.01 U246(mark(X)) -> mark(U246(X)) 101.51/27.01 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.51/27.01 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.51/27.01 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.51/27.01 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.51/27.01 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.51/27.01 U256(mark(X)) -> mark(U256(X)) 101.51/27.01 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.51/27.01 U262(mark(X)) -> mark(U262(X)) 101.51/27.01 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.51/27.01 U272(mark(X)) -> mark(U272(X)) 101.51/27.01 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.51/27.01 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.51/27.01 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.51/27.01 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.51/27.01 s(mark(X)) -> mark(s(X)) 101.51/27.01 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.51/27.01 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.51/27.01 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.51/27.01 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.51/27.01 head(mark(X)) -> mark(head(X)) 101.51/27.01 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.51/27.01 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.51/27.01 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.51/27.01 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.51/27.01 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.51/27.01 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.51/27.01 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.51/27.01 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.51/27.01 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.51/27.01 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.51/27.01 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.51/27.01 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.51/27.01 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.51/27.01 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.51/27.01 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.51/27.01 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.51/27.01 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.51/27.01 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.51/27.01 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.51/27.01 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.51/27.01 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.51/27.01 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.51/27.01 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.51/27.01 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.51/27.01 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.51/27.01 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.51/27.01 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.51/27.01 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.51/27.01 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.51/27.01 fst(mark(X)) -> mark(fst(X)) 101.51/27.01 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.51/27.01 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.51/27.01 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.51/27.01 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.51/27.01 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.51/27.01 U46(mark(X)) -> mark(U46(X)) 101.60/27.02 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.60/27.02 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.60/27.02 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.60/27.02 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.60/27.02 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.60/27.02 U56(mark(X)) -> mark(U56(X)) 101.60/27.02 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.60/27.02 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.60/27.02 U63(mark(X)) -> mark(U63(X)) 101.60/27.02 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.60/27.02 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.60/27.02 U73(mark(X)) -> mark(U73(X)) 101.60/27.02 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.60/27.02 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.60/27.02 U83(mark(X)) -> mark(U83(X)) 101.60/27.02 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.60/27.02 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.60/27.02 U93(mark(X)) -> mark(U93(X)) 101.60/27.02 tail(mark(X)) -> mark(tail(X)) 101.60/27.02 take(mark(X1), X2) -> mark(take(X1, X2)) 101.60/27.02 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.60/27.02 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.60/27.02 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.60/27.02 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(tt) -> ok(tt) 101.60/27.02 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.60/27.02 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.60/27.02 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.60/27.02 proper(isNatural(X)) -> isNatural(proper(X)) 101.60/27.02 proper(U106(X)) -> U106(proper(X)) 101.60/27.02 proper(isLNat(X)) -> isLNat(proper(X)) 101.60/27.02 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.60/27.02 proper(U112(X)) -> U112(proper(X)) 101.60/27.02 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.60/27.02 proper(U122(X)) -> U122(proper(X)) 101.60/27.02 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U131(X)) -> U131(proper(X)) 101.60/27.02 proper(snd(X)) -> snd(proper(X)) 101.60/27.02 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.60/27.02 proper(U141(X)) -> U141(proper(X)) 101.60/27.02 proper(U151(X)) -> U151(proper(X)) 101.60/27.02 proper(U161(X)) -> U161(proper(X)) 101.60/27.02 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.60/27.02 proper(U172(X)) -> U172(proper(X)) 101.60/27.02 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.60/27.02 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.60/27.02 proper(U183(X)) -> U183(proper(X)) 101.60/27.02 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.60/27.02 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.60/27.02 proper(U193(X)) -> U193(proper(X)) 101.60/27.02 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.60/27.02 proper(U206(X)) -> U206(proper(X)) 101.60/27.02 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U211(X)) -> U211(proper(X)) 101.60/27.02 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U221(X)) -> U221(proper(X)) 101.60/27.02 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.60/27.02 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.60/27.02 proper(U232(X)) -> U232(proper(X)) 101.60/27.02 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.60/27.02 proper(U246(X)) -> U246(proper(X)) 101.60/27.02 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.60/27.02 proper(U256(X)) -> U256(proper(X)) 101.60/27.02 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.60/27.02 proper(U262(X)) -> U262(proper(X)) 101.60/27.02 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.60/27.02 proper(U272(X)) -> U272(proper(X)) 101.60/27.02 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.60/27.02 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.60/27.02 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.60/27.02 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.60/27.02 proper(s(X)) -> s(proper(X)) 101.60/27.02 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(head(X)) -> head(proper(X)) 101.60/27.02 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.60/27.02 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.60/27.02 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.60/27.02 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.60/27.02 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.60/27.02 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.60/27.02 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.60/27.02 proper(nil) -> ok(nil) 101.60/27.02 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.60/27.02 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.60/27.02 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.60/27.02 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.60/27.02 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.60/27.02 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.60/27.02 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(fst(X)) -> fst(proper(X)) 101.60/27.02 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.60/27.02 proper(U46(X)) -> U46(proper(X)) 101.60/27.02 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.60/27.02 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.60/27.02 proper(U56(X)) -> U56(proper(X)) 101.60/27.02 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.60/27.02 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.60/27.02 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.60/27.02 proper(U63(X)) -> U63(proper(X)) 101.60/27.02 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.60/27.02 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.60/27.02 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.60/27.02 proper(U73(X)) -> U73(proper(X)) 101.60/27.02 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.60/27.02 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.60/27.02 proper(U83(X)) -> U83(proper(X)) 101.60/27.02 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.60/27.02 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.60/27.02 proper(U93(X)) -> U93(proper(X)) 101.60/27.02 proper(tail(X)) -> tail(proper(X)) 101.60/27.02 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.60/27.02 proper(0') -> ok(0') 101.60/27.02 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.60/27.02 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.60/27.02 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.60/27.02 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.60/27.02 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.60/27.02 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.60/27.02 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.60/27.02 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.60/27.02 isNatural(ok(X)) -> ok(isNatural(X)) 101.60/27.02 U106(ok(X)) -> ok(U106(X)) 101.60/27.02 isLNat(ok(X)) -> ok(isLNat(X)) 101.60/27.02 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.60/27.02 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.60/27.02 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.60/27.02 U112(ok(X)) -> ok(U112(X)) 101.60/27.02 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.60/27.02 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.60/27.02 U122(ok(X)) -> ok(U122(X)) 101.60/27.02 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.60/27.02 U131(ok(X)) -> ok(U131(X)) 101.60/27.02 snd(ok(X)) -> ok(snd(X)) 101.60/27.02 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.60/27.02 U141(ok(X)) -> ok(U141(X)) 101.60/27.02 U151(ok(X)) -> ok(U151(X)) 101.60/27.02 U161(ok(X)) -> ok(U161(X)) 101.60/27.02 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.60/27.02 U172(ok(X)) -> ok(U172(X)) 101.60/27.02 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.60/27.02 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.60/27.02 U183(ok(X)) -> ok(U183(X)) 101.60/27.02 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.60/27.02 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.60/27.02 U193(ok(X)) -> ok(U193(X)) 101.60/27.02 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.60/27.02 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.60/27.02 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.60/27.02 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.60/27.02 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.60/27.02 U206(ok(X)) -> ok(U206(X)) 101.60/27.02 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.60/27.02 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.60/27.02 U211(ok(X)) -> ok(U211(X)) 101.60/27.02 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.60/27.02 U221(ok(X)) -> ok(U221(X)) 101.60/27.02 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.60/27.02 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.60/27.02 U232(ok(X)) -> ok(U232(X)) 101.60/27.02 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.60/27.02 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.60/27.02 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.60/27.02 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.60/27.02 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.60/27.02 U246(ok(X)) -> ok(U246(X)) 101.60/27.02 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.60/27.02 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.60/27.02 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.60/27.02 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.60/27.02 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.60/27.02 U256(ok(X)) -> ok(U256(X)) 101.60/27.02 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.60/27.02 U262(ok(X)) -> ok(U262(X)) 101.60/27.02 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.60/27.02 U272(ok(X)) -> ok(U272(X)) 101.60/27.02 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.60/27.02 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.60/27.02 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.60/27.02 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.60/27.02 s(ok(X)) -> ok(s(X)) 101.60/27.02 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.60/27.02 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.60/27.02 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.60/27.02 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.60/27.02 head(ok(X)) -> ok(head(X)) 101.60/27.02 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.60/27.02 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.60/27.02 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.60/27.02 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.60/27.02 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.60/27.02 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.60/27.02 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.60/27.02 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.60/27.02 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.60/27.02 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.60/27.02 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.60/27.02 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.60/27.02 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.60/27.02 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.60/27.02 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.60/27.02 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.60/27.02 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.60/27.02 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.60/27.02 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.60/27.02 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.60/27.02 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.60/27.02 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.60/27.02 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.60/27.02 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.60/27.02 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.60/27.02 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.60/27.02 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.60/27.02 fst(ok(X)) -> ok(fst(X)) 101.60/27.02 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.60/27.02 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.60/27.02 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.60/27.02 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.60/27.02 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.60/27.02 U46(ok(X)) -> ok(U46(X)) 101.60/27.02 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.60/27.02 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.60/27.02 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.60/27.02 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.60/27.02 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.60/27.02 U56(ok(X)) -> ok(U56(X)) 101.60/27.02 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.60/27.02 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.60/27.02 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.60/27.02 U63(ok(X)) -> ok(U63(X)) 101.60/27.02 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.60/27.02 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.60/27.02 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.60/27.02 U73(ok(X)) -> ok(U73(X)) 101.60/27.02 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.60/27.02 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.60/27.02 U83(ok(X)) -> ok(U83(X)) 101.60/27.02 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.60/27.02 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.60/27.02 U93(ok(X)) -> ok(U93(X)) 101.60/27.02 tail(ok(X)) -> ok(tail(X)) 101.60/27.02 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.60/27.02 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.60/27.02 top(mark(X)) -> top(proper(X)) 101.60/27.02 top(ok(X)) -> top(active(X)) 101.60/27.02 101.60/27.02 Types: 101.60/27.02 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 tt :: tt:mark:nil:0':ok 101.60/27.02 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 nil :: tt:mark:nil:0':ok 101.60/27.02 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 0' :: tt:mark:nil:0':ok 101.60/27.02 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.60/27.02 top :: tt:mark:nil:0':ok -> top 101.60/27.02 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.60/27.02 hole_top2_0 :: top 101.60/27.02 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.60/27.02 101.60/27.02 101.60/27.02 Lemmas: 101.60/27.02 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.60/27.02 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.60/27.02 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.60/27.02 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.60/27.02 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.60/27.02 101.60/27.02 101.60/27.02 Generator Equations: 101.60/27.02 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.60/27.02 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.60/27.02 101.60/27.02 101.60/27.02 The following defined symbols remain to be analysed: 101.60/27.02 isLNat, active, U12, U112, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.60/27.02 101.60/27.02 They will be analysed ascendingly in the following order: 101.60/27.02 isLNat < active 101.60/27.02 U12 < active 101.60/27.02 U112 < active 101.60/27.02 U13 < active 101.60/27.02 U122 < active 101.60/27.02 U14 < active 101.60/27.02 snd < active 101.60/27.02 splitAt < active 101.60/27.02 U172 < active 101.60/27.02 U182 < active 101.60/27.02 U183 < active 101.60/27.02 U192 < active 101.60/27.02 U193 < active 101.60/27.02 U202 < active 101.60/27.02 U203 < active 101.60/27.02 U204 < active 101.60/27.02 U205 < active 101.60/27.02 U206 < active 101.60/27.02 U22 < active 101.60/27.02 U23 < active 101.60/27.02 U24 < active 101.60/27.02 U232 < active 101.60/27.02 U242 < active 101.60/27.02 U243 < active 101.60/27.02 U244 < active 101.60/27.02 U245 < active 101.60/27.02 U246 < active 101.60/27.02 U252 < active 101.60/27.02 U253 < active 101.60/27.02 U254 < active 101.60/27.02 U255 < active 101.60/27.02 U256 < active 101.60/27.02 U262 < active 101.60/27.02 U272 < active 101.60/27.02 U282 < active 101.60/27.02 cons < active 101.60/27.02 natsFrom < active 101.60/27.02 s < active 101.60/27.02 U292 < active 101.60/27.02 U293 < active 101.60/27.02 U294 < active 101.60/27.02 head < active 101.60/27.02 afterNth < active 101.60/27.02 U302 < active 101.60/27.02 U303 < active 101.60/27.02 U304 < active 101.60/27.02 U32 < active 101.60/27.02 U312 < active 101.60/27.02 pair < active 101.60/27.02 U33 < active 101.60/27.02 U322 < active 101.60/27.02 U323 < active 101.60/27.02 U324 < active 101.60/27.02 U325 < active 101.60/27.02 U326 < active 101.60/27.02 U327 < active 101.60/27.02 U34 < active 101.60/27.02 U332 < active 101.60/27.02 U333 < active 101.60/27.02 U334 < active 101.60/27.02 U342 < active 101.60/27.02 U343 < active 101.60/27.02 U344 < active 101.60/27.02 fst < active 101.60/27.02 U42 < active 101.60/27.02 U43 < active 101.60/27.02 U44 < active 101.60/27.02 U45 < active 101.60/27.02 U46 < active 101.60/27.02 U52 < active 101.60/27.02 U53 < active 101.60/27.02 U54 < active 101.60/27.02 U55 < active 101.60/27.02 U56 < active 101.60/27.02 U62 < active 101.60/27.02 isPLNatKind < active 101.60/27.02 U63 < active 101.60/27.02 isPLNat < active 101.60/27.02 U72 < active 101.60/27.02 U73 < active 101.60/27.02 U82 < active 101.60/27.02 U83 < active 101.60/27.02 U92 < active 101.60/27.02 U93 < active 101.60/27.02 U11 < active 101.60/27.02 U21 < active 101.60/27.02 U31 < active 101.60/27.02 U41 < active 101.60/27.02 U51 < active 101.60/27.02 U61 < active 101.60/27.02 U71 < active 101.60/27.02 U81 < active 101.60/27.02 U91 < active 101.60/27.02 U101 < active 101.60/27.02 U111 < active 101.60/27.02 U121 < active 101.60/27.02 U131 < active 101.60/27.02 U141 < active 101.60/27.02 U151 < active 101.60/27.02 U161 < active 101.60/27.02 U171 < active 101.60/27.02 U181 < active 101.60/27.02 U191 < active 101.60/27.02 U201 < active 101.60/27.02 U211 < active 101.60/27.02 U221 < active 101.60/27.02 U231 < active 101.60/27.02 U241 < active 101.60/27.02 U251 < active 101.60/27.02 U261 < active 101.60/27.02 U271 < active 101.60/27.02 U281 < active 101.60/27.02 U291 < active 101.60/27.02 U301 < active 101.60/27.02 U311 < active 101.60/27.02 U321 < active 101.60/27.02 U331 < active 101.60/27.02 U341 < active 101.60/27.02 tail < active 101.60/27.02 take < active 101.60/27.02 sel < active 101.60/27.02 active < top 101.60/27.02 isLNat < proper 101.60/27.02 U12 < proper 101.60/27.02 U112 < proper 101.60/27.02 U13 < proper 101.60/27.02 U122 < proper 101.60/27.02 U14 < proper 101.60/27.02 snd < proper 101.60/27.02 splitAt < proper 101.60/27.02 U172 < proper 101.60/27.02 U182 < proper 101.60/27.02 U183 < proper 101.60/27.02 U192 < proper 101.60/27.02 U193 < proper 101.60/27.02 U202 < proper 101.60/27.02 U203 < proper 101.60/27.02 U204 < proper 101.60/27.02 U205 < proper 101.60/27.02 U206 < proper 101.60/27.02 U22 < proper 101.60/27.02 U23 < proper 101.60/27.02 U24 < proper 101.60/27.02 U232 < proper 101.60/27.02 U242 < proper 101.60/27.02 U243 < proper 101.60/27.02 U244 < proper 101.60/27.02 U245 < proper 101.60/27.02 U246 < proper 101.60/27.02 U252 < proper 101.60/27.02 U253 < proper 101.60/27.02 U254 < proper 101.60/27.02 U255 < proper 101.60/27.02 U256 < proper 101.60/27.02 U262 < proper 101.60/27.02 U272 < proper 101.60/27.02 U282 < proper 101.60/27.02 cons < proper 101.60/27.02 natsFrom < proper 101.60/27.02 s < proper 101.60/27.02 U292 < proper 101.60/27.02 U293 < proper 101.60/27.02 U294 < proper 101.60/27.02 head < proper 101.60/27.02 afterNth < proper 101.60/27.02 U302 < proper 101.60/27.02 U303 < proper 101.60/27.02 U304 < proper 101.60/27.02 U32 < proper 101.60/27.02 U312 < proper 101.60/27.02 pair < proper 101.60/27.02 U33 < proper 101.60/27.02 U322 < proper 101.60/27.02 U323 < proper 101.60/27.02 U324 < proper 101.60/27.02 U325 < proper 101.60/27.02 U326 < proper 101.60/27.02 U327 < proper 101.60/27.02 U34 < proper 101.60/27.02 U332 < proper 101.60/27.02 U333 < proper 101.60/27.02 U334 < proper 101.60/27.02 U342 < proper 101.60/27.02 U343 < proper 101.60/27.02 U344 < proper 101.60/27.02 fst < proper 101.60/27.02 U42 < proper 101.60/27.02 U43 < proper 101.60/27.02 U44 < proper 101.60/27.02 U45 < proper 101.60/27.02 U46 < proper 101.60/27.02 U52 < proper 101.60/27.02 U53 < proper 101.60/27.02 U54 < proper 101.60/27.02 U55 < proper 101.60/27.02 U56 < proper 101.60/27.02 U62 < proper 101.60/27.02 isPLNatKind < proper 101.60/27.02 U63 < proper 101.60/27.02 isPLNat < proper 101.60/27.02 U72 < proper 101.60/27.02 U73 < proper 101.60/27.02 U82 < proper 101.60/27.02 U83 < proper 101.60/27.02 U92 < proper 101.60/27.02 U93 < proper 101.60/27.02 U11 < proper 101.60/27.02 U21 < proper 101.60/27.02 U31 < proper 101.60/27.02 U41 < proper 101.60/27.03 U51 < proper 101.60/27.03 U61 < proper 101.60/27.03 U71 < proper 101.60/27.03 U81 < proper 101.60/27.03 U91 < proper 101.60/27.03 U101 < proper 101.60/27.03 U111 < proper 101.60/27.03 U121 < proper 101.60/27.03 U131 < proper 101.60/27.03 U141 < proper 101.60/27.03 U151 < proper 101.60/27.03 U161 < proper 101.60/27.03 U171 < proper 101.60/27.03 U181 < proper 101.60/27.03 U191 < proper 101.60/27.03 U201 < proper 101.60/27.03 U211 < proper 101.60/27.03 U221 < proper 101.60/27.03 U231 < proper 101.60/27.03 U241 < proper 101.60/27.03 U251 < proper 101.60/27.03 U261 < proper 101.60/27.03 U271 < proper 101.60/27.03 U281 < proper 101.60/27.03 U291 < proper 101.60/27.03 U301 < proper 101.60/27.03 U311 < proper 101.60/27.03 U321 < proper 101.60/27.03 U331 < proper 101.60/27.03 U341 < proper 101.60/27.03 tail < proper 101.60/27.03 take < proper 101.60/27.03 sel < proper 101.60/27.03 proper < top 101.60/27.03 101.60/27.03 ---------------------------------------- 101.60/27.03 101.60/27.03 (39) RewriteLemmaProof (LOWER BOUND(ID)) 101.60/27.03 Proved the following rewrite lemma: 101.60/27.03 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.60/27.03 101.60/27.03 Induction Base: 101.60/27.03 U12(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.60/27.03 101.60/27.03 Induction Step: 101.60/27.03 U12(gen_tt:mark:nil:0':ok3_0(+(1, +(n67850_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.60/27.03 mark(U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.60/27.03 mark(*4_0) 101.60/27.03 101.60/27.03 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.60/27.03 ---------------------------------------- 101.60/27.03 101.60/27.03 (40) 101.60/27.03 Obligation: 101.60/27.03 TRS: 101.60/27.03 Rules: 101.60/27.03 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.60/27.03 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.60/27.03 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.60/27.03 active(U106(tt)) -> mark(tt) 101.60/27.03 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.60/27.03 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.60/27.03 active(U112(tt)) -> mark(tt) 101.60/27.03 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.60/27.03 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.60/27.03 active(U122(tt)) -> mark(tt) 101.60/27.03 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.60/27.03 active(U131(tt)) -> mark(tt) 101.60/27.03 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.60/27.03 active(U141(tt)) -> mark(tt) 101.60/27.03 active(U151(tt)) -> mark(tt) 101.60/27.03 active(U161(tt)) -> mark(tt) 101.60/27.03 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.60/27.03 active(U172(tt)) -> mark(tt) 101.60/27.03 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.60/27.03 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.60/27.03 active(U183(tt)) -> mark(tt) 101.60/27.03 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.60/27.03 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.60/27.03 active(U193(tt)) -> mark(tt) 101.60/27.03 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.60/27.03 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.60/27.03 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.60/27.03 active(U206(tt)) -> mark(tt) 101.60/27.03 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.60/27.03 active(U211(tt)) -> mark(tt) 101.60/27.03 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.60/27.03 active(U221(tt)) -> mark(tt) 101.60/27.03 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.60/27.03 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.60/27.03 active(U232(tt)) -> mark(tt) 101.60/27.03 active(U24(tt, X)) -> mark(X) 101.60/27.03 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.60/27.03 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.60/27.03 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.60/27.03 active(U246(tt)) -> mark(tt) 101.60/27.03 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.60/27.03 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.60/27.03 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.60/27.03 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.60/27.03 active(U256(tt)) -> mark(tt) 101.60/27.03 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.60/27.03 active(U262(tt)) -> mark(tt) 101.60/27.03 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.60/27.03 active(U272(tt)) -> mark(tt) 101.60/27.03 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.60/27.03 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.60/27.03 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.60/27.03 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.03 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.03 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.03 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.03 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.03 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.03 active(U304(tt, Y)) -> mark(Y) 101.64/27.03 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.03 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.03 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.03 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.03 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.03 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.03 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.03 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.03 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.03 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.03 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.03 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.03 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.03 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.03 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.03 active(U334(tt, XS)) -> mark(XS) 101.64/27.03 active(U34(tt, N)) -> mark(N) 101.64/27.03 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.03 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.03 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.03 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.03 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.03 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.03 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.03 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.03 active(U46(tt)) -> mark(tt) 101.64/27.03 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.03 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.03 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.03 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.03 active(U56(tt)) -> mark(tt) 101.64/27.03 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.03 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.03 active(U63(tt)) -> mark(tt) 101.64/27.03 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.03 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.03 active(U73(tt)) -> mark(tt) 101.64/27.03 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.03 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.03 active(U83(tt)) -> mark(tt) 101.64/27.03 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.03 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.03 active(U93(tt)) -> mark(tt) 101.64/27.03 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.03 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.03 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.03 active(isLNat(nil)) -> mark(tt) 101.64/27.03 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.03 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.03 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.03 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.03 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(isLNatKind(nil)) -> mark(tt) 101.64/27.03 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.03 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.03 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.03 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.03 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.03 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.03 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.03 active(isNatural(0')) -> mark(tt) 101.64/27.03 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.03 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.03 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(isNaturalKind(0')) -> mark(tt) 101.64/27.03 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.03 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.03 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.03 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.03 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.03 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.03 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.03 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.03 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.03 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.03 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.03 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.03 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.03 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.03 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.03 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.03 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.03 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.03 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.03 active(U106(X)) -> U106(active(X)) 101.64/27.03 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.03 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.03 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.03 active(U112(X)) -> U112(active(X)) 101.64/27.03 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.03 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.03 active(U122(X)) -> U122(active(X)) 101.64/27.03 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.03 active(U131(X)) -> U131(active(X)) 101.64/27.03 active(snd(X)) -> snd(active(X)) 101.64/27.03 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.03 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.03 active(U141(X)) -> U141(active(X)) 101.64/27.03 active(U151(X)) -> U151(active(X)) 101.64/27.03 active(U161(X)) -> U161(active(X)) 101.64/27.03 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.03 active(U172(X)) -> U172(active(X)) 101.64/27.03 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.03 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.03 active(U183(X)) -> U183(active(X)) 101.64/27.03 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.03 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.03 active(U193(X)) -> U193(active(X)) 101.64/27.03 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.03 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.03 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.03 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.03 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.03 active(U206(X)) -> U206(active(X)) 101.64/27.03 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.03 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.03 active(U211(X)) -> U211(active(X)) 101.64/27.03 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.03 active(U221(X)) -> U221(active(X)) 101.64/27.03 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.03 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.03 active(U232(X)) -> U232(active(X)) 101.64/27.03 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.03 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.03 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.03 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.03 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.03 active(U246(X)) -> U246(active(X)) 101.64/27.03 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.03 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.03 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.03 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.03 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.03 active(U256(X)) -> U256(active(X)) 101.64/27.03 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.03 active(U262(X)) -> U262(active(X)) 101.64/27.03 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.03 active(U272(X)) -> U272(active(X)) 101.64/27.03 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.03 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.03 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.03 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.03 active(s(X)) -> s(active(X)) 101.64/27.03 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.03 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.03 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.03 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.03 active(head(X)) -> head(active(X)) 101.64/27.03 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.03 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.03 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.03 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.03 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.03 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.03 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.03 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.03 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.03 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.03 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.03 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.03 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.03 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.03 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.03 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.03 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.03 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.03 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.03 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.03 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.03 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.03 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.03 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.03 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.03 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.03 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.03 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.03 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.03 active(fst(X)) -> fst(active(X)) 101.64/27.03 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.03 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.03 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.03 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.03 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.03 active(U46(X)) -> U46(active(X)) 101.64/27.03 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.03 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.03 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.03 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.03 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.03 active(U56(X)) -> U56(active(X)) 101.64/27.03 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.03 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.03 active(U63(X)) -> U63(active(X)) 101.64/27.03 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.03 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.03 active(U73(X)) -> U73(active(X)) 101.64/27.03 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.03 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.03 active(U83(X)) -> U83(active(X)) 101.64/27.03 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.03 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.03 active(U93(X)) -> U93(active(X)) 101.64/27.03 active(tail(X)) -> tail(active(X)) 101.64/27.03 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.03 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.03 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.03 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.03 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.03 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.03 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.03 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.03 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.03 U106(mark(X)) -> mark(U106(X)) 101.64/27.03 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.03 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.03 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.03 U112(mark(X)) -> mark(U112(X)) 101.64/27.03 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.04 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.04 U122(mark(X)) -> mark(U122(X)) 101.64/27.04 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.04 U131(mark(X)) -> mark(U131(X)) 101.64/27.04 snd(mark(X)) -> mark(snd(X)) 101.64/27.04 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.04 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.04 U141(mark(X)) -> mark(U141(X)) 101.64/27.04 U151(mark(X)) -> mark(U151(X)) 101.64/27.04 U161(mark(X)) -> mark(U161(X)) 101.64/27.04 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.04 U172(mark(X)) -> mark(U172(X)) 101.64/27.04 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.04 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.04 U183(mark(X)) -> mark(U183(X)) 101.64/27.04 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.04 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.04 U193(mark(X)) -> mark(U193(X)) 101.64/27.04 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.04 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.04 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.04 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.04 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.04 U206(mark(X)) -> mark(U206(X)) 101.64/27.04 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.04 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.04 U211(mark(X)) -> mark(U211(X)) 101.64/27.04 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.04 U221(mark(X)) -> mark(U221(X)) 101.64/27.04 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.04 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.04 U232(mark(X)) -> mark(U232(X)) 101.64/27.04 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.04 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.04 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.04 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.04 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.04 U246(mark(X)) -> mark(U246(X)) 101.64/27.04 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.04 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.04 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.04 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.04 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.04 U256(mark(X)) -> mark(U256(X)) 101.64/27.04 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.04 U262(mark(X)) -> mark(U262(X)) 101.64/27.04 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.04 U272(mark(X)) -> mark(U272(X)) 101.64/27.04 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.04 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.04 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.04 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.04 s(mark(X)) -> mark(s(X)) 101.64/27.04 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.04 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.04 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.04 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.04 head(mark(X)) -> mark(head(X)) 101.64/27.04 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.04 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.04 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.04 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.04 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.04 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.04 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.04 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.04 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.04 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.04 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.04 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.04 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.04 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.04 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.04 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.04 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.04 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.04 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.04 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.04 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.04 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.04 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.04 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.04 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.04 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.04 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.04 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.04 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.04 fst(mark(X)) -> mark(fst(X)) 101.64/27.04 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.04 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.04 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.04 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.04 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.04 U46(mark(X)) -> mark(U46(X)) 101.64/27.04 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.04 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.04 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.04 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.04 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.04 U56(mark(X)) -> mark(U56(X)) 101.64/27.04 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.04 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.04 U63(mark(X)) -> mark(U63(X)) 101.64/27.04 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.04 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.04 U73(mark(X)) -> mark(U73(X)) 101.64/27.04 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.04 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.04 U83(mark(X)) -> mark(U83(X)) 101.64/27.04 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.04 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.04 U93(mark(X)) -> mark(U93(X)) 101.64/27.04 tail(mark(X)) -> mark(tail(X)) 101.64/27.04 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.04 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.04 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.04 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.04 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(tt) -> ok(tt) 101.64/27.04 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.04 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.04 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.04 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.04 proper(U106(X)) -> U106(proper(X)) 101.64/27.04 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.04 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.04 proper(U112(X)) -> U112(proper(X)) 101.64/27.04 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.04 proper(U122(X)) -> U122(proper(X)) 101.64/27.04 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U131(X)) -> U131(proper(X)) 101.64/27.04 proper(snd(X)) -> snd(proper(X)) 101.64/27.04 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.04 proper(U141(X)) -> U141(proper(X)) 101.64/27.04 proper(U151(X)) -> U151(proper(X)) 101.64/27.04 proper(U161(X)) -> U161(proper(X)) 101.64/27.04 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.04 proper(U172(X)) -> U172(proper(X)) 101.64/27.04 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.04 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.04 proper(U183(X)) -> U183(proper(X)) 101.64/27.04 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.04 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.04 proper(U193(X)) -> U193(proper(X)) 101.64/27.04 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.04 proper(U206(X)) -> U206(proper(X)) 101.64/27.04 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U211(X)) -> U211(proper(X)) 101.64/27.04 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U221(X)) -> U221(proper(X)) 101.64/27.04 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.04 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.04 proper(U232(X)) -> U232(proper(X)) 101.64/27.04 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.04 proper(U246(X)) -> U246(proper(X)) 101.64/27.04 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.04 proper(U256(X)) -> U256(proper(X)) 101.64/27.04 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.04 proper(U262(X)) -> U262(proper(X)) 101.64/27.04 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.04 proper(U272(X)) -> U272(proper(X)) 101.64/27.04 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.04 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.04 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.04 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.04 proper(s(X)) -> s(proper(X)) 101.64/27.04 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(head(X)) -> head(proper(X)) 101.64/27.04 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.04 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.04 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.04 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.04 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.04 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.04 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.04 proper(nil) -> ok(nil) 101.64/27.04 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.04 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.04 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.04 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.04 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.04 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.04 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(fst(X)) -> fst(proper(X)) 101.64/27.04 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.04 proper(U46(X)) -> U46(proper(X)) 101.64/27.04 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.04 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.04 proper(U56(X)) -> U56(proper(X)) 101.64/27.04 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.04 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.04 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.04 proper(U63(X)) -> U63(proper(X)) 101.64/27.04 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.04 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.04 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.04 proper(U73(X)) -> U73(proper(X)) 101.64/27.04 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.04 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.04 proper(U83(X)) -> U83(proper(X)) 101.64/27.04 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.04 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.04 proper(U93(X)) -> U93(proper(X)) 101.64/27.04 proper(tail(X)) -> tail(proper(X)) 101.64/27.04 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.04 proper(0') -> ok(0') 101.64/27.04 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.04 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.04 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.04 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.04 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.04 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.04 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.04 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.04 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.04 U106(ok(X)) -> ok(U106(X)) 101.64/27.04 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.04 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.04 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.04 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.04 U112(ok(X)) -> ok(U112(X)) 101.64/27.04 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.04 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.04 U122(ok(X)) -> ok(U122(X)) 101.64/27.04 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.04 U131(ok(X)) -> ok(U131(X)) 101.64/27.04 snd(ok(X)) -> ok(snd(X)) 101.64/27.04 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.04 U141(ok(X)) -> ok(U141(X)) 101.64/27.04 U151(ok(X)) -> ok(U151(X)) 101.64/27.04 U161(ok(X)) -> ok(U161(X)) 101.64/27.04 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.04 U172(ok(X)) -> ok(U172(X)) 101.64/27.04 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.04 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.04 U183(ok(X)) -> ok(U183(X)) 101.64/27.04 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.04 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.04 U193(ok(X)) -> ok(U193(X)) 101.64/27.04 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.04 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.04 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.04 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.04 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.04 U206(ok(X)) -> ok(U206(X)) 101.64/27.04 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.04 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.04 U211(ok(X)) -> ok(U211(X)) 101.64/27.04 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.04 U221(ok(X)) -> ok(U221(X)) 101.64/27.04 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.04 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.04 U232(ok(X)) -> ok(U232(X)) 101.64/27.04 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.04 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.04 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.04 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.04 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.04 U246(ok(X)) -> ok(U246(X)) 101.64/27.04 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.04 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.04 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.04 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.04 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.04 U256(ok(X)) -> ok(U256(X)) 101.64/27.04 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.04 U262(ok(X)) -> ok(U262(X)) 101.64/27.04 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.04 U272(ok(X)) -> ok(U272(X)) 101.64/27.04 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.04 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.04 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.04 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.04 s(ok(X)) -> ok(s(X)) 101.64/27.04 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.04 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.04 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.04 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.04 head(ok(X)) -> ok(head(X)) 101.64/27.04 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.04 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.04 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.04 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.04 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.04 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.04 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.04 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.04 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.04 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.04 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.04 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.04 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.04 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.04 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.04 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.04 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.04 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.04 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.04 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.04 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.04 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.04 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.04 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.04 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.04 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.04 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.04 fst(ok(X)) -> ok(fst(X)) 101.64/27.04 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.04 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.04 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.04 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.04 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.04 U46(ok(X)) -> ok(U46(X)) 101.64/27.04 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.04 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.04 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.04 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.04 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.04 U56(ok(X)) -> ok(U56(X)) 101.64/27.04 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.04 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.04 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.04 U63(ok(X)) -> ok(U63(X)) 101.64/27.04 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.04 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.04 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.04 U73(ok(X)) -> ok(U73(X)) 101.64/27.04 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.04 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.04 U83(ok(X)) -> ok(U83(X)) 101.64/27.04 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.04 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.04 U93(ok(X)) -> ok(U93(X)) 101.64/27.04 tail(ok(X)) -> ok(tail(X)) 101.64/27.04 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.04 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.04 top(mark(X)) -> top(proper(X)) 101.64/27.04 top(ok(X)) -> top(active(X)) 101.64/27.04 101.64/27.04 Types: 101.64/27.04 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 tt :: tt:mark:nil:0':ok 101.64/27.04 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 nil :: tt:mark:nil:0':ok 101.64/27.04 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 0' :: tt:mark:nil:0':ok 101.64/27.04 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.04 top :: tt:mark:nil:0':ok -> top 101.64/27.04 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.04 hole_top2_0 :: top 101.64/27.04 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.04 101.64/27.04 101.64/27.04 Lemmas: 101.64/27.04 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.04 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.04 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.04 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.04 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.04 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.04 101.64/27.04 101.64/27.04 Generator Equations: 101.64/27.04 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.04 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.04 101.64/27.04 101.64/27.04 The following defined symbols remain to be analysed: 101.64/27.04 U112, active, U13, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.04 101.64/27.04 They will be analysed ascendingly in the following order: 101.64/27.04 U112 < active 101.64/27.04 U13 < active 101.64/27.04 U122 < active 101.64/27.04 U14 < active 101.64/27.04 snd < active 101.64/27.04 splitAt < active 101.64/27.04 U172 < active 101.64/27.04 U182 < active 101.64/27.04 U183 < active 101.64/27.04 U192 < active 101.64/27.04 U193 < active 101.64/27.04 U202 < active 101.64/27.04 U203 < active 101.64/27.04 U204 < active 101.64/27.04 U205 < active 101.64/27.04 U206 < active 101.64/27.04 U22 < active 101.64/27.04 U23 < active 101.64/27.04 U24 < active 101.64/27.04 U232 < active 101.64/27.04 U242 < active 101.64/27.04 U243 < active 101.64/27.04 U244 < active 101.64/27.04 U245 < active 101.64/27.04 U246 < active 101.64/27.04 U252 < active 101.64/27.04 U253 < active 101.64/27.04 U254 < active 101.64/27.04 U255 < active 101.64/27.04 U256 < active 101.64/27.04 U262 < active 101.64/27.04 U272 < active 101.64/27.04 U282 < active 101.64/27.04 cons < active 101.64/27.04 natsFrom < active 101.64/27.04 s < active 101.64/27.04 U292 < active 101.64/27.04 U293 < active 101.64/27.04 U294 < active 101.64/27.04 head < active 101.64/27.04 afterNth < active 101.64/27.04 U302 < active 101.64/27.04 U303 < active 101.64/27.04 U304 < active 101.64/27.04 U32 < active 101.64/27.04 U312 < active 101.64/27.04 pair < active 101.64/27.04 U33 < active 101.64/27.04 U322 < active 101.64/27.04 U323 < active 101.64/27.04 U324 < active 101.64/27.04 U325 < active 101.64/27.04 U326 < active 101.64/27.04 U327 < active 101.64/27.04 U34 < active 101.64/27.04 U332 < active 101.64/27.04 U333 < active 101.64/27.04 U334 < active 101.64/27.04 U342 < active 101.64/27.04 U343 < active 101.64/27.04 U344 < active 101.64/27.04 fst < active 101.64/27.04 U42 < active 101.64/27.04 U43 < active 101.64/27.04 U44 < active 101.64/27.04 U45 < active 101.64/27.04 U46 < active 101.64/27.04 U52 < active 101.64/27.04 U53 < active 101.64/27.04 U54 < active 101.64/27.04 U55 < active 101.64/27.04 U56 < active 101.64/27.04 U62 < active 101.64/27.04 isPLNatKind < active 101.64/27.04 U63 < active 101.64/27.04 isPLNat < active 101.64/27.04 U72 < active 101.64/27.04 U73 < active 101.64/27.04 U82 < active 101.64/27.04 U83 < active 101.64/27.04 U92 < active 101.64/27.04 U93 < active 101.64/27.04 U11 < active 101.64/27.04 U21 < active 101.64/27.04 U31 < active 101.64/27.04 U41 < active 101.64/27.04 U51 < active 101.64/27.04 U61 < active 101.64/27.04 U71 < active 101.64/27.04 U81 < active 101.64/27.04 U91 < active 101.64/27.04 U101 < active 101.64/27.04 U111 < active 101.64/27.04 U121 < active 101.64/27.04 U131 < active 101.64/27.04 U141 < active 101.64/27.04 U151 < active 101.64/27.04 U161 < active 101.64/27.04 U171 < active 101.64/27.04 U181 < active 101.64/27.04 U191 < active 101.64/27.04 U201 < active 101.64/27.04 U211 < active 101.64/27.04 U221 < active 101.64/27.04 U231 < active 101.64/27.04 U241 < active 101.64/27.04 U251 < active 101.64/27.04 U261 < active 101.64/27.04 U271 < active 101.64/27.04 U281 < active 101.64/27.04 U291 < active 101.64/27.04 U301 < active 101.64/27.04 U311 < active 101.64/27.04 U321 < active 101.64/27.04 U331 < active 101.64/27.04 U341 < active 101.64/27.04 tail < active 101.64/27.04 take < active 101.64/27.04 sel < active 101.64/27.04 active < top 101.64/27.04 U112 < proper 101.64/27.04 U13 < proper 101.64/27.04 U122 < proper 101.64/27.04 U14 < proper 101.64/27.04 snd < proper 101.64/27.04 splitAt < proper 101.64/27.04 U172 < proper 101.64/27.04 U182 < proper 101.64/27.04 U183 < proper 101.64/27.04 U192 < proper 101.64/27.04 U193 < proper 101.64/27.04 U202 < proper 101.64/27.04 U203 < proper 101.64/27.04 U204 < proper 101.64/27.04 U205 < proper 101.64/27.04 U206 < proper 101.64/27.04 U22 < proper 101.64/27.04 U23 < proper 101.64/27.04 U24 < proper 101.64/27.04 U232 < proper 101.64/27.04 U242 < proper 101.64/27.04 U243 < proper 101.64/27.04 U244 < proper 101.64/27.04 U245 < proper 101.64/27.04 U246 < proper 101.64/27.04 U252 < proper 101.64/27.04 U253 < proper 101.64/27.04 U254 < proper 101.64/27.04 U255 < proper 101.64/27.04 U256 < proper 101.64/27.04 U262 < proper 101.64/27.04 U272 < proper 101.64/27.04 U282 < proper 101.64/27.04 cons < proper 101.64/27.04 natsFrom < proper 101.64/27.04 s < proper 101.64/27.04 U292 < proper 101.64/27.04 U293 < proper 101.64/27.04 U294 < proper 101.64/27.04 head < proper 101.64/27.04 afterNth < proper 101.64/27.04 U302 < proper 101.64/27.04 U303 < proper 101.64/27.04 U304 < proper 101.64/27.04 U32 < proper 101.64/27.04 U312 < proper 101.64/27.04 pair < proper 101.64/27.04 U33 < proper 101.64/27.04 U322 < proper 101.64/27.04 U323 < proper 101.64/27.04 U324 < proper 101.64/27.04 U325 < proper 101.64/27.04 U326 < proper 101.64/27.04 U327 < proper 101.64/27.04 U34 < proper 101.64/27.04 U332 < proper 101.64/27.04 U333 < proper 101.64/27.04 U334 < proper 101.64/27.04 U342 < proper 101.64/27.04 U343 < proper 101.64/27.04 U344 < proper 101.64/27.04 fst < proper 101.64/27.04 U42 < proper 101.64/27.04 U43 < proper 101.64/27.04 U44 < proper 101.64/27.04 U45 < proper 101.64/27.04 U46 < proper 101.64/27.04 U52 < proper 101.64/27.04 U53 < proper 101.64/27.04 U54 < proper 101.64/27.04 U55 < proper 101.64/27.04 U56 < proper 101.64/27.04 U62 < proper 101.64/27.04 isPLNatKind < proper 101.64/27.04 U63 < proper 101.64/27.04 isPLNat < proper 101.64/27.04 U72 < proper 101.64/27.04 U73 < proper 101.64/27.04 U82 < proper 101.64/27.04 U83 < proper 101.64/27.04 U92 < proper 101.64/27.04 U93 < proper 101.64/27.04 U11 < proper 101.64/27.04 U21 < proper 101.64/27.04 U31 < proper 101.64/27.04 U41 < proper 101.64/27.04 U51 < proper 101.64/27.04 U61 < proper 101.64/27.04 U71 < proper 101.64/27.04 U81 < proper 101.64/27.04 U91 < proper 101.64/27.04 U101 < proper 101.64/27.04 U111 < proper 101.64/27.04 U121 < proper 101.64/27.04 U131 < proper 101.64/27.04 U141 < proper 101.64/27.04 U151 < proper 101.64/27.04 U161 < proper 101.64/27.04 U171 < proper 101.64/27.04 U181 < proper 101.64/27.04 U191 < proper 101.64/27.04 U201 < proper 101.64/27.04 U211 < proper 101.64/27.04 U221 < proper 101.64/27.04 U231 < proper 101.64/27.04 U241 < proper 101.64/27.04 U251 < proper 101.64/27.04 U261 < proper 101.64/27.04 U271 < proper 101.64/27.04 U281 < proper 101.64/27.04 U291 < proper 101.64/27.04 U301 < proper 101.64/27.04 U311 < proper 101.64/27.04 U321 < proper 101.64/27.04 U331 < proper 101.64/27.04 U341 < proper 101.64/27.04 tail < proper 101.64/27.04 take < proper 101.64/27.04 sel < proper 101.64/27.04 proper < top 101.64/27.04 101.64/27.04 ---------------------------------------- 101.64/27.04 101.64/27.04 (41) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.04 Proved the following rewrite lemma: 101.64/27.04 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.04 101.64/27.04 Induction Base: 101.64/27.04 U112(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.04 101.64/27.04 Induction Step: 101.64/27.04 U112(gen_tt:mark:nil:0':ok3_0(+(1, +(n87757_0, 1)))) ->_R^Omega(1) 101.64/27.04 mark(U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0)))) ->_IH 101.64/27.04 mark(*4_0) 101.64/27.04 101.64/27.04 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.04 ---------------------------------------- 101.64/27.04 101.64/27.04 (42) 101.64/27.04 Obligation: 101.64/27.04 TRS: 101.64/27.04 Rules: 101.64/27.04 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.04 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.04 active(U106(tt)) -> mark(tt) 101.64/27.04 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.04 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.04 active(U112(tt)) -> mark(tt) 101.64/27.04 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.04 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.04 active(U122(tt)) -> mark(tt) 101.64/27.04 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.04 active(U131(tt)) -> mark(tt) 101.64/27.04 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.04 active(U141(tt)) -> mark(tt) 101.64/27.04 active(U151(tt)) -> mark(tt) 101.64/27.04 active(U161(tt)) -> mark(tt) 101.64/27.04 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.04 active(U172(tt)) -> mark(tt) 101.64/27.04 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.04 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.04 active(U183(tt)) -> mark(tt) 101.64/27.04 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.04 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.04 active(U193(tt)) -> mark(tt) 101.64/27.04 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.04 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.04 active(U206(tt)) -> mark(tt) 101.64/27.04 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.04 active(U211(tt)) -> mark(tt) 101.64/27.04 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.04 active(U221(tt)) -> mark(tt) 101.64/27.04 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.04 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.04 active(U232(tt)) -> mark(tt) 101.64/27.04 active(U24(tt, X)) -> mark(X) 101.64/27.04 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.04 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.04 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.04 active(U246(tt)) -> mark(tt) 101.64/27.04 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.04 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.04 active(U256(tt)) -> mark(tt) 101.64/27.04 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.04 active(U262(tt)) -> mark(tt) 101.64/27.04 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.04 active(U272(tt)) -> mark(tt) 101.64/27.04 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.04 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.04 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.04 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.04 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.04 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.04 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.04 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.04 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.04 active(U304(tt, Y)) -> mark(Y) 101.64/27.04 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.04 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.04 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.04 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.04 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.04 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.04 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.04 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.04 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.04 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.04 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.04 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.04 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.04 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.04 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.04 active(U334(tt, XS)) -> mark(XS) 101.64/27.04 active(U34(tt, N)) -> mark(N) 101.64/27.04 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.04 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.04 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.04 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.04 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.04 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.04 active(U46(tt)) -> mark(tt) 101.64/27.04 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.04 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.04 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.04 active(U56(tt)) -> mark(tt) 101.64/27.04 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.04 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.04 active(U63(tt)) -> mark(tt) 101.64/27.04 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.04 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.04 active(U73(tt)) -> mark(tt) 101.64/27.04 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.04 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.04 active(U83(tt)) -> mark(tt) 101.64/27.04 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.04 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.04 active(U93(tt)) -> mark(tt) 101.64/27.04 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.04 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.04 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.04 active(isLNat(nil)) -> mark(tt) 101.64/27.04 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.04 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.04 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.04 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.04 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(isLNatKind(nil)) -> mark(tt) 101.64/27.04 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.04 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.04 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.04 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.04 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.04 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.04 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.04 active(isNatural(0')) -> mark(tt) 101.64/27.04 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.04 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.04 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(isNaturalKind(0')) -> mark(tt) 101.64/27.04 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.04 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.04 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.04 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.04 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.04 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.04 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.04 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.04 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.04 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.04 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.04 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.04 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.04 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.04 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.04 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.04 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.04 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.04 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.04 active(U106(X)) -> U106(active(X)) 101.64/27.04 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.04 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.04 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.04 active(U112(X)) -> U112(active(X)) 101.64/27.04 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.04 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.04 active(U122(X)) -> U122(active(X)) 101.64/27.04 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.04 active(U131(X)) -> U131(active(X)) 101.64/27.04 active(snd(X)) -> snd(active(X)) 101.64/27.04 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.04 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.04 active(U141(X)) -> U141(active(X)) 101.64/27.04 active(U151(X)) -> U151(active(X)) 101.64/27.04 active(U161(X)) -> U161(active(X)) 101.64/27.04 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.04 active(U172(X)) -> U172(active(X)) 101.64/27.04 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.04 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.04 active(U183(X)) -> U183(active(X)) 101.64/27.04 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.04 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.04 active(U193(X)) -> U193(active(X)) 101.64/27.04 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.04 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.04 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.04 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.04 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.04 active(U206(X)) -> U206(active(X)) 101.64/27.04 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.04 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.04 active(U211(X)) -> U211(active(X)) 101.64/27.04 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.04 active(U221(X)) -> U221(active(X)) 101.64/27.04 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.04 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.04 active(U232(X)) -> U232(active(X)) 101.64/27.04 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.04 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.04 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.04 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.04 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.04 active(U246(X)) -> U246(active(X)) 101.64/27.04 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.04 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.04 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.04 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.04 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.04 active(U256(X)) -> U256(active(X)) 101.64/27.04 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.04 active(U262(X)) -> U262(active(X)) 101.64/27.04 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.04 active(U272(X)) -> U272(active(X)) 101.64/27.04 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.04 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.04 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.04 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.04 active(s(X)) -> s(active(X)) 101.64/27.04 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.04 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.04 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.04 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.04 active(head(X)) -> head(active(X)) 101.64/27.04 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.04 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.04 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.04 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.04 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.04 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.04 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.04 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.04 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.04 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.04 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.04 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.04 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.04 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.04 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.04 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.04 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.04 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.04 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.04 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.04 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.04 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.04 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.04 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.04 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.04 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.04 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.04 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.04 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.04 active(fst(X)) -> fst(active(X)) 101.64/27.04 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.04 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.04 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.04 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.04 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.04 active(U46(X)) -> U46(active(X)) 101.64/27.04 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.04 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.04 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.04 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.04 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.04 active(U56(X)) -> U56(active(X)) 101.64/27.04 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.04 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.04 active(U63(X)) -> U63(active(X)) 101.64/27.04 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.04 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.04 active(U73(X)) -> U73(active(X)) 101.64/27.04 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.04 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.04 active(U83(X)) -> U83(active(X)) 101.64/27.04 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.04 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.04 active(U93(X)) -> U93(active(X)) 101.64/27.04 active(tail(X)) -> tail(active(X)) 101.64/27.04 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.04 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.04 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.04 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.04 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.04 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.04 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.04 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.04 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.04 U106(mark(X)) -> mark(U106(X)) 101.64/27.04 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.04 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.04 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.04 U112(mark(X)) -> mark(U112(X)) 101.64/27.04 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.04 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.04 U122(mark(X)) -> mark(U122(X)) 101.64/27.04 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.04 U131(mark(X)) -> mark(U131(X)) 101.64/27.04 snd(mark(X)) -> mark(snd(X)) 101.64/27.04 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.04 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.04 U141(mark(X)) -> mark(U141(X)) 101.64/27.04 U151(mark(X)) -> mark(U151(X)) 101.64/27.04 U161(mark(X)) -> mark(U161(X)) 101.64/27.04 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.04 U172(mark(X)) -> mark(U172(X)) 101.64/27.04 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.04 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.04 U183(mark(X)) -> mark(U183(X)) 101.64/27.04 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.04 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.04 U193(mark(X)) -> mark(U193(X)) 101.64/27.04 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.04 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.04 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.04 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.04 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.04 U206(mark(X)) -> mark(U206(X)) 101.64/27.04 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.04 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.04 U211(mark(X)) -> mark(U211(X)) 101.64/27.04 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.04 U221(mark(X)) -> mark(U221(X)) 101.64/27.04 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.04 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.04 U232(mark(X)) -> mark(U232(X)) 101.64/27.04 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.04 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.04 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.04 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.04 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.04 U246(mark(X)) -> mark(U246(X)) 101.64/27.04 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.04 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.04 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.04 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.04 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.04 U256(mark(X)) -> mark(U256(X)) 101.64/27.04 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.04 U262(mark(X)) -> mark(U262(X)) 101.64/27.04 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.04 U272(mark(X)) -> mark(U272(X)) 101.64/27.04 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.04 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.04 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.04 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.04 s(mark(X)) -> mark(s(X)) 101.64/27.04 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.04 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.04 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.04 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.04 head(mark(X)) -> mark(head(X)) 101.64/27.04 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.04 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.04 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.04 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.04 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.04 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.04 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.04 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.04 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.04 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.04 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.04 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.04 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.04 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.04 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.04 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.04 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.04 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.04 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.04 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.04 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.04 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.04 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.04 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.04 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.04 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.04 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.04 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.04 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.04 fst(mark(X)) -> mark(fst(X)) 101.64/27.04 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.04 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.04 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.04 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.04 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.04 U46(mark(X)) -> mark(U46(X)) 101.64/27.04 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.04 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.04 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.04 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.04 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.04 U56(mark(X)) -> mark(U56(X)) 101.64/27.04 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.04 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.06 U63(mark(X)) -> mark(U63(X)) 101.64/27.06 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.06 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.06 U73(mark(X)) -> mark(U73(X)) 101.64/27.06 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.06 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.06 U83(mark(X)) -> mark(U83(X)) 101.64/27.06 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.06 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.06 U93(mark(X)) -> mark(U93(X)) 101.64/27.06 tail(mark(X)) -> mark(tail(X)) 101.64/27.06 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.06 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.06 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.06 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.06 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(tt) -> ok(tt) 101.64/27.06 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.06 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.06 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.06 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.06 proper(U106(X)) -> U106(proper(X)) 101.64/27.06 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.06 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.06 proper(U112(X)) -> U112(proper(X)) 101.64/27.06 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.06 proper(U122(X)) -> U122(proper(X)) 101.64/27.06 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U131(X)) -> U131(proper(X)) 101.64/27.06 proper(snd(X)) -> snd(proper(X)) 101.64/27.06 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.06 proper(U141(X)) -> U141(proper(X)) 101.64/27.06 proper(U151(X)) -> U151(proper(X)) 101.64/27.06 proper(U161(X)) -> U161(proper(X)) 101.64/27.06 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.06 proper(U172(X)) -> U172(proper(X)) 101.64/27.06 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.06 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.06 proper(U183(X)) -> U183(proper(X)) 101.64/27.06 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.06 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.06 proper(U193(X)) -> U193(proper(X)) 101.64/27.06 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.06 proper(U206(X)) -> U206(proper(X)) 101.64/27.06 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U211(X)) -> U211(proper(X)) 101.64/27.06 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U221(X)) -> U221(proper(X)) 101.64/27.06 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.06 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.06 proper(U232(X)) -> U232(proper(X)) 101.64/27.06 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.06 proper(U246(X)) -> U246(proper(X)) 101.64/27.06 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.06 proper(U256(X)) -> U256(proper(X)) 101.64/27.06 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.06 proper(U262(X)) -> U262(proper(X)) 101.64/27.06 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.06 proper(U272(X)) -> U272(proper(X)) 101.64/27.06 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.06 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.06 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.06 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.06 proper(s(X)) -> s(proper(X)) 101.64/27.06 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(head(X)) -> head(proper(X)) 101.64/27.06 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.06 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.06 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.06 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.06 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.06 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.06 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.06 proper(nil) -> ok(nil) 101.64/27.06 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.06 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.06 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.06 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.06 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.06 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.06 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(fst(X)) -> fst(proper(X)) 101.64/27.06 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.06 proper(U46(X)) -> U46(proper(X)) 101.64/27.06 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.06 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.06 proper(U56(X)) -> U56(proper(X)) 101.64/27.06 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.06 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.06 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.06 proper(U63(X)) -> U63(proper(X)) 101.64/27.06 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.06 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.06 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.06 proper(U73(X)) -> U73(proper(X)) 101.64/27.06 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.06 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.06 proper(U83(X)) -> U83(proper(X)) 101.64/27.06 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.06 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.06 proper(U93(X)) -> U93(proper(X)) 101.64/27.06 proper(tail(X)) -> tail(proper(X)) 101.64/27.06 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.06 proper(0') -> ok(0') 101.64/27.06 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.06 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.06 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.06 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.06 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.06 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.06 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.06 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.06 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.06 U106(ok(X)) -> ok(U106(X)) 101.64/27.06 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.06 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.06 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.06 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.06 U112(ok(X)) -> ok(U112(X)) 101.64/27.06 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.06 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.06 U122(ok(X)) -> ok(U122(X)) 101.64/27.06 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.06 U131(ok(X)) -> ok(U131(X)) 101.64/27.06 snd(ok(X)) -> ok(snd(X)) 101.64/27.06 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.06 U141(ok(X)) -> ok(U141(X)) 101.64/27.06 U151(ok(X)) -> ok(U151(X)) 101.64/27.06 U161(ok(X)) -> ok(U161(X)) 101.64/27.06 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.06 U172(ok(X)) -> ok(U172(X)) 101.64/27.06 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.06 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.06 U183(ok(X)) -> ok(U183(X)) 101.64/27.06 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.06 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.06 U193(ok(X)) -> ok(U193(X)) 101.64/27.06 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.06 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.06 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.06 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.06 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.06 U206(ok(X)) -> ok(U206(X)) 101.64/27.06 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.06 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.06 U211(ok(X)) -> ok(U211(X)) 101.64/27.06 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.06 U221(ok(X)) -> ok(U221(X)) 101.64/27.06 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.06 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.06 U232(ok(X)) -> ok(U232(X)) 101.64/27.06 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.06 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.06 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.06 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.06 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.06 U246(ok(X)) -> ok(U246(X)) 101.64/27.06 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.06 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.06 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.06 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.06 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.06 U256(ok(X)) -> ok(U256(X)) 101.64/27.06 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.06 U262(ok(X)) -> ok(U262(X)) 101.64/27.06 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.06 U272(ok(X)) -> ok(U272(X)) 101.64/27.06 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.06 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.06 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.06 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.06 s(ok(X)) -> ok(s(X)) 101.64/27.06 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.06 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.06 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.06 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.06 head(ok(X)) -> ok(head(X)) 101.64/27.06 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.06 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.06 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.06 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.06 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.06 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.06 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.06 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.06 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.06 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.06 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.06 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.06 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.06 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.06 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.06 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.06 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.06 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.06 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.06 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.06 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.06 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.06 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.06 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.06 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.06 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.06 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.06 fst(ok(X)) -> ok(fst(X)) 101.64/27.06 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.06 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.06 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.06 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.06 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.06 U46(ok(X)) -> ok(U46(X)) 101.64/27.06 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.06 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.06 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.06 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.06 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.06 U56(ok(X)) -> ok(U56(X)) 101.64/27.06 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.06 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.06 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.06 U63(ok(X)) -> ok(U63(X)) 101.64/27.06 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.06 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.06 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.06 U73(ok(X)) -> ok(U73(X)) 101.64/27.06 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.06 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.06 U83(ok(X)) -> ok(U83(X)) 101.64/27.06 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.06 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.06 U93(ok(X)) -> ok(U93(X)) 101.64/27.06 tail(ok(X)) -> ok(tail(X)) 101.64/27.06 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.06 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.06 top(mark(X)) -> top(proper(X)) 101.64/27.06 top(ok(X)) -> top(active(X)) 101.64/27.06 101.64/27.06 Types: 101.64/27.06 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 tt :: tt:mark:nil:0':ok 101.64/27.06 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 nil :: tt:mark:nil:0':ok 101.64/27.06 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 0' :: tt:mark:nil:0':ok 101.64/27.06 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.06 top :: tt:mark:nil:0':ok -> top 101.64/27.06 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.06 hole_top2_0 :: top 101.64/27.06 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.06 101.64/27.06 101.64/27.06 Lemmas: 101.64/27.06 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.06 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.06 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.06 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.06 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.06 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.06 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.06 101.64/27.06 101.64/27.06 Generator Equations: 101.64/27.06 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.06 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.06 101.64/27.06 101.64/27.06 The following defined symbols remain to be analysed: 101.64/27.06 U13, active, U122, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.06 101.64/27.06 They will be analysed ascendingly in the following order: 101.64/27.06 U13 < active 101.64/27.06 U122 < active 101.64/27.06 U14 < active 101.64/27.06 snd < active 101.64/27.06 splitAt < active 101.64/27.06 U172 < active 101.64/27.06 U182 < active 101.64/27.06 U183 < active 101.64/27.06 U192 < active 101.64/27.06 U193 < active 101.64/27.06 U202 < active 101.64/27.06 U203 < active 101.64/27.06 U204 < active 101.64/27.06 U205 < active 101.64/27.06 U206 < active 101.64/27.06 U22 < active 101.64/27.06 U23 < active 101.64/27.06 U24 < active 101.64/27.06 U232 < active 101.64/27.06 U242 < active 101.64/27.06 U243 < active 101.64/27.06 U244 < active 101.64/27.06 U245 < active 101.64/27.06 U246 < active 101.64/27.06 U252 < active 101.64/27.06 U253 < active 101.64/27.06 U254 < active 101.64/27.06 U255 < active 101.64/27.06 U256 < active 101.64/27.06 U262 < active 101.64/27.06 U272 < active 101.64/27.06 U282 < active 101.64/27.06 cons < active 101.64/27.06 natsFrom < active 101.64/27.06 s < active 101.64/27.06 U292 < active 101.64/27.06 U293 < active 101.64/27.06 U294 < active 101.64/27.06 head < active 101.64/27.06 afterNth < active 101.64/27.06 U302 < active 101.64/27.06 U303 < active 101.64/27.06 U304 < active 101.64/27.06 U32 < active 101.64/27.06 U312 < active 101.64/27.06 pair < active 101.64/27.06 U33 < active 101.64/27.06 U322 < active 101.64/27.06 U323 < active 101.64/27.06 U324 < active 101.64/27.06 U325 < active 101.64/27.06 U326 < active 101.64/27.06 U327 < active 101.64/27.06 U34 < active 101.64/27.06 U332 < active 101.64/27.06 U333 < active 101.64/27.06 U334 < active 101.64/27.06 U342 < active 101.64/27.06 U343 < active 101.64/27.06 U344 < active 101.64/27.06 fst < active 101.64/27.06 U42 < active 101.64/27.06 U43 < active 101.64/27.06 U44 < active 101.64/27.06 U45 < active 101.64/27.06 U46 < active 101.64/27.06 U52 < active 101.64/27.06 U53 < active 101.64/27.06 U54 < active 101.64/27.06 U55 < active 101.64/27.06 U56 < active 101.64/27.06 U62 < active 101.64/27.06 isPLNatKind < active 101.64/27.06 U63 < active 101.64/27.06 isPLNat < active 101.64/27.06 U72 < active 101.64/27.06 U73 < active 101.64/27.06 U82 < active 101.64/27.06 U83 < active 101.64/27.06 U92 < active 101.64/27.06 U93 < active 101.64/27.06 U11 < active 101.64/27.06 U21 < active 101.64/27.06 U31 < active 101.64/27.06 U41 < active 101.64/27.06 U51 < active 101.64/27.06 U61 < active 101.64/27.06 U71 < active 101.64/27.06 U81 < active 101.64/27.06 U91 < active 101.64/27.06 U101 < active 101.64/27.06 U111 < active 101.64/27.06 U121 < active 101.64/27.06 U131 < active 101.64/27.06 U141 < active 101.64/27.06 U151 < active 101.64/27.06 U161 < active 101.64/27.06 U171 < active 101.64/27.06 U181 < active 101.64/27.06 U191 < active 101.64/27.06 U201 < active 101.64/27.06 U211 < active 101.64/27.06 U221 < active 101.64/27.06 U231 < active 101.64/27.06 U241 < active 101.64/27.06 U251 < active 101.64/27.06 U261 < active 101.64/27.06 U271 < active 101.64/27.06 U281 < active 101.64/27.06 U291 < active 101.64/27.06 U301 < active 101.64/27.06 U311 < active 101.64/27.06 U321 < active 101.64/27.06 U331 < active 101.64/27.06 U341 < active 101.64/27.06 tail < active 101.64/27.06 take < active 101.64/27.06 sel < active 101.64/27.06 active < top 101.64/27.06 U13 < proper 101.64/27.06 U122 < proper 101.64/27.06 U14 < proper 101.64/27.06 snd < proper 101.64/27.06 splitAt < proper 101.64/27.06 U172 < proper 101.64/27.06 U182 < proper 101.64/27.06 U183 < proper 101.64/27.06 U192 < proper 101.64/27.06 U193 < proper 101.64/27.06 U202 < proper 101.64/27.06 U203 < proper 101.64/27.06 U204 < proper 101.64/27.06 U205 < proper 101.64/27.06 U206 < proper 101.64/27.06 U22 < proper 101.64/27.06 U23 < proper 101.64/27.06 U24 < proper 101.64/27.06 U232 < proper 101.64/27.06 U242 < proper 101.64/27.06 U243 < proper 101.64/27.06 U244 < proper 101.64/27.06 U245 < proper 101.64/27.06 U246 < proper 101.64/27.06 U252 < proper 101.64/27.06 U253 < proper 101.64/27.06 U254 < proper 101.64/27.06 U255 < proper 101.64/27.06 U256 < proper 101.64/27.06 U262 < proper 101.64/27.06 U272 < proper 101.64/27.06 U282 < proper 101.64/27.06 cons < proper 101.64/27.06 natsFrom < proper 101.64/27.06 s < proper 101.64/27.06 U292 < proper 101.64/27.06 U293 < proper 101.64/27.06 U294 < proper 101.64/27.06 head < proper 101.64/27.06 afterNth < proper 101.64/27.06 U302 < proper 101.64/27.06 U303 < proper 101.64/27.06 U304 < proper 101.64/27.06 U32 < proper 101.64/27.06 U312 < proper 101.64/27.06 pair < proper 101.64/27.06 U33 < proper 101.64/27.06 U322 < proper 101.64/27.06 U323 < proper 101.64/27.06 U324 < proper 101.64/27.06 U325 < proper 101.64/27.06 U326 < proper 101.64/27.06 U327 < proper 101.64/27.06 U34 < proper 101.64/27.06 U332 < proper 101.64/27.06 U333 < proper 101.64/27.06 U334 < proper 101.64/27.06 U342 < proper 101.64/27.06 U343 < proper 101.64/27.06 U344 < proper 101.64/27.06 fst < proper 101.64/27.06 U42 < proper 101.64/27.06 U43 < proper 101.64/27.06 U44 < proper 101.64/27.06 U45 < proper 101.64/27.06 U46 < proper 101.64/27.06 U52 < proper 101.64/27.06 U53 < proper 101.64/27.06 U54 < proper 101.64/27.06 U55 < proper 101.64/27.06 U56 < proper 101.64/27.06 U62 < proper 101.64/27.06 isPLNatKind < proper 101.64/27.06 U63 < proper 101.64/27.06 isPLNat < proper 101.64/27.06 U72 < proper 101.64/27.06 U73 < proper 101.64/27.06 U82 < proper 101.64/27.06 U83 < proper 101.64/27.06 U92 < proper 101.64/27.06 U93 < proper 101.64/27.06 U11 < proper 101.64/27.06 U21 < proper 101.64/27.06 U31 < proper 101.64/27.06 U41 < proper 101.64/27.06 U51 < proper 101.64/27.06 U61 < proper 101.64/27.06 U71 < proper 101.64/27.06 U81 < proper 101.64/27.06 U91 < proper 101.64/27.06 U101 < proper 101.64/27.06 U111 < proper 101.64/27.06 U121 < proper 101.64/27.06 U131 < proper 101.64/27.06 U141 < proper 101.64/27.06 U151 < proper 101.64/27.06 U161 < proper 101.64/27.06 U171 < proper 101.64/27.06 U181 < proper 101.64/27.06 U191 < proper 101.64/27.06 U201 < proper 101.64/27.06 U211 < proper 101.64/27.06 U221 < proper 101.64/27.06 U231 < proper 101.64/27.06 U241 < proper 101.64/27.06 U251 < proper 101.64/27.06 U261 < proper 101.64/27.06 U271 < proper 101.64/27.06 U281 < proper 101.64/27.06 U291 < proper 101.64/27.06 U301 < proper 101.64/27.06 U311 < proper 101.64/27.06 U321 < proper 101.64/27.06 U331 < proper 101.64/27.06 U341 < proper 101.64/27.06 tail < proper 101.64/27.06 take < proper 101.64/27.06 sel < proper 101.64/27.06 proper < top 101.64/27.06 101.64/27.06 ---------------------------------------- 101.64/27.06 101.64/27.06 (43) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.06 Proved the following rewrite lemma: 101.64/27.06 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.06 101.64/27.06 Induction Base: 101.64/27.06 U13(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.64/27.06 101.64/27.06 Induction Step: 101.64/27.06 U13(gen_tt:mark:nil:0':ok3_0(+(1, +(n91075_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.64/27.06 mark(U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.64/27.06 mark(*4_0) 101.64/27.06 101.64/27.06 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.06 ---------------------------------------- 101.64/27.06 101.64/27.06 (44) 101.64/27.06 Obligation: 101.64/27.06 TRS: 101.64/27.06 Rules: 101.64/27.06 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.06 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.06 active(U106(tt)) -> mark(tt) 101.64/27.06 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.06 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.06 active(U112(tt)) -> mark(tt) 101.64/27.06 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.06 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.06 active(U122(tt)) -> mark(tt) 101.64/27.06 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.06 active(U131(tt)) -> mark(tt) 101.64/27.06 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.06 active(U141(tt)) -> mark(tt) 101.64/27.06 active(U151(tt)) -> mark(tt) 101.64/27.06 active(U161(tt)) -> mark(tt) 101.64/27.06 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.06 active(U172(tt)) -> mark(tt) 101.64/27.06 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.06 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.06 active(U183(tt)) -> mark(tt) 101.64/27.06 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.06 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.06 active(U193(tt)) -> mark(tt) 101.64/27.06 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.06 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.06 active(U206(tt)) -> mark(tt) 101.64/27.06 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.06 active(U211(tt)) -> mark(tt) 101.64/27.06 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.06 active(U221(tt)) -> mark(tt) 101.64/27.06 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.06 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.06 active(U232(tt)) -> mark(tt) 101.64/27.06 active(U24(tt, X)) -> mark(X) 101.64/27.06 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.06 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.06 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.06 active(U246(tt)) -> mark(tt) 101.64/27.06 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.06 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.06 active(U256(tt)) -> mark(tt) 101.64/27.06 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.06 active(U262(tt)) -> mark(tt) 101.64/27.06 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.06 active(U272(tt)) -> mark(tt) 101.64/27.06 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.06 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.06 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.06 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.06 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.06 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.06 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.06 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.06 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.06 active(U304(tt, Y)) -> mark(Y) 101.64/27.06 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.06 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.06 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.06 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.06 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.06 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.06 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.06 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.06 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.06 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.06 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.06 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.06 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.06 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.06 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.06 active(U334(tt, XS)) -> mark(XS) 101.64/27.06 active(U34(tt, N)) -> mark(N) 101.64/27.06 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.06 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.06 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.06 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.06 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.06 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.06 active(U46(tt)) -> mark(tt) 101.64/27.06 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.06 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.06 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.06 active(U56(tt)) -> mark(tt) 101.64/27.06 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.06 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.06 active(U63(tt)) -> mark(tt) 101.64/27.06 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.06 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.06 active(U73(tt)) -> mark(tt) 101.64/27.06 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.06 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.06 active(U83(tt)) -> mark(tt) 101.64/27.06 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.06 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.06 active(U93(tt)) -> mark(tt) 101.64/27.06 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.06 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.06 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.06 active(isLNat(nil)) -> mark(tt) 101.64/27.06 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.06 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.06 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.06 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.06 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(isLNatKind(nil)) -> mark(tt) 101.64/27.06 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.06 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.06 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.06 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.06 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.06 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.06 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.06 active(isNatural(0')) -> mark(tt) 101.64/27.06 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.06 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.06 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(isNaturalKind(0')) -> mark(tt) 101.64/27.06 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.06 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.06 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.06 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.06 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.06 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.06 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.06 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.06 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.06 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.06 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.06 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.06 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.06 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.06 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.06 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.06 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.06 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.06 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.06 active(U106(X)) -> U106(active(X)) 101.64/27.06 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.06 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.06 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.06 active(U112(X)) -> U112(active(X)) 101.64/27.06 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.06 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.06 active(U122(X)) -> U122(active(X)) 101.64/27.06 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.06 active(U131(X)) -> U131(active(X)) 101.64/27.06 active(snd(X)) -> snd(active(X)) 101.64/27.06 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.06 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.06 active(U141(X)) -> U141(active(X)) 101.64/27.06 active(U151(X)) -> U151(active(X)) 101.64/27.06 active(U161(X)) -> U161(active(X)) 101.64/27.06 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.06 active(U172(X)) -> U172(active(X)) 101.64/27.06 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.06 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.06 active(U183(X)) -> U183(active(X)) 101.64/27.06 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.06 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.06 active(U193(X)) -> U193(active(X)) 101.64/27.06 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.06 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.06 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.06 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.06 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.06 active(U206(X)) -> U206(active(X)) 101.64/27.06 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.06 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.06 active(U211(X)) -> U211(active(X)) 101.64/27.06 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.06 active(U221(X)) -> U221(active(X)) 101.64/27.06 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.06 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.06 active(U232(X)) -> U232(active(X)) 101.64/27.06 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.06 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.06 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.06 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.06 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.06 active(U246(X)) -> U246(active(X)) 101.64/27.06 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.06 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.06 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.06 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.06 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.06 active(U256(X)) -> U256(active(X)) 101.64/27.06 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.06 active(U262(X)) -> U262(active(X)) 101.64/27.06 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.06 active(U272(X)) -> U272(active(X)) 101.64/27.06 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.06 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.06 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.06 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.06 active(s(X)) -> s(active(X)) 101.64/27.06 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.06 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.06 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.06 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.06 active(head(X)) -> head(active(X)) 101.64/27.06 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.06 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.06 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.06 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.06 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.06 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.06 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.06 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.06 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.06 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.06 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.06 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.06 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.06 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.06 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.06 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.06 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.06 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.06 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.06 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.06 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.06 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.06 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.06 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.06 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.06 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.06 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.06 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.06 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.06 active(fst(X)) -> fst(active(X)) 101.64/27.06 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.06 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.06 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.06 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.06 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.06 active(U46(X)) -> U46(active(X)) 101.64/27.06 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.06 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.06 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.06 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.06 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.06 active(U56(X)) -> U56(active(X)) 101.64/27.06 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.06 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.06 active(U63(X)) -> U63(active(X)) 101.64/27.06 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.06 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.06 active(U73(X)) -> U73(active(X)) 101.64/27.06 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.06 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.06 active(U83(X)) -> U83(active(X)) 101.64/27.06 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.06 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.06 active(U93(X)) -> U93(active(X)) 101.64/27.06 active(tail(X)) -> tail(active(X)) 101.64/27.06 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.06 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.06 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.06 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.06 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.06 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.06 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.06 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.06 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.06 U106(mark(X)) -> mark(U106(X)) 101.64/27.06 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.06 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.06 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.06 U112(mark(X)) -> mark(U112(X)) 101.64/27.06 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.06 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.06 U122(mark(X)) -> mark(U122(X)) 101.64/27.06 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.06 U131(mark(X)) -> mark(U131(X)) 101.64/27.06 snd(mark(X)) -> mark(snd(X)) 101.64/27.06 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.06 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.06 U141(mark(X)) -> mark(U141(X)) 101.64/27.06 U151(mark(X)) -> mark(U151(X)) 101.64/27.06 U161(mark(X)) -> mark(U161(X)) 101.64/27.06 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.06 U172(mark(X)) -> mark(U172(X)) 101.64/27.06 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.06 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.06 U183(mark(X)) -> mark(U183(X)) 101.64/27.06 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.06 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.06 U193(mark(X)) -> mark(U193(X)) 101.64/27.06 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.06 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.06 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.06 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.06 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.06 U206(mark(X)) -> mark(U206(X)) 101.64/27.06 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.06 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.06 U211(mark(X)) -> mark(U211(X)) 101.64/27.06 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.06 U221(mark(X)) -> mark(U221(X)) 101.64/27.06 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.06 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.06 U232(mark(X)) -> mark(U232(X)) 101.64/27.06 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.06 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.06 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.06 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.06 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.06 U246(mark(X)) -> mark(U246(X)) 101.64/27.06 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.06 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.06 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.06 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.06 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.06 U256(mark(X)) -> mark(U256(X)) 101.64/27.06 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.06 U262(mark(X)) -> mark(U262(X)) 101.64/27.06 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.06 U272(mark(X)) -> mark(U272(X)) 101.64/27.06 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.06 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.06 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.06 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.06 s(mark(X)) -> mark(s(X)) 101.64/27.06 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.06 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.06 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.07 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.07 head(mark(X)) -> mark(head(X)) 101.64/27.07 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.07 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.07 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.07 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.07 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.07 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.07 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.07 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.07 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.07 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.07 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.07 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.07 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.07 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.07 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.07 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.07 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.07 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.07 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.07 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.07 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.07 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.07 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.07 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.07 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.07 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.07 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.07 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.07 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.07 fst(mark(X)) -> mark(fst(X)) 101.64/27.07 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.07 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.07 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.07 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.07 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.07 U46(mark(X)) -> mark(U46(X)) 101.64/27.07 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.07 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.07 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.07 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.07 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.07 U56(mark(X)) -> mark(U56(X)) 101.64/27.07 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.07 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.07 U63(mark(X)) -> mark(U63(X)) 101.64/27.07 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.07 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.07 U73(mark(X)) -> mark(U73(X)) 101.64/27.07 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.07 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.07 U83(mark(X)) -> mark(U83(X)) 101.64/27.07 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.07 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.07 U93(mark(X)) -> mark(U93(X)) 101.64/27.07 tail(mark(X)) -> mark(tail(X)) 101.64/27.07 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.07 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.07 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.07 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.07 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(tt) -> ok(tt) 101.64/27.07 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.07 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.07 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.07 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.07 proper(U106(X)) -> U106(proper(X)) 101.64/27.07 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.07 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.07 proper(U112(X)) -> U112(proper(X)) 101.64/27.07 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.07 proper(U122(X)) -> U122(proper(X)) 101.64/27.07 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U131(X)) -> U131(proper(X)) 101.64/27.07 proper(snd(X)) -> snd(proper(X)) 101.64/27.07 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.07 proper(U141(X)) -> U141(proper(X)) 101.64/27.07 proper(U151(X)) -> U151(proper(X)) 101.64/27.07 proper(U161(X)) -> U161(proper(X)) 101.64/27.07 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.07 proper(U172(X)) -> U172(proper(X)) 101.64/27.07 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.07 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.07 proper(U183(X)) -> U183(proper(X)) 101.64/27.07 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.07 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.07 proper(U193(X)) -> U193(proper(X)) 101.64/27.07 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.07 proper(U206(X)) -> U206(proper(X)) 101.64/27.07 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U211(X)) -> U211(proper(X)) 101.64/27.07 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U221(X)) -> U221(proper(X)) 101.64/27.07 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.07 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.07 proper(U232(X)) -> U232(proper(X)) 101.64/27.07 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.07 proper(U246(X)) -> U246(proper(X)) 101.64/27.07 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.07 proper(U256(X)) -> U256(proper(X)) 101.64/27.07 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.07 proper(U262(X)) -> U262(proper(X)) 101.64/27.07 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.07 proper(U272(X)) -> U272(proper(X)) 101.64/27.07 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.07 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.07 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.07 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.07 proper(s(X)) -> s(proper(X)) 101.64/27.07 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(head(X)) -> head(proper(X)) 101.64/27.07 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.07 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.07 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.07 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.07 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.07 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.07 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.07 proper(nil) -> ok(nil) 101.64/27.07 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.07 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.07 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.07 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.07 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.07 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(fst(X)) -> fst(proper(X)) 101.64/27.07 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.07 proper(U46(X)) -> U46(proper(X)) 101.64/27.07 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.07 proper(U56(X)) -> U56(proper(X)) 101.64/27.07 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.07 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.07 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.07 proper(U63(X)) -> U63(proper(X)) 101.64/27.07 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.07 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.07 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.07 proper(U73(X)) -> U73(proper(X)) 101.64/27.07 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.07 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.07 proper(U83(X)) -> U83(proper(X)) 101.64/27.07 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.07 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.07 proper(U93(X)) -> U93(proper(X)) 101.64/27.07 proper(tail(X)) -> tail(proper(X)) 101.64/27.07 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.07 proper(0') -> ok(0') 101.64/27.07 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.07 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.07 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.07 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.07 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.07 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.07 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.07 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.07 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.07 U106(ok(X)) -> ok(U106(X)) 101.64/27.07 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.07 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.07 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.07 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.07 U112(ok(X)) -> ok(U112(X)) 101.64/27.07 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.07 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.07 U122(ok(X)) -> ok(U122(X)) 101.64/27.07 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.07 U131(ok(X)) -> ok(U131(X)) 101.64/27.07 snd(ok(X)) -> ok(snd(X)) 101.64/27.07 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.07 U141(ok(X)) -> ok(U141(X)) 101.64/27.07 U151(ok(X)) -> ok(U151(X)) 101.64/27.07 U161(ok(X)) -> ok(U161(X)) 101.64/27.07 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.07 U172(ok(X)) -> ok(U172(X)) 101.64/27.07 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.07 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.07 U183(ok(X)) -> ok(U183(X)) 101.64/27.07 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.07 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.07 U193(ok(X)) -> ok(U193(X)) 101.64/27.07 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.07 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.07 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.07 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.07 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.07 U206(ok(X)) -> ok(U206(X)) 101.64/27.07 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.07 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.07 U211(ok(X)) -> ok(U211(X)) 101.64/27.07 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.07 U221(ok(X)) -> ok(U221(X)) 101.64/27.07 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.07 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.07 U232(ok(X)) -> ok(U232(X)) 101.64/27.07 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.07 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.07 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.07 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.07 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.07 U246(ok(X)) -> ok(U246(X)) 101.64/27.07 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.07 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.07 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.07 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.07 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.07 U256(ok(X)) -> ok(U256(X)) 101.64/27.07 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.07 U262(ok(X)) -> ok(U262(X)) 101.64/27.07 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.07 U272(ok(X)) -> ok(U272(X)) 101.64/27.07 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.07 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.07 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.07 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.07 s(ok(X)) -> ok(s(X)) 101.64/27.07 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.07 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.07 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.07 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.07 head(ok(X)) -> ok(head(X)) 101.64/27.07 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.07 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.07 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.07 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.07 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.07 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.07 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.07 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.07 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.07 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.07 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.07 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.07 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.07 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.07 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.07 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.07 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.07 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.07 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.07 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.07 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.07 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.07 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.07 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.07 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.07 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.07 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.07 fst(ok(X)) -> ok(fst(X)) 101.64/27.07 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.07 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.07 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.07 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.07 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.07 U46(ok(X)) -> ok(U46(X)) 101.64/27.07 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.07 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.07 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.07 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.07 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.07 U56(ok(X)) -> ok(U56(X)) 101.64/27.07 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.07 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.07 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.07 U63(ok(X)) -> ok(U63(X)) 101.64/27.07 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.07 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.07 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.07 U73(ok(X)) -> ok(U73(X)) 101.64/27.07 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.07 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.07 U83(ok(X)) -> ok(U83(X)) 101.64/27.07 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.07 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.07 U93(ok(X)) -> ok(U93(X)) 101.64/27.07 tail(ok(X)) -> ok(tail(X)) 101.64/27.07 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.07 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.07 top(mark(X)) -> top(proper(X)) 101.64/27.07 top(ok(X)) -> top(active(X)) 101.64/27.07 101.64/27.07 Types: 101.64/27.07 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 tt :: tt:mark:nil:0':ok 101.64/27.07 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 nil :: tt:mark:nil:0':ok 101.64/27.07 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 0' :: tt:mark:nil:0':ok 101.64/27.07 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 top :: tt:mark:nil:0':ok -> top 101.64/27.07 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.07 hole_top2_0 :: top 101.64/27.07 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.07 101.64/27.07 101.64/27.07 Lemmas: 101.64/27.07 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.07 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.07 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.07 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.07 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.07 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.07 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.07 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.07 101.64/27.07 101.64/27.07 Generator Equations: 101.64/27.07 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.07 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.07 101.64/27.07 101.64/27.07 The following defined symbols remain to be analysed: 101.64/27.07 U122, active, U14, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.07 101.64/27.07 They will be analysed ascendingly in the following order: 101.64/27.07 U122 < active 101.64/27.07 U14 < active 101.64/27.07 snd < active 101.64/27.07 splitAt < active 101.64/27.07 U172 < active 101.64/27.07 U182 < active 101.64/27.07 U183 < active 101.64/27.07 U192 < active 101.64/27.07 U193 < active 101.64/27.07 U202 < active 101.64/27.07 U203 < active 101.64/27.07 U204 < active 101.64/27.07 U205 < active 101.64/27.07 U206 < active 101.64/27.07 U22 < active 101.64/27.07 U23 < active 101.64/27.07 U24 < active 101.64/27.07 U232 < active 101.64/27.07 U242 < active 101.64/27.07 U243 < active 101.64/27.07 U244 < active 101.64/27.07 U245 < active 101.64/27.07 U246 < active 101.64/27.07 U252 < active 101.64/27.07 U253 < active 101.64/27.07 U254 < active 101.64/27.07 U255 < active 101.64/27.07 U256 < active 101.64/27.07 U262 < active 101.64/27.07 U272 < active 101.64/27.07 U282 < active 101.64/27.07 cons < active 101.64/27.07 natsFrom < active 101.64/27.07 s < active 101.64/27.07 U292 < active 101.64/27.07 U293 < active 101.64/27.07 U294 < active 101.64/27.07 head < active 101.64/27.07 afterNth < active 101.64/27.07 U302 < active 101.64/27.07 U303 < active 101.64/27.07 U304 < active 101.64/27.07 U32 < active 101.64/27.07 U312 < active 101.64/27.07 pair < active 101.64/27.07 U33 < active 101.64/27.07 U322 < active 101.64/27.07 U323 < active 101.64/27.07 U324 < active 101.64/27.07 U325 < active 101.64/27.07 U326 < active 101.64/27.07 U327 < active 101.64/27.07 U34 < active 101.64/27.07 U332 < active 101.64/27.07 U333 < active 101.64/27.07 U334 < active 101.64/27.07 U342 < active 101.64/27.07 U343 < active 101.64/27.07 U344 < active 101.64/27.07 fst < active 101.64/27.07 U42 < active 101.64/27.07 U43 < active 101.64/27.07 U44 < active 101.64/27.07 U45 < active 101.64/27.07 U46 < active 101.64/27.07 U52 < active 101.64/27.07 U53 < active 101.64/27.07 U54 < active 101.64/27.07 U55 < active 101.64/27.07 U56 < active 101.64/27.07 U62 < active 101.64/27.07 isPLNatKind < active 101.64/27.07 U63 < active 101.64/27.07 isPLNat < active 101.64/27.07 U72 < active 101.64/27.07 U73 < active 101.64/27.07 U82 < active 101.64/27.07 U83 < active 101.64/27.07 U92 < active 101.64/27.07 U93 < active 101.64/27.07 U11 < active 101.64/27.07 U21 < active 101.64/27.07 U31 < active 101.64/27.07 U41 < active 101.64/27.07 U51 < active 101.64/27.07 U61 < active 101.64/27.07 U71 < active 101.64/27.07 U81 < active 101.64/27.07 U91 < active 101.64/27.07 U101 < active 101.64/27.07 U111 < active 101.64/27.07 U121 < active 101.64/27.07 U131 < active 101.64/27.07 U141 < active 101.64/27.07 U151 < active 101.64/27.07 U161 < active 101.64/27.07 U171 < active 101.64/27.07 U181 < active 101.64/27.07 U191 < active 101.64/27.07 U201 < active 101.64/27.07 U211 < active 101.64/27.07 U221 < active 101.64/27.07 U231 < active 101.64/27.07 U241 < active 101.64/27.07 U251 < active 101.64/27.07 U261 < active 101.64/27.07 U271 < active 101.64/27.07 U281 < active 101.64/27.07 U291 < active 101.64/27.07 U301 < active 101.64/27.07 U311 < active 101.64/27.07 U321 < active 101.64/27.07 U331 < active 101.64/27.07 U341 < active 101.64/27.07 tail < active 101.64/27.07 take < active 101.64/27.07 sel < active 101.64/27.07 active < top 101.64/27.07 U122 < proper 101.64/27.07 U14 < proper 101.64/27.07 snd < proper 101.64/27.07 splitAt < proper 101.64/27.07 U172 < proper 101.64/27.07 U182 < proper 101.64/27.07 U183 < proper 101.64/27.07 U192 < proper 101.64/27.07 U193 < proper 101.64/27.07 U202 < proper 101.64/27.07 U203 < proper 101.64/27.07 U204 < proper 101.64/27.07 U205 < proper 101.64/27.07 U206 < proper 101.64/27.07 U22 < proper 101.64/27.07 U23 < proper 101.64/27.07 U24 < proper 101.64/27.07 U232 < proper 101.64/27.07 U242 < proper 101.64/27.07 U243 < proper 101.64/27.07 U244 < proper 101.64/27.07 U245 < proper 101.64/27.07 U246 < proper 101.64/27.07 U252 < proper 101.64/27.07 U253 < proper 101.64/27.07 U254 < proper 101.64/27.07 U255 < proper 101.64/27.07 U256 < proper 101.64/27.07 U262 < proper 101.64/27.07 U272 < proper 101.64/27.07 U282 < proper 101.64/27.07 cons < proper 101.64/27.07 natsFrom < proper 101.64/27.07 s < proper 101.64/27.07 U292 < proper 101.64/27.07 U293 < proper 101.64/27.07 U294 < proper 101.64/27.07 head < proper 101.64/27.07 afterNth < proper 101.64/27.07 U302 < proper 101.64/27.07 U303 < proper 101.64/27.07 U304 < proper 101.64/27.07 U32 < proper 101.64/27.07 U312 < proper 101.64/27.07 pair < proper 101.64/27.07 U33 < proper 101.64/27.07 U322 < proper 101.64/27.07 U323 < proper 101.64/27.07 U324 < proper 101.64/27.07 U325 < proper 101.64/27.07 U326 < proper 101.64/27.07 U327 < proper 101.64/27.07 U34 < proper 101.64/27.07 U332 < proper 101.64/27.07 U333 < proper 101.64/27.07 U334 < proper 101.64/27.07 U342 < proper 101.64/27.07 U343 < proper 101.64/27.07 U344 < proper 101.64/27.07 fst < proper 101.64/27.07 U42 < proper 101.64/27.07 U43 < proper 101.64/27.07 U44 < proper 101.64/27.07 U45 < proper 101.64/27.07 U46 < proper 101.64/27.07 U52 < proper 101.64/27.07 U53 < proper 101.64/27.07 U54 < proper 101.64/27.07 U55 < proper 101.64/27.07 U56 < proper 101.64/27.07 U62 < proper 101.64/27.07 isPLNatKind < proper 101.64/27.07 U63 < proper 101.64/27.07 isPLNat < proper 101.64/27.07 U72 < proper 101.64/27.07 U73 < proper 101.64/27.07 U82 < proper 101.64/27.07 U83 < proper 101.64/27.07 U92 < proper 101.64/27.07 U93 < proper 101.64/27.07 U11 < proper 101.64/27.07 U21 < proper 101.64/27.07 U31 < proper 101.64/27.07 U41 < proper 101.64/27.07 U51 < proper 101.64/27.07 U61 < proper 101.64/27.07 U71 < proper 101.64/27.07 U81 < proper 101.64/27.07 U91 < proper 101.64/27.07 U101 < proper 101.64/27.07 U111 < proper 101.64/27.07 U121 < proper 101.64/27.07 U131 < proper 101.64/27.07 U141 < proper 101.64/27.07 U151 < proper 101.64/27.07 U161 < proper 101.64/27.07 U171 < proper 101.64/27.07 U181 < proper 101.64/27.07 U191 < proper 101.64/27.07 U201 < proper 101.64/27.07 U211 < proper 101.64/27.07 U221 < proper 101.64/27.07 U231 < proper 101.64/27.07 U241 < proper 101.64/27.07 U251 < proper 101.64/27.07 U261 < proper 101.64/27.07 U271 < proper 101.64/27.07 U281 < proper 101.64/27.07 U291 < proper 101.64/27.07 U301 < proper 101.64/27.07 U311 < proper 101.64/27.07 U321 < proper 101.64/27.07 U331 < proper 101.64/27.07 U341 < proper 101.64/27.07 tail < proper 101.64/27.07 take < proper 101.64/27.07 sel < proper 101.64/27.07 proper < top 101.64/27.07 101.64/27.07 ---------------------------------------- 101.64/27.07 101.64/27.07 (45) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.07 Proved the following rewrite lemma: 101.64/27.07 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.07 101.64/27.07 Induction Base: 101.64/27.07 U122(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.07 101.64/27.07 Induction Step: 101.64/27.07 U122(gen_tt:mark:nil:0':ok3_0(+(1, +(n111906_0, 1)))) ->_R^Omega(1) 101.64/27.07 mark(U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0)))) ->_IH 101.64/27.07 mark(*4_0) 101.64/27.07 101.64/27.07 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.07 ---------------------------------------- 101.64/27.07 101.64/27.07 (46) 101.64/27.07 Obligation: 101.64/27.07 TRS: 101.64/27.07 Rules: 101.64/27.07 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.07 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.07 active(U106(tt)) -> mark(tt) 101.64/27.07 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.07 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.07 active(U112(tt)) -> mark(tt) 101.64/27.07 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.07 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.07 active(U122(tt)) -> mark(tt) 101.64/27.07 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.07 active(U131(tt)) -> mark(tt) 101.64/27.07 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.07 active(U141(tt)) -> mark(tt) 101.64/27.07 active(U151(tt)) -> mark(tt) 101.64/27.07 active(U161(tt)) -> mark(tt) 101.64/27.07 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.07 active(U172(tt)) -> mark(tt) 101.64/27.07 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.07 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.07 active(U183(tt)) -> mark(tt) 101.64/27.07 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.07 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.07 active(U193(tt)) -> mark(tt) 101.64/27.07 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.07 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.07 active(U206(tt)) -> mark(tt) 101.64/27.07 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.07 active(U211(tt)) -> mark(tt) 101.64/27.07 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.07 active(U221(tt)) -> mark(tt) 101.64/27.07 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.07 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.07 active(U232(tt)) -> mark(tt) 101.64/27.07 active(U24(tt, X)) -> mark(X) 101.64/27.07 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.07 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.07 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.07 active(U246(tt)) -> mark(tt) 101.64/27.07 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.07 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.07 active(U256(tt)) -> mark(tt) 101.64/27.07 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.07 active(U262(tt)) -> mark(tt) 101.64/27.07 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.07 active(U272(tt)) -> mark(tt) 101.64/27.07 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.07 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.07 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.07 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.07 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.07 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.07 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.07 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.07 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.07 active(U304(tt, Y)) -> mark(Y) 101.64/27.07 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.07 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.07 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.07 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.07 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.07 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.07 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.07 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.07 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.07 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.07 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.07 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.07 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.07 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.07 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.07 active(U334(tt, XS)) -> mark(XS) 101.64/27.07 active(U34(tt, N)) -> mark(N) 101.64/27.07 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.07 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.07 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.07 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.07 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.07 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.07 active(U46(tt)) -> mark(tt) 101.64/27.07 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.07 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.07 active(U56(tt)) -> mark(tt) 101.64/27.07 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.07 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.07 active(U63(tt)) -> mark(tt) 101.64/27.07 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.07 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.07 active(U73(tt)) -> mark(tt) 101.64/27.07 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.07 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.07 active(U83(tt)) -> mark(tt) 101.64/27.07 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.07 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.07 active(U93(tt)) -> mark(tt) 101.64/27.07 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.07 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.07 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.07 active(isLNat(nil)) -> mark(tt) 101.64/27.07 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.07 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.07 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.07 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.07 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNatKind(nil)) -> mark(tt) 101.64/27.07 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.07 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.07 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.07 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.07 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.07 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.07 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.07 active(isNatural(0')) -> mark(tt) 101.64/27.07 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.07 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.07 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isNaturalKind(0')) -> mark(tt) 101.64/27.07 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.07 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.07 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.07 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.07 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.07 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.07 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.07 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.07 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.07 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.07 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.07 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.07 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.07 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.07 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.07 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.07 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.07 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.07 active(U106(X)) -> U106(active(X)) 101.64/27.07 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.07 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.07 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.07 active(U112(X)) -> U112(active(X)) 101.64/27.07 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.07 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.07 active(U122(X)) -> U122(active(X)) 101.64/27.07 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.07 active(U131(X)) -> U131(active(X)) 101.64/27.07 active(snd(X)) -> snd(active(X)) 101.64/27.07 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.07 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.07 active(U141(X)) -> U141(active(X)) 101.64/27.07 active(U151(X)) -> U151(active(X)) 101.64/27.07 active(U161(X)) -> U161(active(X)) 101.64/27.07 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.07 active(U172(X)) -> U172(active(X)) 101.64/27.07 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.07 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.07 active(U183(X)) -> U183(active(X)) 101.64/27.07 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.07 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.07 active(U193(X)) -> U193(active(X)) 101.64/27.07 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.07 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.07 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.07 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.07 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.07 active(U206(X)) -> U206(active(X)) 101.64/27.07 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.07 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.07 active(U211(X)) -> U211(active(X)) 101.64/27.07 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.07 active(U221(X)) -> U221(active(X)) 101.64/27.07 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.07 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.07 active(U232(X)) -> U232(active(X)) 101.64/27.07 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.07 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.07 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.07 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.07 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.07 active(U246(X)) -> U246(active(X)) 101.64/27.07 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.07 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.07 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.07 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.07 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.07 active(U256(X)) -> U256(active(X)) 101.64/27.07 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.07 active(U262(X)) -> U262(active(X)) 101.64/27.07 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.07 active(U272(X)) -> U272(active(X)) 101.64/27.07 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.07 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.07 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.07 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.07 active(s(X)) -> s(active(X)) 101.64/27.07 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.07 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.07 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.07 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.07 active(head(X)) -> head(active(X)) 101.64/27.07 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.07 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.07 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.07 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.07 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.07 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.07 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.07 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.07 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.07 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.07 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.07 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.07 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.07 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.07 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.07 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.07 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.07 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.07 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.07 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.07 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.07 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.07 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.07 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.07 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.07 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.07 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.07 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.07 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.07 active(fst(X)) -> fst(active(X)) 101.64/27.07 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.07 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.07 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.07 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.07 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.07 active(U46(X)) -> U46(active(X)) 101.64/27.07 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.07 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.07 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.07 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.07 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.07 active(U56(X)) -> U56(active(X)) 101.64/27.07 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.07 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.07 active(U63(X)) -> U63(active(X)) 101.64/27.07 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.07 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.07 active(U73(X)) -> U73(active(X)) 101.64/27.07 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.07 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.07 active(U83(X)) -> U83(active(X)) 101.64/27.07 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.07 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.07 active(U93(X)) -> U93(active(X)) 101.64/27.07 active(tail(X)) -> tail(active(X)) 101.64/27.07 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.07 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.07 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.07 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.07 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.07 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.07 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.07 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.07 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.07 U106(mark(X)) -> mark(U106(X)) 101.64/27.07 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.07 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.07 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.07 U112(mark(X)) -> mark(U112(X)) 101.64/27.07 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.07 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.07 U122(mark(X)) -> mark(U122(X)) 101.64/27.07 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.07 U131(mark(X)) -> mark(U131(X)) 101.64/27.07 snd(mark(X)) -> mark(snd(X)) 101.64/27.07 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.07 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.07 U141(mark(X)) -> mark(U141(X)) 101.64/27.07 U151(mark(X)) -> mark(U151(X)) 101.64/27.07 U161(mark(X)) -> mark(U161(X)) 101.64/27.07 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.07 U172(mark(X)) -> mark(U172(X)) 101.64/27.07 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.07 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.07 U183(mark(X)) -> mark(U183(X)) 101.64/27.07 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.07 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.07 U193(mark(X)) -> mark(U193(X)) 101.64/27.07 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.07 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.07 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.07 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.07 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.07 U206(mark(X)) -> mark(U206(X)) 101.64/27.07 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.07 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.07 U211(mark(X)) -> mark(U211(X)) 101.64/27.07 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.07 U221(mark(X)) -> mark(U221(X)) 101.64/27.07 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.07 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.07 U232(mark(X)) -> mark(U232(X)) 101.64/27.07 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.07 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.07 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.07 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.07 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.07 U246(mark(X)) -> mark(U246(X)) 101.64/27.07 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.07 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.07 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.07 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.07 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.07 U256(mark(X)) -> mark(U256(X)) 101.64/27.07 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.07 U262(mark(X)) -> mark(U262(X)) 101.64/27.07 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.07 U272(mark(X)) -> mark(U272(X)) 101.64/27.07 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.07 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.07 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.07 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.07 s(mark(X)) -> mark(s(X)) 101.64/27.07 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.07 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.07 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.07 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.07 head(mark(X)) -> mark(head(X)) 101.64/27.07 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.07 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.07 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.07 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.07 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.07 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.07 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.07 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.07 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.07 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.07 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.07 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.07 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.07 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.07 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.07 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.07 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.07 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.07 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.07 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.07 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.07 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.07 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.07 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.07 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.07 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.07 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.07 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.07 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.07 fst(mark(X)) -> mark(fst(X)) 101.64/27.07 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.07 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.07 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.07 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.07 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.07 U46(mark(X)) -> mark(U46(X)) 101.64/27.07 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.07 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.07 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.07 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.07 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.07 U56(mark(X)) -> mark(U56(X)) 101.64/27.07 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.07 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.07 U63(mark(X)) -> mark(U63(X)) 101.64/27.07 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.07 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.07 U73(mark(X)) -> mark(U73(X)) 101.64/27.07 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.07 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.07 U83(mark(X)) -> mark(U83(X)) 101.64/27.07 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.07 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.07 U93(mark(X)) -> mark(U93(X)) 101.64/27.07 tail(mark(X)) -> mark(tail(X)) 101.64/27.07 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.07 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.07 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.07 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.07 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(tt) -> ok(tt) 101.64/27.07 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.07 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.07 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.07 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.07 proper(U106(X)) -> U106(proper(X)) 101.64/27.07 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.07 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.07 proper(U112(X)) -> U112(proper(X)) 101.64/27.07 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.07 proper(U122(X)) -> U122(proper(X)) 101.64/27.07 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U131(X)) -> U131(proper(X)) 101.64/27.07 proper(snd(X)) -> snd(proper(X)) 101.64/27.07 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.07 proper(U141(X)) -> U141(proper(X)) 101.64/27.07 proper(U151(X)) -> U151(proper(X)) 101.64/27.07 proper(U161(X)) -> U161(proper(X)) 101.64/27.07 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.07 proper(U172(X)) -> U172(proper(X)) 101.64/27.07 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.07 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.07 proper(U183(X)) -> U183(proper(X)) 101.64/27.07 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.07 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.07 proper(U193(X)) -> U193(proper(X)) 101.64/27.07 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.07 proper(U206(X)) -> U206(proper(X)) 101.64/27.07 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U211(X)) -> U211(proper(X)) 101.64/27.07 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U221(X)) -> U221(proper(X)) 101.64/27.07 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.07 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.07 proper(U232(X)) -> U232(proper(X)) 101.64/27.07 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.07 proper(U246(X)) -> U246(proper(X)) 101.64/27.07 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.07 proper(U256(X)) -> U256(proper(X)) 101.64/27.07 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.07 proper(U262(X)) -> U262(proper(X)) 101.64/27.07 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.07 proper(U272(X)) -> U272(proper(X)) 101.64/27.07 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.07 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.07 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.07 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.07 proper(s(X)) -> s(proper(X)) 101.64/27.07 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(head(X)) -> head(proper(X)) 101.64/27.07 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.07 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.07 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.07 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.07 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.07 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.07 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.07 proper(nil) -> ok(nil) 101.64/27.07 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.07 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.07 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.07 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.07 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.07 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.07 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(fst(X)) -> fst(proper(X)) 101.64/27.07 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.07 proper(U46(X)) -> U46(proper(X)) 101.64/27.07 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.07 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.07 proper(U56(X)) -> U56(proper(X)) 101.64/27.07 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.07 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.07 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.07 proper(U63(X)) -> U63(proper(X)) 101.64/27.07 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.07 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.07 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.07 proper(U73(X)) -> U73(proper(X)) 101.64/27.07 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.07 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.07 proper(U83(X)) -> U83(proper(X)) 101.64/27.07 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.07 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.07 proper(U93(X)) -> U93(proper(X)) 101.64/27.07 proper(tail(X)) -> tail(proper(X)) 101.64/27.07 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.07 proper(0') -> ok(0') 101.64/27.07 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.07 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.07 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.07 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.07 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.07 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.07 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.07 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.07 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.07 U106(ok(X)) -> ok(U106(X)) 101.64/27.07 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.07 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.07 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.07 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.07 U112(ok(X)) -> ok(U112(X)) 101.64/27.07 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.07 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.07 U122(ok(X)) -> ok(U122(X)) 101.64/27.07 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.07 U131(ok(X)) -> ok(U131(X)) 101.64/27.07 snd(ok(X)) -> ok(snd(X)) 101.64/27.07 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.07 U141(ok(X)) -> ok(U141(X)) 101.64/27.07 U151(ok(X)) -> ok(U151(X)) 101.64/27.07 U161(ok(X)) -> ok(U161(X)) 101.64/27.07 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.07 U172(ok(X)) -> ok(U172(X)) 101.64/27.07 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.07 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.07 U183(ok(X)) -> ok(U183(X)) 101.64/27.07 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.07 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.07 U193(ok(X)) -> ok(U193(X)) 101.64/27.07 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.07 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.07 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.07 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.07 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.07 U206(ok(X)) -> ok(U206(X)) 101.64/27.07 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.07 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.07 U211(ok(X)) -> ok(U211(X)) 101.64/27.07 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.07 U221(ok(X)) -> ok(U221(X)) 101.64/27.07 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.07 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.07 U232(ok(X)) -> ok(U232(X)) 101.64/27.07 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.07 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.07 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.07 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.07 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.07 U246(ok(X)) -> ok(U246(X)) 101.64/27.07 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.07 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.07 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.07 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.07 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.07 U256(ok(X)) -> ok(U256(X)) 101.64/27.07 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.07 U262(ok(X)) -> ok(U262(X)) 101.64/27.07 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.07 U272(ok(X)) -> ok(U272(X)) 101.64/27.07 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.07 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.07 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.07 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.07 s(ok(X)) -> ok(s(X)) 101.64/27.07 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.07 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.07 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.07 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.07 head(ok(X)) -> ok(head(X)) 101.64/27.07 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.07 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.07 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.07 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.07 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.07 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.07 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.07 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.07 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.07 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.07 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.07 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.07 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.07 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.07 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.07 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.07 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.07 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.07 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.07 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.07 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.07 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.07 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.07 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.07 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.07 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.07 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.07 fst(ok(X)) -> ok(fst(X)) 101.64/27.07 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.07 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.07 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.07 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.07 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.07 U46(ok(X)) -> ok(U46(X)) 101.64/27.07 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.07 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.07 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.07 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.07 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.07 U56(ok(X)) -> ok(U56(X)) 101.64/27.07 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.07 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.07 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.07 U63(ok(X)) -> ok(U63(X)) 101.64/27.07 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.07 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.07 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.07 U73(ok(X)) -> ok(U73(X)) 101.64/27.07 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.07 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.07 U83(ok(X)) -> ok(U83(X)) 101.64/27.07 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.07 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.07 U93(ok(X)) -> ok(U93(X)) 101.64/27.07 tail(ok(X)) -> ok(tail(X)) 101.64/27.07 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.07 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.07 top(mark(X)) -> top(proper(X)) 101.64/27.07 top(ok(X)) -> top(active(X)) 101.64/27.07 101.64/27.07 Types: 101.64/27.07 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 tt :: tt:mark:nil:0':ok 101.64/27.07 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 nil :: tt:mark:nil:0':ok 101.64/27.07 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 0' :: tt:mark:nil:0':ok 101.64/27.07 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.07 top :: tt:mark:nil:0':ok -> top 101.64/27.07 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.07 hole_top2_0 :: top 101.64/27.07 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.07 101.64/27.07 101.64/27.07 Lemmas: 101.64/27.07 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.07 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.07 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.07 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.07 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.07 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.07 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.07 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.07 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.07 101.64/27.07 101.64/27.07 Generator Equations: 101.64/27.07 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.07 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.07 101.64/27.07 101.64/27.07 The following defined symbols remain to be analysed: 101.64/27.07 U14, active, snd, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.07 101.64/27.07 They will be analysed ascendingly in the following order: 101.64/27.07 U14 < active 101.64/27.07 snd < active 101.64/27.07 splitAt < active 101.64/27.07 U172 < active 101.64/27.07 U182 < active 101.64/27.07 U183 < active 101.64/27.07 U192 < active 101.64/27.07 U193 < active 101.64/27.07 U202 < active 101.64/27.07 U203 < active 101.64/27.07 U204 < active 101.64/27.07 U205 < active 101.64/27.07 U206 < active 101.64/27.07 U22 < active 101.64/27.07 U23 < active 101.64/27.07 U24 < active 101.64/27.07 U232 < active 101.64/27.07 U242 < active 101.64/27.07 U243 < active 101.64/27.07 U244 < active 101.64/27.07 U245 < active 101.64/27.07 U246 < active 101.64/27.07 U252 < active 101.64/27.07 U253 < active 101.64/27.07 U254 < active 101.64/27.07 U255 < active 101.64/27.07 U256 < active 101.64/27.07 U262 < active 101.64/27.07 U272 < active 101.64/27.07 U282 < active 101.64/27.07 cons < active 101.64/27.07 natsFrom < active 101.64/27.07 s < active 101.64/27.07 U292 < active 101.64/27.07 U293 < active 101.64/27.07 U294 < active 101.64/27.07 head < active 101.64/27.07 afterNth < active 101.64/27.07 U302 < active 101.64/27.07 U303 < active 101.64/27.07 U304 < active 101.64/27.07 U32 < active 101.64/27.07 U312 < active 101.64/27.07 pair < active 101.64/27.07 U33 < active 101.64/27.07 U322 < active 101.64/27.07 U323 < active 101.64/27.07 U324 < active 101.64/27.07 U325 < active 101.64/27.07 U326 < active 101.64/27.07 U327 < active 101.64/27.07 U34 < active 101.64/27.07 U332 < active 101.64/27.07 U333 < active 101.64/27.07 U334 < active 101.64/27.07 U342 < active 101.64/27.07 U343 < active 101.64/27.07 U344 < active 101.64/27.07 fst < active 101.64/27.07 U42 < active 101.64/27.07 U43 < active 101.64/27.07 U44 < active 101.64/27.07 U45 < active 101.64/27.07 U46 < active 101.64/27.07 U52 < active 101.64/27.07 U53 < active 101.64/27.07 U54 < active 101.64/27.07 U55 < active 101.64/27.07 U56 < active 101.64/27.07 U62 < active 101.64/27.07 isPLNatKind < active 101.64/27.07 U63 < active 101.64/27.07 isPLNat < active 101.64/27.07 U72 < active 101.64/27.07 U73 < active 101.64/27.07 U82 < active 101.64/27.07 U83 < active 101.64/27.07 U92 < active 101.64/27.07 U93 < active 101.64/27.07 U11 < active 101.64/27.07 U21 < active 101.64/27.07 U31 < active 101.64/27.07 U41 < active 101.64/27.07 U51 < active 101.64/27.07 U61 < active 101.64/27.07 U71 < active 101.64/27.07 U81 < active 101.64/27.07 U91 < active 101.64/27.07 U101 < active 101.64/27.07 U111 < active 101.64/27.07 U121 < active 101.64/27.07 U131 < active 101.64/27.07 U141 < active 101.64/27.07 U151 < active 101.64/27.07 U161 < active 101.64/27.07 U171 < active 101.64/27.07 U181 < active 101.64/27.07 U191 < active 101.64/27.07 U201 < active 101.64/27.07 U211 < active 101.64/27.07 U221 < active 101.64/27.07 U231 < active 101.64/27.07 U241 < active 101.64/27.07 U251 < active 101.64/27.07 U261 < active 101.64/27.07 U271 < active 101.64/27.07 U281 < active 101.64/27.07 U291 < active 101.64/27.07 U301 < active 101.64/27.07 U311 < active 101.64/27.07 U321 < active 101.64/27.07 U331 < active 101.64/27.07 U341 < active 101.64/27.07 tail < active 101.64/27.07 take < active 101.64/27.07 sel < active 101.64/27.07 active < top 101.64/27.07 U14 < proper 101.64/27.07 snd < proper 101.64/27.07 splitAt < proper 101.64/27.07 U172 < proper 101.64/27.07 U182 < proper 101.64/27.07 U183 < proper 101.64/27.07 U192 < proper 101.64/27.07 U193 < proper 101.64/27.07 U202 < proper 101.64/27.07 U203 < proper 101.64/27.07 U204 < proper 101.64/27.07 U205 < proper 101.64/27.07 U206 < proper 101.64/27.07 U22 < proper 101.64/27.07 U23 < proper 101.64/27.07 U24 < proper 101.64/27.07 U232 < proper 101.64/27.07 U242 < proper 101.64/27.07 U243 < proper 101.64/27.07 U244 < proper 101.64/27.07 U245 < proper 101.64/27.07 U246 < proper 101.64/27.07 U252 < proper 101.64/27.07 U253 < proper 101.64/27.07 U254 < proper 101.64/27.07 U255 < proper 101.64/27.07 U256 < proper 101.64/27.07 U262 < proper 101.64/27.07 U272 < proper 101.64/27.07 U282 < proper 101.64/27.07 cons < proper 101.64/27.07 natsFrom < proper 101.64/27.07 s < proper 101.64/27.07 U292 < proper 101.64/27.07 U293 < proper 101.64/27.07 U294 < proper 101.64/27.07 head < proper 101.64/27.07 afterNth < proper 101.64/27.07 U302 < proper 101.64/27.07 U303 < proper 101.64/27.07 U304 < proper 101.64/27.07 U32 < proper 101.64/27.07 U312 < proper 101.64/27.07 pair < proper 101.64/27.07 U33 < proper 101.64/27.07 U322 < proper 101.64/27.07 U323 < proper 101.64/27.07 U324 < proper 101.64/27.07 U325 < proper 101.64/27.07 U326 < proper 101.64/27.07 U327 < proper 101.64/27.07 U34 < proper 101.64/27.07 U332 < proper 101.64/27.07 U333 < proper 101.64/27.07 U334 < proper 101.64/27.07 U342 < proper 101.64/27.07 U343 < proper 101.64/27.07 U344 < proper 101.64/27.07 fst < proper 101.64/27.07 U42 < proper 101.64/27.07 U43 < proper 101.64/27.07 U44 < proper 101.64/27.07 U45 < proper 101.64/27.07 U46 < proper 101.64/27.07 U52 < proper 101.64/27.07 U53 < proper 101.64/27.07 U54 < proper 101.64/27.07 U55 < proper 101.64/27.07 U56 < proper 101.64/27.07 U62 < proper 101.64/27.07 isPLNatKind < proper 101.64/27.07 U63 < proper 101.64/27.07 isPLNat < proper 101.64/27.07 U72 < proper 101.64/27.07 U73 < proper 101.64/27.07 U82 < proper 101.64/27.07 U83 < proper 101.64/27.07 U92 < proper 101.64/27.07 U93 < proper 101.64/27.07 U11 < proper 101.64/27.07 U21 < proper 101.64/27.07 U31 < proper 101.64/27.07 U41 < proper 101.64/27.07 U51 < proper 101.64/27.07 U61 < proper 101.64/27.07 U71 < proper 101.64/27.07 U81 < proper 101.64/27.07 U91 < proper 101.64/27.07 U101 < proper 101.64/27.07 U111 < proper 101.64/27.07 U121 < proper 101.64/27.07 U131 < proper 101.64/27.07 U141 < proper 101.64/27.07 U151 < proper 101.64/27.07 U161 < proper 101.64/27.07 U171 < proper 101.64/27.07 U181 < proper 101.64/27.07 U191 < proper 101.64/27.07 U201 < proper 101.64/27.07 U211 < proper 101.64/27.07 U221 < proper 101.64/27.07 U231 < proper 101.64/27.07 U241 < proper 101.64/27.07 U251 < proper 101.64/27.07 U261 < proper 101.64/27.07 U271 < proper 101.64/27.07 U281 < proper 101.64/27.07 U291 < proper 101.64/27.07 U301 < proper 101.64/27.07 U311 < proper 101.64/27.07 U321 < proper 101.64/27.07 U331 < proper 101.64/27.07 U341 < proper 101.64/27.07 tail < proper 101.64/27.07 take < proper 101.64/27.07 sel < proper 101.64/27.07 proper < top 101.64/27.07 101.64/27.07 ---------------------------------------- 101.64/27.07 101.64/27.07 (47) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.07 Proved the following rewrite lemma: 101.64/27.07 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.07 101.64/27.07 Induction Base: 101.64/27.07 U14(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.64/27.07 101.64/27.07 Induction Step: 101.64/27.07 U14(gen_tt:mark:nil:0':ok3_0(+(1, +(n115524_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.64/27.07 mark(U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.64/27.07 mark(*4_0) 101.64/27.07 101.64/27.07 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.07 ---------------------------------------- 101.64/27.07 101.64/27.07 (48) 101.64/27.07 Obligation: 101.64/27.07 TRS: 101.64/27.07 Rules: 101.64/27.07 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.07 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.07 active(U106(tt)) -> mark(tt) 101.64/27.07 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.07 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.07 active(U112(tt)) -> mark(tt) 101.64/27.07 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.07 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.07 active(U122(tt)) -> mark(tt) 101.64/27.07 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.07 active(U131(tt)) -> mark(tt) 101.64/27.07 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.07 active(U141(tt)) -> mark(tt) 101.64/27.07 active(U151(tt)) -> mark(tt) 101.64/27.07 active(U161(tt)) -> mark(tt) 101.64/27.07 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.07 active(U172(tt)) -> mark(tt) 101.64/27.07 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.07 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.07 active(U183(tt)) -> mark(tt) 101.64/27.07 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.07 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.07 active(U193(tt)) -> mark(tt) 101.64/27.07 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.07 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.07 active(U206(tt)) -> mark(tt) 101.64/27.07 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.07 active(U211(tt)) -> mark(tt) 101.64/27.07 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.07 active(U221(tt)) -> mark(tt) 101.64/27.07 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.07 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.07 active(U232(tt)) -> mark(tt) 101.64/27.07 active(U24(tt, X)) -> mark(X) 101.64/27.07 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.07 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.07 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.07 active(U246(tt)) -> mark(tt) 101.64/27.07 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.07 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.07 active(U256(tt)) -> mark(tt) 101.64/27.07 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.07 active(U262(tt)) -> mark(tt) 101.64/27.07 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.07 active(U272(tt)) -> mark(tt) 101.64/27.07 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.07 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.07 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.07 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.07 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.07 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.07 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.07 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.07 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.07 active(U304(tt, Y)) -> mark(Y) 101.64/27.07 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.07 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.07 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.07 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.07 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.07 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.07 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.07 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.07 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.07 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.07 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.07 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.07 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.07 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.07 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.07 active(U334(tt, XS)) -> mark(XS) 101.64/27.07 active(U34(tt, N)) -> mark(N) 101.64/27.07 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.07 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.07 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.07 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.07 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.07 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.07 active(U46(tt)) -> mark(tt) 101.64/27.07 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.07 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.07 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.07 active(U56(tt)) -> mark(tt) 101.64/27.07 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.07 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.07 active(U63(tt)) -> mark(tt) 101.64/27.07 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.07 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.07 active(U73(tt)) -> mark(tt) 101.64/27.07 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.07 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.07 active(U83(tt)) -> mark(tt) 101.64/27.07 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.07 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.07 active(U93(tt)) -> mark(tt) 101.64/27.07 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.07 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.07 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.07 active(isLNat(nil)) -> mark(tt) 101.64/27.07 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.07 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.07 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.07 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.07 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isLNatKind(nil)) -> mark(tt) 101.64/27.07 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.07 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.07 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.07 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.07 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.07 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.07 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.07 active(isNatural(0')) -> mark(tt) 101.64/27.07 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.07 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.07 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isNaturalKind(0')) -> mark(tt) 101.64/27.07 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.07 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.07 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.07 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.07 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.07 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.07 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.07 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.07 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.07 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.07 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.07 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.07 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.07 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.07 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.07 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.07 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.07 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.07 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.07 active(U106(X)) -> U106(active(X)) 101.64/27.07 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.08 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.08 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.08 active(U112(X)) -> U112(active(X)) 101.64/27.08 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.08 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.08 active(U122(X)) -> U122(active(X)) 101.64/27.08 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.08 active(U131(X)) -> U131(active(X)) 101.64/27.08 active(snd(X)) -> snd(active(X)) 101.64/27.08 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.08 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.08 active(U141(X)) -> U141(active(X)) 101.64/27.08 active(U151(X)) -> U151(active(X)) 101.64/27.08 active(U161(X)) -> U161(active(X)) 101.64/27.08 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.08 active(U172(X)) -> U172(active(X)) 101.64/27.08 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.08 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.08 active(U183(X)) -> U183(active(X)) 101.64/27.08 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.08 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.08 active(U193(X)) -> U193(active(X)) 101.64/27.08 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.08 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.08 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.08 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.08 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.08 active(U206(X)) -> U206(active(X)) 101.64/27.08 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.08 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.08 active(U211(X)) -> U211(active(X)) 101.64/27.08 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.08 active(U221(X)) -> U221(active(X)) 101.64/27.08 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.08 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.08 active(U232(X)) -> U232(active(X)) 101.64/27.08 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.08 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.08 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.08 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.08 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.08 active(U246(X)) -> U246(active(X)) 101.64/27.08 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.08 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.08 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.08 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.08 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.08 active(U256(X)) -> U256(active(X)) 101.64/27.08 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.08 active(U262(X)) -> U262(active(X)) 101.64/27.08 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.08 active(U272(X)) -> U272(active(X)) 101.64/27.08 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.08 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.08 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.08 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.08 active(s(X)) -> s(active(X)) 101.64/27.08 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.08 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.08 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.08 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.08 active(head(X)) -> head(active(X)) 101.64/27.08 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.08 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.08 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.08 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.08 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.08 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.08 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.08 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.08 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.08 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.08 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.08 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.08 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.08 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.08 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.08 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.08 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.08 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.08 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.08 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.08 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.08 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.08 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.08 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.08 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.08 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.08 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.08 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.08 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.08 active(fst(X)) -> fst(active(X)) 101.64/27.08 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.08 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.08 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.08 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.08 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.08 active(U46(X)) -> U46(active(X)) 101.64/27.08 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.08 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.08 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.08 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.08 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.08 active(U56(X)) -> U56(active(X)) 101.64/27.08 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.08 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.08 active(U63(X)) -> U63(active(X)) 101.64/27.08 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.08 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.08 active(U73(X)) -> U73(active(X)) 101.64/27.08 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.08 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.08 active(U83(X)) -> U83(active(X)) 101.64/27.08 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.08 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.08 active(U93(X)) -> U93(active(X)) 101.64/27.08 active(tail(X)) -> tail(active(X)) 101.64/27.08 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.08 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.08 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.08 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.08 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.08 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.08 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.08 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.08 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.08 U106(mark(X)) -> mark(U106(X)) 101.64/27.08 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.08 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.08 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.08 U112(mark(X)) -> mark(U112(X)) 101.64/27.08 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.08 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.08 U122(mark(X)) -> mark(U122(X)) 101.64/27.08 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.08 U131(mark(X)) -> mark(U131(X)) 101.64/27.08 snd(mark(X)) -> mark(snd(X)) 101.64/27.08 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.08 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.08 U141(mark(X)) -> mark(U141(X)) 101.64/27.08 U151(mark(X)) -> mark(U151(X)) 101.64/27.08 U161(mark(X)) -> mark(U161(X)) 101.64/27.08 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.08 U172(mark(X)) -> mark(U172(X)) 101.64/27.08 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.08 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.08 U183(mark(X)) -> mark(U183(X)) 101.64/27.08 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.08 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.08 U193(mark(X)) -> mark(U193(X)) 101.64/27.08 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.08 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.08 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.08 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.08 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.08 U206(mark(X)) -> mark(U206(X)) 101.64/27.08 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.08 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.08 U211(mark(X)) -> mark(U211(X)) 101.64/27.08 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.08 U221(mark(X)) -> mark(U221(X)) 101.64/27.08 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.08 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.08 U232(mark(X)) -> mark(U232(X)) 101.64/27.08 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.08 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.08 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.08 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.08 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.08 U246(mark(X)) -> mark(U246(X)) 101.64/27.08 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.08 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.08 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.08 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.08 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.08 U256(mark(X)) -> mark(U256(X)) 101.64/27.08 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.08 U262(mark(X)) -> mark(U262(X)) 101.64/27.08 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.08 U272(mark(X)) -> mark(U272(X)) 101.64/27.08 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.08 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.08 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.08 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.08 s(mark(X)) -> mark(s(X)) 101.64/27.08 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.08 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.08 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.08 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.08 head(mark(X)) -> mark(head(X)) 101.64/27.08 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.08 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.08 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.08 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.08 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.08 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.08 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.08 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.08 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.08 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.08 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.08 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.08 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.08 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.08 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.08 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.08 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.08 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.08 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.08 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.08 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.08 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.08 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.08 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.08 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.08 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.08 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.08 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.08 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.08 fst(mark(X)) -> mark(fst(X)) 101.64/27.08 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.08 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.08 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.08 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.08 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.08 U46(mark(X)) -> mark(U46(X)) 101.64/27.08 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.08 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.08 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.08 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.08 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.08 U56(mark(X)) -> mark(U56(X)) 101.64/27.08 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.08 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.08 U63(mark(X)) -> mark(U63(X)) 101.64/27.08 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.08 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.08 U73(mark(X)) -> mark(U73(X)) 101.64/27.08 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.08 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.08 U83(mark(X)) -> mark(U83(X)) 101.64/27.08 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.08 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.08 U93(mark(X)) -> mark(U93(X)) 101.64/27.08 tail(mark(X)) -> mark(tail(X)) 101.64/27.08 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.08 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.08 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.08 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.08 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(tt) -> ok(tt) 101.64/27.08 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.08 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.08 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.08 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.08 proper(U106(X)) -> U106(proper(X)) 101.64/27.08 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.08 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.08 proper(U112(X)) -> U112(proper(X)) 101.64/27.08 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.08 proper(U122(X)) -> U122(proper(X)) 101.64/27.08 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U131(X)) -> U131(proper(X)) 101.64/27.08 proper(snd(X)) -> snd(proper(X)) 101.64/27.08 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.08 proper(U141(X)) -> U141(proper(X)) 101.64/27.08 proper(U151(X)) -> U151(proper(X)) 101.64/27.08 proper(U161(X)) -> U161(proper(X)) 101.64/27.08 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.08 proper(U172(X)) -> U172(proper(X)) 101.64/27.08 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.08 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.08 proper(U183(X)) -> U183(proper(X)) 101.64/27.08 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.08 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.08 proper(U193(X)) -> U193(proper(X)) 101.64/27.08 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.08 proper(U206(X)) -> U206(proper(X)) 101.64/27.08 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U211(X)) -> U211(proper(X)) 101.64/27.08 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U221(X)) -> U221(proper(X)) 101.64/27.08 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.08 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.08 proper(U232(X)) -> U232(proper(X)) 101.64/27.08 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.08 proper(U246(X)) -> U246(proper(X)) 101.64/27.08 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.08 proper(U256(X)) -> U256(proper(X)) 101.64/27.08 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.08 proper(U262(X)) -> U262(proper(X)) 101.64/27.08 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.08 proper(U272(X)) -> U272(proper(X)) 101.64/27.08 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.08 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.08 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.08 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.08 proper(s(X)) -> s(proper(X)) 101.64/27.08 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(head(X)) -> head(proper(X)) 101.64/27.08 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.08 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.08 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.08 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.08 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.08 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.08 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.08 proper(nil) -> ok(nil) 101.64/27.08 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.08 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.08 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.08 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.08 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.08 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(fst(X)) -> fst(proper(X)) 101.64/27.08 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.08 proper(U46(X)) -> U46(proper(X)) 101.64/27.08 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.08 proper(U56(X)) -> U56(proper(X)) 101.64/27.08 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.08 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.08 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.08 proper(U63(X)) -> U63(proper(X)) 101.64/27.08 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.08 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.08 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.08 proper(U73(X)) -> U73(proper(X)) 101.64/27.08 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.08 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.08 proper(U83(X)) -> U83(proper(X)) 101.64/27.08 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.08 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.08 proper(U93(X)) -> U93(proper(X)) 101.64/27.08 proper(tail(X)) -> tail(proper(X)) 101.64/27.08 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.08 proper(0') -> ok(0') 101.64/27.08 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.08 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.08 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.08 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.08 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.08 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.08 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.08 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.08 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.08 U106(ok(X)) -> ok(U106(X)) 101.64/27.08 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.08 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.08 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.08 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.08 U112(ok(X)) -> ok(U112(X)) 101.64/27.08 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.08 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.08 U122(ok(X)) -> ok(U122(X)) 101.64/27.08 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.08 U131(ok(X)) -> ok(U131(X)) 101.64/27.08 snd(ok(X)) -> ok(snd(X)) 101.64/27.08 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.08 U141(ok(X)) -> ok(U141(X)) 101.64/27.08 U151(ok(X)) -> ok(U151(X)) 101.64/27.08 U161(ok(X)) -> ok(U161(X)) 101.64/27.08 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.08 U172(ok(X)) -> ok(U172(X)) 101.64/27.08 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.08 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.08 U183(ok(X)) -> ok(U183(X)) 101.64/27.08 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.08 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.08 U193(ok(X)) -> ok(U193(X)) 101.64/27.08 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.08 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.08 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.08 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.08 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.08 U206(ok(X)) -> ok(U206(X)) 101.64/27.08 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.08 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.08 U211(ok(X)) -> ok(U211(X)) 101.64/27.08 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.08 U221(ok(X)) -> ok(U221(X)) 101.64/27.08 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.08 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.08 U232(ok(X)) -> ok(U232(X)) 101.64/27.08 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.08 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.08 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.08 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.08 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.08 U246(ok(X)) -> ok(U246(X)) 101.64/27.08 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.08 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.08 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.08 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.08 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.08 U256(ok(X)) -> ok(U256(X)) 101.64/27.08 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.08 U262(ok(X)) -> ok(U262(X)) 101.64/27.08 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.08 U272(ok(X)) -> ok(U272(X)) 101.64/27.08 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.08 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.08 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.08 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.08 s(ok(X)) -> ok(s(X)) 101.64/27.08 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.08 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.08 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.08 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.08 head(ok(X)) -> ok(head(X)) 101.64/27.08 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.08 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.08 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.08 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.08 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.08 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.08 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.08 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.08 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.08 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.08 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.08 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.08 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.08 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.08 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.08 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.08 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.08 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.08 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.08 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.08 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.08 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.08 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.08 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.08 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.08 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.08 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.08 fst(ok(X)) -> ok(fst(X)) 101.64/27.08 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.08 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.08 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.08 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.08 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.08 U46(ok(X)) -> ok(U46(X)) 101.64/27.08 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.08 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.08 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.08 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.08 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.08 U56(ok(X)) -> ok(U56(X)) 101.64/27.08 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.08 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.08 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.08 U63(ok(X)) -> ok(U63(X)) 101.64/27.08 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.08 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.08 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.08 U73(ok(X)) -> ok(U73(X)) 101.64/27.08 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.08 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.08 U83(ok(X)) -> ok(U83(X)) 101.64/27.08 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.08 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.08 U93(ok(X)) -> ok(U93(X)) 101.64/27.08 tail(ok(X)) -> ok(tail(X)) 101.64/27.08 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.08 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.08 top(mark(X)) -> top(proper(X)) 101.64/27.08 top(ok(X)) -> top(active(X)) 101.64/27.08 101.64/27.08 Types: 101.64/27.08 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 tt :: tt:mark:nil:0':ok 101.64/27.08 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 nil :: tt:mark:nil:0':ok 101.64/27.08 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 0' :: tt:mark:nil:0':ok 101.64/27.08 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 top :: tt:mark:nil:0':ok -> top 101.64/27.08 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.08 hole_top2_0 :: top 101.64/27.08 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.08 101.64/27.08 101.64/27.08 Lemmas: 101.64/27.08 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.08 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.08 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.08 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.08 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.08 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.08 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.08 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.08 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.08 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.08 101.64/27.08 101.64/27.08 Generator Equations: 101.64/27.08 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.08 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.08 101.64/27.08 101.64/27.08 The following defined symbols remain to be analysed: 101.64/27.08 snd, active, splitAt, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.08 101.64/27.08 They will be analysed ascendingly in the following order: 101.64/27.08 snd < active 101.64/27.08 splitAt < active 101.64/27.08 U172 < active 101.64/27.08 U182 < active 101.64/27.08 U183 < active 101.64/27.08 U192 < active 101.64/27.08 U193 < active 101.64/27.08 U202 < active 101.64/27.08 U203 < active 101.64/27.08 U204 < active 101.64/27.08 U205 < active 101.64/27.08 U206 < active 101.64/27.08 U22 < active 101.64/27.08 U23 < active 101.64/27.08 U24 < active 101.64/27.08 U232 < active 101.64/27.08 U242 < active 101.64/27.08 U243 < active 101.64/27.08 U244 < active 101.64/27.08 U245 < active 101.64/27.08 U246 < active 101.64/27.08 U252 < active 101.64/27.08 U253 < active 101.64/27.08 U254 < active 101.64/27.08 U255 < active 101.64/27.08 U256 < active 101.64/27.08 U262 < active 101.64/27.08 U272 < active 101.64/27.08 U282 < active 101.64/27.08 cons < active 101.64/27.08 natsFrom < active 101.64/27.08 s < active 101.64/27.08 U292 < active 101.64/27.08 U293 < active 101.64/27.08 U294 < active 101.64/27.08 head < active 101.64/27.08 afterNth < active 101.64/27.08 U302 < active 101.64/27.08 U303 < active 101.64/27.08 U304 < active 101.64/27.08 U32 < active 101.64/27.08 U312 < active 101.64/27.08 pair < active 101.64/27.08 U33 < active 101.64/27.08 U322 < active 101.64/27.08 U323 < active 101.64/27.08 U324 < active 101.64/27.08 U325 < active 101.64/27.08 U326 < active 101.64/27.08 U327 < active 101.64/27.08 U34 < active 101.64/27.08 U332 < active 101.64/27.08 U333 < active 101.64/27.08 U334 < active 101.64/27.08 U342 < active 101.64/27.08 U343 < active 101.64/27.08 U344 < active 101.64/27.08 fst < active 101.64/27.08 U42 < active 101.64/27.08 U43 < active 101.64/27.08 U44 < active 101.64/27.08 U45 < active 101.64/27.08 U46 < active 101.64/27.08 U52 < active 101.64/27.08 U53 < active 101.64/27.08 U54 < active 101.64/27.08 U55 < active 101.64/27.08 U56 < active 101.64/27.08 U62 < active 101.64/27.08 isPLNatKind < active 101.64/27.08 U63 < active 101.64/27.08 isPLNat < active 101.64/27.08 U72 < active 101.64/27.08 U73 < active 101.64/27.08 U82 < active 101.64/27.08 U83 < active 101.64/27.08 U92 < active 101.64/27.08 U93 < active 101.64/27.08 U11 < active 101.64/27.08 U21 < active 101.64/27.08 U31 < active 101.64/27.08 U41 < active 101.64/27.08 U51 < active 101.64/27.08 U61 < active 101.64/27.08 U71 < active 101.64/27.08 U81 < active 101.64/27.08 U91 < active 101.64/27.08 U101 < active 101.64/27.08 U111 < active 101.64/27.08 U121 < active 101.64/27.08 U131 < active 101.64/27.08 U141 < active 101.64/27.08 U151 < active 101.64/27.08 U161 < active 101.64/27.08 U171 < active 101.64/27.08 U181 < active 101.64/27.08 U191 < active 101.64/27.08 U201 < active 101.64/27.08 U211 < active 101.64/27.08 U221 < active 101.64/27.08 U231 < active 101.64/27.08 U241 < active 101.64/27.08 U251 < active 101.64/27.08 U261 < active 101.64/27.08 U271 < active 101.64/27.08 U281 < active 101.64/27.08 U291 < active 101.64/27.08 U301 < active 101.64/27.08 U311 < active 101.64/27.08 U321 < active 101.64/27.08 U331 < active 101.64/27.08 U341 < active 101.64/27.08 tail < active 101.64/27.08 take < active 101.64/27.08 sel < active 101.64/27.08 active < top 101.64/27.08 snd < proper 101.64/27.08 splitAt < proper 101.64/27.08 U172 < proper 101.64/27.08 U182 < proper 101.64/27.08 U183 < proper 101.64/27.08 U192 < proper 101.64/27.08 U193 < proper 101.64/27.08 U202 < proper 101.64/27.08 U203 < proper 101.64/27.08 U204 < proper 101.64/27.08 U205 < proper 101.64/27.08 U206 < proper 101.64/27.08 U22 < proper 101.64/27.08 U23 < proper 101.64/27.08 U24 < proper 101.64/27.08 U232 < proper 101.64/27.08 U242 < proper 101.64/27.08 U243 < proper 101.64/27.08 U244 < proper 101.64/27.08 U245 < proper 101.64/27.08 U246 < proper 101.64/27.08 U252 < proper 101.64/27.08 U253 < proper 101.64/27.08 U254 < proper 101.64/27.08 U255 < proper 101.64/27.08 U256 < proper 101.64/27.08 U262 < proper 101.64/27.08 U272 < proper 101.64/27.08 U282 < proper 101.64/27.08 cons < proper 101.64/27.08 natsFrom < proper 101.64/27.08 s < proper 101.64/27.08 U292 < proper 101.64/27.08 U293 < proper 101.64/27.08 U294 < proper 101.64/27.08 head < proper 101.64/27.08 afterNth < proper 101.64/27.08 U302 < proper 101.64/27.08 U303 < proper 101.64/27.08 U304 < proper 101.64/27.08 U32 < proper 101.64/27.08 U312 < proper 101.64/27.08 pair < proper 101.64/27.08 U33 < proper 101.64/27.08 U322 < proper 101.64/27.08 U323 < proper 101.64/27.08 U324 < proper 101.64/27.08 U325 < proper 101.64/27.08 U326 < proper 101.64/27.08 U327 < proper 101.64/27.08 U34 < proper 101.64/27.08 U332 < proper 101.64/27.08 U333 < proper 101.64/27.08 U334 < proper 101.64/27.08 U342 < proper 101.64/27.08 U343 < proper 101.64/27.08 U344 < proper 101.64/27.08 fst < proper 101.64/27.08 U42 < proper 101.64/27.08 U43 < proper 101.64/27.08 U44 < proper 101.64/27.08 U45 < proper 101.64/27.08 U46 < proper 101.64/27.08 U52 < proper 101.64/27.08 U53 < proper 101.64/27.08 U54 < proper 101.64/27.08 U55 < proper 101.64/27.08 U56 < proper 101.64/27.08 U62 < proper 101.64/27.08 isPLNatKind < proper 101.64/27.08 U63 < proper 101.64/27.08 isPLNat < proper 101.64/27.08 U72 < proper 101.64/27.08 U73 < proper 101.64/27.08 U82 < proper 101.64/27.08 U83 < proper 101.64/27.08 U92 < proper 101.64/27.08 U93 < proper 101.64/27.08 U11 < proper 101.64/27.08 U21 < proper 101.64/27.08 U31 < proper 101.64/27.08 U41 < proper 101.64/27.08 U51 < proper 101.64/27.08 U61 < proper 101.64/27.08 U71 < proper 101.64/27.08 U81 < proper 101.64/27.08 U91 < proper 101.64/27.08 U101 < proper 101.64/27.08 U111 < proper 101.64/27.08 U121 < proper 101.64/27.08 U131 < proper 101.64/27.08 U141 < proper 101.64/27.08 U151 < proper 101.64/27.08 U161 < proper 101.64/27.08 U171 < proper 101.64/27.08 U181 < proper 101.64/27.08 U191 < proper 101.64/27.08 U201 < proper 101.64/27.08 U211 < proper 101.64/27.08 U221 < proper 101.64/27.08 U231 < proper 101.64/27.08 U241 < proper 101.64/27.08 U251 < proper 101.64/27.08 U261 < proper 101.64/27.08 U271 < proper 101.64/27.08 U281 < proper 101.64/27.08 U291 < proper 101.64/27.08 U301 < proper 101.64/27.08 U311 < proper 101.64/27.08 U321 < proper 101.64/27.08 U331 < proper 101.64/27.08 U341 < proper 101.64/27.08 tail < proper 101.64/27.08 take < proper 101.64/27.08 sel < proper 101.64/27.08 proper < top 101.64/27.08 101.64/27.08 ---------------------------------------- 101.64/27.08 101.64/27.08 (49) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.08 Proved the following rewrite lemma: 101.64/27.08 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.08 101.64/27.08 Induction Base: 101.64/27.08 snd(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.08 101.64/27.08 Induction Step: 101.64/27.08 snd(gen_tt:mark:nil:0':ok3_0(+(1, +(n137279_0, 1)))) ->_R^Omega(1) 101.64/27.08 mark(snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0)))) ->_IH 101.64/27.08 mark(*4_0) 101.64/27.08 101.64/27.08 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.08 ---------------------------------------- 101.64/27.08 101.64/27.08 (50) 101.64/27.08 Obligation: 101.64/27.08 TRS: 101.64/27.08 Rules: 101.64/27.08 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.08 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.08 active(U106(tt)) -> mark(tt) 101.64/27.08 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.08 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.08 active(U112(tt)) -> mark(tt) 101.64/27.08 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.08 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.08 active(U122(tt)) -> mark(tt) 101.64/27.08 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.08 active(U131(tt)) -> mark(tt) 101.64/27.08 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.08 active(U141(tt)) -> mark(tt) 101.64/27.08 active(U151(tt)) -> mark(tt) 101.64/27.08 active(U161(tt)) -> mark(tt) 101.64/27.08 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.08 active(U172(tt)) -> mark(tt) 101.64/27.08 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.08 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.08 active(U183(tt)) -> mark(tt) 101.64/27.08 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.08 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.08 active(U193(tt)) -> mark(tt) 101.64/27.08 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.08 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.08 active(U206(tt)) -> mark(tt) 101.64/27.08 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.08 active(U211(tt)) -> mark(tt) 101.64/27.08 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.08 active(U221(tt)) -> mark(tt) 101.64/27.08 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.08 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.08 active(U232(tt)) -> mark(tt) 101.64/27.08 active(U24(tt, X)) -> mark(X) 101.64/27.08 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.08 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.08 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.08 active(U246(tt)) -> mark(tt) 101.64/27.08 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.08 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.08 active(U256(tt)) -> mark(tt) 101.64/27.08 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.08 active(U262(tt)) -> mark(tt) 101.64/27.08 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.08 active(U272(tt)) -> mark(tt) 101.64/27.08 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.08 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.08 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.08 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.08 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.08 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.08 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.08 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.08 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.08 active(U304(tt, Y)) -> mark(Y) 101.64/27.08 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.08 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.08 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.08 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.08 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.08 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.08 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.08 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.08 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.08 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.08 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.08 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.08 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.08 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.08 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.08 active(U334(tt, XS)) -> mark(XS) 101.64/27.08 active(U34(tt, N)) -> mark(N) 101.64/27.08 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.08 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.08 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.08 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.08 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.08 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.08 active(U46(tt)) -> mark(tt) 101.64/27.08 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.08 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.08 active(U56(tt)) -> mark(tt) 101.64/27.08 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.08 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.08 active(U63(tt)) -> mark(tt) 101.64/27.08 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.08 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.08 active(U73(tt)) -> mark(tt) 101.64/27.08 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.08 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.08 active(U83(tt)) -> mark(tt) 101.64/27.08 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.08 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.08 active(U93(tt)) -> mark(tt) 101.64/27.08 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.08 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.08 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.08 active(isLNat(nil)) -> mark(tt) 101.64/27.08 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.08 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.08 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.08 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.08 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(isLNatKind(nil)) -> mark(tt) 101.64/27.08 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.08 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.08 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.08 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.08 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.08 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.08 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.08 active(isNatural(0')) -> mark(tt) 101.64/27.08 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.08 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.08 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(isNaturalKind(0')) -> mark(tt) 101.64/27.08 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.08 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.08 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.08 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.08 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.08 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.08 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.08 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.08 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.08 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.08 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.08 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.08 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.08 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.08 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.08 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.08 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.08 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.08 active(U106(X)) -> U106(active(X)) 101.64/27.08 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.08 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.08 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.08 active(U112(X)) -> U112(active(X)) 101.64/27.08 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.08 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.08 active(U122(X)) -> U122(active(X)) 101.64/27.08 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.08 active(U131(X)) -> U131(active(X)) 101.64/27.08 active(snd(X)) -> snd(active(X)) 101.64/27.08 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.08 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.08 active(U141(X)) -> U141(active(X)) 101.64/27.08 active(U151(X)) -> U151(active(X)) 101.64/27.08 active(U161(X)) -> U161(active(X)) 101.64/27.08 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.08 active(U172(X)) -> U172(active(X)) 101.64/27.08 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.08 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.08 active(U183(X)) -> U183(active(X)) 101.64/27.08 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.08 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.08 active(U193(X)) -> U193(active(X)) 101.64/27.08 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.08 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.08 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.08 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.08 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.08 active(U206(X)) -> U206(active(X)) 101.64/27.08 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.08 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.08 active(U211(X)) -> U211(active(X)) 101.64/27.08 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.08 active(U221(X)) -> U221(active(X)) 101.64/27.08 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.08 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.08 active(U232(X)) -> U232(active(X)) 101.64/27.08 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.08 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.08 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.08 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.08 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.08 active(U246(X)) -> U246(active(X)) 101.64/27.08 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.08 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.08 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.08 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.08 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.08 active(U256(X)) -> U256(active(X)) 101.64/27.08 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.08 active(U262(X)) -> U262(active(X)) 101.64/27.08 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.08 active(U272(X)) -> U272(active(X)) 101.64/27.08 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.08 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.08 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.08 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.08 active(s(X)) -> s(active(X)) 101.64/27.08 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.08 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.08 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.08 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.08 active(head(X)) -> head(active(X)) 101.64/27.08 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.08 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.08 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.08 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.08 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.08 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.08 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.08 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.08 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.08 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.08 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.08 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.08 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.08 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.08 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.08 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.08 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.08 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.08 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.08 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.08 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.08 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.08 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.08 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.08 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.08 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.08 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.08 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.08 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.08 active(fst(X)) -> fst(active(X)) 101.64/27.08 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.08 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.08 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.08 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.08 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.08 active(U46(X)) -> U46(active(X)) 101.64/27.08 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.08 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.08 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.08 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.08 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.08 active(U56(X)) -> U56(active(X)) 101.64/27.08 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.08 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.08 active(U63(X)) -> U63(active(X)) 101.64/27.08 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.08 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.08 active(U73(X)) -> U73(active(X)) 101.64/27.08 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.08 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.08 active(U83(X)) -> U83(active(X)) 101.64/27.08 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.08 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.08 active(U93(X)) -> U93(active(X)) 101.64/27.08 active(tail(X)) -> tail(active(X)) 101.64/27.08 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.08 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.08 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.08 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.08 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.08 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.08 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.08 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.08 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.08 U106(mark(X)) -> mark(U106(X)) 101.64/27.08 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.08 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.08 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.08 U112(mark(X)) -> mark(U112(X)) 101.64/27.08 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.08 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.08 U122(mark(X)) -> mark(U122(X)) 101.64/27.08 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.08 U131(mark(X)) -> mark(U131(X)) 101.64/27.08 snd(mark(X)) -> mark(snd(X)) 101.64/27.08 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.08 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.08 U141(mark(X)) -> mark(U141(X)) 101.64/27.08 U151(mark(X)) -> mark(U151(X)) 101.64/27.08 U161(mark(X)) -> mark(U161(X)) 101.64/27.08 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.08 U172(mark(X)) -> mark(U172(X)) 101.64/27.08 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.08 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.08 U183(mark(X)) -> mark(U183(X)) 101.64/27.08 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.08 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.08 U193(mark(X)) -> mark(U193(X)) 101.64/27.08 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.08 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.08 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.08 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.08 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.08 U206(mark(X)) -> mark(U206(X)) 101.64/27.08 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.08 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.08 U211(mark(X)) -> mark(U211(X)) 101.64/27.08 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.08 U221(mark(X)) -> mark(U221(X)) 101.64/27.08 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.08 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.08 U232(mark(X)) -> mark(U232(X)) 101.64/27.08 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.08 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.08 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.08 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.08 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.08 U246(mark(X)) -> mark(U246(X)) 101.64/27.08 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.08 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.08 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.08 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.08 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.08 U256(mark(X)) -> mark(U256(X)) 101.64/27.08 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.08 U262(mark(X)) -> mark(U262(X)) 101.64/27.08 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.08 U272(mark(X)) -> mark(U272(X)) 101.64/27.08 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.08 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.08 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.08 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.08 s(mark(X)) -> mark(s(X)) 101.64/27.08 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.08 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.08 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.08 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.08 head(mark(X)) -> mark(head(X)) 101.64/27.08 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.08 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.08 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.08 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.08 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.08 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.08 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.08 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.08 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.08 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.08 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.08 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.08 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.08 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.08 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.08 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.08 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.08 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.08 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.08 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.08 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.08 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.08 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.08 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.08 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.08 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.08 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.08 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.08 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.08 fst(mark(X)) -> mark(fst(X)) 101.64/27.08 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.08 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.08 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.08 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.08 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.08 U46(mark(X)) -> mark(U46(X)) 101.64/27.08 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.08 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.08 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.08 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.08 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.08 U56(mark(X)) -> mark(U56(X)) 101.64/27.08 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.08 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.08 U63(mark(X)) -> mark(U63(X)) 101.64/27.08 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.08 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.08 U73(mark(X)) -> mark(U73(X)) 101.64/27.08 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.08 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.08 U83(mark(X)) -> mark(U83(X)) 101.64/27.08 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.08 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.08 U93(mark(X)) -> mark(U93(X)) 101.64/27.08 tail(mark(X)) -> mark(tail(X)) 101.64/27.08 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.08 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.08 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.08 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.08 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(tt) -> ok(tt) 101.64/27.08 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.08 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.08 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.08 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.08 proper(U106(X)) -> U106(proper(X)) 101.64/27.08 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.08 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.08 proper(U112(X)) -> U112(proper(X)) 101.64/27.08 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.08 proper(U122(X)) -> U122(proper(X)) 101.64/27.08 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U131(X)) -> U131(proper(X)) 101.64/27.08 proper(snd(X)) -> snd(proper(X)) 101.64/27.08 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.08 proper(U141(X)) -> U141(proper(X)) 101.64/27.08 proper(U151(X)) -> U151(proper(X)) 101.64/27.08 proper(U161(X)) -> U161(proper(X)) 101.64/27.08 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.08 proper(U172(X)) -> U172(proper(X)) 101.64/27.08 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.08 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.08 proper(U183(X)) -> U183(proper(X)) 101.64/27.08 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.08 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.08 proper(U193(X)) -> U193(proper(X)) 101.64/27.08 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.08 proper(U206(X)) -> U206(proper(X)) 101.64/27.08 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U211(X)) -> U211(proper(X)) 101.64/27.08 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U221(X)) -> U221(proper(X)) 101.64/27.08 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.08 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.08 proper(U232(X)) -> U232(proper(X)) 101.64/27.08 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.08 proper(U246(X)) -> U246(proper(X)) 101.64/27.08 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.08 proper(U256(X)) -> U256(proper(X)) 101.64/27.08 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.08 proper(U262(X)) -> U262(proper(X)) 101.64/27.08 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.08 proper(U272(X)) -> U272(proper(X)) 101.64/27.08 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.08 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.08 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.08 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.08 proper(s(X)) -> s(proper(X)) 101.64/27.08 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(head(X)) -> head(proper(X)) 101.64/27.08 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.08 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.08 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.08 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.08 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.08 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.08 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.08 proper(nil) -> ok(nil) 101.64/27.08 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.08 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.08 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.08 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.08 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.08 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.08 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(fst(X)) -> fst(proper(X)) 101.64/27.08 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.08 proper(U46(X)) -> U46(proper(X)) 101.64/27.08 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.08 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.08 proper(U56(X)) -> U56(proper(X)) 101.64/27.08 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.08 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.08 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.08 proper(U63(X)) -> U63(proper(X)) 101.64/27.08 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.08 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.08 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.08 proper(U73(X)) -> U73(proper(X)) 101.64/27.08 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.08 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.08 proper(U83(X)) -> U83(proper(X)) 101.64/27.08 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.08 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.08 proper(U93(X)) -> U93(proper(X)) 101.64/27.08 proper(tail(X)) -> tail(proper(X)) 101.64/27.08 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.08 proper(0') -> ok(0') 101.64/27.08 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.08 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.08 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.08 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.08 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.08 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.08 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.08 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.08 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.08 U106(ok(X)) -> ok(U106(X)) 101.64/27.08 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.08 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.08 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.08 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.08 U112(ok(X)) -> ok(U112(X)) 101.64/27.08 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.08 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.08 U122(ok(X)) -> ok(U122(X)) 101.64/27.08 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.08 U131(ok(X)) -> ok(U131(X)) 101.64/27.08 snd(ok(X)) -> ok(snd(X)) 101.64/27.08 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.08 U141(ok(X)) -> ok(U141(X)) 101.64/27.08 U151(ok(X)) -> ok(U151(X)) 101.64/27.08 U161(ok(X)) -> ok(U161(X)) 101.64/27.08 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.08 U172(ok(X)) -> ok(U172(X)) 101.64/27.08 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.08 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.08 U183(ok(X)) -> ok(U183(X)) 101.64/27.08 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.08 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.08 U193(ok(X)) -> ok(U193(X)) 101.64/27.08 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.08 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.08 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.08 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.08 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.08 U206(ok(X)) -> ok(U206(X)) 101.64/27.08 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.08 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.08 U211(ok(X)) -> ok(U211(X)) 101.64/27.08 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.08 U221(ok(X)) -> ok(U221(X)) 101.64/27.08 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.08 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.08 U232(ok(X)) -> ok(U232(X)) 101.64/27.08 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.08 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.08 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.08 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.08 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.08 U246(ok(X)) -> ok(U246(X)) 101.64/27.08 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.08 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.08 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.08 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.08 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.08 U256(ok(X)) -> ok(U256(X)) 101.64/27.08 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.08 U262(ok(X)) -> ok(U262(X)) 101.64/27.08 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.08 U272(ok(X)) -> ok(U272(X)) 101.64/27.08 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.08 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.08 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.08 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.08 s(ok(X)) -> ok(s(X)) 101.64/27.08 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.08 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.08 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.08 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.08 head(ok(X)) -> ok(head(X)) 101.64/27.08 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.08 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.08 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.08 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.08 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.08 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.08 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.08 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.08 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.08 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.08 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.08 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.08 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.08 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.08 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.08 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.08 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.08 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.08 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.08 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.08 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.08 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.08 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.08 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.08 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.08 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.08 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.08 fst(ok(X)) -> ok(fst(X)) 101.64/27.08 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.08 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.08 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.08 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.08 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.08 U46(ok(X)) -> ok(U46(X)) 101.64/27.08 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.08 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.08 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.08 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.08 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.08 U56(ok(X)) -> ok(U56(X)) 101.64/27.08 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.08 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.08 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.08 U63(ok(X)) -> ok(U63(X)) 101.64/27.08 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.08 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.08 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.08 U73(ok(X)) -> ok(U73(X)) 101.64/27.08 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.08 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.08 U83(ok(X)) -> ok(U83(X)) 101.64/27.08 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.08 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.08 U93(ok(X)) -> ok(U93(X)) 101.64/27.08 tail(ok(X)) -> ok(tail(X)) 101.64/27.08 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.08 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.08 top(mark(X)) -> top(proper(X)) 101.64/27.08 top(ok(X)) -> top(active(X)) 101.64/27.08 101.64/27.08 Types: 101.64/27.08 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 tt :: tt:mark:nil:0':ok 101.64/27.08 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 nil :: tt:mark:nil:0':ok 101.64/27.08 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 0' :: tt:mark:nil:0':ok 101.64/27.08 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.08 top :: tt:mark:nil:0':ok -> top 101.64/27.08 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.08 hole_top2_0 :: top 101.64/27.08 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.08 101.64/27.08 101.64/27.08 Lemmas: 101.64/27.08 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.08 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.08 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.08 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.08 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.08 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.08 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.08 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.08 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.08 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.08 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.08 101.64/27.08 101.64/27.08 Generator Equations: 101.64/27.08 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.08 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.08 101.64/27.08 101.64/27.08 The following defined symbols remain to be analysed: 101.64/27.08 splitAt, active, U172, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.08 101.64/27.08 They will be analysed ascendingly in the following order: 101.64/27.08 splitAt < active 101.64/27.08 U172 < active 101.64/27.08 U182 < active 101.64/27.08 U183 < active 101.64/27.08 U192 < active 101.64/27.08 U193 < active 101.64/27.08 U202 < active 101.64/27.08 U203 < active 101.64/27.08 U204 < active 101.64/27.08 U205 < active 101.64/27.08 U206 < active 101.64/27.08 U22 < active 101.64/27.08 U23 < active 101.64/27.08 U24 < active 101.64/27.08 U232 < active 101.64/27.08 U242 < active 101.64/27.08 U243 < active 101.64/27.08 U244 < active 101.64/27.08 U245 < active 101.64/27.08 U246 < active 101.64/27.08 U252 < active 101.64/27.08 U253 < active 101.64/27.08 U254 < active 101.64/27.08 U255 < active 101.64/27.08 U256 < active 101.64/27.08 U262 < active 101.64/27.08 U272 < active 101.64/27.08 U282 < active 101.64/27.08 cons < active 101.64/27.08 natsFrom < active 101.64/27.08 s < active 101.64/27.08 U292 < active 101.64/27.08 U293 < active 101.64/27.08 U294 < active 101.64/27.08 head < active 101.64/27.08 afterNth < active 101.64/27.08 U302 < active 101.64/27.08 U303 < active 101.64/27.08 U304 < active 101.64/27.08 U32 < active 101.64/27.08 U312 < active 101.64/27.08 pair < active 101.64/27.08 U33 < active 101.64/27.08 U322 < active 101.64/27.08 U323 < active 101.64/27.08 U324 < active 101.64/27.08 U325 < active 101.64/27.08 U326 < active 101.64/27.08 U327 < active 101.64/27.08 U34 < active 101.64/27.08 U332 < active 101.64/27.08 U333 < active 101.64/27.08 U334 < active 101.64/27.08 U342 < active 101.64/27.08 U343 < active 101.64/27.08 U344 < active 101.64/27.08 fst < active 101.64/27.08 U42 < active 101.64/27.08 U43 < active 101.64/27.08 U44 < active 101.64/27.08 U45 < active 101.64/27.08 U46 < active 101.64/27.08 U52 < active 101.64/27.08 U53 < active 101.64/27.08 U54 < active 101.64/27.08 U55 < active 101.64/27.08 U56 < active 101.64/27.08 U62 < active 101.64/27.08 isPLNatKind < active 101.64/27.08 U63 < active 101.64/27.08 isPLNat < active 101.64/27.08 U72 < active 101.64/27.08 U73 < active 101.64/27.08 U82 < active 101.64/27.08 U83 < active 101.64/27.08 U92 < active 101.64/27.08 U93 < active 101.64/27.08 U11 < active 101.64/27.08 U21 < active 101.64/27.08 U31 < active 101.64/27.08 U41 < active 101.64/27.08 U51 < active 101.64/27.08 U61 < active 101.64/27.08 U71 < active 101.64/27.08 U81 < active 101.64/27.08 U91 < active 101.64/27.08 U101 < active 101.64/27.08 U111 < active 101.64/27.08 U121 < active 101.64/27.08 U131 < active 101.64/27.08 U141 < active 101.64/27.08 U151 < active 101.64/27.08 U161 < active 101.64/27.08 U171 < active 101.64/27.08 U181 < active 101.64/27.08 U191 < active 101.64/27.08 U201 < active 101.64/27.08 U211 < active 101.64/27.08 U221 < active 101.64/27.08 U231 < active 101.64/27.08 U241 < active 101.64/27.08 U251 < active 101.64/27.08 U261 < active 101.64/27.08 U271 < active 101.64/27.08 U281 < active 101.64/27.08 U291 < active 101.64/27.08 U301 < active 101.64/27.08 U311 < active 101.64/27.08 U321 < active 101.64/27.08 U331 < active 101.64/27.08 U341 < active 101.64/27.08 tail < active 101.64/27.08 take < active 101.64/27.08 sel < active 101.64/27.08 active < top 101.64/27.08 splitAt < proper 101.64/27.08 U172 < proper 101.64/27.08 U182 < proper 101.64/27.08 U183 < proper 101.64/27.08 U192 < proper 101.64/27.08 U193 < proper 101.64/27.08 U202 < proper 101.64/27.08 U203 < proper 101.64/27.08 U204 < proper 101.64/27.08 U205 < proper 101.64/27.08 U206 < proper 101.64/27.08 U22 < proper 101.64/27.08 U23 < proper 101.64/27.08 U24 < proper 101.64/27.08 U232 < proper 101.64/27.08 U242 < proper 101.64/27.08 U243 < proper 101.64/27.08 U244 < proper 101.64/27.08 U245 < proper 101.64/27.08 U246 < proper 101.64/27.08 U252 < proper 101.64/27.08 U253 < proper 101.64/27.08 U254 < proper 101.64/27.08 U255 < proper 101.64/27.08 U256 < proper 101.64/27.08 U262 < proper 101.64/27.08 U272 < proper 101.64/27.08 U282 < proper 101.64/27.08 cons < proper 101.64/27.08 natsFrom < proper 101.64/27.08 s < proper 101.64/27.08 U292 < proper 101.64/27.08 U293 < proper 101.64/27.08 U294 < proper 101.64/27.08 head < proper 101.64/27.08 afterNth < proper 101.64/27.08 U302 < proper 101.64/27.08 U303 < proper 101.64/27.08 U304 < proper 101.64/27.08 U32 < proper 101.64/27.08 U312 < proper 101.64/27.08 pair < proper 101.64/27.08 U33 < proper 101.64/27.08 U322 < proper 101.64/27.08 U323 < proper 101.64/27.08 U324 < proper 101.64/27.08 U325 < proper 101.64/27.08 U326 < proper 101.64/27.08 U327 < proper 101.64/27.08 U34 < proper 101.64/27.08 U332 < proper 101.64/27.08 U333 < proper 101.64/27.08 U334 < proper 101.64/27.08 U342 < proper 101.64/27.08 U343 < proper 101.64/27.08 U344 < proper 101.64/27.08 fst < proper 101.64/27.08 U42 < proper 101.64/27.08 U43 < proper 101.64/27.08 U44 < proper 101.64/27.08 U45 < proper 101.64/27.08 U46 < proper 101.64/27.08 U52 < proper 101.64/27.08 U53 < proper 101.64/27.08 U54 < proper 101.64/27.08 U55 < proper 101.64/27.08 U56 < proper 101.64/27.08 U62 < proper 101.64/27.08 isPLNatKind < proper 101.64/27.08 U63 < proper 101.64/27.08 isPLNat < proper 101.64/27.08 U72 < proper 101.64/27.08 U73 < proper 101.64/27.08 U82 < proper 101.64/27.08 U83 < proper 101.64/27.08 U92 < proper 101.64/27.08 U93 < proper 101.64/27.08 U11 < proper 101.64/27.08 U21 < proper 101.64/27.08 U31 < proper 101.64/27.08 U41 < proper 101.64/27.08 U51 < proper 101.64/27.08 U61 < proper 101.64/27.08 U71 < proper 101.64/27.08 U81 < proper 101.64/27.08 U91 < proper 101.64/27.08 U101 < proper 101.64/27.08 U111 < proper 101.64/27.08 U121 < proper 101.64/27.08 U131 < proper 101.64/27.08 U141 < proper 101.64/27.08 U151 < proper 101.64/27.08 U161 < proper 101.64/27.08 U171 < proper 101.64/27.08 U181 < proper 101.64/27.08 U191 < proper 101.64/27.08 U201 < proper 101.64/27.08 U211 < proper 101.64/27.08 U221 < proper 101.64/27.08 U231 < proper 101.64/27.08 U241 < proper 101.64/27.08 U251 < proper 101.64/27.08 U261 < proper 101.64/27.08 U271 < proper 101.64/27.08 U281 < proper 101.64/27.08 U291 < proper 101.64/27.08 U301 < proper 101.64/27.08 U311 < proper 101.64/27.08 U321 < proper 101.64/27.08 U331 < proper 101.64/27.08 U341 < proper 101.64/27.08 tail < proper 101.64/27.08 take < proper 101.64/27.08 sel < proper 101.64/27.08 proper < top 101.64/27.08 101.64/27.08 ---------------------------------------- 101.64/27.08 101.64/27.08 (51) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.08 Proved the following rewrite lemma: 101.64/27.08 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.08 101.64/27.08 Induction Base: 101.64/27.08 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.64/27.08 101.64/27.08 Induction Step: 101.64/27.08 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, +(n141197_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.64/27.08 mark(splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.64/27.08 mark(*4_0) 101.64/27.08 101.64/27.08 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.08 ---------------------------------------- 101.64/27.08 101.64/27.08 (52) 101.64/27.08 Obligation: 101.64/27.08 TRS: 101.64/27.08 Rules: 101.64/27.08 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.08 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.08 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.08 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.08 active(U106(tt)) -> mark(tt) 101.64/27.08 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.08 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.08 active(U112(tt)) -> mark(tt) 101.64/27.08 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.08 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.08 active(U122(tt)) -> mark(tt) 101.64/27.08 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.08 active(U131(tt)) -> mark(tt) 101.64/27.09 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.09 active(U141(tt)) -> mark(tt) 101.64/27.09 active(U151(tt)) -> mark(tt) 101.64/27.09 active(U161(tt)) -> mark(tt) 101.64/27.09 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.09 active(U172(tt)) -> mark(tt) 101.64/27.09 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.09 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.09 active(U183(tt)) -> mark(tt) 101.64/27.09 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.09 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.09 active(U193(tt)) -> mark(tt) 101.64/27.09 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.09 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.09 active(U206(tt)) -> mark(tt) 101.64/27.09 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.09 active(U211(tt)) -> mark(tt) 101.64/27.09 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.09 active(U221(tt)) -> mark(tt) 101.64/27.09 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.09 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.09 active(U232(tt)) -> mark(tt) 101.64/27.09 active(U24(tt, X)) -> mark(X) 101.64/27.09 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.09 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.09 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.09 active(U246(tt)) -> mark(tt) 101.64/27.09 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.09 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.09 active(U256(tt)) -> mark(tt) 101.64/27.09 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.09 active(U262(tt)) -> mark(tt) 101.64/27.09 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.09 active(U272(tt)) -> mark(tt) 101.64/27.09 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.09 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.09 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.09 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.09 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.09 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.09 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.09 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.09 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.09 active(U304(tt, Y)) -> mark(Y) 101.64/27.09 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.09 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.09 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.09 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.09 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.09 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.09 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.09 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.09 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.09 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.09 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.09 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.09 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.09 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.09 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.09 active(U334(tt, XS)) -> mark(XS) 101.64/27.09 active(U34(tt, N)) -> mark(N) 101.64/27.09 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.09 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.09 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.09 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.09 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.09 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.09 active(U46(tt)) -> mark(tt) 101.64/27.09 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.09 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.09 active(U56(tt)) -> mark(tt) 101.64/27.09 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.09 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.09 active(U63(tt)) -> mark(tt) 101.64/27.09 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.09 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.09 active(U73(tt)) -> mark(tt) 101.64/27.09 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.09 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.09 active(U83(tt)) -> mark(tt) 101.64/27.09 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.09 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.09 active(U93(tt)) -> mark(tt) 101.64/27.09 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.09 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.09 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.09 active(isLNat(nil)) -> mark(tt) 101.64/27.09 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.09 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.09 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.09 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.09 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNatKind(nil)) -> mark(tt) 101.64/27.09 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.09 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.09 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.09 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.09 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.09 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.09 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.09 active(isNatural(0')) -> mark(tt) 101.64/27.09 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.09 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.09 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isNaturalKind(0')) -> mark(tt) 101.64/27.09 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.09 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.09 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.09 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.09 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.09 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.09 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.09 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.09 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.09 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.09 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.09 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.09 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.09 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.09 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.09 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.09 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.09 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.09 active(U106(X)) -> U106(active(X)) 101.64/27.09 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.09 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.09 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.09 active(U112(X)) -> U112(active(X)) 101.64/27.09 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.09 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.09 active(U122(X)) -> U122(active(X)) 101.64/27.09 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.09 active(U131(X)) -> U131(active(X)) 101.64/27.09 active(snd(X)) -> snd(active(X)) 101.64/27.09 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.09 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.09 active(U141(X)) -> U141(active(X)) 101.64/27.09 active(U151(X)) -> U151(active(X)) 101.64/27.09 active(U161(X)) -> U161(active(X)) 101.64/27.09 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.09 active(U172(X)) -> U172(active(X)) 101.64/27.09 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.09 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.09 active(U183(X)) -> U183(active(X)) 101.64/27.09 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.09 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.09 active(U193(X)) -> U193(active(X)) 101.64/27.09 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.09 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.09 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.09 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.09 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.09 active(U206(X)) -> U206(active(X)) 101.64/27.09 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.09 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.09 active(U211(X)) -> U211(active(X)) 101.64/27.09 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.09 active(U221(X)) -> U221(active(X)) 101.64/27.09 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.09 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.09 active(U232(X)) -> U232(active(X)) 101.64/27.09 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.09 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.09 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.09 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.09 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.09 active(U246(X)) -> U246(active(X)) 101.64/27.09 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.09 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.09 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.09 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.09 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.09 active(U256(X)) -> U256(active(X)) 101.64/27.09 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.09 active(U262(X)) -> U262(active(X)) 101.64/27.09 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.09 active(U272(X)) -> U272(active(X)) 101.64/27.09 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.09 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.09 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.09 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.09 active(s(X)) -> s(active(X)) 101.64/27.09 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.09 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.09 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.09 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.09 active(head(X)) -> head(active(X)) 101.64/27.09 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.09 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.09 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.09 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.09 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.09 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.09 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.09 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.09 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.09 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.09 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.09 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.09 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.09 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.09 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.09 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.09 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.09 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.09 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.09 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.09 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.09 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.09 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.09 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.09 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.09 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.09 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.09 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.09 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.09 active(fst(X)) -> fst(active(X)) 101.64/27.09 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.09 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.09 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.09 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.09 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.09 active(U46(X)) -> U46(active(X)) 101.64/27.09 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.09 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.09 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.09 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.09 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.09 active(U56(X)) -> U56(active(X)) 101.64/27.09 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.09 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.09 active(U63(X)) -> U63(active(X)) 101.64/27.09 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.09 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.09 active(U73(X)) -> U73(active(X)) 101.64/27.09 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.09 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.09 active(U83(X)) -> U83(active(X)) 101.64/27.09 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.09 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.09 active(U93(X)) -> U93(active(X)) 101.64/27.09 active(tail(X)) -> tail(active(X)) 101.64/27.09 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.09 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.09 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.09 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.09 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.09 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.09 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.09 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.09 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.09 U106(mark(X)) -> mark(U106(X)) 101.64/27.09 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.09 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.09 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.09 U112(mark(X)) -> mark(U112(X)) 101.64/27.09 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.09 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.09 U122(mark(X)) -> mark(U122(X)) 101.64/27.09 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.09 U131(mark(X)) -> mark(U131(X)) 101.64/27.09 snd(mark(X)) -> mark(snd(X)) 101.64/27.09 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.09 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.09 U141(mark(X)) -> mark(U141(X)) 101.64/27.09 U151(mark(X)) -> mark(U151(X)) 101.64/27.09 U161(mark(X)) -> mark(U161(X)) 101.64/27.09 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.09 U172(mark(X)) -> mark(U172(X)) 101.64/27.09 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.09 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.09 U183(mark(X)) -> mark(U183(X)) 101.64/27.09 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.09 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.09 U193(mark(X)) -> mark(U193(X)) 101.64/27.09 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.09 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.09 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.09 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.09 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.09 U206(mark(X)) -> mark(U206(X)) 101.64/27.09 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.09 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.09 U211(mark(X)) -> mark(U211(X)) 101.64/27.09 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.09 U221(mark(X)) -> mark(U221(X)) 101.64/27.09 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.09 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.09 U232(mark(X)) -> mark(U232(X)) 101.64/27.09 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.09 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.09 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.09 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.09 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.09 U246(mark(X)) -> mark(U246(X)) 101.64/27.09 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.09 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.09 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.09 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.09 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.09 U256(mark(X)) -> mark(U256(X)) 101.64/27.09 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.09 U262(mark(X)) -> mark(U262(X)) 101.64/27.09 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.09 U272(mark(X)) -> mark(U272(X)) 101.64/27.09 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.09 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.09 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.09 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.09 s(mark(X)) -> mark(s(X)) 101.64/27.09 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.09 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.09 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.09 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.09 head(mark(X)) -> mark(head(X)) 101.64/27.09 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.09 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.09 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.09 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.09 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.09 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.09 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.09 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.09 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.09 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.09 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.09 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.09 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.09 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.09 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.09 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.09 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.09 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.09 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.09 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.09 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.09 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.09 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.09 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.09 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.09 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.09 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.09 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.09 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.09 fst(mark(X)) -> mark(fst(X)) 101.64/27.09 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.09 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.09 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.09 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.09 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.09 U46(mark(X)) -> mark(U46(X)) 101.64/27.09 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.09 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.09 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.09 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.09 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.09 U56(mark(X)) -> mark(U56(X)) 101.64/27.09 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.09 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.09 U63(mark(X)) -> mark(U63(X)) 101.64/27.09 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.09 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.09 U73(mark(X)) -> mark(U73(X)) 101.64/27.09 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.09 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.09 U83(mark(X)) -> mark(U83(X)) 101.64/27.09 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.09 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.09 U93(mark(X)) -> mark(U93(X)) 101.64/27.09 tail(mark(X)) -> mark(tail(X)) 101.64/27.09 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.09 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.09 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.09 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.09 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(tt) -> ok(tt) 101.64/27.09 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.09 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.09 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.09 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.09 proper(U106(X)) -> U106(proper(X)) 101.64/27.09 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.09 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.09 proper(U112(X)) -> U112(proper(X)) 101.64/27.09 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.09 proper(U122(X)) -> U122(proper(X)) 101.64/27.09 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U131(X)) -> U131(proper(X)) 101.64/27.09 proper(snd(X)) -> snd(proper(X)) 101.64/27.09 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.09 proper(U141(X)) -> U141(proper(X)) 101.64/27.09 proper(U151(X)) -> U151(proper(X)) 101.64/27.09 proper(U161(X)) -> U161(proper(X)) 101.64/27.09 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.09 proper(U172(X)) -> U172(proper(X)) 101.64/27.09 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.09 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.09 proper(U183(X)) -> U183(proper(X)) 101.64/27.09 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.09 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.09 proper(U193(X)) -> U193(proper(X)) 101.64/27.09 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.09 proper(U206(X)) -> U206(proper(X)) 101.64/27.09 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U211(X)) -> U211(proper(X)) 101.64/27.09 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U221(X)) -> U221(proper(X)) 101.64/27.09 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.09 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.09 proper(U232(X)) -> U232(proper(X)) 101.64/27.09 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.09 proper(U246(X)) -> U246(proper(X)) 101.64/27.09 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.09 proper(U256(X)) -> U256(proper(X)) 101.64/27.09 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.09 proper(U262(X)) -> U262(proper(X)) 101.64/27.09 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.09 proper(U272(X)) -> U272(proper(X)) 101.64/27.09 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.09 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.09 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.09 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.09 proper(s(X)) -> s(proper(X)) 101.64/27.09 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(head(X)) -> head(proper(X)) 101.64/27.09 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.09 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.09 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.09 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.09 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.09 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.09 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.09 proper(nil) -> ok(nil) 101.64/27.09 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.09 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.09 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.09 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.09 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.09 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(fst(X)) -> fst(proper(X)) 101.64/27.09 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.09 proper(U46(X)) -> U46(proper(X)) 101.64/27.09 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.09 proper(U56(X)) -> U56(proper(X)) 101.64/27.09 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.09 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.09 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.09 proper(U63(X)) -> U63(proper(X)) 101.64/27.09 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.09 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.09 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.09 proper(U73(X)) -> U73(proper(X)) 101.64/27.09 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.09 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.09 proper(U83(X)) -> U83(proper(X)) 101.64/27.09 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.09 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.09 proper(U93(X)) -> U93(proper(X)) 101.64/27.09 proper(tail(X)) -> tail(proper(X)) 101.64/27.09 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.09 proper(0') -> ok(0') 101.64/27.09 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.09 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.09 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.09 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.09 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.09 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.09 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.09 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.09 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.09 U106(ok(X)) -> ok(U106(X)) 101.64/27.09 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.09 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.09 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.09 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.09 U112(ok(X)) -> ok(U112(X)) 101.64/27.09 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.09 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.09 U122(ok(X)) -> ok(U122(X)) 101.64/27.09 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.09 U131(ok(X)) -> ok(U131(X)) 101.64/27.09 snd(ok(X)) -> ok(snd(X)) 101.64/27.09 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.09 U141(ok(X)) -> ok(U141(X)) 101.64/27.09 U151(ok(X)) -> ok(U151(X)) 101.64/27.09 U161(ok(X)) -> ok(U161(X)) 101.64/27.09 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.09 U172(ok(X)) -> ok(U172(X)) 101.64/27.09 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.09 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.09 U183(ok(X)) -> ok(U183(X)) 101.64/27.09 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.09 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.09 U193(ok(X)) -> ok(U193(X)) 101.64/27.09 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.09 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.09 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.09 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.09 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.09 U206(ok(X)) -> ok(U206(X)) 101.64/27.09 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.09 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.09 U211(ok(X)) -> ok(U211(X)) 101.64/27.09 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.09 U221(ok(X)) -> ok(U221(X)) 101.64/27.09 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.09 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.09 U232(ok(X)) -> ok(U232(X)) 101.64/27.09 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.09 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.09 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.09 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.09 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.09 U246(ok(X)) -> ok(U246(X)) 101.64/27.09 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.09 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.09 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.09 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.09 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.09 U256(ok(X)) -> ok(U256(X)) 101.64/27.09 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.09 U262(ok(X)) -> ok(U262(X)) 101.64/27.09 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.09 U272(ok(X)) -> ok(U272(X)) 101.64/27.09 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.09 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.09 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.09 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.09 s(ok(X)) -> ok(s(X)) 101.64/27.09 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.09 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.09 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.09 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.09 head(ok(X)) -> ok(head(X)) 101.64/27.09 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.09 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.09 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.09 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.09 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.09 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.09 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.09 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.09 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.09 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.09 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.09 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.09 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.09 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.09 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.09 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.09 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.09 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.09 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.09 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.09 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.09 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.09 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.09 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.09 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.09 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.09 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.09 fst(ok(X)) -> ok(fst(X)) 101.64/27.09 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.09 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.09 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.09 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.09 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.09 U46(ok(X)) -> ok(U46(X)) 101.64/27.09 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.09 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.09 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.09 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.09 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.09 U56(ok(X)) -> ok(U56(X)) 101.64/27.09 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.09 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.09 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.09 U63(ok(X)) -> ok(U63(X)) 101.64/27.09 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.09 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.09 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.09 U73(ok(X)) -> ok(U73(X)) 101.64/27.09 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.09 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.09 U83(ok(X)) -> ok(U83(X)) 101.64/27.09 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.09 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.09 U93(ok(X)) -> ok(U93(X)) 101.64/27.09 tail(ok(X)) -> ok(tail(X)) 101.64/27.09 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.09 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.09 top(mark(X)) -> top(proper(X)) 101.64/27.09 top(ok(X)) -> top(active(X)) 101.64/27.09 101.64/27.09 Types: 101.64/27.09 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 tt :: tt:mark:nil:0':ok 101.64/27.09 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 nil :: tt:mark:nil:0':ok 101.64/27.09 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 0' :: tt:mark:nil:0':ok 101.64/27.09 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 top :: tt:mark:nil:0':ok -> top 101.64/27.09 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.09 hole_top2_0 :: top 101.64/27.09 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.09 101.64/27.09 101.64/27.09 Lemmas: 101.64/27.09 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.09 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.09 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.09 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.09 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.09 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.09 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.09 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.09 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.09 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.09 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.09 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.09 101.64/27.09 101.64/27.09 Generator Equations: 101.64/27.09 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.09 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.09 101.64/27.09 101.64/27.09 The following defined symbols remain to be analysed: 101.64/27.09 U172, active, U182, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.09 101.64/27.09 They will be analysed ascendingly in the following order: 101.64/27.09 U172 < active 101.64/27.09 U182 < active 101.64/27.09 U183 < active 101.64/27.09 U192 < active 101.64/27.09 U193 < active 101.64/27.09 U202 < active 101.64/27.09 U203 < active 101.64/27.09 U204 < active 101.64/27.09 U205 < active 101.64/27.09 U206 < active 101.64/27.09 U22 < active 101.64/27.09 U23 < active 101.64/27.09 U24 < active 101.64/27.09 U232 < active 101.64/27.09 U242 < active 101.64/27.09 U243 < active 101.64/27.09 U244 < active 101.64/27.09 U245 < active 101.64/27.09 U246 < active 101.64/27.09 U252 < active 101.64/27.09 U253 < active 101.64/27.09 U254 < active 101.64/27.09 U255 < active 101.64/27.09 U256 < active 101.64/27.09 U262 < active 101.64/27.09 U272 < active 101.64/27.09 U282 < active 101.64/27.09 cons < active 101.64/27.09 natsFrom < active 101.64/27.09 s < active 101.64/27.09 U292 < active 101.64/27.09 U293 < active 101.64/27.09 U294 < active 101.64/27.09 head < active 101.64/27.09 afterNth < active 101.64/27.09 U302 < active 101.64/27.09 U303 < active 101.64/27.09 U304 < active 101.64/27.09 U32 < active 101.64/27.09 U312 < active 101.64/27.09 pair < active 101.64/27.09 U33 < active 101.64/27.09 U322 < active 101.64/27.09 U323 < active 101.64/27.09 U324 < active 101.64/27.09 U325 < active 101.64/27.09 U326 < active 101.64/27.09 U327 < active 101.64/27.09 U34 < active 101.64/27.09 U332 < active 101.64/27.09 U333 < active 101.64/27.09 U334 < active 101.64/27.09 U342 < active 101.64/27.09 U343 < active 101.64/27.09 U344 < active 101.64/27.09 fst < active 101.64/27.09 U42 < active 101.64/27.09 U43 < active 101.64/27.09 U44 < active 101.64/27.09 U45 < active 101.64/27.09 U46 < active 101.64/27.09 U52 < active 101.64/27.09 U53 < active 101.64/27.09 U54 < active 101.64/27.09 U55 < active 101.64/27.09 U56 < active 101.64/27.09 U62 < active 101.64/27.09 isPLNatKind < active 101.64/27.09 U63 < active 101.64/27.09 isPLNat < active 101.64/27.09 U72 < active 101.64/27.09 U73 < active 101.64/27.09 U82 < active 101.64/27.09 U83 < active 101.64/27.09 U92 < active 101.64/27.09 U93 < active 101.64/27.09 U11 < active 101.64/27.09 U21 < active 101.64/27.09 U31 < active 101.64/27.09 U41 < active 101.64/27.09 U51 < active 101.64/27.09 U61 < active 101.64/27.09 U71 < active 101.64/27.09 U81 < active 101.64/27.09 U91 < active 101.64/27.09 U101 < active 101.64/27.09 U111 < active 101.64/27.09 U121 < active 101.64/27.09 U131 < active 101.64/27.09 U141 < active 101.64/27.09 U151 < active 101.64/27.09 U161 < active 101.64/27.09 U171 < active 101.64/27.09 U181 < active 101.64/27.09 U191 < active 101.64/27.09 U201 < active 101.64/27.09 U211 < active 101.64/27.09 U221 < active 101.64/27.09 U231 < active 101.64/27.09 U241 < active 101.64/27.09 U251 < active 101.64/27.09 U261 < active 101.64/27.09 U271 < active 101.64/27.09 U281 < active 101.64/27.09 U291 < active 101.64/27.09 U301 < active 101.64/27.09 U311 < active 101.64/27.09 U321 < active 101.64/27.09 U331 < active 101.64/27.09 U341 < active 101.64/27.09 tail < active 101.64/27.09 take < active 101.64/27.09 sel < active 101.64/27.09 active < top 101.64/27.09 U172 < proper 101.64/27.09 U182 < proper 101.64/27.09 U183 < proper 101.64/27.09 U192 < proper 101.64/27.09 U193 < proper 101.64/27.09 U202 < proper 101.64/27.09 U203 < proper 101.64/27.09 U204 < proper 101.64/27.09 U205 < proper 101.64/27.09 U206 < proper 101.64/27.09 U22 < proper 101.64/27.09 U23 < proper 101.64/27.09 U24 < proper 101.64/27.09 U232 < proper 101.64/27.09 U242 < proper 101.64/27.09 U243 < proper 101.64/27.09 U244 < proper 101.64/27.09 U245 < proper 101.64/27.09 U246 < proper 101.64/27.09 U252 < proper 101.64/27.09 U253 < proper 101.64/27.09 U254 < proper 101.64/27.09 U255 < proper 101.64/27.09 U256 < proper 101.64/27.09 U262 < proper 101.64/27.09 U272 < proper 101.64/27.09 U282 < proper 101.64/27.09 cons < proper 101.64/27.09 natsFrom < proper 101.64/27.09 s < proper 101.64/27.09 U292 < proper 101.64/27.09 U293 < proper 101.64/27.09 U294 < proper 101.64/27.09 head < proper 101.64/27.09 afterNth < proper 101.64/27.09 U302 < proper 101.64/27.09 U303 < proper 101.64/27.09 U304 < proper 101.64/27.09 U32 < proper 101.64/27.09 U312 < proper 101.64/27.09 pair < proper 101.64/27.09 U33 < proper 101.64/27.09 U322 < proper 101.64/27.09 U323 < proper 101.64/27.09 U324 < proper 101.64/27.09 U325 < proper 101.64/27.09 U326 < proper 101.64/27.09 U327 < proper 101.64/27.09 U34 < proper 101.64/27.09 U332 < proper 101.64/27.09 U333 < proper 101.64/27.09 U334 < proper 101.64/27.09 U342 < proper 101.64/27.09 U343 < proper 101.64/27.09 U344 < proper 101.64/27.09 fst < proper 101.64/27.09 U42 < proper 101.64/27.09 U43 < proper 101.64/27.09 U44 < proper 101.64/27.09 U45 < proper 101.64/27.09 U46 < proper 101.64/27.09 U52 < proper 101.64/27.09 U53 < proper 101.64/27.09 U54 < proper 101.64/27.09 U55 < proper 101.64/27.09 U56 < proper 101.64/27.09 U62 < proper 101.64/27.09 isPLNatKind < proper 101.64/27.09 U63 < proper 101.64/27.09 isPLNat < proper 101.64/27.09 U72 < proper 101.64/27.09 U73 < proper 101.64/27.09 U82 < proper 101.64/27.09 U83 < proper 101.64/27.09 U92 < proper 101.64/27.09 U93 < proper 101.64/27.09 U11 < proper 101.64/27.09 U21 < proper 101.64/27.09 U31 < proper 101.64/27.09 U41 < proper 101.64/27.09 U51 < proper 101.64/27.09 U61 < proper 101.64/27.09 U71 < proper 101.64/27.09 U81 < proper 101.64/27.09 U91 < proper 101.64/27.09 U101 < proper 101.64/27.09 U111 < proper 101.64/27.09 U121 < proper 101.64/27.09 U131 < proper 101.64/27.09 U141 < proper 101.64/27.09 U151 < proper 101.64/27.09 U161 < proper 101.64/27.09 U171 < proper 101.64/27.09 U181 < proper 101.64/27.09 U191 < proper 101.64/27.09 U201 < proper 101.64/27.09 U211 < proper 101.64/27.09 U221 < proper 101.64/27.09 U231 < proper 101.64/27.09 U241 < proper 101.64/27.09 U251 < proper 101.64/27.09 U261 < proper 101.64/27.09 U271 < proper 101.64/27.09 U281 < proper 101.64/27.09 U291 < proper 101.64/27.09 U301 < proper 101.64/27.09 U311 < proper 101.64/27.09 U321 < proper 101.64/27.09 U331 < proper 101.64/27.09 U341 < proper 101.64/27.09 tail < proper 101.64/27.09 take < proper 101.64/27.09 sel < proper 101.64/27.09 proper < top 101.64/27.09 101.64/27.09 ---------------------------------------- 101.64/27.09 101.64/27.09 (53) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.09 Proved the following rewrite lemma: 101.64/27.09 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.64/27.09 101.64/27.09 Induction Base: 101.64/27.09 U172(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.09 101.64/27.09 Induction Step: 101.64/27.09 U172(gen_tt:mark:nil:0':ok3_0(+(1, +(n154745_0, 1)))) ->_R^Omega(1) 101.64/27.09 mark(U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0)))) ->_IH 101.64/27.09 mark(*4_0) 101.64/27.09 101.64/27.09 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.09 ---------------------------------------- 101.64/27.09 101.64/27.09 (54) 101.64/27.09 Obligation: 101.64/27.09 TRS: 101.64/27.09 Rules: 101.64/27.09 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.09 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.09 active(U106(tt)) -> mark(tt) 101.64/27.09 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.09 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.09 active(U112(tt)) -> mark(tt) 101.64/27.09 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.09 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.09 active(U122(tt)) -> mark(tt) 101.64/27.09 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.09 active(U131(tt)) -> mark(tt) 101.64/27.09 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.09 active(U141(tt)) -> mark(tt) 101.64/27.09 active(U151(tt)) -> mark(tt) 101.64/27.09 active(U161(tt)) -> mark(tt) 101.64/27.09 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.09 active(U172(tt)) -> mark(tt) 101.64/27.09 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.09 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.09 active(U183(tt)) -> mark(tt) 101.64/27.09 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.09 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.09 active(U193(tt)) -> mark(tt) 101.64/27.09 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.09 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.09 active(U206(tt)) -> mark(tt) 101.64/27.09 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.09 active(U211(tt)) -> mark(tt) 101.64/27.09 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.09 active(U221(tt)) -> mark(tt) 101.64/27.09 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.09 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.09 active(U232(tt)) -> mark(tt) 101.64/27.09 active(U24(tt, X)) -> mark(X) 101.64/27.09 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.09 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.09 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.09 active(U246(tt)) -> mark(tt) 101.64/27.09 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.09 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.09 active(U256(tt)) -> mark(tt) 101.64/27.09 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.09 active(U262(tt)) -> mark(tt) 101.64/27.09 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.09 active(U272(tt)) -> mark(tt) 101.64/27.09 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.09 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.09 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.09 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.09 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.09 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.09 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.09 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.09 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.09 active(U304(tt, Y)) -> mark(Y) 101.64/27.09 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.09 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.09 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.09 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.09 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.09 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.09 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.09 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.09 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.09 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.09 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.09 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.09 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.09 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.09 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.09 active(U334(tt, XS)) -> mark(XS) 101.64/27.09 active(U34(tt, N)) -> mark(N) 101.64/27.09 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.09 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.09 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.09 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.09 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.09 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.09 active(U46(tt)) -> mark(tt) 101.64/27.09 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.09 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.09 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.09 active(U56(tt)) -> mark(tt) 101.64/27.09 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.09 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.09 active(U63(tt)) -> mark(tt) 101.64/27.09 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.09 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.09 active(U73(tt)) -> mark(tt) 101.64/27.09 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.09 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.09 active(U83(tt)) -> mark(tt) 101.64/27.09 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.09 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.09 active(U93(tt)) -> mark(tt) 101.64/27.09 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.09 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.09 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.09 active(isLNat(nil)) -> mark(tt) 101.64/27.09 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.09 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.09 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.09 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.09 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isLNatKind(nil)) -> mark(tt) 101.64/27.09 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.09 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.09 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.09 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.09 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.09 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.09 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.09 active(isNatural(0')) -> mark(tt) 101.64/27.09 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.09 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.09 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isNaturalKind(0')) -> mark(tt) 101.64/27.09 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.09 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.09 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.09 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.09 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.09 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.09 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.09 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.09 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.09 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.09 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.09 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.09 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.09 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.09 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.09 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.09 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.09 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.09 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.09 active(U106(X)) -> U106(active(X)) 101.64/27.09 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.09 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.09 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.09 active(U112(X)) -> U112(active(X)) 101.64/27.09 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.09 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.09 active(U122(X)) -> U122(active(X)) 101.64/27.09 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.09 active(U131(X)) -> U131(active(X)) 101.64/27.09 active(snd(X)) -> snd(active(X)) 101.64/27.09 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.09 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.09 active(U141(X)) -> U141(active(X)) 101.64/27.09 active(U151(X)) -> U151(active(X)) 101.64/27.09 active(U161(X)) -> U161(active(X)) 101.64/27.09 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.09 active(U172(X)) -> U172(active(X)) 101.64/27.09 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.09 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.09 active(U183(X)) -> U183(active(X)) 101.64/27.09 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.09 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.09 active(U193(X)) -> U193(active(X)) 101.64/27.09 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.09 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.09 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.09 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.09 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.09 active(U206(X)) -> U206(active(X)) 101.64/27.09 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.09 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.09 active(U211(X)) -> U211(active(X)) 101.64/27.09 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.09 active(U221(X)) -> U221(active(X)) 101.64/27.09 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.09 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.09 active(U232(X)) -> U232(active(X)) 101.64/27.09 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.09 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.09 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.09 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.09 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.09 active(U246(X)) -> U246(active(X)) 101.64/27.09 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.09 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.09 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.09 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.09 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.09 active(U256(X)) -> U256(active(X)) 101.64/27.09 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.09 active(U262(X)) -> U262(active(X)) 101.64/27.09 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.09 active(U272(X)) -> U272(active(X)) 101.64/27.09 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.09 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.09 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.09 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.09 active(s(X)) -> s(active(X)) 101.64/27.09 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.09 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.09 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.09 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.09 active(head(X)) -> head(active(X)) 101.64/27.09 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.09 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.09 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.09 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.09 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.09 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.09 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.09 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.09 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.09 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.09 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.09 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.09 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.09 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.09 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.09 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.09 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.09 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.09 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.09 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.09 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.09 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.09 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.09 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.09 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.09 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.09 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.09 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.09 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.09 active(fst(X)) -> fst(active(X)) 101.64/27.09 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.09 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.09 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.09 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.09 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.09 active(U46(X)) -> U46(active(X)) 101.64/27.09 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.09 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.09 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.09 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.09 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.09 active(U56(X)) -> U56(active(X)) 101.64/27.09 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.09 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.09 active(U63(X)) -> U63(active(X)) 101.64/27.09 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.09 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.09 active(U73(X)) -> U73(active(X)) 101.64/27.09 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.09 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.09 active(U83(X)) -> U83(active(X)) 101.64/27.09 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.09 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.09 active(U93(X)) -> U93(active(X)) 101.64/27.09 active(tail(X)) -> tail(active(X)) 101.64/27.09 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.09 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.09 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.09 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.09 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.09 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.09 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.09 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.09 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.09 U106(mark(X)) -> mark(U106(X)) 101.64/27.09 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.09 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.09 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.09 U112(mark(X)) -> mark(U112(X)) 101.64/27.09 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.09 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.09 U122(mark(X)) -> mark(U122(X)) 101.64/27.09 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.09 U131(mark(X)) -> mark(U131(X)) 101.64/27.09 snd(mark(X)) -> mark(snd(X)) 101.64/27.09 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.09 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.09 U141(mark(X)) -> mark(U141(X)) 101.64/27.09 U151(mark(X)) -> mark(U151(X)) 101.64/27.09 U161(mark(X)) -> mark(U161(X)) 101.64/27.09 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.09 U172(mark(X)) -> mark(U172(X)) 101.64/27.09 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.09 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.09 U183(mark(X)) -> mark(U183(X)) 101.64/27.09 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.09 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.09 U193(mark(X)) -> mark(U193(X)) 101.64/27.09 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.09 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.09 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.09 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.09 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.09 U206(mark(X)) -> mark(U206(X)) 101.64/27.09 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.09 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.09 U211(mark(X)) -> mark(U211(X)) 101.64/27.09 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.09 U221(mark(X)) -> mark(U221(X)) 101.64/27.09 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.09 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.09 U232(mark(X)) -> mark(U232(X)) 101.64/27.09 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.09 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.09 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.09 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.09 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.09 U246(mark(X)) -> mark(U246(X)) 101.64/27.09 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.09 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.09 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.09 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.09 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.09 U256(mark(X)) -> mark(U256(X)) 101.64/27.09 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.09 U262(mark(X)) -> mark(U262(X)) 101.64/27.09 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.09 U272(mark(X)) -> mark(U272(X)) 101.64/27.09 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.09 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.09 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.09 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.09 s(mark(X)) -> mark(s(X)) 101.64/27.09 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.09 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.09 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.09 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.09 head(mark(X)) -> mark(head(X)) 101.64/27.09 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.09 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.09 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.09 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.09 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.09 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.09 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.09 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.09 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.09 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.09 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.09 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.09 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.09 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.09 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.09 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.09 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.09 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.09 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.09 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.09 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.09 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.09 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.09 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.09 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.09 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.09 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.09 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.09 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.09 fst(mark(X)) -> mark(fst(X)) 101.64/27.09 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.09 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.09 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.09 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.09 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.09 U46(mark(X)) -> mark(U46(X)) 101.64/27.09 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.09 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.09 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.09 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.09 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.09 U56(mark(X)) -> mark(U56(X)) 101.64/27.09 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.09 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.09 U63(mark(X)) -> mark(U63(X)) 101.64/27.09 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.09 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.09 U73(mark(X)) -> mark(U73(X)) 101.64/27.09 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.09 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.09 U83(mark(X)) -> mark(U83(X)) 101.64/27.09 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.09 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.09 U93(mark(X)) -> mark(U93(X)) 101.64/27.09 tail(mark(X)) -> mark(tail(X)) 101.64/27.09 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.09 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.09 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.09 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.09 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(tt) -> ok(tt) 101.64/27.09 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.09 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.09 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.09 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.09 proper(U106(X)) -> U106(proper(X)) 101.64/27.09 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.09 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.09 proper(U112(X)) -> U112(proper(X)) 101.64/27.09 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.09 proper(U122(X)) -> U122(proper(X)) 101.64/27.09 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U131(X)) -> U131(proper(X)) 101.64/27.09 proper(snd(X)) -> snd(proper(X)) 101.64/27.09 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.09 proper(U141(X)) -> U141(proper(X)) 101.64/27.09 proper(U151(X)) -> U151(proper(X)) 101.64/27.09 proper(U161(X)) -> U161(proper(X)) 101.64/27.09 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.09 proper(U172(X)) -> U172(proper(X)) 101.64/27.09 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.09 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.09 proper(U183(X)) -> U183(proper(X)) 101.64/27.09 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.09 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.09 proper(U193(X)) -> U193(proper(X)) 101.64/27.09 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.09 proper(U206(X)) -> U206(proper(X)) 101.64/27.09 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U211(X)) -> U211(proper(X)) 101.64/27.09 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U221(X)) -> U221(proper(X)) 101.64/27.09 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.09 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.09 proper(U232(X)) -> U232(proper(X)) 101.64/27.09 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.09 proper(U246(X)) -> U246(proper(X)) 101.64/27.09 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.09 proper(U256(X)) -> U256(proper(X)) 101.64/27.09 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.09 proper(U262(X)) -> U262(proper(X)) 101.64/27.09 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.09 proper(U272(X)) -> U272(proper(X)) 101.64/27.09 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.09 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.09 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.09 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.09 proper(s(X)) -> s(proper(X)) 101.64/27.09 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(head(X)) -> head(proper(X)) 101.64/27.09 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.09 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.09 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.09 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.09 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.09 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.09 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.09 proper(nil) -> ok(nil) 101.64/27.09 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.09 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.09 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.09 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.09 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.09 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.09 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(fst(X)) -> fst(proper(X)) 101.64/27.09 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.09 proper(U46(X)) -> U46(proper(X)) 101.64/27.09 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.09 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.09 proper(U56(X)) -> U56(proper(X)) 101.64/27.09 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.09 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.09 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.09 proper(U63(X)) -> U63(proper(X)) 101.64/27.09 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.09 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.09 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.09 proper(U73(X)) -> U73(proper(X)) 101.64/27.09 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.09 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.09 proper(U83(X)) -> U83(proper(X)) 101.64/27.09 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.09 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.09 proper(U93(X)) -> U93(proper(X)) 101.64/27.09 proper(tail(X)) -> tail(proper(X)) 101.64/27.09 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.09 proper(0') -> ok(0') 101.64/27.09 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.09 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.09 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.09 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.09 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.09 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.09 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.09 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.09 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.09 U106(ok(X)) -> ok(U106(X)) 101.64/27.09 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.09 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.09 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.09 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.09 U112(ok(X)) -> ok(U112(X)) 101.64/27.09 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.09 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.09 U122(ok(X)) -> ok(U122(X)) 101.64/27.09 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.09 U131(ok(X)) -> ok(U131(X)) 101.64/27.09 snd(ok(X)) -> ok(snd(X)) 101.64/27.09 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.09 U141(ok(X)) -> ok(U141(X)) 101.64/27.09 U151(ok(X)) -> ok(U151(X)) 101.64/27.09 U161(ok(X)) -> ok(U161(X)) 101.64/27.09 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.09 U172(ok(X)) -> ok(U172(X)) 101.64/27.09 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.09 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.09 U183(ok(X)) -> ok(U183(X)) 101.64/27.09 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.09 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.09 U193(ok(X)) -> ok(U193(X)) 101.64/27.09 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.09 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.09 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.09 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.09 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.09 U206(ok(X)) -> ok(U206(X)) 101.64/27.09 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.09 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.09 U211(ok(X)) -> ok(U211(X)) 101.64/27.09 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.09 U221(ok(X)) -> ok(U221(X)) 101.64/27.09 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.09 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.09 U232(ok(X)) -> ok(U232(X)) 101.64/27.09 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.09 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.09 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.09 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.09 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.09 U246(ok(X)) -> ok(U246(X)) 101.64/27.09 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.09 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.09 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.09 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.09 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.09 U256(ok(X)) -> ok(U256(X)) 101.64/27.09 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.09 U262(ok(X)) -> ok(U262(X)) 101.64/27.09 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.09 U272(ok(X)) -> ok(U272(X)) 101.64/27.09 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.09 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.09 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.09 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.09 s(ok(X)) -> ok(s(X)) 101.64/27.09 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.09 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.09 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.09 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.09 head(ok(X)) -> ok(head(X)) 101.64/27.09 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.09 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.09 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.09 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.09 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.09 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.09 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.09 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.09 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.09 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.09 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.09 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.09 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.09 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.09 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.09 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.09 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.09 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.09 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.09 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.09 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.09 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.09 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.09 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.09 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.09 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.09 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.09 fst(ok(X)) -> ok(fst(X)) 101.64/27.09 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.09 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.09 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.09 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.09 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.09 U46(ok(X)) -> ok(U46(X)) 101.64/27.09 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.09 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.09 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.09 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.09 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.09 U56(ok(X)) -> ok(U56(X)) 101.64/27.09 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.09 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.09 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.09 U63(ok(X)) -> ok(U63(X)) 101.64/27.09 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.09 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.09 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.09 U73(ok(X)) -> ok(U73(X)) 101.64/27.09 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.09 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.09 U83(ok(X)) -> ok(U83(X)) 101.64/27.09 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.09 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.09 U93(ok(X)) -> ok(U93(X)) 101.64/27.09 tail(ok(X)) -> ok(tail(X)) 101.64/27.09 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.09 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.09 top(mark(X)) -> top(proper(X)) 101.64/27.09 top(ok(X)) -> top(active(X)) 101.64/27.09 101.64/27.09 Types: 101.64/27.09 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 tt :: tt:mark:nil:0':ok 101.64/27.09 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 nil :: tt:mark:nil:0':ok 101.64/27.09 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 0' :: tt:mark:nil:0':ok 101.64/27.09 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.09 top :: tt:mark:nil:0':ok -> top 101.64/27.09 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.09 hole_top2_0 :: top 101.64/27.09 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.09 101.64/27.09 101.64/27.09 Lemmas: 101.64/27.09 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.09 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.09 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.09 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.09 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.09 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.09 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.09 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.09 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.09 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.09 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.09 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.09 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.64/27.09 101.64/27.09 101.64/27.09 Generator Equations: 101.64/27.09 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.09 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.09 101.64/27.09 101.64/27.09 The following defined symbols remain to be analysed: 101.64/27.09 U182, active, U183, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.09 101.64/27.09 They will be analysed ascendingly in the following order: 101.64/27.09 U182 < active 101.64/27.09 U183 < active 101.64/27.09 U192 < active 101.64/27.09 U193 < active 101.64/27.09 U202 < active 101.64/27.09 U203 < active 101.64/27.09 U204 < active 101.64/27.09 U205 < active 101.64/27.09 U206 < active 101.64/27.09 U22 < active 101.64/27.09 U23 < active 101.64/27.09 U24 < active 101.64/27.09 U232 < active 101.64/27.09 U242 < active 101.64/27.09 U243 < active 101.64/27.09 U244 < active 101.64/27.09 U245 < active 101.64/27.09 U246 < active 101.64/27.09 U252 < active 101.64/27.09 U253 < active 101.64/27.09 U254 < active 101.64/27.09 U255 < active 101.64/27.09 U256 < active 101.64/27.09 U262 < active 101.64/27.09 U272 < active 101.64/27.09 U282 < active 101.64/27.09 cons < active 101.64/27.09 natsFrom < active 101.64/27.09 s < active 101.64/27.09 U292 < active 101.64/27.09 U293 < active 101.64/27.09 U294 < active 101.64/27.09 head < active 101.64/27.09 afterNth < active 101.64/27.09 U302 < active 101.64/27.09 U303 < active 101.64/27.09 U304 < active 101.64/27.09 U32 < active 101.64/27.09 U312 < active 101.64/27.09 pair < active 101.64/27.09 U33 < active 101.64/27.09 U322 < active 101.64/27.09 U323 < active 101.64/27.09 U324 < active 101.64/27.09 U325 < active 101.64/27.09 U326 < active 101.64/27.09 U327 < active 101.64/27.09 U34 < active 101.64/27.09 U332 < active 101.64/27.09 U333 < active 101.64/27.09 U334 < active 101.64/27.09 U342 < active 101.64/27.09 U343 < active 101.64/27.09 U344 < active 101.64/27.09 fst < active 101.64/27.09 U42 < active 101.64/27.09 U43 < active 101.64/27.09 U44 < active 101.64/27.09 U45 < active 101.64/27.09 U46 < active 101.64/27.09 U52 < active 101.64/27.09 U53 < active 101.64/27.09 U54 < active 101.64/27.09 U55 < active 101.64/27.09 U56 < active 101.64/27.09 U62 < active 101.64/27.09 isPLNatKind < active 101.64/27.09 U63 < active 101.64/27.09 isPLNat < active 101.64/27.09 U72 < active 101.64/27.09 U73 < active 101.64/27.09 U82 < active 101.64/27.09 U83 < active 101.64/27.09 U92 < active 101.64/27.09 U93 < active 101.64/27.09 U11 < active 101.64/27.09 U21 < active 101.64/27.09 U31 < active 101.64/27.09 U41 < active 101.64/27.09 U51 < active 101.64/27.09 U61 < active 101.64/27.09 U71 < active 101.64/27.09 U81 < active 101.64/27.09 U91 < active 101.64/27.09 U101 < active 101.64/27.09 U111 < active 101.64/27.09 U121 < active 101.64/27.09 U131 < active 101.64/27.09 U141 < active 101.64/27.09 U151 < active 101.64/27.09 U161 < active 101.64/27.09 U171 < active 101.64/27.09 U181 < active 101.64/27.09 U191 < active 101.64/27.09 U201 < active 101.64/27.09 U211 < active 101.64/27.09 U221 < active 101.64/27.09 U231 < active 101.64/27.09 U241 < active 101.64/27.09 U251 < active 101.64/27.09 U261 < active 101.64/27.09 U271 < active 101.64/27.09 U281 < active 101.64/27.09 U291 < active 101.64/27.09 U301 < active 101.64/27.09 U311 < active 101.64/27.09 U321 < active 101.64/27.09 U331 < active 101.64/27.09 U341 < active 101.64/27.09 tail < active 101.64/27.09 take < active 101.64/27.09 sel < active 101.64/27.09 active < top 101.64/27.09 U182 < proper 101.64/27.09 U183 < proper 101.64/27.09 U192 < proper 101.64/27.09 U193 < proper 101.64/27.09 U202 < proper 101.64/27.09 U203 < proper 101.64/27.09 U204 < proper 101.64/27.09 U205 < proper 101.64/27.09 U206 < proper 101.64/27.09 U22 < proper 101.64/27.09 U23 < proper 101.64/27.09 U24 < proper 101.64/27.09 U232 < proper 101.64/27.09 U242 < proper 101.64/27.09 U243 < proper 101.64/27.09 U244 < proper 101.64/27.09 U245 < proper 101.64/27.09 U246 < proper 101.64/27.09 U252 < proper 101.64/27.09 U253 < proper 101.64/27.09 U254 < proper 101.64/27.09 U255 < proper 101.64/27.09 U256 < proper 101.64/27.09 U262 < proper 101.64/27.09 U272 < proper 101.64/27.09 U282 < proper 101.64/27.09 cons < proper 101.64/27.09 natsFrom < proper 101.64/27.10 s < proper 101.64/27.10 U292 < proper 101.64/27.10 U293 < proper 101.64/27.10 U294 < proper 101.64/27.10 head < proper 101.64/27.10 afterNth < proper 101.64/27.10 U302 < proper 101.64/27.10 U303 < proper 101.64/27.10 U304 < proper 101.64/27.10 U32 < proper 101.64/27.10 U312 < proper 101.64/27.10 pair < proper 101.64/27.10 U33 < proper 101.64/27.10 U322 < proper 101.64/27.10 U323 < proper 101.64/27.10 U324 < proper 101.64/27.10 U325 < proper 101.64/27.10 U326 < proper 101.64/27.10 U327 < proper 101.64/27.10 U34 < proper 101.64/27.10 U332 < proper 101.64/27.10 U333 < proper 101.64/27.10 U334 < proper 101.64/27.10 U342 < proper 101.64/27.10 U343 < proper 101.64/27.10 U344 < proper 101.64/27.10 fst < proper 101.64/27.10 U42 < proper 101.64/27.10 U43 < proper 101.64/27.10 U44 < proper 101.64/27.10 U45 < proper 101.64/27.10 U46 < proper 101.64/27.10 U52 < proper 101.64/27.10 U53 < proper 101.64/27.10 U54 < proper 101.64/27.10 U55 < proper 101.64/27.10 U56 < proper 101.64/27.10 U62 < proper 101.64/27.10 isPLNatKind < proper 101.64/27.10 U63 < proper 101.64/27.10 isPLNat < proper 101.64/27.10 U72 < proper 101.64/27.10 U73 < proper 101.64/27.10 U82 < proper 101.64/27.10 U83 < proper 101.64/27.10 U92 < proper 101.64/27.10 U93 < proper 101.64/27.10 U11 < proper 101.64/27.10 U21 < proper 101.64/27.10 U31 < proper 101.64/27.10 U41 < proper 101.64/27.10 U51 < proper 101.64/27.10 U61 < proper 101.64/27.10 U71 < proper 101.64/27.10 U81 < proper 101.64/27.10 U91 < proper 101.64/27.10 U101 < proper 101.64/27.10 U111 < proper 101.64/27.10 U121 < proper 101.64/27.10 U131 < proper 101.64/27.10 U141 < proper 101.64/27.10 U151 < proper 101.64/27.10 U161 < proper 101.64/27.10 U171 < proper 101.64/27.10 U181 < proper 101.64/27.10 U191 < proper 101.64/27.10 U201 < proper 101.64/27.10 U211 < proper 101.64/27.10 U221 < proper 101.64/27.10 U231 < proper 101.64/27.10 U241 < proper 101.64/27.10 U251 < proper 101.64/27.10 U261 < proper 101.64/27.10 U271 < proper 101.64/27.10 U281 < proper 101.64/27.10 U291 < proper 101.64/27.10 U301 < proper 101.64/27.10 U311 < proper 101.64/27.10 U321 < proper 101.64/27.10 U331 < proper 101.64/27.10 U341 < proper 101.64/27.10 tail < proper 101.64/27.10 take < proper 101.64/27.10 sel < proper 101.64/27.10 proper < top 101.64/27.10 101.64/27.10 ---------------------------------------- 101.64/27.10 101.64/27.10 (55) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.10 Proved the following rewrite lemma: 101.64/27.10 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.64/27.10 101.64/27.10 Induction Base: 101.64/27.10 U182(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.64/27.10 101.64/27.10 Induction Step: 101.64/27.10 U182(gen_tt:mark:nil:0':ok3_0(+(1, +(n158914_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.64/27.10 mark(U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.64/27.10 mark(*4_0) 101.64/27.10 101.64/27.10 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.10 ---------------------------------------- 101.64/27.10 101.64/27.10 (56) 101.64/27.10 Obligation: 101.64/27.10 TRS: 101.64/27.10 Rules: 101.64/27.10 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.10 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.10 active(U106(tt)) -> mark(tt) 101.64/27.10 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.10 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.10 active(U112(tt)) -> mark(tt) 101.64/27.10 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.10 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.10 active(U122(tt)) -> mark(tt) 101.64/27.10 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.10 active(U131(tt)) -> mark(tt) 101.64/27.10 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.10 active(U141(tt)) -> mark(tt) 101.64/27.10 active(U151(tt)) -> mark(tt) 101.64/27.10 active(U161(tt)) -> mark(tt) 101.64/27.10 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.10 active(U172(tt)) -> mark(tt) 101.64/27.10 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.10 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.10 active(U183(tt)) -> mark(tt) 101.64/27.10 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.10 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.10 active(U193(tt)) -> mark(tt) 101.64/27.10 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.10 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.10 active(U206(tt)) -> mark(tt) 101.64/27.10 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.10 active(U211(tt)) -> mark(tt) 101.64/27.10 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.10 active(U221(tt)) -> mark(tt) 101.64/27.10 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.10 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.10 active(U232(tt)) -> mark(tt) 101.64/27.10 active(U24(tt, X)) -> mark(X) 101.64/27.10 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.10 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.10 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.10 active(U246(tt)) -> mark(tt) 101.64/27.10 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.10 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.10 active(U256(tt)) -> mark(tt) 101.64/27.10 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.10 active(U262(tt)) -> mark(tt) 101.64/27.10 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.10 active(U272(tt)) -> mark(tt) 101.64/27.10 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.10 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.10 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.10 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.10 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.10 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.10 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.10 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.10 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.10 active(U304(tt, Y)) -> mark(Y) 101.64/27.10 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.10 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.10 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.10 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.10 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.10 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.10 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.10 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.10 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.10 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.10 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.10 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.10 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.10 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.10 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.10 active(U334(tt, XS)) -> mark(XS) 101.64/27.10 active(U34(tt, N)) -> mark(N) 101.64/27.10 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.10 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.10 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.10 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.10 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.10 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.10 active(U46(tt)) -> mark(tt) 101.64/27.10 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.10 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.10 active(U56(tt)) -> mark(tt) 101.64/27.10 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.10 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.10 active(U63(tt)) -> mark(tt) 101.64/27.10 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.10 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.10 active(U73(tt)) -> mark(tt) 101.64/27.10 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.10 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.10 active(U83(tt)) -> mark(tt) 101.64/27.10 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.10 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.10 active(U93(tt)) -> mark(tt) 101.64/27.10 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.10 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.10 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.10 active(isLNat(nil)) -> mark(tt) 101.64/27.10 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.10 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.10 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.10 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.10 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNatKind(nil)) -> mark(tt) 101.64/27.10 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.10 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.10 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.10 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.10 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.10 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.10 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.10 active(isNatural(0')) -> mark(tt) 101.64/27.10 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.10 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.10 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isNaturalKind(0')) -> mark(tt) 101.64/27.10 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.10 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.10 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.10 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.10 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.10 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.10 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.10 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.10 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.10 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.10 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.10 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.10 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.10 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.10 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.10 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.10 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.10 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.10 active(U106(X)) -> U106(active(X)) 101.64/27.10 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.10 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.10 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.10 active(U112(X)) -> U112(active(X)) 101.64/27.10 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.10 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.10 active(U122(X)) -> U122(active(X)) 101.64/27.10 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.10 active(U131(X)) -> U131(active(X)) 101.64/27.10 active(snd(X)) -> snd(active(X)) 101.64/27.10 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.10 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.10 active(U141(X)) -> U141(active(X)) 101.64/27.10 active(U151(X)) -> U151(active(X)) 101.64/27.10 active(U161(X)) -> U161(active(X)) 101.64/27.10 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.10 active(U172(X)) -> U172(active(X)) 101.64/27.10 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.10 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.10 active(U183(X)) -> U183(active(X)) 101.64/27.10 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.10 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.10 active(U193(X)) -> U193(active(X)) 101.64/27.10 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.10 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.10 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.10 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.10 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.10 active(U206(X)) -> U206(active(X)) 101.64/27.10 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.10 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.10 active(U211(X)) -> U211(active(X)) 101.64/27.10 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.10 active(U221(X)) -> U221(active(X)) 101.64/27.10 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.10 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.10 active(U232(X)) -> U232(active(X)) 101.64/27.10 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.10 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.10 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.10 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.10 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.10 active(U246(X)) -> U246(active(X)) 101.64/27.10 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.10 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.10 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.10 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.10 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.10 active(U256(X)) -> U256(active(X)) 101.64/27.10 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.10 active(U262(X)) -> U262(active(X)) 101.64/27.10 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.10 active(U272(X)) -> U272(active(X)) 101.64/27.10 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.10 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.10 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.10 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.10 active(s(X)) -> s(active(X)) 101.64/27.10 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.10 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.10 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.10 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.10 active(head(X)) -> head(active(X)) 101.64/27.10 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.10 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.10 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.10 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.10 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.10 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.10 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.10 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.10 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.10 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.10 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.10 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.10 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.10 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.10 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.10 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.10 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.10 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.10 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.10 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.10 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.10 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.10 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.10 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.10 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.10 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.10 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.10 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.10 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.10 active(fst(X)) -> fst(active(X)) 101.64/27.10 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.10 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.10 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.10 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.10 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.10 active(U46(X)) -> U46(active(X)) 101.64/27.10 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.10 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.10 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.10 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.10 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.10 active(U56(X)) -> U56(active(X)) 101.64/27.10 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.10 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.10 active(U63(X)) -> U63(active(X)) 101.64/27.10 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.10 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.10 active(U73(X)) -> U73(active(X)) 101.64/27.10 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.10 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.10 active(U83(X)) -> U83(active(X)) 101.64/27.10 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.10 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.10 active(U93(X)) -> U93(active(X)) 101.64/27.10 active(tail(X)) -> tail(active(X)) 101.64/27.10 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.10 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.10 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.10 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.10 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.10 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.10 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.10 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.10 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.10 U106(mark(X)) -> mark(U106(X)) 101.64/27.10 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.10 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.10 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.10 U112(mark(X)) -> mark(U112(X)) 101.64/27.10 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.10 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.10 U122(mark(X)) -> mark(U122(X)) 101.64/27.10 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.10 U131(mark(X)) -> mark(U131(X)) 101.64/27.10 snd(mark(X)) -> mark(snd(X)) 101.64/27.10 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.10 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.10 U141(mark(X)) -> mark(U141(X)) 101.64/27.10 U151(mark(X)) -> mark(U151(X)) 101.64/27.10 U161(mark(X)) -> mark(U161(X)) 101.64/27.10 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.10 U172(mark(X)) -> mark(U172(X)) 101.64/27.10 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.10 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.10 U183(mark(X)) -> mark(U183(X)) 101.64/27.10 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.10 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.10 U193(mark(X)) -> mark(U193(X)) 101.64/27.10 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.10 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.10 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.10 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.10 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.10 U206(mark(X)) -> mark(U206(X)) 101.64/27.10 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.10 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.10 U211(mark(X)) -> mark(U211(X)) 101.64/27.10 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.10 U221(mark(X)) -> mark(U221(X)) 101.64/27.10 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.10 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.10 U232(mark(X)) -> mark(U232(X)) 101.64/27.10 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.10 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.10 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.10 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.10 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.10 U246(mark(X)) -> mark(U246(X)) 101.64/27.10 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.10 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.10 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.10 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.10 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.10 U256(mark(X)) -> mark(U256(X)) 101.64/27.10 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.10 U262(mark(X)) -> mark(U262(X)) 101.64/27.10 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.10 U272(mark(X)) -> mark(U272(X)) 101.64/27.10 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.10 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.10 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.10 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.10 s(mark(X)) -> mark(s(X)) 101.64/27.10 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.10 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.10 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.10 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.10 head(mark(X)) -> mark(head(X)) 101.64/27.10 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.10 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.10 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.10 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.10 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.10 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.10 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.10 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.10 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.10 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.10 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.10 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.10 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.10 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.10 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.10 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.10 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.10 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.10 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.10 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.10 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.10 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.10 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.10 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.10 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.10 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.10 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.10 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.10 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.10 fst(mark(X)) -> mark(fst(X)) 101.64/27.10 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.10 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.10 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.10 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.10 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.10 U46(mark(X)) -> mark(U46(X)) 101.64/27.10 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.10 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.10 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.10 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.10 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.10 U56(mark(X)) -> mark(U56(X)) 101.64/27.10 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.10 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.10 U63(mark(X)) -> mark(U63(X)) 101.64/27.10 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.10 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.10 U73(mark(X)) -> mark(U73(X)) 101.64/27.10 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.10 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.10 U83(mark(X)) -> mark(U83(X)) 101.64/27.10 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.10 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.10 U93(mark(X)) -> mark(U93(X)) 101.64/27.10 tail(mark(X)) -> mark(tail(X)) 101.64/27.10 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.10 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.10 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.10 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.10 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(tt) -> ok(tt) 101.64/27.10 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.10 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.10 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.10 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.10 proper(U106(X)) -> U106(proper(X)) 101.64/27.10 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.10 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.10 proper(U112(X)) -> U112(proper(X)) 101.64/27.10 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.10 proper(U122(X)) -> U122(proper(X)) 101.64/27.10 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U131(X)) -> U131(proper(X)) 101.64/27.10 proper(snd(X)) -> snd(proper(X)) 101.64/27.10 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.10 proper(U141(X)) -> U141(proper(X)) 101.64/27.10 proper(U151(X)) -> U151(proper(X)) 101.64/27.10 proper(U161(X)) -> U161(proper(X)) 101.64/27.10 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.10 proper(U172(X)) -> U172(proper(X)) 101.64/27.10 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.10 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.10 proper(U183(X)) -> U183(proper(X)) 101.64/27.10 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.10 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.10 proper(U193(X)) -> U193(proper(X)) 101.64/27.10 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.10 proper(U206(X)) -> U206(proper(X)) 101.64/27.10 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U211(X)) -> U211(proper(X)) 101.64/27.10 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U221(X)) -> U221(proper(X)) 101.64/27.10 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.10 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.10 proper(U232(X)) -> U232(proper(X)) 101.64/27.10 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.10 proper(U246(X)) -> U246(proper(X)) 101.64/27.10 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.10 proper(U256(X)) -> U256(proper(X)) 101.64/27.10 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.10 proper(U262(X)) -> U262(proper(X)) 101.64/27.10 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.10 proper(U272(X)) -> U272(proper(X)) 101.64/27.10 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.10 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.10 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.10 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.10 proper(s(X)) -> s(proper(X)) 101.64/27.10 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(head(X)) -> head(proper(X)) 101.64/27.10 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.10 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.10 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.10 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.10 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.10 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.10 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.10 proper(nil) -> ok(nil) 101.64/27.10 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.10 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.10 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.10 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.10 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.10 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(fst(X)) -> fst(proper(X)) 101.64/27.10 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.10 proper(U46(X)) -> U46(proper(X)) 101.64/27.10 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.10 proper(U56(X)) -> U56(proper(X)) 101.64/27.10 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.10 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.10 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.10 proper(U63(X)) -> U63(proper(X)) 101.64/27.10 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.10 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.10 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.10 proper(U73(X)) -> U73(proper(X)) 101.64/27.10 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.10 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.10 proper(U83(X)) -> U83(proper(X)) 101.64/27.10 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.10 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.10 proper(U93(X)) -> U93(proper(X)) 101.64/27.10 proper(tail(X)) -> tail(proper(X)) 101.64/27.10 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.10 proper(0') -> ok(0') 101.64/27.10 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.10 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.10 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.10 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.10 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.10 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.10 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.10 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.10 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.10 U106(ok(X)) -> ok(U106(X)) 101.64/27.10 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.10 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.10 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.10 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.10 U112(ok(X)) -> ok(U112(X)) 101.64/27.10 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.10 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.10 U122(ok(X)) -> ok(U122(X)) 101.64/27.10 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.10 U131(ok(X)) -> ok(U131(X)) 101.64/27.10 snd(ok(X)) -> ok(snd(X)) 101.64/27.10 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.10 U141(ok(X)) -> ok(U141(X)) 101.64/27.10 U151(ok(X)) -> ok(U151(X)) 101.64/27.10 U161(ok(X)) -> ok(U161(X)) 101.64/27.10 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.10 U172(ok(X)) -> ok(U172(X)) 101.64/27.10 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.10 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.10 U183(ok(X)) -> ok(U183(X)) 101.64/27.10 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.10 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.10 U193(ok(X)) -> ok(U193(X)) 101.64/27.10 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.10 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.10 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.10 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.10 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.10 U206(ok(X)) -> ok(U206(X)) 101.64/27.10 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.10 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.10 U211(ok(X)) -> ok(U211(X)) 101.64/27.10 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.10 U221(ok(X)) -> ok(U221(X)) 101.64/27.10 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.10 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.10 U232(ok(X)) -> ok(U232(X)) 101.64/27.10 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.10 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.10 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.10 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.10 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.10 U246(ok(X)) -> ok(U246(X)) 101.64/27.10 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.10 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.10 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.10 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.10 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.10 U256(ok(X)) -> ok(U256(X)) 101.64/27.10 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.10 U262(ok(X)) -> ok(U262(X)) 101.64/27.10 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.10 U272(ok(X)) -> ok(U272(X)) 101.64/27.10 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.10 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.10 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.10 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.10 s(ok(X)) -> ok(s(X)) 101.64/27.10 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.10 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.10 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.10 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.10 head(ok(X)) -> ok(head(X)) 101.64/27.10 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.10 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.10 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.10 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.10 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.10 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.10 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.10 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.10 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.10 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.10 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.10 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.10 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.10 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.10 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.10 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.10 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.10 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.10 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.10 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.10 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.10 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.10 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.10 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.10 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.10 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.10 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.10 fst(ok(X)) -> ok(fst(X)) 101.64/27.10 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.10 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.10 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.10 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.10 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.10 U46(ok(X)) -> ok(U46(X)) 101.64/27.10 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.10 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.10 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.10 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.10 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.10 U56(ok(X)) -> ok(U56(X)) 101.64/27.10 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.10 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.10 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.10 U63(ok(X)) -> ok(U63(X)) 101.64/27.10 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.10 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.10 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.10 U73(ok(X)) -> ok(U73(X)) 101.64/27.10 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.10 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.10 U83(ok(X)) -> ok(U83(X)) 101.64/27.10 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.10 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.10 U93(ok(X)) -> ok(U93(X)) 101.64/27.10 tail(ok(X)) -> ok(tail(X)) 101.64/27.10 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.10 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.10 top(mark(X)) -> top(proper(X)) 101.64/27.10 top(ok(X)) -> top(active(X)) 101.64/27.10 101.64/27.10 Types: 101.64/27.10 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 tt :: tt:mark:nil:0':ok 101.64/27.10 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 nil :: tt:mark:nil:0':ok 101.64/27.10 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 0' :: tt:mark:nil:0':ok 101.64/27.10 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 top :: tt:mark:nil:0':ok -> top 101.64/27.10 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.10 hole_top2_0 :: top 101.64/27.10 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.10 101.64/27.10 101.64/27.10 Lemmas: 101.64/27.10 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.10 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.10 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.10 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.10 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.10 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.10 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.10 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.10 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.10 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.10 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.10 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.10 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.64/27.10 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.64/27.10 101.64/27.10 101.64/27.10 Generator Equations: 101.64/27.10 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.10 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.10 101.64/27.10 101.64/27.10 The following defined symbols remain to be analysed: 101.64/27.10 U183, active, U192, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.10 101.64/27.10 They will be analysed ascendingly in the following order: 101.64/27.10 U183 < active 101.64/27.10 U192 < active 101.64/27.10 U193 < active 101.64/27.10 U202 < active 101.64/27.10 U203 < active 101.64/27.10 U204 < active 101.64/27.10 U205 < active 101.64/27.10 U206 < active 101.64/27.10 U22 < active 101.64/27.10 U23 < active 101.64/27.10 U24 < active 101.64/27.10 U232 < active 101.64/27.10 U242 < active 101.64/27.10 U243 < active 101.64/27.10 U244 < active 101.64/27.10 U245 < active 101.64/27.10 U246 < active 101.64/27.10 U252 < active 101.64/27.10 U253 < active 101.64/27.10 U254 < active 101.64/27.10 U255 < active 101.64/27.10 U256 < active 101.64/27.10 U262 < active 101.64/27.10 U272 < active 101.64/27.10 U282 < active 101.64/27.10 cons < active 101.64/27.10 natsFrom < active 101.64/27.10 s < active 101.64/27.10 U292 < active 101.64/27.10 U293 < active 101.64/27.10 U294 < active 101.64/27.10 head < active 101.64/27.10 afterNth < active 101.64/27.10 U302 < active 101.64/27.10 U303 < active 101.64/27.10 U304 < active 101.64/27.10 U32 < active 101.64/27.10 U312 < active 101.64/27.10 pair < active 101.64/27.10 U33 < active 101.64/27.10 U322 < active 101.64/27.10 U323 < active 101.64/27.10 U324 < active 101.64/27.10 U325 < active 101.64/27.10 U326 < active 101.64/27.10 U327 < active 101.64/27.10 U34 < active 101.64/27.10 U332 < active 101.64/27.10 U333 < active 101.64/27.10 U334 < active 101.64/27.10 U342 < active 101.64/27.10 U343 < active 101.64/27.10 U344 < active 101.64/27.10 fst < active 101.64/27.10 U42 < active 101.64/27.10 U43 < active 101.64/27.10 U44 < active 101.64/27.10 U45 < active 101.64/27.10 U46 < active 101.64/27.10 U52 < active 101.64/27.10 U53 < active 101.64/27.10 U54 < active 101.64/27.10 U55 < active 101.64/27.10 U56 < active 101.64/27.10 U62 < active 101.64/27.10 isPLNatKind < active 101.64/27.10 U63 < active 101.64/27.10 isPLNat < active 101.64/27.10 U72 < active 101.64/27.10 U73 < active 101.64/27.10 U82 < active 101.64/27.10 U83 < active 101.64/27.10 U92 < active 101.64/27.10 U93 < active 101.64/27.10 U11 < active 101.64/27.10 U21 < active 101.64/27.10 U31 < active 101.64/27.10 U41 < active 101.64/27.10 U51 < active 101.64/27.10 U61 < active 101.64/27.10 U71 < active 101.64/27.10 U81 < active 101.64/27.10 U91 < active 101.64/27.10 U101 < active 101.64/27.10 U111 < active 101.64/27.10 U121 < active 101.64/27.10 U131 < active 101.64/27.10 U141 < active 101.64/27.10 U151 < active 101.64/27.10 U161 < active 101.64/27.10 U171 < active 101.64/27.10 U181 < active 101.64/27.10 U191 < active 101.64/27.10 U201 < active 101.64/27.10 U211 < active 101.64/27.10 U221 < active 101.64/27.10 U231 < active 101.64/27.10 U241 < active 101.64/27.10 U251 < active 101.64/27.10 U261 < active 101.64/27.10 U271 < active 101.64/27.10 U281 < active 101.64/27.10 U291 < active 101.64/27.10 U301 < active 101.64/27.10 U311 < active 101.64/27.10 U321 < active 101.64/27.10 U331 < active 101.64/27.10 U341 < active 101.64/27.10 tail < active 101.64/27.10 take < active 101.64/27.10 sel < active 101.64/27.10 active < top 101.64/27.10 U183 < proper 101.64/27.10 U192 < proper 101.64/27.10 U193 < proper 101.64/27.10 U202 < proper 101.64/27.10 U203 < proper 101.64/27.10 U204 < proper 101.64/27.10 U205 < proper 101.64/27.10 U206 < proper 101.64/27.10 U22 < proper 101.64/27.10 U23 < proper 101.64/27.10 U24 < proper 101.64/27.10 U232 < proper 101.64/27.10 U242 < proper 101.64/27.10 U243 < proper 101.64/27.10 U244 < proper 101.64/27.10 U245 < proper 101.64/27.10 U246 < proper 101.64/27.10 U252 < proper 101.64/27.10 U253 < proper 101.64/27.10 U254 < proper 101.64/27.10 U255 < proper 101.64/27.10 U256 < proper 101.64/27.10 U262 < proper 101.64/27.10 U272 < proper 101.64/27.10 U282 < proper 101.64/27.10 cons < proper 101.64/27.10 natsFrom < proper 101.64/27.10 s < proper 101.64/27.10 U292 < proper 101.64/27.10 U293 < proper 101.64/27.10 U294 < proper 101.64/27.10 head < proper 101.64/27.10 afterNth < proper 101.64/27.10 U302 < proper 101.64/27.10 U303 < proper 101.64/27.10 U304 < proper 101.64/27.10 U32 < proper 101.64/27.10 U312 < proper 101.64/27.10 pair < proper 101.64/27.10 U33 < proper 101.64/27.10 U322 < proper 101.64/27.10 U323 < proper 101.64/27.10 U324 < proper 101.64/27.10 U325 < proper 101.64/27.10 U326 < proper 101.64/27.10 U327 < proper 101.64/27.10 U34 < proper 101.64/27.10 U332 < proper 101.64/27.10 U333 < proper 101.64/27.10 U334 < proper 101.64/27.10 U342 < proper 101.64/27.10 U343 < proper 101.64/27.10 U344 < proper 101.64/27.10 fst < proper 101.64/27.10 U42 < proper 101.64/27.10 U43 < proper 101.64/27.10 U44 < proper 101.64/27.10 U45 < proper 101.64/27.10 U46 < proper 101.64/27.10 U52 < proper 101.64/27.10 U53 < proper 101.64/27.10 U54 < proper 101.64/27.10 U55 < proper 101.64/27.10 U56 < proper 101.64/27.10 U62 < proper 101.64/27.10 isPLNatKind < proper 101.64/27.10 U63 < proper 101.64/27.10 isPLNat < proper 101.64/27.10 U72 < proper 101.64/27.10 U73 < proper 101.64/27.10 U82 < proper 101.64/27.10 U83 < proper 101.64/27.10 U92 < proper 101.64/27.10 U93 < proper 101.64/27.10 U11 < proper 101.64/27.10 U21 < proper 101.64/27.10 U31 < proper 101.64/27.10 U41 < proper 101.64/27.10 U51 < proper 101.64/27.10 U61 < proper 101.64/27.10 U71 < proper 101.64/27.10 U81 < proper 101.64/27.10 U91 < proper 101.64/27.10 U101 < proper 101.64/27.10 U111 < proper 101.64/27.10 U121 < proper 101.64/27.10 U131 < proper 101.64/27.10 U141 < proper 101.64/27.10 U151 < proper 101.64/27.10 U161 < proper 101.64/27.10 U171 < proper 101.64/27.10 U181 < proper 101.64/27.10 U191 < proper 101.64/27.10 U201 < proper 101.64/27.10 U211 < proper 101.64/27.10 U221 < proper 101.64/27.10 U231 < proper 101.64/27.10 U241 < proper 101.64/27.10 U251 < proper 101.64/27.10 U261 < proper 101.64/27.10 U271 < proper 101.64/27.10 U281 < proper 101.64/27.10 U291 < proper 101.64/27.10 U301 < proper 101.64/27.10 U311 < proper 101.64/27.10 U321 < proper 101.64/27.10 U331 < proper 101.64/27.10 U341 < proper 101.64/27.10 tail < proper 101.64/27.10 take < proper 101.64/27.10 sel < proper 101.64/27.10 proper < top 101.64/27.10 101.64/27.10 ---------------------------------------- 101.64/27.10 101.64/27.10 (57) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.10 Proved the following rewrite lemma: 101.64/27.10 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.64/27.10 101.64/27.10 Induction Base: 101.64/27.10 U183(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.10 101.64/27.10 Induction Step: 101.64/27.10 U183(gen_tt:mark:nil:0':ok3_0(+(1, +(n172777_0, 1)))) ->_R^Omega(1) 101.64/27.10 mark(U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0)))) ->_IH 101.64/27.10 mark(*4_0) 101.64/27.10 101.64/27.10 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.10 ---------------------------------------- 101.64/27.10 101.64/27.10 (58) 101.64/27.10 Obligation: 101.64/27.10 TRS: 101.64/27.10 Rules: 101.64/27.10 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.10 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.10 active(U106(tt)) -> mark(tt) 101.64/27.10 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.10 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.10 active(U112(tt)) -> mark(tt) 101.64/27.10 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.10 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.10 active(U122(tt)) -> mark(tt) 101.64/27.10 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.10 active(U131(tt)) -> mark(tt) 101.64/27.10 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.10 active(U141(tt)) -> mark(tt) 101.64/27.10 active(U151(tt)) -> mark(tt) 101.64/27.10 active(U161(tt)) -> mark(tt) 101.64/27.10 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.10 active(U172(tt)) -> mark(tt) 101.64/27.10 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.10 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.10 active(U183(tt)) -> mark(tt) 101.64/27.10 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.10 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.10 active(U193(tt)) -> mark(tt) 101.64/27.10 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.10 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.10 active(U206(tt)) -> mark(tt) 101.64/27.10 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.10 active(U211(tt)) -> mark(tt) 101.64/27.10 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.10 active(U221(tt)) -> mark(tt) 101.64/27.10 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.10 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.10 active(U232(tt)) -> mark(tt) 101.64/27.10 active(U24(tt, X)) -> mark(X) 101.64/27.10 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.10 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.10 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.10 active(U246(tt)) -> mark(tt) 101.64/27.10 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.10 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.10 active(U256(tt)) -> mark(tt) 101.64/27.10 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.10 active(U262(tt)) -> mark(tt) 101.64/27.10 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.10 active(U272(tt)) -> mark(tt) 101.64/27.10 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.10 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.10 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.10 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.10 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.10 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.10 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.10 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.10 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.10 active(U304(tt, Y)) -> mark(Y) 101.64/27.10 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.10 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.10 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.10 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.10 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.10 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.10 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.10 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.10 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.10 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.10 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.10 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.10 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.10 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.10 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.10 active(U334(tt, XS)) -> mark(XS) 101.64/27.10 active(U34(tt, N)) -> mark(N) 101.64/27.10 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.10 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.10 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.10 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.10 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.10 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.10 active(U46(tt)) -> mark(tt) 101.64/27.10 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.10 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.10 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.10 active(U56(tt)) -> mark(tt) 101.64/27.10 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.10 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.10 active(U63(tt)) -> mark(tt) 101.64/27.10 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.10 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.10 active(U73(tt)) -> mark(tt) 101.64/27.10 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.10 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.10 active(U83(tt)) -> mark(tt) 101.64/27.10 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.10 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.10 active(U93(tt)) -> mark(tt) 101.64/27.10 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.10 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.10 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.10 active(isLNat(nil)) -> mark(tt) 101.64/27.10 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.10 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.10 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.10 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.10 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isLNatKind(nil)) -> mark(tt) 101.64/27.10 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.10 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.10 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.10 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.10 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.10 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.10 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.10 active(isNatural(0')) -> mark(tt) 101.64/27.10 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.10 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.10 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isNaturalKind(0')) -> mark(tt) 101.64/27.10 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.10 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.10 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.10 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.10 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.10 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.10 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.10 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.10 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.10 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.10 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.10 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.10 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.10 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.10 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.10 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.10 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.10 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.10 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.10 active(U106(X)) -> U106(active(X)) 101.64/27.10 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.10 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.10 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.10 active(U112(X)) -> U112(active(X)) 101.64/27.10 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.10 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.10 active(U122(X)) -> U122(active(X)) 101.64/27.10 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.10 active(U131(X)) -> U131(active(X)) 101.64/27.10 active(snd(X)) -> snd(active(X)) 101.64/27.10 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.10 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.10 active(U141(X)) -> U141(active(X)) 101.64/27.10 active(U151(X)) -> U151(active(X)) 101.64/27.10 active(U161(X)) -> U161(active(X)) 101.64/27.10 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.10 active(U172(X)) -> U172(active(X)) 101.64/27.10 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.10 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.10 active(U183(X)) -> U183(active(X)) 101.64/27.10 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.10 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.10 active(U193(X)) -> U193(active(X)) 101.64/27.10 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.10 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.10 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.10 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.10 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.10 active(U206(X)) -> U206(active(X)) 101.64/27.10 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.10 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.10 active(U211(X)) -> U211(active(X)) 101.64/27.10 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.10 active(U221(X)) -> U221(active(X)) 101.64/27.10 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.10 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.10 active(U232(X)) -> U232(active(X)) 101.64/27.10 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.10 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.10 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.10 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.10 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.10 active(U246(X)) -> U246(active(X)) 101.64/27.10 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.10 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.10 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.10 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.10 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.10 active(U256(X)) -> U256(active(X)) 101.64/27.10 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.10 active(U262(X)) -> U262(active(X)) 101.64/27.10 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.10 active(U272(X)) -> U272(active(X)) 101.64/27.10 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.10 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.10 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.10 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.10 active(s(X)) -> s(active(X)) 101.64/27.10 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.10 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.10 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.10 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.10 active(head(X)) -> head(active(X)) 101.64/27.10 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.10 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.10 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.10 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.10 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.10 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.10 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.10 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.10 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.10 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.10 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.10 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.10 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.10 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.10 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.10 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.10 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.10 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.10 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.10 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.10 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.10 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.10 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.10 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.10 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.10 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.10 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.10 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.10 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.10 active(fst(X)) -> fst(active(X)) 101.64/27.10 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.10 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.10 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.10 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.10 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.10 active(U46(X)) -> U46(active(X)) 101.64/27.10 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.10 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.10 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.10 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.10 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.10 active(U56(X)) -> U56(active(X)) 101.64/27.10 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.10 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.10 active(U63(X)) -> U63(active(X)) 101.64/27.10 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.10 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.10 active(U73(X)) -> U73(active(X)) 101.64/27.10 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.10 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.10 active(U83(X)) -> U83(active(X)) 101.64/27.10 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.10 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.10 active(U93(X)) -> U93(active(X)) 101.64/27.10 active(tail(X)) -> tail(active(X)) 101.64/27.10 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.10 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.10 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.10 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.10 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.10 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.10 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.10 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.10 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.10 U106(mark(X)) -> mark(U106(X)) 101.64/27.10 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.10 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.10 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.10 U112(mark(X)) -> mark(U112(X)) 101.64/27.10 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.10 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.10 U122(mark(X)) -> mark(U122(X)) 101.64/27.10 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.10 U131(mark(X)) -> mark(U131(X)) 101.64/27.10 snd(mark(X)) -> mark(snd(X)) 101.64/27.10 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.10 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.10 U141(mark(X)) -> mark(U141(X)) 101.64/27.10 U151(mark(X)) -> mark(U151(X)) 101.64/27.10 U161(mark(X)) -> mark(U161(X)) 101.64/27.10 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.10 U172(mark(X)) -> mark(U172(X)) 101.64/27.10 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.10 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.10 U183(mark(X)) -> mark(U183(X)) 101.64/27.10 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.10 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.10 U193(mark(X)) -> mark(U193(X)) 101.64/27.10 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.10 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.10 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.10 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.10 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.10 U206(mark(X)) -> mark(U206(X)) 101.64/27.10 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.10 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.10 U211(mark(X)) -> mark(U211(X)) 101.64/27.10 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.10 U221(mark(X)) -> mark(U221(X)) 101.64/27.10 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.10 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.10 U232(mark(X)) -> mark(U232(X)) 101.64/27.10 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.10 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.10 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.10 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.10 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.10 U246(mark(X)) -> mark(U246(X)) 101.64/27.10 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.10 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.10 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.10 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.10 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.10 U256(mark(X)) -> mark(U256(X)) 101.64/27.10 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.10 U262(mark(X)) -> mark(U262(X)) 101.64/27.10 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.10 U272(mark(X)) -> mark(U272(X)) 101.64/27.10 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.10 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.10 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.10 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.10 s(mark(X)) -> mark(s(X)) 101.64/27.10 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.10 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.10 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.10 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.10 head(mark(X)) -> mark(head(X)) 101.64/27.10 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.10 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.10 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.10 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.10 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.10 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.10 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.10 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.10 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.10 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.10 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.10 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.10 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.10 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.10 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.10 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.10 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.10 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.10 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.10 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.10 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.10 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.10 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.10 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.10 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.10 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.10 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.10 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.10 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.10 fst(mark(X)) -> mark(fst(X)) 101.64/27.10 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.10 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.10 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.10 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.10 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.10 U46(mark(X)) -> mark(U46(X)) 101.64/27.10 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.10 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.10 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.10 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.10 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.10 U56(mark(X)) -> mark(U56(X)) 101.64/27.10 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.10 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.10 U63(mark(X)) -> mark(U63(X)) 101.64/27.10 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.10 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.10 U73(mark(X)) -> mark(U73(X)) 101.64/27.10 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.10 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.10 U83(mark(X)) -> mark(U83(X)) 101.64/27.10 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.10 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.10 U93(mark(X)) -> mark(U93(X)) 101.64/27.10 tail(mark(X)) -> mark(tail(X)) 101.64/27.10 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.10 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.10 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.10 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.10 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(tt) -> ok(tt) 101.64/27.10 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.10 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.10 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.10 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.10 proper(U106(X)) -> U106(proper(X)) 101.64/27.10 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.10 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.10 proper(U112(X)) -> U112(proper(X)) 101.64/27.10 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.10 proper(U122(X)) -> U122(proper(X)) 101.64/27.10 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U131(X)) -> U131(proper(X)) 101.64/27.10 proper(snd(X)) -> snd(proper(X)) 101.64/27.10 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.10 proper(U141(X)) -> U141(proper(X)) 101.64/27.10 proper(U151(X)) -> U151(proper(X)) 101.64/27.10 proper(U161(X)) -> U161(proper(X)) 101.64/27.10 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.10 proper(U172(X)) -> U172(proper(X)) 101.64/27.10 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.10 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.10 proper(U183(X)) -> U183(proper(X)) 101.64/27.10 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.10 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.10 proper(U193(X)) -> U193(proper(X)) 101.64/27.10 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.10 proper(U206(X)) -> U206(proper(X)) 101.64/27.10 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U211(X)) -> U211(proper(X)) 101.64/27.10 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U221(X)) -> U221(proper(X)) 101.64/27.10 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.10 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.10 proper(U232(X)) -> U232(proper(X)) 101.64/27.10 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.10 proper(U246(X)) -> U246(proper(X)) 101.64/27.10 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.10 proper(U256(X)) -> U256(proper(X)) 101.64/27.10 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.10 proper(U262(X)) -> U262(proper(X)) 101.64/27.10 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.10 proper(U272(X)) -> U272(proper(X)) 101.64/27.10 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.10 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.10 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.10 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.10 proper(s(X)) -> s(proper(X)) 101.64/27.10 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(head(X)) -> head(proper(X)) 101.64/27.10 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.10 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.10 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.10 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.10 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.10 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.10 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.10 proper(nil) -> ok(nil) 101.64/27.10 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.10 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.10 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.10 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.10 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.10 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.10 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(fst(X)) -> fst(proper(X)) 101.64/27.10 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.10 proper(U46(X)) -> U46(proper(X)) 101.64/27.10 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.10 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.10 proper(U56(X)) -> U56(proper(X)) 101.64/27.10 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.10 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.10 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.10 proper(U63(X)) -> U63(proper(X)) 101.64/27.10 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.10 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.10 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.10 proper(U73(X)) -> U73(proper(X)) 101.64/27.10 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.10 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.10 proper(U83(X)) -> U83(proper(X)) 101.64/27.10 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.10 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.10 proper(U93(X)) -> U93(proper(X)) 101.64/27.10 proper(tail(X)) -> tail(proper(X)) 101.64/27.10 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.10 proper(0') -> ok(0') 101.64/27.10 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.10 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.10 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.10 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.10 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.10 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.10 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.10 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.10 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.10 U106(ok(X)) -> ok(U106(X)) 101.64/27.10 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.10 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.10 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.10 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.10 U112(ok(X)) -> ok(U112(X)) 101.64/27.10 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.10 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.10 U122(ok(X)) -> ok(U122(X)) 101.64/27.10 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.10 U131(ok(X)) -> ok(U131(X)) 101.64/27.10 snd(ok(X)) -> ok(snd(X)) 101.64/27.10 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.10 U141(ok(X)) -> ok(U141(X)) 101.64/27.10 U151(ok(X)) -> ok(U151(X)) 101.64/27.10 U161(ok(X)) -> ok(U161(X)) 101.64/27.10 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.10 U172(ok(X)) -> ok(U172(X)) 101.64/27.10 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.10 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.10 U183(ok(X)) -> ok(U183(X)) 101.64/27.10 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.10 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.10 U193(ok(X)) -> ok(U193(X)) 101.64/27.10 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.10 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.10 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.10 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.10 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.10 U206(ok(X)) -> ok(U206(X)) 101.64/27.10 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.10 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.10 U211(ok(X)) -> ok(U211(X)) 101.64/27.10 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.10 U221(ok(X)) -> ok(U221(X)) 101.64/27.10 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.10 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.10 U232(ok(X)) -> ok(U232(X)) 101.64/27.10 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.10 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.10 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.10 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.10 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.10 U246(ok(X)) -> ok(U246(X)) 101.64/27.10 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.10 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.10 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.10 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.10 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.10 U256(ok(X)) -> ok(U256(X)) 101.64/27.10 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.10 U262(ok(X)) -> ok(U262(X)) 101.64/27.10 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.10 U272(ok(X)) -> ok(U272(X)) 101.64/27.10 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.10 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.10 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.10 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.10 s(ok(X)) -> ok(s(X)) 101.64/27.10 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.10 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.10 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.10 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.10 head(ok(X)) -> ok(head(X)) 101.64/27.10 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.10 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.10 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.10 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.10 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.10 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.10 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.10 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.10 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.10 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.10 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.10 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.10 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.10 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.10 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.10 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.10 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.10 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.10 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.10 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.10 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.10 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.10 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.10 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.10 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.10 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.10 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.10 fst(ok(X)) -> ok(fst(X)) 101.64/27.10 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.10 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.10 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.10 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.10 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.10 U46(ok(X)) -> ok(U46(X)) 101.64/27.10 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.10 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.10 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.10 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.10 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.10 U56(ok(X)) -> ok(U56(X)) 101.64/27.10 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.10 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.10 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.10 U63(ok(X)) -> ok(U63(X)) 101.64/27.10 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.10 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.10 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.10 U73(ok(X)) -> ok(U73(X)) 101.64/27.10 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.10 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.10 U83(ok(X)) -> ok(U83(X)) 101.64/27.10 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.10 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.10 U93(ok(X)) -> ok(U93(X)) 101.64/27.10 tail(ok(X)) -> ok(tail(X)) 101.64/27.10 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.10 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.10 top(mark(X)) -> top(proper(X)) 101.64/27.10 top(ok(X)) -> top(active(X)) 101.64/27.10 101.64/27.10 Types: 101.64/27.10 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 tt :: tt:mark:nil:0':ok 101.64/27.10 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.10 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 nil :: tt:mark:nil:0':ok 101.64/27.11 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 0' :: tt:mark:nil:0':ok 101.64/27.11 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 top :: tt:mark:nil:0':ok -> top 101.64/27.11 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.11 hole_top2_0 :: top 101.64/27.11 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.11 101.64/27.11 101.64/27.11 Lemmas: 101.64/27.11 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.11 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.11 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.11 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.11 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.11 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.11 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.11 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.11 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.11 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.11 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.11 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.11 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.64/27.11 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.64/27.11 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.64/27.11 101.64/27.11 101.64/27.11 Generator Equations: 101.64/27.11 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.11 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.11 101.64/27.11 101.64/27.11 The following defined symbols remain to be analysed: 101.64/27.11 U192, active, U193, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.11 101.64/27.11 They will be analysed ascendingly in the following order: 101.64/27.11 U192 < active 101.64/27.11 U193 < active 101.64/27.11 U202 < active 101.64/27.11 U203 < active 101.64/27.11 U204 < active 101.64/27.11 U205 < active 101.64/27.11 U206 < active 101.64/27.11 U22 < active 101.64/27.11 U23 < active 101.64/27.11 U24 < active 101.64/27.11 U232 < active 101.64/27.11 U242 < active 101.64/27.11 U243 < active 101.64/27.11 U244 < active 101.64/27.11 U245 < active 101.64/27.11 U246 < active 101.64/27.11 U252 < active 101.64/27.11 U253 < active 101.64/27.11 U254 < active 101.64/27.11 U255 < active 101.64/27.11 U256 < active 101.64/27.11 U262 < active 101.64/27.11 U272 < active 101.64/27.11 U282 < active 101.64/27.11 cons < active 101.64/27.11 natsFrom < active 101.64/27.11 s < active 101.64/27.11 U292 < active 101.64/27.11 U293 < active 101.64/27.11 U294 < active 101.64/27.11 head < active 101.64/27.11 afterNth < active 101.64/27.11 U302 < active 101.64/27.11 U303 < active 101.64/27.11 U304 < active 101.64/27.11 U32 < active 101.64/27.11 U312 < active 101.64/27.11 pair < active 101.64/27.11 U33 < active 101.64/27.11 U322 < active 101.64/27.11 U323 < active 101.64/27.11 U324 < active 101.64/27.11 U325 < active 101.64/27.11 U326 < active 101.64/27.11 U327 < active 101.64/27.11 U34 < active 101.64/27.11 U332 < active 101.64/27.11 U333 < active 101.64/27.11 U334 < active 101.64/27.11 U342 < active 101.64/27.11 U343 < active 101.64/27.11 U344 < active 101.64/27.11 fst < active 101.64/27.11 U42 < active 101.64/27.11 U43 < active 101.64/27.11 U44 < active 101.64/27.11 U45 < active 101.64/27.11 U46 < active 101.64/27.11 U52 < active 101.64/27.11 U53 < active 101.64/27.11 U54 < active 101.64/27.11 U55 < active 101.64/27.11 U56 < active 101.64/27.11 U62 < active 101.64/27.11 isPLNatKind < active 101.64/27.11 U63 < active 101.64/27.11 isPLNat < active 101.64/27.11 U72 < active 101.64/27.11 U73 < active 101.64/27.11 U82 < active 101.64/27.11 U83 < active 101.64/27.11 U92 < active 101.64/27.11 U93 < active 101.64/27.11 U11 < active 101.64/27.11 U21 < active 101.64/27.11 U31 < active 101.64/27.11 U41 < active 101.64/27.11 U51 < active 101.64/27.11 U61 < active 101.64/27.11 U71 < active 101.64/27.11 U81 < active 101.64/27.11 U91 < active 101.64/27.11 U101 < active 101.64/27.11 U111 < active 101.64/27.11 U121 < active 101.64/27.11 U131 < active 101.64/27.11 U141 < active 101.64/27.11 U151 < active 101.64/27.11 U161 < active 101.64/27.11 U171 < active 101.64/27.11 U181 < active 101.64/27.11 U191 < active 101.64/27.11 U201 < active 101.64/27.11 U211 < active 101.64/27.11 U221 < active 101.64/27.11 U231 < active 101.64/27.11 U241 < active 101.64/27.11 U251 < active 101.64/27.11 U261 < active 101.64/27.11 U271 < active 101.64/27.11 U281 < active 101.64/27.11 U291 < active 101.64/27.11 U301 < active 101.64/27.11 U311 < active 101.64/27.11 U321 < active 101.64/27.11 U331 < active 101.64/27.11 U341 < active 101.64/27.11 tail < active 101.64/27.11 take < active 101.64/27.11 sel < active 101.64/27.11 active < top 101.64/27.11 U192 < proper 101.64/27.11 U193 < proper 101.64/27.11 U202 < proper 101.64/27.11 U203 < proper 101.64/27.11 U204 < proper 101.64/27.11 U205 < proper 101.64/27.11 U206 < proper 101.64/27.11 U22 < proper 101.64/27.11 U23 < proper 101.64/27.11 U24 < proper 101.64/27.11 U232 < proper 101.64/27.11 U242 < proper 101.64/27.11 U243 < proper 101.64/27.11 U244 < proper 101.64/27.11 U245 < proper 101.64/27.11 U246 < proper 101.64/27.11 U252 < proper 101.64/27.11 U253 < proper 101.64/27.11 U254 < proper 101.64/27.11 U255 < proper 101.64/27.11 U256 < proper 101.64/27.11 U262 < proper 101.64/27.11 U272 < proper 101.64/27.11 U282 < proper 101.64/27.11 cons < proper 101.64/27.11 natsFrom < proper 101.64/27.11 s < proper 101.64/27.11 U292 < proper 101.64/27.11 U293 < proper 101.64/27.11 U294 < proper 101.64/27.11 head < proper 101.64/27.11 afterNth < proper 101.64/27.11 U302 < proper 101.64/27.11 U303 < proper 101.64/27.11 U304 < proper 101.64/27.11 U32 < proper 101.64/27.11 U312 < proper 101.64/27.11 pair < proper 101.64/27.11 U33 < proper 101.64/27.11 U322 < proper 101.64/27.11 U323 < proper 101.64/27.11 U324 < proper 101.64/27.11 U325 < proper 101.64/27.11 U326 < proper 101.64/27.11 U327 < proper 101.64/27.11 U34 < proper 101.64/27.11 U332 < proper 101.64/27.11 U333 < proper 101.64/27.11 U334 < proper 101.64/27.11 U342 < proper 101.64/27.11 U343 < proper 101.64/27.11 U344 < proper 101.64/27.11 fst < proper 101.64/27.11 U42 < proper 101.64/27.11 U43 < proper 101.64/27.11 U44 < proper 101.64/27.11 U45 < proper 101.64/27.11 U46 < proper 101.64/27.11 U52 < proper 101.64/27.11 U53 < proper 101.64/27.11 U54 < proper 101.64/27.11 U55 < proper 101.64/27.11 U56 < proper 101.64/27.11 U62 < proper 101.64/27.11 isPLNatKind < proper 101.64/27.11 U63 < proper 101.64/27.11 isPLNat < proper 101.64/27.11 U72 < proper 101.64/27.11 U73 < proper 101.64/27.11 U82 < proper 101.64/27.11 U83 < proper 101.64/27.11 U92 < proper 101.64/27.11 U93 < proper 101.64/27.11 U11 < proper 101.64/27.11 U21 < proper 101.64/27.11 U31 < proper 101.64/27.11 U41 < proper 101.64/27.11 U51 < proper 101.64/27.11 U61 < proper 101.64/27.11 U71 < proper 101.64/27.11 U81 < proper 101.64/27.11 U91 < proper 101.64/27.11 U101 < proper 101.64/27.11 U111 < proper 101.64/27.11 U121 < proper 101.64/27.11 U131 < proper 101.64/27.11 U141 < proper 101.64/27.11 U151 < proper 101.64/27.11 U161 < proper 101.64/27.11 U171 < proper 101.64/27.11 U181 < proper 101.64/27.11 U191 < proper 101.64/27.11 U201 < proper 101.64/27.11 U211 < proper 101.64/27.11 U221 < proper 101.64/27.11 U231 < proper 101.64/27.11 U241 < proper 101.64/27.11 U251 < proper 101.64/27.11 U261 < proper 101.64/27.11 U271 < proper 101.64/27.11 U281 < proper 101.64/27.11 U291 < proper 101.64/27.11 U301 < proper 101.64/27.11 U311 < proper 101.64/27.11 U321 < proper 101.64/27.11 U331 < proper 101.64/27.11 U341 < proper 101.64/27.11 tail < proper 101.64/27.11 take < proper 101.64/27.11 sel < proper 101.64/27.11 proper < top 101.64/27.11 101.64/27.11 ---------------------------------------- 101.64/27.11 101.64/27.11 (59) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.11 Proved the following rewrite lemma: 101.64/27.11 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.64/27.11 101.64/27.11 Induction Base: 101.64/27.11 U192(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.64/27.11 101.64/27.11 Induction Step: 101.64/27.11 U192(gen_tt:mark:nil:0':ok3_0(+(1, +(n177197_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.64/27.11 mark(U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.64/27.11 mark(*4_0) 101.64/27.11 101.64/27.11 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.11 ---------------------------------------- 101.64/27.11 101.64/27.11 (60) 101.64/27.11 Obligation: 101.64/27.11 TRS: 101.64/27.11 Rules: 101.64/27.11 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.11 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.11 active(U106(tt)) -> mark(tt) 101.64/27.11 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.11 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.11 active(U112(tt)) -> mark(tt) 101.64/27.11 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.11 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.11 active(U122(tt)) -> mark(tt) 101.64/27.11 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.11 active(U131(tt)) -> mark(tt) 101.64/27.11 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.11 active(U141(tt)) -> mark(tt) 101.64/27.11 active(U151(tt)) -> mark(tt) 101.64/27.11 active(U161(tt)) -> mark(tt) 101.64/27.11 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.11 active(U172(tt)) -> mark(tt) 101.64/27.11 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.11 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.11 active(U183(tt)) -> mark(tt) 101.64/27.11 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.11 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.11 active(U193(tt)) -> mark(tt) 101.64/27.11 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.11 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.11 active(U206(tt)) -> mark(tt) 101.64/27.11 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.11 active(U211(tt)) -> mark(tt) 101.64/27.11 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.11 active(U221(tt)) -> mark(tt) 101.64/27.11 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.11 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.11 active(U232(tt)) -> mark(tt) 101.64/27.11 active(U24(tt, X)) -> mark(X) 101.64/27.11 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.11 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.11 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.11 active(U246(tt)) -> mark(tt) 101.64/27.11 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.11 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.11 active(U256(tt)) -> mark(tt) 101.64/27.11 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.11 active(U262(tt)) -> mark(tt) 101.64/27.11 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.11 active(U272(tt)) -> mark(tt) 101.64/27.11 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.11 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.11 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.11 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.11 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.11 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.11 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.11 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.11 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.11 active(U304(tt, Y)) -> mark(Y) 101.64/27.11 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.11 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.11 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.11 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.11 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.11 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.11 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.11 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.11 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.11 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.11 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.11 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.11 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.11 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.11 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.11 active(U334(tt, XS)) -> mark(XS) 101.64/27.11 active(U34(tt, N)) -> mark(N) 101.64/27.11 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.11 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.11 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.11 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.11 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.11 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.11 active(U46(tt)) -> mark(tt) 101.64/27.11 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.11 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.11 active(U56(tt)) -> mark(tt) 101.64/27.11 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.11 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.11 active(U63(tt)) -> mark(tt) 101.64/27.11 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.11 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.11 active(U73(tt)) -> mark(tt) 101.64/27.11 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.11 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.11 active(U83(tt)) -> mark(tt) 101.64/27.11 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.11 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.11 active(U93(tt)) -> mark(tt) 101.64/27.11 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.11 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.11 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.11 active(isLNat(nil)) -> mark(tt) 101.64/27.11 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.11 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.11 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.11 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.11 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNatKind(nil)) -> mark(tt) 101.64/27.11 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.11 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.11 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.11 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.11 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.11 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.11 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.11 active(isNatural(0')) -> mark(tt) 101.64/27.11 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.11 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.11 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isNaturalKind(0')) -> mark(tt) 101.64/27.11 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.11 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.11 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.11 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.11 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.11 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.11 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.11 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.11 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.11 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.11 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.11 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.11 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.11 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.11 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.11 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.11 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.11 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.11 active(U106(X)) -> U106(active(X)) 101.64/27.11 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.11 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.11 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.11 active(U112(X)) -> U112(active(X)) 101.64/27.11 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.64/27.11 active(U121(X1, X2)) -> U121(active(X1), X2) 101.64/27.11 active(U122(X)) -> U122(active(X)) 101.64/27.11 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.64/27.11 active(U131(X)) -> U131(active(X)) 101.64/27.11 active(snd(X)) -> snd(active(X)) 101.64/27.11 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.64/27.11 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.64/27.11 active(U141(X)) -> U141(active(X)) 101.64/27.11 active(U151(X)) -> U151(active(X)) 101.64/27.11 active(U161(X)) -> U161(active(X)) 101.64/27.11 active(U171(X1, X2)) -> U171(active(X1), X2) 101.64/27.11 active(U172(X)) -> U172(active(X)) 101.64/27.11 active(U181(X1, X2)) -> U181(active(X1), X2) 101.64/27.11 active(U182(X1, X2)) -> U182(active(X1), X2) 101.64/27.11 active(U183(X)) -> U183(active(X)) 101.64/27.11 active(U191(X1, X2)) -> U191(active(X1), X2) 101.64/27.11 active(U192(X1, X2)) -> U192(active(X1), X2) 101.64/27.11 active(U193(X)) -> U193(active(X)) 101.64/27.11 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.64/27.11 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.64/27.11 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.64/27.11 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.64/27.11 active(U205(X1, X2)) -> U205(active(X1), X2) 101.64/27.11 active(U206(X)) -> U206(active(X)) 101.64/27.11 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.64/27.11 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.64/27.11 active(U211(X)) -> U211(active(X)) 101.64/27.11 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.64/27.11 active(U221(X)) -> U221(active(X)) 101.64/27.11 active(U24(X1, X2)) -> U24(active(X1), X2) 101.64/27.11 active(U231(X1, X2)) -> U231(active(X1), X2) 101.64/27.11 active(U232(X)) -> U232(active(X)) 101.64/27.11 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.64/27.11 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.64/27.11 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.64/27.11 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.64/27.11 active(U245(X1, X2)) -> U245(active(X1), X2) 101.64/27.11 active(U246(X)) -> U246(active(X)) 101.64/27.11 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.64/27.11 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.64/27.11 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.64/27.11 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.64/27.11 active(U255(X1, X2)) -> U255(active(X1), X2) 101.64/27.11 active(U256(X)) -> U256(active(X)) 101.64/27.11 active(U261(X1, X2)) -> U261(active(X1), X2) 101.64/27.11 active(U262(X)) -> U262(active(X)) 101.64/27.11 active(U271(X1, X2)) -> U271(active(X1), X2) 101.64/27.11 active(U272(X)) -> U272(active(X)) 101.64/27.11 active(U281(X1, X2)) -> U281(active(X1), X2) 101.64/27.11 active(U282(X1, X2)) -> U282(active(X1), X2) 101.64/27.11 active(cons(X1, X2)) -> cons(active(X1), X2) 101.64/27.11 active(natsFrom(X)) -> natsFrom(active(X)) 101.64/27.11 active(s(X)) -> s(active(X)) 101.64/27.11 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.64/27.11 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.64/27.11 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.64/27.11 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.64/27.11 active(head(X)) -> head(active(X)) 101.64/27.11 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.64/27.11 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.64/27.11 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.64/27.11 active(U302(X1, X2)) -> U302(active(X1), X2) 101.64/27.11 active(U303(X1, X2)) -> U303(active(X1), X2) 101.64/27.11 active(U304(X1, X2)) -> U304(active(X1), X2) 101.64/27.11 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.64/27.11 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.64/27.11 active(U311(X1, X2)) -> U311(active(X1), X2) 101.64/27.11 active(U312(X1, X2)) -> U312(active(X1), X2) 101.64/27.11 active(pair(X1, X2)) -> pair(active(X1), X2) 101.64/27.11 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.64/27.11 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.64/27.11 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.64/27.11 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.64/27.11 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.64/27.11 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.64/27.11 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.64/27.11 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.64/27.11 active(U327(X1, X2)) -> U327(active(X1), X2) 101.64/27.11 active(U34(X1, X2)) -> U34(active(X1), X2) 101.64/27.11 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.64/27.11 active(U332(X1, X2)) -> U332(active(X1), X2) 101.64/27.11 active(U333(X1, X2)) -> U333(active(X1), X2) 101.64/27.11 active(U334(X1, X2)) -> U334(active(X1), X2) 101.64/27.11 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.64/27.11 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.64/27.11 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.64/27.11 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.64/27.11 active(fst(X)) -> fst(active(X)) 101.64/27.11 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.64/27.11 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.64/27.11 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.64/27.11 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.64/27.11 active(U45(X1, X2)) -> U45(active(X1), X2) 101.64/27.11 active(U46(X)) -> U46(active(X)) 101.64/27.11 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.64/27.11 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.64/27.11 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.64/27.11 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.64/27.11 active(U55(X1, X2)) -> U55(active(X1), X2) 101.64/27.11 active(U56(X)) -> U56(active(X)) 101.64/27.11 active(U61(X1, X2)) -> U61(active(X1), X2) 101.64/27.11 active(U62(X1, X2)) -> U62(active(X1), X2) 101.64/27.11 active(U63(X)) -> U63(active(X)) 101.64/27.11 active(U71(X1, X2)) -> U71(active(X1), X2) 101.64/27.11 active(U72(X1, X2)) -> U72(active(X1), X2) 101.64/27.11 active(U73(X)) -> U73(active(X)) 101.64/27.11 active(U81(X1, X2)) -> U81(active(X1), X2) 101.64/27.11 active(U82(X1, X2)) -> U82(active(X1), X2) 101.64/27.11 active(U83(X)) -> U83(active(X)) 101.64/27.11 active(U91(X1, X2)) -> U91(active(X1), X2) 101.64/27.11 active(U92(X1, X2)) -> U92(active(X1), X2) 101.64/27.11 active(U93(X)) -> U93(active(X)) 101.64/27.11 active(tail(X)) -> tail(active(X)) 101.64/27.11 active(take(X1, X2)) -> take(active(X1), X2) 101.64/27.11 active(take(X1, X2)) -> take(X1, active(X2)) 101.64/27.11 active(sel(X1, X2)) -> sel(active(X1), X2) 101.64/27.11 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.64/27.11 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.64/27.11 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.64/27.11 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.64/27.11 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.64/27.11 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.64/27.11 U106(mark(X)) -> mark(U106(X)) 101.64/27.11 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.64/27.11 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.64/27.11 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.64/27.11 U112(mark(X)) -> mark(U112(X)) 101.64/27.11 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.64/27.11 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.64/27.11 U122(mark(X)) -> mark(U122(X)) 101.64/27.11 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.64/27.11 U131(mark(X)) -> mark(U131(X)) 101.64/27.11 snd(mark(X)) -> mark(snd(X)) 101.64/27.11 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.64/27.11 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.64/27.11 U141(mark(X)) -> mark(U141(X)) 101.64/27.11 U151(mark(X)) -> mark(U151(X)) 101.64/27.11 U161(mark(X)) -> mark(U161(X)) 101.64/27.11 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.64/27.11 U172(mark(X)) -> mark(U172(X)) 101.64/27.11 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.64/27.11 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.64/27.11 U183(mark(X)) -> mark(U183(X)) 101.64/27.11 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.64/27.11 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.64/27.11 U193(mark(X)) -> mark(U193(X)) 101.64/27.11 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.64/27.11 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.64/27.11 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.64/27.11 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.64/27.11 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.64/27.11 U206(mark(X)) -> mark(U206(X)) 101.64/27.11 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.64/27.11 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.64/27.11 U211(mark(X)) -> mark(U211(X)) 101.64/27.11 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.64/27.11 U221(mark(X)) -> mark(U221(X)) 101.64/27.11 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.64/27.11 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.64/27.11 U232(mark(X)) -> mark(U232(X)) 101.64/27.11 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.64/27.11 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.64/27.11 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.64/27.11 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.64/27.11 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.64/27.11 U246(mark(X)) -> mark(U246(X)) 101.64/27.11 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.64/27.11 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.64/27.11 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.64/27.11 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.64/27.11 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.64/27.11 U256(mark(X)) -> mark(U256(X)) 101.64/27.11 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.64/27.11 U262(mark(X)) -> mark(U262(X)) 101.64/27.11 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.64/27.11 U272(mark(X)) -> mark(U272(X)) 101.64/27.11 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.64/27.11 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.64/27.11 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.64/27.11 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.64/27.11 s(mark(X)) -> mark(s(X)) 101.64/27.11 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.64/27.11 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.64/27.11 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.64/27.11 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.64/27.11 head(mark(X)) -> mark(head(X)) 101.64/27.11 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.64/27.11 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.64/27.11 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.64/27.11 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.64/27.11 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.64/27.11 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.64/27.11 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.64/27.11 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.64/27.11 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.64/27.11 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.64/27.11 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.64/27.11 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.64/27.11 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.64/27.11 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.64/27.11 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.64/27.11 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.64/27.11 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.64/27.11 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.64/27.11 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.64/27.11 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.64/27.11 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.64/27.11 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.64/27.11 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.64/27.11 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.64/27.11 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.64/27.11 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.64/27.11 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.64/27.11 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.64/27.11 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.64/27.11 fst(mark(X)) -> mark(fst(X)) 101.64/27.11 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.64/27.11 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.64/27.11 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.64/27.11 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.64/27.11 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.64/27.11 U46(mark(X)) -> mark(U46(X)) 101.64/27.11 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.64/27.11 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.64/27.11 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.64/27.11 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.64/27.11 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.64/27.11 U56(mark(X)) -> mark(U56(X)) 101.64/27.11 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.64/27.11 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.64/27.11 U63(mark(X)) -> mark(U63(X)) 101.64/27.11 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.64/27.11 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.64/27.11 U73(mark(X)) -> mark(U73(X)) 101.64/27.11 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.64/27.11 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.64/27.11 U83(mark(X)) -> mark(U83(X)) 101.64/27.11 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.64/27.11 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.64/27.11 U93(mark(X)) -> mark(U93(X)) 101.64/27.11 tail(mark(X)) -> mark(tail(X)) 101.64/27.11 take(mark(X1), X2) -> mark(take(X1, X2)) 101.64/27.11 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.64/27.11 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.64/27.11 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.64/27.11 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(tt) -> ok(tt) 101.64/27.11 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.64/27.11 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.64/27.11 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.64/27.11 proper(isNatural(X)) -> isNatural(proper(X)) 101.64/27.11 proper(U106(X)) -> U106(proper(X)) 101.64/27.11 proper(isLNat(X)) -> isLNat(proper(X)) 101.64/27.11 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.64/27.11 proper(U112(X)) -> U112(proper(X)) 101.64/27.11 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.64/27.11 proper(U122(X)) -> U122(proper(X)) 101.64/27.11 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U131(X)) -> U131(proper(X)) 101.64/27.11 proper(snd(X)) -> snd(proper(X)) 101.64/27.11 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.64/27.11 proper(U141(X)) -> U141(proper(X)) 101.64/27.11 proper(U151(X)) -> U151(proper(X)) 101.64/27.11 proper(U161(X)) -> U161(proper(X)) 101.64/27.11 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.64/27.11 proper(U172(X)) -> U172(proper(X)) 101.64/27.11 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.64/27.11 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.64/27.11 proper(U183(X)) -> U183(proper(X)) 101.64/27.11 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.64/27.11 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.64/27.11 proper(U193(X)) -> U193(proper(X)) 101.64/27.11 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.64/27.11 proper(U206(X)) -> U206(proper(X)) 101.64/27.11 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U211(X)) -> U211(proper(X)) 101.64/27.11 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U221(X)) -> U221(proper(X)) 101.64/27.11 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.64/27.11 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.64/27.11 proper(U232(X)) -> U232(proper(X)) 101.64/27.11 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.64/27.11 proper(U246(X)) -> U246(proper(X)) 101.64/27.11 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.64/27.11 proper(U256(X)) -> U256(proper(X)) 101.64/27.11 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.64/27.11 proper(U262(X)) -> U262(proper(X)) 101.64/27.11 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.64/27.11 proper(U272(X)) -> U272(proper(X)) 101.64/27.11 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.64/27.11 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.64/27.11 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.64/27.11 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.64/27.11 proper(s(X)) -> s(proper(X)) 101.64/27.11 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(head(X)) -> head(proper(X)) 101.64/27.11 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.64/27.11 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.64/27.11 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.64/27.11 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.64/27.11 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.64/27.11 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.64/27.11 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.64/27.11 proper(nil) -> ok(nil) 101.64/27.11 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.64/27.11 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.64/27.11 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.64/27.11 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.64/27.11 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.64/27.11 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.64/27.11 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(fst(X)) -> fst(proper(X)) 101.64/27.11 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.64/27.11 proper(U46(X)) -> U46(proper(X)) 101.64/27.11 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.64/27.11 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.64/27.11 proper(U56(X)) -> U56(proper(X)) 101.64/27.11 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.64/27.11 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.64/27.11 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.64/27.11 proper(U63(X)) -> U63(proper(X)) 101.64/27.11 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.64/27.11 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.64/27.11 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.64/27.11 proper(U73(X)) -> U73(proper(X)) 101.64/27.11 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.64/27.11 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.64/27.11 proper(U83(X)) -> U83(proper(X)) 101.64/27.11 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.64/27.11 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.64/27.11 proper(U93(X)) -> U93(proper(X)) 101.64/27.11 proper(tail(X)) -> tail(proper(X)) 101.64/27.11 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.64/27.11 proper(0') -> ok(0') 101.64/27.11 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.64/27.11 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.64/27.11 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.64/27.11 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.64/27.11 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.64/27.11 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.64/27.11 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.64/27.11 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.64/27.11 isNatural(ok(X)) -> ok(isNatural(X)) 101.64/27.11 U106(ok(X)) -> ok(U106(X)) 101.64/27.11 isLNat(ok(X)) -> ok(isLNat(X)) 101.64/27.11 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.64/27.11 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.64/27.11 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.64/27.11 U112(ok(X)) -> ok(U112(X)) 101.64/27.11 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.64/27.11 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.64/27.11 U122(ok(X)) -> ok(U122(X)) 101.64/27.11 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.64/27.11 U131(ok(X)) -> ok(U131(X)) 101.64/27.11 snd(ok(X)) -> ok(snd(X)) 101.64/27.11 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.64/27.11 U141(ok(X)) -> ok(U141(X)) 101.64/27.11 U151(ok(X)) -> ok(U151(X)) 101.64/27.11 U161(ok(X)) -> ok(U161(X)) 101.64/27.11 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.64/27.11 U172(ok(X)) -> ok(U172(X)) 101.64/27.11 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.64/27.11 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.64/27.11 U183(ok(X)) -> ok(U183(X)) 101.64/27.11 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.64/27.11 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.64/27.11 U193(ok(X)) -> ok(U193(X)) 101.64/27.11 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.64/27.11 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.64/27.11 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.64/27.11 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.64/27.11 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.64/27.11 U206(ok(X)) -> ok(U206(X)) 101.64/27.11 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.64/27.11 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.64/27.11 U211(ok(X)) -> ok(U211(X)) 101.64/27.11 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.64/27.11 U221(ok(X)) -> ok(U221(X)) 101.64/27.11 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.64/27.11 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.64/27.11 U232(ok(X)) -> ok(U232(X)) 101.64/27.11 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.64/27.11 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.64/27.11 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.64/27.11 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.64/27.11 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.64/27.11 U246(ok(X)) -> ok(U246(X)) 101.64/27.11 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.64/27.11 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.64/27.11 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.64/27.11 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.64/27.11 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.64/27.11 U256(ok(X)) -> ok(U256(X)) 101.64/27.11 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.64/27.11 U262(ok(X)) -> ok(U262(X)) 101.64/27.11 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.64/27.11 U272(ok(X)) -> ok(U272(X)) 101.64/27.11 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.64/27.11 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.64/27.11 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.64/27.11 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.64/27.11 s(ok(X)) -> ok(s(X)) 101.64/27.11 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.64/27.11 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.64/27.11 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.64/27.11 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.64/27.11 head(ok(X)) -> ok(head(X)) 101.64/27.11 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.64/27.11 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.64/27.11 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.64/27.11 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.64/27.11 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.64/27.11 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.64/27.11 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.64/27.11 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.64/27.11 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.64/27.11 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.64/27.11 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.64/27.11 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.64/27.11 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.64/27.11 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.64/27.11 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.64/27.11 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.64/27.11 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.64/27.11 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.64/27.11 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.64/27.11 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.64/27.11 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.64/27.11 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.64/27.11 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.64/27.11 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.64/27.11 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.64/27.11 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.64/27.11 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.64/27.11 fst(ok(X)) -> ok(fst(X)) 101.64/27.11 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.64/27.11 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.64/27.11 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.64/27.11 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.64/27.11 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.64/27.11 U46(ok(X)) -> ok(U46(X)) 101.64/27.11 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.64/27.11 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.64/27.11 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.64/27.11 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.64/27.11 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.64/27.11 U56(ok(X)) -> ok(U56(X)) 101.64/27.11 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.64/27.11 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.64/27.11 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.64/27.11 U63(ok(X)) -> ok(U63(X)) 101.64/27.11 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.64/27.11 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.64/27.11 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.64/27.11 U73(ok(X)) -> ok(U73(X)) 101.64/27.11 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.64/27.11 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.64/27.11 U83(ok(X)) -> ok(U83(X)) 101.64/27.11 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.64/27.11 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.64/27.11 U93(ok(X)) -> ok(U93(X)) 101.64/27.11 tail(ok(X)) -> ok(tail(X)) 101.64/27.11 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.64/27.11 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.64/27.11 top(mark(X)) -> top(proper(X)) 101.64/27.11 top(ok(X)) -> top(active(X)) 101.64/27.11 101.64/27.11 Types: 101.64/27.11 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 tt :: tt:mark:nil:0':ok 101.64/27.11 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 nil :: tt:mark:nil:0':ok 101.64/27.11 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 0' :: tt:mark:nil:0':ok 101.64/27.11 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.64/27.11 top :: tt:mark:nil:0':ok -> top 101.64/27.11 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.64/27.11 hole_top2_0 :: top 101.64/27.11 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.64/27.11 101.64/27.11 101.64/27.11 Lemmas: 101.64/27.11 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.64/27.11 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.64/27.11 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.64/27.11 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.64/27.11 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.64/27.11 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.64/27.11 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.64/27.11 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.64/27.11 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.64/27.11 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.64/27.11 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.64/27.11 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.64/27.11 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.64/27.11 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.64/27.11 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.64/27.11 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.64/27.11 101.64/27.11 101.64/27.11 Generator Equations: 101.64/27.11 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.64/27.11 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.64/27.11 101.64/27.11 101.64/27.11 The following defined symbols remain to be analysed: 101.64/27.11 U193, active, U202, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.64/27.11 101.64/27.11 They will be analysed ascendingly in the following order: 101.64/27.11 U193 < active 101.64/27.11 U202 < active 101.64/27.11 U203 < active 101.64/27.11 U204 < active 101.64/27.11 U205 < active 101.64/27.11 U206 < active 101.64/27.11 U22 < active 101.64/27.11 U23 < active 101.64/27.11 U24 < active 101.64/27.11 U232 < active 101.64/27.11 U242 < active 101.64/27.11 U243 < active 101.64/27.11 U244 < active 101.64/27.11 U245 < active 101.64/27.11 U246 < active 101.64/27.11 U252 < active 101.64/27.11 U253 < active 101.64/27.11 U254 < active 101.64/27.11 U255 < active 101.64/27.11 U256 < active 101.64/27.11 U262 < active 101.64/27.11 U272 < active 101.64/27.11 U282 < active 101.64/27.11 cons < active 101.64/27.11 natsFrom < active 101.64/27.11 s < active 101.64/27.11 U292 < active 101.64/27.11 U293 < active 101.64/27.11 U294 < active 101.64/27.11 head < active 101.64/27.11 afterNth < active 101.64/27.11 U302 < active 101.64/27.11 U303 < active 101.64/27.11 U304 < active 101.64/27.11 U32 < active 101.64/27.11 U312 < active 101.64/27.11 pair < active 101.64/27.11 U33 < active 101.64/27.11 U322 < active 101.64/27.11 U323 < active 101.64/27.11 U324 < active 101.64/27.11 U325 < active 101.64/27.11 U326 < active 101.64/27.11 U327 < active 101.64/27.11 U34 < active 101.64/27.11 U332 < active 101.64/27.11 U333 < active 101.64/27.11 U334 < active 101.64/27.11 U342 < active 101.64/27.11 U343 < active 101.64/27.11 U344 < active 101.64/27.11 fst < active 101.64/27.11 U42 < active 101.64/27.11 U43 < active 101.64/27.11 U44 < active 101.64/27.11 U45 < active 101.64/27.11 U46 < active 101.64/27.11 U52 < active 101.64/27.11 U53 < active 101.64/27.11 U54 < active 101.64/27.11 U55 < active 101.64/27.11 U56 < active 101.64/27.11 U62 < active 101.64/27.11 isPLNatKind < active 101.64/27.11 U63 < active 101.64/27.11 isPLNat < active 101.64/27.11 U72 < active 101.64/27.11 U73 < active 101.64/27.11 U82 < active 101.64/27.11 U83 < active 101.64/27.11 U92 < active 101.64/27.11 U93 < active 101.64/27.11 U11 < active 101.64/27.11 U21 < active 101.64/27.11 U31 < active 101.64/27.11 U41 < active 101.64/27.11 U51 < active 101.64/27.11 U61 < active 101.64/27.11 U71 < active 101.64/27.11 U81 < active 101.64/27.11 U91 < active 101.64/27.11 U101 < active 101.64/27.11 U111 < active 101.64/27.11 U121 < active 101.64/27.11 U131 < active 101.64/27.11 U141 < active 101.64/27.11 U151 < active 101.64/27.11 U161 < active 101.64/27.11 U171 < active 101.64/27.11 U181 < active 101.64/27.11 U191 < active 101.64/27.11 U201 < active 101.64/27.11 U211 < active 101.64/27.11 U221 < active 101.64/27.11 U231 < active 101.64/27.11 U241 < active 101.64/27.11 U251 < active 101.64/27.11 U261 < active 101.64/27.11 U271 < active 101.64/27.11 U281 < active 101.64/27.11 U291 < active 101.64/27.11 U301 < active 101.64/27.11 U311 < active 101.64/27.11 U321 < active 101.64/27.11 U331 < active 101.64/27.11 U341 < active 101.64/27.11 tail < active 101.64/27.11 take < active 101.64/27.11 sel < active 101.64/27.11 active < top 101.64/27.11 U193 < proper 101.64/27.11 U202 < proper 101.64/27.11 U203 < proper 101.64/27.11 U204 < proper 101.64/27.11 U205 < proper 101.64/27.11 U206 < proper 101.64/27.11 U22 < proper 101.64/27.11 U23 < proper 101.64/27.11 U24 < proper 101.64/27.11 U232 < proper 101.64/27.11 U242 < proper 101.64/27.11 U243 < proper 101.64/27.11 U244 < proper 101.64/27.11 U245 < proper 101.64/27.11 U246 < proper 101.64/27.11 U252 < proper 101.64/27.11 U253 < proper 101.64/27.11 U254 < proper 101.64/27.11 U255 < proper 101.64/27.11 U256 < proper 101.64/27.11 U262 < proper 101.64/27.11 U272 < proper 101.64/27.11 U282 < proper 101.64/27.11 cons < proper 101.64/27.11 natsFrom < proper 101.64/27.11 s < proper 101.64/27.11 U292 < proper 101.64/27.11 U293 < proper 101.64/27.11 U294 < proper 101.64/27.11 head < proper 101.64/27.11 afterNth < proper 101.64/27.11 U302 < proper 101.64/27.11 U303 < proper 101.64/27.11 U304 < proper 101.64/27.11 U32 < proper 101.64/27.11 U312 < proper 101.64/27.11 pair < proper 101.64/27.11 U33 < proper 101.64/27.11 U322 < proper 101.64/27.11 U323 < proper 101.64/27.11 U324 < proper 101.64/27.11 U325 < proper 101.64/27.11 U326 < proper 101.64/27.11 U327 < proper 101.64/27.11 U34 < proper 101.64/27.11 U332 < proper 101.64/27.11 U333 < proper 101.64/27.11 U334 < proper 101.64/27.11 U342 < proper 101.64/27.11 U343 < proper 101.64/27.11 U344 < proper 101.64/27.11 fst < proper 101.64/27.11 U42 < proper 101.64/27.11 U43 < proper 101.64/27.11 U44 < proper 101.64/27.11 U45 < proper 101.64/27.11 U46 < proper 101.64/27.11 U52 < proper 101.64/27.11 U53 < proper 101.64/27.11 U54 < proper 101.64/27.11 U55 < proper 101.64/27.11 U56 < proper 101.64/27.11 U62 < proper 101.64/27.11 isPLNatKind < proper 101.64/27.11 U63 < proper 101.64/27.11 isPLNat < proper 101.64/27.11 U72 < proper 101.64/27.11 U73 < proper 101.64/27.11 U82 < proper 101.64/27.11 U83 < proper 101.64/27.11 U92 < proper 101.64/27.11 U93 < proper 101.64/27.11 U11 < proper 101.64/27.11 U21 < proper 101.64/27.11 U31 < proper 101.64/27.11 U41 < proper 101.64/27.11 U51 < proper 101.64/27.11 U61 < proper 101.64/27.11 U71 < proper 101.64/27.11 U81 < proper 101.64/27.11 U91 < proper 101.64/27.11 U101 < proper 101.64/27.11 U111 < proper 101.64/27.11 U121 < proper 101.64/27.11 U131 < proper 101.64/27.11 U141 < proper 101.64/27.11 U151 < proper 101.64/27.11 U161 < proper 101.64/27.11 U171 < proper 101.64/27.11 U181 < proper 101.64/27.11 U191 < proper 101.64/27.11 U201 < proper 101.64/27.11 U211 < proper 101.64/27.11 U221 < proper 101.64/27.11 U231 < proper 101.64/27.11 U241 < proper 101.64/27.11 U251 < proper 101.64/27.11 U261 < proper 101.64/27.11 U271 < proper 101.64/27.11 U281 < proper 101.64/27.11 U291 < proper 101.64/27.11 U301 < proper 101.64/27.11 U311 < proper 101.64/27.11 U321 < proper 101.64/27.11 U331 < proper 101.64/27.11 U341 < proper 101.64/27.11 tail < proper 101.64/27.11 take < proper 101.64/27.11 sel < proper 101.64/27.11 proper < top 101.64/27.11 101.64/27.11 ---------------------------------------- 101.64/27.11 101.64/27.11 (61) RewriteLemmaProof (LOWER BOUND(ID)) 101.64/27.11 Proved the following rewrite lemma: 101.64/27.11 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.64/27.11 101.64/27.11 Induction Base: 101.64/27.11 U193(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.64/27.11 101.64/27.11 Induction Step: 101.64/27.11 U193(gen_tt:mark:nil:0':ok3_0(+(1, +(n191574_0, 1)))) ->_R^Omega(1) 101.64/27.11 mark(U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0)))) ->_IH 101.64/27.11 mark(*4_0) 101.64/27.11 101.64/27.11 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.64/27.11 ---------------------------------------- 101.64/27.11 101.64/27.11 (62) 101.64/27.11 Obligation: 101.64/27.11 TRS: 101.64/27.11 Rules: 101.64/27.11 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.64/27.11 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.64/27.11 active(U106(tt)) -> mark(tt) 101.64/27.11 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.64/27.11 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.64/27.11 active(U112(tt)) -> mark(tt) 101.64/27.11 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.64/27.11 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.64/27.11 active(U122(tt)) -> mark(tt) 101.64/27.11 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.64/27.11 active(U131(tt)) -> mark(tt) 101.64/27.11 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.64/27.11 active(U141(tt)) -> mark(tt) 101.64/27.11 active(U151(tt)) -> mark(tt) 101.64/27.11 active(U161(tt)) -> mark(tt) 101.64/27.11 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.64/27.11 active(U172(tt)) -> mark(tt) 101.64/27.11 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.64/27.11 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.64/27.11 active(U183(tt)) -> mark(tt) 101.64/27.11 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.64/27.11 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.64/27.11 active(U193(tt)) -> mark(tt) 101.64/27.11 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.64/27.11 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.64/27.11 active(U206(tt)) -> mark(tt) 101.64/27.11 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.64/27.11 active(U211(tt)) -> mark(tt) 101.64/27.11 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.64/27.11 active(U221(tt)) -> mark(tt) 101.64/27.11 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.64/27.11 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.64/27.11 active(U232(tt)) -> mark(tt) 101.64/27.11 active(U24(tt, X)) -> mark(X) 101.64/27.11 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.64/27.11 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.64/27.11 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.64/27.11 active(U246(tt)) -> mark(tt) 101.64/27.11 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.64/27.11 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.64/27.11 active(U256(tt)) -> mark(tt) 101.64/27.11 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.64/27.11 active(U262(tt)) -> mark(tt) 101.64/27.11 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.64/27.11 active(U272(tt)) -> mark(tt) 101.64/27.11 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.64/27.11 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.64/27.11 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.64/27.11 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.64/27.11 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.64/27.11 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.64/27.11 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.64/27.11 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.64/27.11 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.64/27.11 active(U304(tt, Y)) -> mark(Y) 101.64/27.11 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.64/27.11 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.64/27.11 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.64/27.11 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.64/27.11 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.64/27.11 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.64/27.11 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.64/27.11 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.64/27.11 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.64/27.11 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.64/27.11 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.64/27.11 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.64/27.11 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.64/27.11 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.64/27.11 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.64/27.11 active(U334(tt, XS)) -> mark(XS) 101.64/27.11 active(U34(tt, N)) -> mark(N) 101.64/27.11 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.64/27.11 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.64/27.11 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.64/27.11 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.64/27.11 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.64/27.11 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.64/27.11 active(U46(tt)) -> mark(tt) 101.64/27.11 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.64/27.11 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.64/27.11 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.64/27.11 active(U56(tt)) -> mark(tt) 101.64/27.11 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.64/27.11 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.64/27.11 active(U63(tt)) -> mark(tt) 101.64/27.11 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.64/27.11 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.64/27.11 active(U73(tt)) -> mark(tt) 101.64/27.11 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.64/27.11 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.64/27.11 active(U83(tt)) -> mark(tt) 101.64/27.11 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.64/27.11 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.64/27.11 active(U93(tt)) -> mark(tt) 101.64/27.11 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.64/27.11 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.64/27.11 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.64/27.11 active(isLNat(nil)) -> mark(tt) 101.64/27.11 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.64/27.11 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.64/27.11 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.64/27.11 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.64/27.11 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isLNatKind(nil)) -> mark(tt) 101.64/27.11 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.64/27.11 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.64/27.11 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.64/27.11 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.64/27.11 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.64/27.11 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.64/27.11 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.64/27.11 active(isNatural(0')) -> mark(tt) 101.64/27.11 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.64/27.11 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.64/27.11 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isNaturalKind(0')) -> mark(tt) 101.64/27.11 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.64/27.11 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.64/27.11 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.64/27.11 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.64/27.11 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.64/27.11 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.64/27.11 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.64/27.11 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.64/27.11 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.64/27.11 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.64/27.11 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.64/27.11 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.64/27.11 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.64/27.11 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.64/27.11 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.64/27.11 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.64/27.11 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.64/27.11 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.64/27.11 active(U105(X1, X2)) -> U105(active(X1), X2) 101.64/27.11 active(U106(X)) -> U106(active(X)) 101.64/27.11 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.64/27.11 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.64/27.11 active(U111(X1, X2)) -> U111(active(X1), X2) 101.64/27.11 active(U112(X)) -> U112(active(X)) 101.91/27.11 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.11 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.11 active(U122(X)) -> U122(active(X)) 101.91/27.11 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.11 active(U131(X)) -> U131(active(X)) 101.91/27.11 active(snd(X)) -> snd(active(X)) 101.91/27.11 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.11 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.11 active(U141(X)) -> U141(active(X)) 101.91/27.11 active(U151(X)) -> U151(active(X)) 101.91/27.11 active(U161(X)) -> U161(active(X)) 101.91/27.11 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.11 active(U172(X)) -> U172(active(X)) 101.91/27.11 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.11 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.11 active(U183(X)) -> U183(active(X)) 101.91/27.11 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.11 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.11 active(U193(X)) -> U193(active(X)) 101.91/27.11 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.11 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.11 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.11 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.11 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.11 active(U206(X)) -> U206(active(X)) 101.91/27.11 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.11 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.11 active(U211(X)) -> U211(active(X)) 101.91/27.11 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.11 active(U221(X)) -> U221(active(X)) 101.91/27.11 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.11 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.11 active(U232(X)) -> U232(active(X)) 101.91/27.11 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.11 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.11 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.11 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.11 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.11 active(U246(X)) -> U246(active(X)) 101.91/27.11 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.11 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.11 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.11 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.11 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.11 active(U256(X)) -> U256(active(X)) 101.91/27.11 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.11 active(U262(X)) -> U262(active(X)) 101.91/27.11 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.11 active(U272(X)) -> U272(active(X)) 101.91/27.11 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.11 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.11 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.11 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.11 active(s(X)) -> s(active(X)) 101.91/27.11 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.11 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.11 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.11 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.11 active(head(X)) -> head(active(X)) 101.91/27.11 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.11 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.11 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.11 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.11 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.11 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.11 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.11 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.11 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.11 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.11 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.11 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.11 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.11 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.11 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.11 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.11 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.11 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.11 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.11 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.11 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.11 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.11 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.11 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.11 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.11 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.11 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.11 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.11 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.11 active(fst(X)) -> fst(active(X)) 101.91/27.11 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.11 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.11 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.11 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.11 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.11 active(U46(X)) -> U46(active(X)) 101.91/27.11 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.11 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.11 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.11 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.11 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.11 active(U56(X)) -> U56(active(X)) 101.91/27.11 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.11 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.11 active(U63(X)) -> U63(active(X)) 101.91/27.11 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.11 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.11 active(U73(X)) -> U73(active(X)) 101.91/27.11 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.11 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.11 active(U83(X)) -> U83(active(X)) 101.91/27.11 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.11 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.11 active(U93(X)) -> U93(active(X)) 101.91/27.11 active(tail(X)) -> tail(active(X)) 101.91/27.11 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.11 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.11 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.11 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.11 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.11 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.11 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.11 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.11 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.11 U106(mark(X)) -> mark(U106(X)) 101.91/27.11 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.11 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.11 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.11 U112(mark(X)) -> mark(U112(X)) 101.91/27.11 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.11 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.11 U122(mark(X)) -> mark(U122(X)) 101.91/27.11 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.11 U131(mark(X)) -> mark(U131(X)) 101.91/27.11 snd(mark(X)) -> mark(snd(X)) 101.91/27.11 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.11 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.11 U141(mark(X)) -> mark(U141(X)) 101.91/27.11 U151(mark(X)) -> mark(U151(X)) 101.91/27.11 U161(mark(X)) -> mark(U161(X)) 101.91/27.11 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.11 U172(mark(X)) -> mark(U172(X)) 101.91/27.11 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.11 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.11 U183(mark(X)) -> mark(U183(X)) 101.91/27.11 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.11 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.11 U193(mark(X)) -> mark(U193(X)) 101.91/27.11 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.11 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.11 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.11 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.11 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.11 U206(mark(X)) -> mark(U206(X)) 101.91/27.11 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.11 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.11 U211(mark(X)) -> mark(U211(X)) 101.91/27.11 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.11 U221(mark(X)) -> mark(U221(X)) 101.91/27.11 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.11 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.11 U232(mark(X)) -> mark(U232(X)) 101.91/27.11 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.11 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.11 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.11 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.11 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.11 U246(mark(X)) -> mark(U246(X)) 101.91/27.11 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.11 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.11 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.11 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.11 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.11 U256(mark(X)) -> mark(U256(X)) 101.91/27.11 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.11 U262(mark(X)) -> mark(U262(X)) 101.91/27.11 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.11 U272(mark(X)) -> mark(U272(X)) 101.91/27.11 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.11 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.11 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.11 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.11 s(mark(X)) -> mark(s(X)) 101.91/27.11 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.11 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.11 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.11 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.11 head(mark(X)) -> mark(head(X)) 101.91/27.11 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.11 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.11 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.11 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.11 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.11 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.11 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.11 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.11 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.11 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.11 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.11 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.11 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.11 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.11 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.11 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.11 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.11 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.11 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.11 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.11 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.11 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.11 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.11 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.11 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.11 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.11 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.11 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.11 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.11 fst(mark(X)) -> mark(fst(X)) 101.91/27.11 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.11 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.11 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.11 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.11 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.11 U46(mark(X)) -> mark(U46(X)) 101.91/27.11 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.11 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.11 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.11 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.11 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.11 U56(mark(X)) -> mark(U56(X)) 101.91/27.11 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.11 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.11 U63(mark(X)) -> mark(U63(X)) 101.91/27.11 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.11 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.11 U73(mark(X)) -> mark(U73(X)) 101.91/27.11 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.11 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.11 U83(mark(X)) -> mark(U83(X)) 101.91/27.11 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.11 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.11 U93(mark(X)) -> mark(U93(X)) 101.91/27.11 tail(mark(X)) -> mark(tail(X)) 101.91/27.11 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.11 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.11 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.11 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.11 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(tt) -> ok(tt) 101.91/27.11 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.11 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.11 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.11 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.11 proper(U106(X)) -> U106(proper(X)) 101.91/27.11 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.11 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.11 proper(U112(X)) -> U112(proper(X)) 101.91/27.11 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.11 proper(U122(X)) -> U122(proper(X)) 101.91/27.11 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U131(X)) -> U131(proper(X)) 101.91/27.11 proper(snd(X)) -> snd(proper(X)) 101.91/27.11 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.11 proper(U141(X)) -> U141(proper(X)) 101.91/27.11 proper(U151(X)) -> U151(proper(X)) 101.91/27.11 proper(U161(X)) -> U161(proper(X)) 101.91/27.11 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.11 proper(U172(X)) -> U172(proper(X)) 101.91/27.11 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.11 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.11 proper(U183(X)) -> U183(proper(X)) 101.91/27.11 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.11 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.11 proper(U193(X)) -> U193(proper(X)) 101.91/27.11 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.11 proper(U206(X)) -> U206(proper(X)) 101.91/27.11 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U211(X)) -> U211(proper(X)) 101.91/27.11 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U221(X)) -> U221(proper(X)) 101.91/27.11 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.11 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.11 proper(U232(X)) -> U232(proper(X)) 101.91/27.11 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.11 proper(U246(X)) -> U246(proper(X)) 101.91/27.11 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.11 proper(U256(X)) -> U256(proper(X)) 101.91/27.11 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.11 proper(U262(X)) -> U262(proper(X)) 101.91/27.11 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.11 proper(U272(X)) -> U272(proper(X)) 101.91/27.11 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.11 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.11 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.11 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.11 proper(s(X)) -> s(proper(X)) 101.91/27.11 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(head(X)) -> head(proper(X)) 101.91/27.11 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.11 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.11 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.11 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.11 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.11 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.11 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.11 proper(nil) -> ok(nil) 101.91/27.11 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.11 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.11 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.11 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.11 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.11 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.11 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(fst(X)) -> fst(proper(X)) 101.91/27.11 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.11 proper(U46(X)) -> U46(proper(X)) 101.91/27.11 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.11 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.11 proper(U56(X)) -> U56(proper(X)) 101.91/27.11 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.11 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.11 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.11 proper(U63(X)) -> U63(proper(X)) 101.91/27.11 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.11 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.11 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.11 proper(U73(X)) -> U73(proper(X)) 101.91/27.11 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.11 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.11 proper(U83(X)) -> U83(proper(X)) 101.91/27.11 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.11 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.11 proper(U93(X)) -> U93(proper(X)) 101.91/27.11 proper(tail(X)) -> tail(proper(X)) 101.91/27.11 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.11 proper(0') -> ok(0') 101.91/27.11 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.11 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.11 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.11 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.11 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.11 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.11 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.11 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.11 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.11 U106(ok(X)) -> ok(U106(X)) 101.91/27.11 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.11 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.11 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.11 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.11 U112(ok(X)) -> ok(U112(X)) 101.91/27.11 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.11 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.11 U122(ok(X)) -> ok(U122(X)) 101.91/27.11 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.11 U131(ok(X)) -> ok(U131(X)) 101.91/27.11 snd(ok(X)) -> ok(snd(X)) 101.91/27.11 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.11 U141(ok(X)) -> ok(U141(X)) 101.91/27.11 U151(ok(X)) -> ok(U151(X)) 101.91/27.11 U161(ok(X)) -> ok(U161(X)) 101.91/27.11 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.11 U172(ok(X)) -> ok(U172(X)) 101.91/27.11 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.11 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.11 U183(ok(X)) -> ok(U183(X)) 101.91/27.11 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.11 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.11 U193(ok(X)) -> ok(U193(X)) 101.91/27.11 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.11 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.11 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.11 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.11 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.11 U206(ok(X)) -> ok(U206(X)) 101.91/27.11 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.11 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.11 U211(ok(X)) -> ok(U211(X)) 101.91/27.11 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.11 U221(ok(X)) -> ok(U221(X)) 101.91/27.11 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.11 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.11 U232(ok(X)) -> ok(U232(X)) 101.91/27.11 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.11 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.11 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.11 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.11 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.11 U246(ok(X)) -> ok(U246(X)) 101.91/27.11 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.11 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.11 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.11 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.11 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.11 U256(ok(X)) -> ok(U256(X)) 101.91/27.11 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.11 U262(ok(X)) -> ok(U262(X)) 101.91/27.11 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.11 U272(ok(X)) -> ok(U272(X)) 101.91/27.11 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.11 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.12 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.12 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.12 s(ok(X)) -> ok(s(X)) 101.91/27.12 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.12 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.12 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.12 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.12 head(ok(X)) -> ok(head(X)) 101.91/27.12 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.12 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.12 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.12 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.12 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.12 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.12 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.12 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.12 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.12 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.12 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.12 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.12 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.12 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.12 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.12 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.12 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.12 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.12 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.12 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.12 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.12 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.12 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.12 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.12 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.12 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.12 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.12 fst(ok(X)) -> ok(fst(X)) 101.91/27.12 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.12 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.12 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.12 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.12 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.12 U46(ok(X)) -> ok(U46(X)) 101.91/27.12 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.12 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.12 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.12 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.12 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.12 U56(ok(X)) -> ok(U56(X)) 101.91/27.12 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.12 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.12 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.12 U63(ok(X)) -> ok(U63(X)) 101.91/27.12 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.12 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.12 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.12 U73(ok(X)) -> ok(U73(X)) 101.91/27.12 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.12 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.12 U83(ok(X)) -> ok(U83(X)) 101.91/27.12 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.12 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.12 U93(ok(X)) -> ok(U93(X)) 101.91/27.12 tail(ok(X)) -> ok(tail(X)) 101.91/27.12 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.12 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.12 top(mark(X)) -> top(proper(X)) 101.91/27.12 top(ok(X)) -> top(active(X)) 101.91/27.12 101.91/27.12 Types: 101.91/27.12 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 tt :: tt:mark:nil:0':ok 101.91/27.12 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 nil :: tt:mark:nil:0':ok 101.91/27.12 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 0' :: tt:mark:nil:0':ok 101.91/27.12 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 top :: tt:mark:nil:0':ok -> top 101.91/27.12 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.12 hole_top2_0 :: top 101.91/27.12 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.12 101.91/27.12 101.91/27.12 Lemmas: 101.91/27.12 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.12 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.12 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.12 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.12 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.12 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.12 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.12 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.12 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.12 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.12 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.12 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.12 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.12 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.12 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.12 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.12 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.12 101.91/27.12 101.91/27.12 Generator Equations: 101.91/27.12 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.12 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.12 101.91/27.12 101.91/27.12 The following defined symbols remain to be analysed: 101.91/27.12 U202, active, U203, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.12 101.91/27.12 They will be analysed ascendingly in the following order: 101.91/27.12 U202 < active 101.91/27.12 U203 < active 101.91/27.12 U204 < active 101.91/27.12 U205 < active 101.91/27.12 U206 < active 101.91/27.12 U22 < active 101.91/27.12 U23 < active 101.91/27.12 U24 < active 101.91/27.12 U232 < active 101.91/27.12 U242 < active 101.91/27.12 U243 < active 101.91/27.12 U244 < active 101.91/27.12 U245 < active 101.91/27.12 U246 < active 101.91/27.12 U252 < active 101.91/27.12 U253 < active 101.91/27.12 U254 < active 101.91/27.12 U255 < active 101.91/27.12 U256 < active 101.91/27.12 U262 < active 101.91/27.12 U272 < active 101.91/27.12 U282 < active 101.91/27.12 cons < active 101.91/27.12 natsFrom < active 101.91/27.12 s < active 101.91/27.12 U292 < active 101.91/27.12 U293 < active 101.91/27.12 U294 < active 101.91/27.12 head < active 101.91/27.12 afterNth < active 101.91/27.12 U302 < active 101.91/27.12 U303 < active 101.91/27.12 U304 < active 101.91/27.12 U32 < active 101.91/27.12 U312 < active 101.91/27.12 pair < active 101.91/27.12 U33 < active 101.91/27.12 U322 < active 101.91/27.12 U323 < active 101.91/27.12 U324 < active 101.91/27.12 U325 < active 101.91/27.12 U326 < active 101.91/27.12 U327 < active 101.91/27.12 U34 < active 101.91/27.12 U332 < active 101.91/27.12 U333 < active 101.91/27.12 U334 < active 101.91/27.12 U342 < active 101.91/27.12 U343 < active 101.91/27.12 U344 < active 101.91/27.12 fst < active 101.91/27.12 U42 < active 101.91/27.12 U43 < active 101.91/27.12 U44 < active 101.91/27.12 U45 < active 101.91/27.12 U46 < active 101.91/27.12 U52 < active 101.91/27.12 U53 < active 101.91/27.12 U54 < active 101.91/27.12 U55 < active 101.91/27.12 U56 < active 101.91/27.12 U62 < active 101.91/27.12 isPLNatKind < active 101.91/27.12 U63 < active 101.91/27.12 isPLNat < active 101.91/27.12 U72 < active 101.91/27.12 U73 < active 101.91/27.12 U82 < active 101.91/27.12 U83 < active 101.91/27.12 U92 < active 101.91/27.12 U93 < active 101.91/27.12 U11 < active 101.91/27.12 U21 < active 101.91/27.12 U31 < active 101.91/27.12 U41 < active 101.91/27.12 U51 < active 101.91/27.12 U61 < active 101.91/27.12 U71 < active 101.91/27.12 U81 < active 101.91/27.12 U91 < active 101.91/27.12 U101 < active 101.91/27.12 U111 < active 101.91/27.12 U121 < active 101.91/27.12 U131 < active 101.91/27.12 U141 < active 101.91/27.12 U151 < active 101.91/27.12 U161 < active 101.91/27.12 U171 < active 101.91/27.12 U181 < active 101.91/27.12 U191 < active 101.91/27.12 U201 < active 101.91/27.12 U211 < active 101.91/27.12 U221 < active 101.91/27.12 U231 < active 101.91/27.12 U241 < active 101.91/27.12 U251 < active 101.91/27.12 U261 < active 101.91/27.12 U271 < active 101.91/27.12 U281 < active 101.91/27.12 U291 < active 101.91/27.12 U301 < active 101.91/27.12 U311 < active 101.91/27.12 U321 < active 101.91/27.12 U331 < active 101.91/27.12 U341 < active 101.91/27.12 tail < active 101.91/27.12 take < active 101.91/27.12 sel < active 101.91/27.12 active < top 101.91/27.12 U202 < proper 101.91/27.12 U203 < proper 101.91/27.12 U204 < proper 101.91/27.12 U205 < proper 101.91/27.12 U206 < proper 101.91/27.12 U22 < proper 101.91/27.12 U23 < proper 101.91/27.12 U24 < proper 101.91/27.12 U232 < proper 101.91/27.12 U242 < proper 101.91/27.12 U243 < proper 101.91/27.12 U244 < proper 101.91/27.12 U245 < proper 101.91/27.12 U246 < proper 101.91/27.12 U252 < proper 101.91/27.12 U253 < proper 101.91/27.12 U254 < proper 101.91/27.12 U255 < proper 101.91/27.12 U256 < proper 101.91/27.12 U262 < proper 101.91/27.12 U272 < proper 101.91/27.12 U282 < proper 101.91/27.12 cons < proper 101.91/27.12 natsFrom < proper 101.91/27.12 s < proper 101.91/27.12 U292 < proper 101.91/27.12 U293 < proper 101.91/27.12 U294 < proper 101.91/27.12 head < proper 101.91/27.12 afterNth < proper 101.91/27.12 U302 < proper 101.91/27.12 U303 < proper 101.91/27.12 U304 < proper 101.91/27.12 U32 < proper 101.91/27.12 U312 < proper 101.91/27.12 pair < proper 101.91/27.12 U33 < proper 101.91/27.12 U322 < proper 101.91/27.12 U323 < proper 101.91/27.12 U324 < proper 101.91/27.12 U325 < proper 101.91/27.12 U326 < proper 101.91/27.12 U327 < proper 101.91/27.12 U34 < proper 101.91/27.12 U332 < proper 101.91/27.12 U333 < proper 101.91/27.12 U334 < proper 101.91/27.12 U342 < proper 101.91/27.12 U343 < proper 101.91/27.12 U344 < proper 101.91/27.12 fst < proper 101.91/27.12 U42 < proper 101.91/27.12 U43 < proper 101.91/27.12 U44 < proper 101.91/27.12 U45 < proper 101.91/27.12 U46 < proper 101.91/27.12 U52 < proper 101.91/27.12 U53 < proper 101.91/27.12 U54 < proper 101.91/27.12 U55 < proper 101.91/27.12 U56 < proper 101.91/27.12 U62 < proper 101.91/27.12 isPLNatKind < proper 101.91/27.12 U63 < proper 101.91/27.12 isPLNat < proper 101.91/27.12 U72 < proper 101.91/27.12 U73 < proper 101.91/27.12 U82 < proper 101.91/27.12 U83 < proper 101.91/27.12 U92 < proper 101.91/27.12 U93 < proper 101.91/27.12 U11 < proper 101.91/27.12 U21 < proper 101.91/27.12 U31 < proper 101.91/27.12 U41 < proper 101.91/27.12 U51 < proper 101.91/27.12 U61 < proper 101.91/27.12 U71 < proper 101.91/27.12 U81 < proper 101.91/27.12 U91 < proper 101.91/27.12 U101 < proper 101.91/27.12 U111 < proper 101.91/27.12 U121 < proper 101.91/27.12 U131 < proper 101.91/27.12 U141 < proper 101.91/27.12 U151 < proper 101.91/27.12 U161 < proper 101.91/27.12 U171 < proper 101.91/27.12 U181 < proper 101.91/27.12 U191 < proper 101.91/27.12 U201 < proper 101.91/27.12 U211 < proper 101.91/27.12 U221 < proper 101.91/27.12 U231 < proper 101.91/27.12 U241 < proper 101.91/27.12 U251 < proper 101.91/27.12 U261 < proper 101.91/27.12 U271 < proper 101.91/27.12 U281 < proper 101.91/27.12 U291 < proper 101.91/27.12 U301 < proper 101.91/27.12 U311 < proper 101.91/27.12 U321 < proper 101.91/27.12 U331 < proper 101.91/27.12 U341 < proper 101.91/27.12 tail < proper 101.91/27.12 take < proper 101.91/27.12 sel < proper 101.91/27.12 proper < top 101.91/27.12 101.91/27.12 ---------------------------------------- 101.91/27.12 101.91/27.12 (63) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.12 Proved the following rewrite lemma: 101.91/27.12 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.12 101.91/27.12 Induction Base: 101.91/27.12 U202(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.12 101.91/27.12 Induction Step: 101.91/27.12 U202(gen_tt:mark:nil:0':ok3_0(+(1, +(n196245_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.12 mark(U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.12 mark(*4_0) 101.91/27.12 101.91/27.12 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.12 ---------------------------------------- 101.91/27.12 101.91/27.12 (64) 101.91/27.12 Obligation: 101.91/27.12 TRS: 101.91/27.12 Rules: 101.91/27.12 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.12 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.12 active(U106(tt)) -> mark(tt) 101.91/27.12 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.12 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.12 active(U112(tt)) -> mark(tt) 101.91/27.12 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.12 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.12 active(U122(tt)) -> mark(tt) 101.91/27.12 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.12 active(U131(tt)) -> mark(tt) 101.91/27.12 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.12 active(U141(tt)) -> mark(tt) 101.91/27.12 active(U151(tt)) -> mark(tt) 101.91/27.12 active(U161(tt)) -> mark(tt) 101.91/27.12 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.12 active(U172(tt)) -> mark(tt) 101.91/27.12 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.12 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.12 active(U183(tt)) -> mark(tt) 101.91/27.12 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.12 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.12 active(U193(tt)) -> mark(tt) 101.91/27.12 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.12 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.12 active(U206(tt)) -> mark(tt) 101.91/27.12 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.12 active(U211(tt)) -> mark(tt) 101.91/27.12 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.12 active(U221(tt)) -> mark(tt) 101.91/27.12 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.12 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.12 active(U232(tt)) -> mark(tt) 101.91/27.12 active(U24(tt, X)) -> mark(X) 101.91/27.12 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.12 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.12 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.12 active(U246(tt)) -> mark(tt) 101.91/27.12 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.12 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.12 active(U256(tt)) -> mark(tt) 101.91/27.12 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.12 active(U262(tt)) -> mark(tt) 101.91/27.12 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.12 active(U272(tt)) -> mark(tt) 101.91/27.12 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.12 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.12 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.12 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.12 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.12 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.12 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.12 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.12 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.12 active(U304(tt, Y)) -> mark(Y) 101.91/27.12 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.12 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.12 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.12 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.12 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.12 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.12 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.12 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.12 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.12 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.12 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.12 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.12 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.12 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.12 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.12 active(U334(tt, XS)) -> mark(XS) 101.91/27.12 active(U34(tt, N)) -> mark(N) 101.91/27.12 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.12 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.12 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.12 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.12 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.12 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.12 active(U46(tt)) -> mark(tt) 101.91/27.12 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.12 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.12 active(U56(tt)) -> mark(tt) 101.91/27.12 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.12 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.12 active(U63(tt)) -> mark(tt) 101.91/27.12 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.12 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.12 active(U73(tt)) -> mark(tt) 101.91/27.12 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.12 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.12 active(U83(tt)) -> mark(tt) 101.91/27.12 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.12 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.12 active(U93(tt)) -> mark(tt) 101.91/27.12 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.12 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.12 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.12 active(isLNat(nil)) -> mark(tt) 101.91/27.12 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.12 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.12 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.12 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.12 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNatKind(nil)) -> mark(tt) 101.91/27.12 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.12 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.12 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.12 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.12 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.12 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.12 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.12 active(isNatural(0')) -> mark(tt) 101.91/27.12 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.12 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.12 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isNaturalKind(0')) -> mark(tt) 101.91/27.12 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.12 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.12 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.12 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.12 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.12 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.12 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.12 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.12 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.12 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.12 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.12 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.12 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.12 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.12 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.12 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.12 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.12 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.12 active(U106(X)) -> U106(active(X)) 101.91/27.12 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.12 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.12 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.12 active(U112(X)) -> U112(active(X)) 101.91/27.12 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.12 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.12 active(U122(X)) -> U122(active(X)) 101.91/27.12 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.12 active(U131(X)) -> U131(active(X)) 101.91/27.12 active(snd(X)) -> snd(active(X)) 101.91/27.12 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.12 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.12 active(U141(X)) -> U141(active(X)) 101.91/27.12 active(U151(X)) -> U151(active(X)) 101.91/27.12 active(U161(X)) -> U161(active(X)) 101.91/27.12 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.12 active(U172(X)) -> U172(active(X)) 101.91/27.12 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.12 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.12 active(U183(X)) -> U183(active(X)) 101.91/27.12 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.12 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.12 active(U193(X)) -> U193(active(X)) 101.91/27.12 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.12 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.12 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.12 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.12 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.12 active(U206(X)) -> U206(active(X)) 101.91/27.12 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.12 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.12 active(U211(X)) -> U211(active(X)) 101.91/27.12 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.12 active(U221(X)) -> U221(active(X)) 101.91/27.12 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.12 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.12 active(U232(X)) -> U232(active(X)) 101.91/27.12 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.12 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.12 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.12 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.12 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.12 active(U246(X)) -> U246(active(X)) 101.91/27.12 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.12 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.12 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.12 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.12 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.12 active(U256(X)) -> U256(active(X)) 101.91/27.12 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.12 active(U262(X)) -> U262(active(X)) 101.91/27.12 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.12 active(U272(X)) -> U272(active(X)) 101.91/27.12 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.12 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.12 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.12 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.12 active(s(X)) -> s(active(X)) 101.91/27.12 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.12 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.12 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.12 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.12 active(head(X)) -> head(active(X)) 101.91/27.12 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.12 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.12 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.12 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.12 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.12 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.12 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.12 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.12 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.12 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.12 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.12 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.12 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.12 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.12 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.12 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.12 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.12 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.12 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.12 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.12 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.12 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.12 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.12 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.12 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.12 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.12 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.12 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.12 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.12 active(fst(X)) -> fst(active(X)) 101.91/27.12 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.12 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.12 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.12 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.12 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.12 active(U46(X)) -> U46(active(X)) 101.91/27.12 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.12 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.12 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.12 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.12 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.12 active(U56(X)) -> U56(active(X)) 101.91/27.12 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.12 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.12 active(U63(X)) -> U63(active(X)) 101.91/27.12 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.12 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.12 active(U73(X)) -> U73(active(X)) 101.91/27.12 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.12 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.12 active(U83(X)) -> U83(active(X)) 101.91/27.12 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.12 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.12 active(U93(X)) -> U93(active(X)) 101.91/27.12 active(tail(X)) -> tail(active(X)) 101.91/27.12 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.12 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.12 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.12 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.12 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.12 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.12 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.12 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.12 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.12 U106(mark(X)) -> mark(U106(X)) 101.91/27.12 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.12 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.12 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.12 U112(mark(X)) -> mark(U112(X)) 101.91/27.12 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.12 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.12 U122(mark(X)) -> mark(U122(X)) 101.91/27.12 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.12 U131(mark(X)) -> mark(U131(X)) 101.91/27.12 snd(mark(X)) -> mark(snd(X)) 101.91/27.12 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.12 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.12 U141(mark(X)) -> mark(U141(X)) 101.91/27.12 U151(mark(X)) -> mark(U151(X)) 101.91/27.12 U161(mark(X)) -> mark(U161(X)) 101.91/27.12 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.12 U172(mark(X)) -> mark(U172(X)) 101.91/27.12 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.12 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.12 U183(mark(X)) -> mark(U183(X)) 101.91/27.12 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.12 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.12 U193(mark(X)) -> mark(U193(X)) 101.91/27.12 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.12 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.12 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.12 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.12 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.12 U206(mark(X)) -> mark(U206(X)) 101.91/27.12 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.12 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.12 U211(mark(X)) -> mark(U211(X)) 101.91/27.12 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.12 U221(mark(X)) -> mark(U221(X)) 101.91/27.12 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.12 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.12 U232(mark(X)) -> mark(U232(X)) 101.91/27.12 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.12 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.12 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.12 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.12 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.12 U246(mark(X)) -> mark(U246(X)) 101.91/27.12 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.12 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.12 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.12 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.12 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.12 U256(mark(X)) -> mark(U256(X)) 101.91/27.12 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.12 U262(mark(X)) -> mark(U262(X)) 101.91/27.12 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.12 U272(mark(X)) -> mark(U272(X)) 101.91/27.12 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.12 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.12 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.12 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.12 s(mark(X)) -> mark(s(X)) 101.91/27.12 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.12 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.12 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.12 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.12 head(mark(X)) -> mark(head(X)) 101.91/27.12 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.12 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.12 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.12 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.12 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.12 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.12 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.12 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.12 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.12 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.12 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.12 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.12 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.12 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.12 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.12 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.12 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.12 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.12 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.12 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.12 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.12 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.12 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.12 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.12 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.12 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.12 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.12 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.12 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.12 fst(mark(X)) -> mark(fst(X)) 101.91/27.12 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.12 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.12 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.12 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.12 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.12 U46(mark(X)) -> mark(U46(X)) 101.91/27.12 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.12 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.12 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.12 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.12 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.12 U56(mark(X)) -> mark(U56(X)) 101.91/27.12 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.12 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.12 U63(mark(X)) -> mark(U63(X)) 101.91/27.12 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.12 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.12 U73(mark(X)) -> mark(U73(X)) 101.91/27.12 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.12 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.12 U83(mark(X)) -> mark(U83(X)) 101.91/27.12 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.12 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.12 U93(mark(X)) -> mark(U93(X)) 101.91/27.12 tail(mark(X)) -> mark(tail(X)) 101.91/27.12 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.12 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.12 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.12 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.12 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(tt) -> ok(tt) 101.91/27.12 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.12 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.12 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.12 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.12 proper(U106(X)) -> U106(proper(X)) 101.91/27.12 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.12 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.12 proper(U112(X)) -> U112(proper(X)) 101.91/27.12 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.12 proper(U122(X)) -> U122(proper(X)) 101.91/27.12 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U131(X)) -> U131(proper(X)) 101.91/27.12 proper(snd(X)) -> snd(proper(X)) 101.91/27.12 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.12 proper(U141(X)) -> U141(proper(X)) 101.91/27.12 proper(U151(X)) -> U151(proper(X)) 101.91/27.12 proper(U161(X)) -> U161(proper(X)) 101.91/27.12 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.12 proper(U172(X)) -> U172(proper(X)) 101.91/27.12 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.12 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.12 proper(U183(X)) -> U183(proper(X)) 101.91/27.12 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.12 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.12 proper(U193(X)) -> U193(proper(X)) 101.91/27.12 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.12 proper(U206(X)) -> U206(proper(X)) 101.91/27.12 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U211(X)) -> U211(proper(X)) 101.91/27.12 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U221(X)) -> U221(proper(X)) 101.91/27.12 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.12 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.12 proper(U232(X)) -> U232(proper(X)) 101.91/27.12 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.12 proper(U246(X)) -> U246(proper(X)) 101.91/27.12 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.12 proper(U256(X)) -> U256(proper(X)) 101.91/27.12 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.12 proper(U262(X)) -> U262(proper(X)) 101.91/27.12 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.12 proper(U272(X)) -> U272(proper(X)) 101.91/27.12 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.12 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.12 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.12 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.12 proper(s(X)) -> s(proper(X)) 101.91/27.12 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(head(X)) -> head(proper(X)) 101.91/27.12 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.12 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.12 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.12 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.12 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.12 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.12 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.12 proper(nil) -> ok(nil) 101.91/27.12 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.12 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.12 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.12 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.12 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.12 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.12 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(fst(X)) -> fst(proper(X)) 101.91/27.12 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.12 proper(U46(X)) -> U46(proper(X)) 101.91/27.12 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.12 proper(U56(X)) -> U56(proper(X)) 101.91/27.12 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.12 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.12 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.12 proper(U63(X)) -> U63(proper(X)) 101.91/27.12 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.12 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.12 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.12 proper(U73(X)) -> U73(proper(X)) 101.91/27.12 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.12 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.12 proper(U83(X)) -> U83(proper(X)) 101.91/27.12 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.12 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.12 proper(U93(X)) -> U93(proper(X)) 101.91/27.12 proper(tail(X)) -> tail(proper(X)) 101.91/27.12 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.12 proper(0') -> ok(0') 101.91/27.12 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.12 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.12 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.12 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.12 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.12 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.12 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.12 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.12 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.12 U106(ok(X)) -> ok(U106(X)) 101.91/27.12 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.12 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.12 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.12 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.12 U112(ok(X)) -> ok(U112(X)) 101.91/27.12 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.12 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.12 U122(ok(X)) -> ok(U122(X)) 101.91/27.12 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.12 U131(ok(X)) -> ok(U131(X)) 101.91/27.12 snd(ok(X)) -> ok(snd(X)) 101.91/27.12 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.12 U141(ok(X)) -> ok(U141(X)) 101.91/27.12 U151(ok(X)) -> ok(U151(X)) 101.91/27.12 U161(ok(X)) -> ok(U161(X)) 101.91/27.12 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.12 U172(ok(X)) -> ok(U172(X)) 101.91/27.12 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.12 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.12 U183(ok(X)) -> ok(U183(X)) 101.91/27.12 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.12 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.12 U193(ok(X)) -> ok(U193(X)) 101.91/27.12 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.12 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.12 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.12 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.12 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.12 U206(ok(X)) -> ok(U206(X)) 101.91/27.12 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.12 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.12 U211(ok(X)) -> ok(U211(X)) 101.91/27.12 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.12 U221(ok(X)) -> ok(U221(X)) 101.91/27.12 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.12 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.12 U232(ok(X)) -> ok(U232(X)) 101.91/27.12 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.12 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.12 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.12 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.12 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.12 U246(ok(X)) -> ok(U246(X)) 101.91/27.12 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.12 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.12 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.12 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.12 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.12 U256(ok(X)) -> ok(U256(X)) 101.91/27.12 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.12 U262(ok(X)) -> ok(U262(X)) 101.91/27.12 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.12 U272(ok(X)) -> ok(U272(X)) 101.91/27.12 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.12 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.12 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.12 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.12 s(ok(X)) -> ok(s(X)) 101.91/27.12 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.12 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.12 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.12 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.12 head(ok(X)) -> ok(head(X)) 101.91/27.12 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.12 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.12 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.12 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.12 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.12 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.12 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.12 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.12 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.12 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.12 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.12 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.12 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.12 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.12 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.12 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.12 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.12 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.12 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.12 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.12 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.12 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.12 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.12 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.12 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.12 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.12 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.12 fst(ok(X)) -> ok(fst(X)) 101.91/27.12 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.12 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.12 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.12 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.12 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.12 U46(ok(X)) -> ok(U46(X)) 101.91/27.12 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.12 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.12 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.12 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.12 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.12 U56(ok(X)) -> ok(U56(X)) 101.91/27.12 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.12 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.12 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.12 U63(ok(X)) -> ok(U63(X)) 101.91/27.12 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.12 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.12 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.12 U73(ok(X)) -> ok(U73(X)) 101.91/27.12 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.12 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.12 U83(ok(X)) -> ok(U83(X)) 101.91/27.12 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.12 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.12 U93(ok(X)) -> ok(U93(X)) 101.91/27.12 tail(ok(X)) -> ok(tail(X)) 101.91/27.12 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.12 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.12 top(mark(X)) -> top(proper(X)) 101.91/27.12 top(ok(X)) -> top(active(X)) 101.91/27.12 101.91/27.12 Types: 101.91/27.12 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 tt :: tt:mark:nil:0':ok 101.91/27.12 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 nil :: tt:mark:nil:0':ok 101.91/27.12 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 0' :: tt:mark:nil:0':ok 101.91/27.12 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.12 top :: tt:mark:nil:0':ok -> top 101.91/27.12 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.12 hole_top2_0 :: top 101.91/27.12 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.12 101.91/27.12 101.91/27.12 Lemmas: 101.91/27.12 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.12 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.12 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.12 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.12 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.12 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.12 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.12 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.12 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.12 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.12 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.12 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.12 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.12 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.12 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.12 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.12 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.12 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.12 101.91/27.12 101.91/27.12 Generator Equations: 101.91/27.12 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.12 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.12 101.91/27.12 101.91/27.12 The following defined symbols remain to be analysed: 101.91/27.12 U203, active, U204, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.12 101.91/27.12 They will be analysed ascendingly in the following order: 101.91/27.12 U203 < active 101.91/27.12 U204 < active 101.91/27.12 U205 < active 101.91/27.12 U206 < active 101.91/27.12 U22 < active 101.91/27.12 U23 < active 101.91/27.12 U24 < active 101.91/27.12 U232 < active 101.91/27.12 U242 < active 101.91/27.12 U243 < active 101.91/27.12 U244 < active 101.91/27.12 U245 < active 101.91/27.12 U246 < active 101.91/27.12 U252 < active 101.91/27.12 U253 < active 101.91/27.12 U254 < active 101.91/27.12 U255 < active 101.91/27.12 U256 < active 101.91/27.12 U262 < active 101.91/27.12 U272 < active 101.91/27.12 U282 < active 101.91/27.12 cons < active 101.91/27.12 natsFrom < active 101.91/27.12 s < active 101.91/27.12 U292 < active 101.91/27.12 U293 < active 101.91/27.12 U294 < active 101.91/27.12 head < active 101.91/27.12 afterNth < active 101.91/27.12 U302 < active 101.91/27.12 U303 < active 101.91/27.12 U304 < active 101.91/27.12 U32 < active 101.91/27.12 U312 < active 101.91/27.12 pair < active 101.91/27.12 U33 < active 101.91/27.12 U322 < active 101.91/27.12 U323 < active 101.91/27.12 U324 < active 101.91/27.12 U325 < active 101.91/27.12 U326 < active 101.91/27.12 U327 < active 101.91/27.12 U34 < active 101.91/27.12 U332 < active 101.91/27.12 U333 < active 101.91/27.12 U334 < active 101.91/27.12 U342 < active 101.91/27.12 U343 < active 101.91/27.12 U344 < active 101.91/27.12 fst < active 101.91/27.12 U42 < active 101.91/27.12 U43 < active 101.91/27.12 U44 < active 101.91/27.12 U45 < active 101.91/27.12 U46 < active 101.91/27.12 U52 < active 101.91/27.12 U53 < active 101.91/27.12 U54 < active 101.91/27.12 U55 < active 101.91/27.12 U56 < active 101.91/27.12 U62 < active 101.91/27.12 isPLNatKind < active 101.91/27.12 U63 < active 101.91/27.12 isPLNat < active 101.91/27.12 U72 < active 101.91/27.12 U73 < active 101.91/27.12 U82 < active 101.91/27.12 U83 < active 101.91/27.12 U92 < active 101.91/27.12 U93 < active 101.91/27.12 U11 < active 101.91/27.12 U21 < active 101.91/27.12 U31 < active 101.91/27.12 U41 < active 101.91/27.12 U51 < active 101.91/27.12 U61 < active 101.91/27.12 U71 < active 101.91/27.12 U81 < active 101.91/27.12 U91 < active 101.91/27.12 U101 < active 101.91/27.12 U111 < active 101.91/27.12 U121 < active 101.91/27.12 U131 < active 101.91/27.12 U141 < active 101.91/27.12 U151 < active 101.91/27.12 U161 < active 101.91/27.12 U171 < active 101.91/27.12 U181 < active 101.91/27.12 U191 < active 101.91/27.12 U201 < active 101.91/27.12 U211 < active 101.91/27.12 U221 < active 101.91/27.12 U231 < active 101.91/27.12 U241 < active 101.91/27.12 U251 < active 101.91/27.12 U261 < active 101.91/27.12 U271 < active 101.91/27.12 U281 < active 101.91/27.12 U291 < active 101.91/27.12 U301 < active 101.91/27.12 U311 < active 101.91/27.12 U321 < active 101.91/27.12 U331 < active 101.91/27.12 U341 < active 101.91/27.12 tail < active 101.91/27.12 take < active 101.91/27.12 sel < active 101.91/27.12 active < top 101.91/27.12 U203 < proper 101.91/27.12 U204 < proper 101.91/27.12 U205 < proper 101.91/27.12 U206 < proper 101.91/27.12 U22 < proper 101.91/27.12 U23 < proper 101.91/27.12 U24 < proper 101.91/27.12 U232 < proper 101.91/27.12 U242 < proper 101.91/27.12 U243 < proper 101.91/27.12 U244 < proper 101.91/27.12 U245 < proper 101.91/27.12 U246 < proper 101.91/27.12 U252 < proper 101.91/27.12 U253 < proper 101.91/27.12 U254 < proper 101.91/27.12 U255 < proper 101.91/27.12 U256 < proper 101.91/27.12 U262 < proper 101.91/27.12 U272 < proper 101.91/27.12 U282 < proper 101.91/27.12 cons < proper 101.91/27.12 natsFrom < proper 101.91/27.12 s < proper 101.91/27.12 U292 < proper 101.91/27.12 U293 < proper 101.91/27.12 U294 < proper 101.91/27.12 head < proper 101.91/27.12 afterNth < proper 101.91/27.12 U302 < proper 101.91/27.12 U303 < proper 101.91/27.12 U304 < proper 101.91/27.12 U32 < proper 101.91/27.12 U312 < proper 101.91/27.12 pair < proper 101.91/27.12 U33 < proper 101.91/27.12 U322 < proper 101.91/27.12 U323 < proper 101.91/27.12 U324 < proper 101.91/27.12 U325 < proper 101.91/27.12 U326 < proper 101.91/27.12 U327 < proper 101.91/27.12 U34 < proper 101.91/27.12 U332 < proper 101.91/27.12 U333 < proper 101.91/27.12 U334 < proper 101.91/27.12 U342 < proper 101.91/27.12 U343 < proper 101.91/27.12 U344 < proper 101.91/27.12 fst < proper 101.91/27.12 U42 < proper 101.91/27.12 U43 < proper 101.91/27.12 U44 < proper 101.91/27.12 U45 < proper 101.91/27.12 U46 < proper 101.91/27.12 U52 < proper 101.91/27.12 U53 < proper 101.91/27.12 U54 < proper 101.91/27.12 U55 < proper 101.91/27.12 U56 < proper 101.91/27.12 U62 < proper 101.91/27.12 isPLNatKind < proper 101.91/27.12 U63 < proper 101.91/27.12 isPLNat < proper 101.91/27.12 U72 < proper 101.91/27.12 U73 < proper 101.91/27.12 U82 < proper 101.91/27.12 U83 < proper 101.91/27.12 U92 < proper 101.91/27.12 U93 < proper 101.91/27.12 U11 < proper 101.91/27.12 U21 < proper 101.91/27.12 U31 < proper 101.91/27.12 U41 < proper 101.91/27.12 U51 < proper 101.91/27.12 U61 < proper 101.91/27.12 U71 < proper 101.91/27.12 U81 < proper 101.91/27.12 U91 < proper 101.91/27.12 U101 < proper 101.91/27.12 U111 < proper 101.91/27.12 U121 < proper 101.91/27.12 U131 < proper 101.91/27.12 U141 < proper 101.91/27.12 U151 < proper 101.91/27.12 U161 < proper 101.91/27.12 U171 < proper 101.91/27.12 U181 < proper 101.91/27.12 U191 < proper 101.91/27.12 U201 < proper 101.91/27.12 U211 < proper 101.91/27.12 U221 < proper 101.91/27.12 U231 < proper 101.91/27.12 U241 < proper 101.91/27.12 U251 < proper 101.91/27.12 U261 < proper 101.91/27.12 U271 < proper 101.91/27.12 U281 < proper 101.91/27.12 U291 < proper 101.91/27.12 U301 < proper 101.91/27.12 U311 < proper 101.91/27.12 U321 < proper 101.91/27.12 U331 < proper 101.91/27.12 U341 < proper 101.91/27.12 tail < proper 101.91/27.12 take < proper 101.91/27.12 sel < proper 101.91/27.12 proper < top 101.91/27.12 101.91/27.12 ---------------------------------------- 101.91/27.12 101.91/27.12 (65) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.12 Proved the following rewrite lemma: 101.91/27.12 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.12 101.91/27.12 Induction Base: 101.91/27.12 U203(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.12 101.91/27.12 Induction Step: 101.91/27.12 U203(gen_tt:mark:nil:0':ok3_0(+(1, +(n221255_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.12 mark(U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.12 mark(*4_0) 101.91/27.12 101.91/27.12 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.12 ---------------------------------------- 101.91/27.12 101.91/27.12 (66) 101.91/27.12 Obligation: 101.91/27.12 TRS: 101.91/27.12 Rules: 101.91/27.12 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.12 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.12 active(U106(tt)) -> mark(tt) 101.91/27.12 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.12 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.12 active(U112(tt)) -> mark(tt) 101.91/27.12 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.12 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.12 active(U122(tt)) -> mark(tt) 101.91/27.12 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.12 active(U131(tt)) -> mark(tt) 101.91/27.12 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.12 active(U141(tt)) -> mark(tt) 101.91/27.12 active(U151(tt)) -> mark(tt) 101.91/27.12 active(U161(tt)) -> mark(tt) 101.91/27.12 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.12 active(U172(tt)) -> mark(tt) 101.91/27.12 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.12 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.12 active(U183(tt)) -> mark(tt) 101.91/27.12 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.12 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.12 active(U193(tt)) -> mark(tt) 101.91/27.12 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.12 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.12 active(U206(tt)) -> mark(tt) 101.91/27.12 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.12 active(U211(tt)) -> mark(tt) 101.91/27.12 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.12 active(U221(tt)) -> mark(tt) 101.91/27.12 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.12 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.12 active(U232(tt)) -> mark(tt) 101.91/27.12 active(U24(tt, X)) -> mark(X) 101.91/27.12 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.12 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.12 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.12 active(U246(tt)) -> mark(tt) 101.91/27.12 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.12 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.12 active(U256(tt)) -> mark(tt) 101.91/27.12 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.12 active(U262(tt)) -> mark(tt) 101.91/27.12 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.12 active(U272(tt)) -> mark(tt) 101.91/27.12 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.12 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.12 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.12 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.12 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.12 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.12 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.12 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.12 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.12 active(U304(tt, Y)) -> mark(Y) 101.91/27.12 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.12 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.12 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.12 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.12 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.12 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.12 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.12 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.12 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.12 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.12 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.12 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.12 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.12 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.12 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.12 active(U334(tt, XS)) -> mark(XS) 101.91/27.12 active(U34(tt, N)) -> mark(N) 101.91/27.12 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.12 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.12 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.12 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.12 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.12 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.12 active(U46(tt)) -> mark(tt) 101.91/27.12 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.12 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.12 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.12 active(U56(tt)) -> mark(tt) 101.91/27.12 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.12 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.12 active(U63(tt)) -> mark(tt) 101.91/27.12 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.12 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.12 active(U73(tt)) -> mark(tt) 101.91/27.12 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.12 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.12 active(U83(tt)) -> mark(tt) 101.91/27.12 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.12 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.12 active(U93(tt)) -> mark(tt) 101.91/27.12 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.12 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.12 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.12 active(isLNat(nil)) -> mark(tt) 101.91/27.12 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.12 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.12 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.12 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.12 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isLNatKind(nil)) -> mark(tt) 101.91/27.12 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.12 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.12 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.12 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.12 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.12 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.12 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.12 active(isNatural(0')) -> mark(tt) 101.91/27.12 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.12 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.12 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isNaturalKind(0')) -> mark(tt) 101.91/27.12 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.12 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.12 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.12 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.12 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.12 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.12 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.12 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.12 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.12 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.12 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.12 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.12 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.12 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.12 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.12 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.12 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.12 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.12 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.12 active(U106(X)) -> U106(active(X)) 101.91/27.12 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.12 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.12 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.12 active(U112(X)) -> U112(active(X)) 101.91/27.12 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.12 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.12 active(U122(X)) -> U122(active(X)) 101.91/27.12 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.12 active(U131(X)) -> U131(active(X)) 101.91/27.12 active(snd(X)) -> snd(active(X)) 101.91/27.12 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.12 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.12 active(U141(X)) -> U141(active(X)) 101.91/27.12 active(U151(X)) -> U151(active(X)) 101.91/27.12 active(U161(X)) -> U161(active(X)) 101.91/27.12 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.12 active(U172(X)) -> U172(active(X)) 101.91/27.12 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.12 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.12 active(U183(X)) -> U183(active(X)) 101.91/27.12 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.12 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.12 active(U193(X)) -> U193(active(X)) 101.91/27.12 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.12 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.12 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.12 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.12 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.12 active(U206(X)) -> U206(active(X)) 101.91/27.12 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.12 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.12 active(U211(X)) -> U211(active(X)) 101.91/27.12 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.12 active(U221(X)) -> U221(active(X)) 101.91/27.12 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.12 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.12 active(U232(X)) -> U232(active(X)) 101.91/27.12 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.12 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.12 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.12 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.12 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.12 active(U246(X)) -> U246(active(X)) 101.91/27.12 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.12 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.12 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.12 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.12 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.12 active(U256(X)) -> U256(active(X)) 101.91/27.12 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.12 active(U262(X)) -> U262(active(X)) 101.91/27.12 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.12 active(U272(X)) -> U272(active(X)) 101.91/27.12 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.12 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.12 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.12 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.12 active(s(X)) -> s(active(X)) 101.91/27.12 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.12 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.12 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.12 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.12 active(head(X)) -> head(active(X)) 101.91/27.12 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.12 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.12 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.12 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.12 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.12 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.12 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.12 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.12 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.12 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.12 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.12 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.12 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.12 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.12 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.12 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.12 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.12 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.12 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.12 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.12 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.12 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.12 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.12 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.12 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.12 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.12 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.12 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.12 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.12 active(fst(X)) -> fst(active(X)) 101.91/27.12 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.12 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.12 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.12 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.12 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.12 active(U46(X)) -> U46(active(X)) 101.91/27.12 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.12 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.12 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.12 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.12 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.12 active(U56(X)) -> U56(active(X)) 101.91/27.12 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.12 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.12 active(U63(X)) -> U63(active(X)) 101.91/27.12 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.12 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.12 active(U73(X)) -> U73(active(X)) 101.91/27.12 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.12 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.12 active(U83(X)) -> U83(active(X)) 101.91/27.12 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.12 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.12 active(U93(X)) -> U93(active(X)) 101.91/27.12 active(tail(X)) -> tail(active(X)) 101.91/27.12 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.12 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.12 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.12 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.12 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.12 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.12 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.12 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.12 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.12 U106(mark(X)) -> mark(U106(X)) 101.91/27.12 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.12 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.12 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.12 U112(mark(X)) -> mark(U112(X)) 101.91/27.12 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.12 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.12 U122(mark(X)) -> mark(U122(X)) 101.91/27.12 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.12 U131(mark(X)) -> mark(U131(X)) 101.91/27.12 snd(mark(X)) -> mark(snd(X)) 101.91/27.12 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.12 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.12 U141(mark(X)) -> mark(U141(X)) 101.91/27.12 U151(mark(X)) -> mark(U151(X)) 101.91/27.12 U161(mark(X)) -> mark(U161(X)) 101.91/27.12 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.12 U172(mark(X)) -> mark(U172(X)) 101.91/27.12 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.12 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.12 U183(mark(X)) -> mark(U183(X)) 101.91/27.12 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.12 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.12 U193(mark(X)) -> mark(U193(X)) 101.91/27.12 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.12 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.12 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.12 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.12 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.12 U206(mark(X)) -> mark(U206(X)) 101.91/27.12 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.12 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.12 U211(mark(X)) -> mark(U211(X)) 101.91/27.12 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.12 U221(mark(X)) -> mark(U221(X)) 101.91/27.12 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.12 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.12 U232(mark(X)) -> mark(U232(X)) 101.91/27.12 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.12 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.12 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.12 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.12 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.12 U246(mark(X)) -> mark(U246(X)) 101.91/27.12 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.12 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.12 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.12 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.12 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.12 U256(mark(X)) -> mark(U256(X)) 101.91/27.12 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.12 U262(mark(X)) -> mark(U262(X)) 101.91/27.12 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.12 U272(mark(X)) -> mark(U272(X)) 101.91/27.12 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.12 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.12 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.12 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.12 s(mark(X)) -> mark(s(X)) 101.91/27.12 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.12 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.12 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.12 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.12 head(mark(X)) -> mark(head(X)) 101.91/27.12 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.12 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.12 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.12 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.12 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.12 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.12 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.12 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.12 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.12 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.12 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.12 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.12 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.12 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.12 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.12 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.12 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.12 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.12 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.12 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.12 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.12 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.12 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.12 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.12 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.12 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.12 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.12 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.12 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.12 fst(mark(X)) -> mark(fst(X)) 101.91/27.12 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.12 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.12 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.12 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.12 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.12 U46(mark(X)) -> mark(U46(X)) 101.91/27.12 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.12 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.12 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.12 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.12 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.12 U56(mark(X)) -> mark(U56(X)) 101.91/27.12 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.12 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.12 U63(mark(X)) -> mark(U63(X)) 101.91/27.12 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.12 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.12 U73(mark(X)) -> mark(U73(X)) 101.91/27.12 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.12 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.12 U83(mark(X)) -> mark(U83(X)) 101.91/27.12 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.12 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.12 U93(mark(X)) -> mark(U93(X)) 101.91/27.12 tail(mark(X)) -> mark(tail(X)) 101.91/27.12 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.12 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.12 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.12 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.12 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.12 proper(tt) -> ok(tt) 101.91/27.13 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.13 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.13 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.13 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.13 proper(U106(X)) -> U106(proper(X)) 101.91/27.13 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.13 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.13 proper(U112(X)) -> U112(proper(X)) 101.91/27.13 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.13 proper(U122(X)) -> U122(proper(X)) 101.91/27.13 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U131(X)) -> U131(proper(X)) 101.91/27.13 proper(snd(X)) -> snd(proper(X)) 101.91/27.13 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.13 proper(U141(X)) -> U141(proper(X)) 101.91/27.13 proper(U151(X)) -> U151(proper(X)) 101.91/27.13 proper(U161(X)) -> U161(proper(X)) 101.91/27.13 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.13 proper(U172(X)) -> U172(proper(X)) 101.91/27.13 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.13 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.13 proper(U183(X)) -> U183(proper(X)) 101.91/27.13 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.13 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.13 proper(U193(X)) -> U193(proper(X)) 101.91/27.13 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.13 proper(U206(X)) -> U206(proper(X)) 101.91/27.13 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U211(X)) -> U211(proper(X)) 101.91/27.13 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U221(X)) -> U221(proper(X)) 101.91/27.13 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.13 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.13 proper(U232(X)) -> U232(proper(X)) 101.91/27.13 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.13 proper(U246(X)) -> U246(proper(X)) 101.91/27.13 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.13 proper(U256(X)) -> U256(proper(X)) 101.91/27.13 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.13 proper(U262(X)) -> U262(proper(X)) 101.91/27.13 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.13 proper(U272(X)) -> U272(proper(X)) 101.91/27.13 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.13 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.13 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.13 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.13 proper(s(X)) -> s(proper(X)) 101.91/27.13 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(head(X)) -> head(proper(X)) 101.91/27.13 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.13 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.13 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.13 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.13 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.13 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.13 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.13 proper(nil) -> ok(nil) 101.91/27.13 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.13 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.13 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.13 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.13 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.13 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(fst(X)) -> fst(proper(X)) 101.91/27.13 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.13 proper(U46(X)) -> U46(proper(X)) 101.91/27.13 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.13 proper(U56(X)) -> U56(proper(X)) 101.91/27.13 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.13 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.13 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.13 proper(U63(X)) -> U63(proper(X)) 101.91/27.13 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.13 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.13 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.13 proper(U73(X)) -> U73(proper(X)) 101.91/27.13 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.13 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.13 proper(U83(X)) -> U83(proper(X)) 101.91/27.13 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.13 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.13 proper(U93(X)) -> U93(proper(X)) 101.91/27.13 proper(tail(X)) -> tail(proper(X)) 101.91/27.13 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.13 proper(0') -> ok(0') 101.91/27.13 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.13 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.13 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.13 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.13 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.13 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.13 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.13 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.13 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.13 U106(ok(X)) -> ok(U106(X)) 101.91/27.13 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.13 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.13 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.13 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.13 U112(ok(X)) -> ok(U112(X)) 101.91/27.13 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.13 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.13 U122(ok(X)) -> ok(U122(X)) 101.91/27.13 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.13 U131(ok(X)) -> ok(U131(X)) 101.91/27.13 snd(ok(X)) -> ok(snd(X)) 101.91/27.13 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.13 U141(ok(X)) -> ok(U141(X)) 101.91/27.13 U151(ok(X)) -> ok(U151(X)) 101.91/27.13 U161(ok(X)) -> ok(U161(X)) 101.91/27.13 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.13 U172(ok(X)) -> ok(U172(X)) 101.91/27.13 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.13 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.13 U183(ok(X)) -> ok(U183(X)) 101.91/27.13 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.13 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.13 U193(ok(X)) -> ok(U193(X)) 101.91/27.13 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.13 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.13 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.13 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.13 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.13 U206(ok(X)) -> ok(U206(X)) 101.91/27.13 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.13 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.13 U211(ok(X)) -> ok(U211(X)) 101.91/27.13 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.13 U221(ok(X)) -> ok(U221(X)) 101.91/27.13 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.13 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.13 U232(ok(X)) -> ok(U232(X)) 101.91/27.13 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.13 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.13 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.13 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.13 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.13 U246(ok(X)) -> ok(U246(X)) 101.91/27.13 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.13 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.13 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.13 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.13 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.13 U256(ok(X)) -> ok(U256(X)) 101.91/27.13 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.13 U262(ok(X)) -> ok(U262(X)) 101.91/27.13 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.13 U272(ok(X)) -> ok(U272(X)) 101.91/27.13 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.13 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.13 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.13 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.13 s(ok(X)) -> ok(s(X)) 101.91/27.13 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.13 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.13 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.13 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.13 head(ok(X)) -> ok(head(X)) 101.91/27.13 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.13 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.13 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.13 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.13 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.13 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.13 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.13 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.13 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.13 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.13 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.13 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.13 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.13 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.13 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.13 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.13 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.13 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.13 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.13 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.13 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.13 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.13 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.13 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.13 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.13 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.13 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.13 fst(ok(X)) -> ok(fst(X)) 101.91/27.13 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.13 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.13 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.13 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.13 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.13 U46(ok(X)) -> ok(U46(X)) 101.91/27.13 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.13 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.13 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.13 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.13 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.13 U56(ok(X)) -> ok(U56(X)) 101.91/27.13 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.13 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.13 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.13 U63(ok(X)) -> ok(U63(X)) 101.91/27.13 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.13 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.13 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.13 U73(ok(X)) -> ok(U73(X)) 101.91/27.13 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.13 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.13 U83(ok(X)) -> ok(U83(X)) 101.91/27.13 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.13 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.13 U93(ok(X)) -> ok(U93(X)) 101.91/27.13 tail(ok(X)) -> ok(tail(X)) 101.91/27.13 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.13 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.13 top(mark(X)) -> top(proper(X)) 101.91/27.13 top(ok(X)) -> top(active(X)) 101.91/27.13 101.91/27.13 Types: 101.91/27.13 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 tt :: tt:mark:nil:0':ok 101.91/27.13 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 nil :: tt:mark:nil:0':ok 101.91/27.13 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 0' :: tt:mark:nil:0':ok 101.91/27.13 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 top :: tt:mark:nil:0':ok -> top 101.91/27.13 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.13 hole_top2_0 :: top 101.91/27.13 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.13 101.91/27.13 101.91/27.13 Lemmas: 101.91/27.13 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.13 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.13 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.13 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.13 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.13 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.13 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.13 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.13 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.13 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.13 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.13 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.13 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.13 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.13 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.13 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.13 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.13 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.13 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.13 101.91/27.13 101.91/27.13 Generator Equations: 101.91/27.13 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.13 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.13 101.91/27.13 101.91/27.13 The following defined symbols remain to be analysed: 101.91/27.13 U204, active, U205, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.13 101.91/27.13 They will be analysed ascendingly in the following order: 101.91/27.13 U204 < active 101.91/27.13 U205 < active 101.91/27.13 U206 < active 101.91/27.13 U22 < active 101.91/27.13 U23 < active 101.91/27.13 U24 < active 101.91/27.13 U232 < active 101.91/27.13 U242 < active 101.91/27.13 U243 < active 101.91/27.13 U244 < active 101.91/27.13 U245 < active 101.91/27.13 U246 < active 101.91/27.13 U252 < active 101.91/27.13 U253 < active 101.91/27.13 U254 < active 101.91/27.13 U255 < active 101.91/27.13 U256 < active 101.91/27.13 U262 < active 101.91/27.13 U272 < active 101.91/27.13 U282 < active 101.91/27.13 cons < active 101.91/27.13 natsFrom < active 101.91/27.13 s < active 101.91/27.13 U292 < active 101.91/27.13 U293 < active 101.91/27.13 U294 < active 101.91/27.13 head < active 101.91/27.13 afterNth < active 101.91/27.13 U302 < active 101.91/27.13 U303 < active 101.91/27.13 U304 < active 101.91/27.13 U32 < active 101.91/27.13 U312 < active 101.91/27.13 pair < active 101.91/27.13 U33 < active 101.91/27.13 U322 < active 101.91/27.13 U323 < active 101.91/27.13 U324 < active 101.91/27.13 U325 < active 101.91/27.13 U326 < active 101.91/27.13 U327 < active 101.91/27.13 U34 < active 101.91/27.13 U332 < active 101.91/27.13 U333 < active 101.91/27.13 U334 < active 101.91/27.13 U342 < active 101.91/27.13 U343 < active 101.91/27.13 U344 < active 101.91/27.13 fst < active 101.91/27.13 U42 < active 101.91/27.13 U43 < active 101.91/27.13 U44 < active 101.91/27.13 U45 < active 101.91/27.13 U46 < active 101.91/27.13 U52 < active 101.91/27.13 U53 < active 101.91/27.13 U54 < active 101.91/27.13 U55 < active 101.91/27.13 U56 < active 101.91/27.13 U62 < active 101.91/27.13 isPLNatKind < active 101.91/27.13 U63 < active 101.91/27.13 isPLNat < active 101.91/27.13 U72 < active 101.91/27.13 U73 < active 101.91/27.13 U82 < active 101.91/27.13 U83 < active 101.91/27.13 U92 < active 101.91/27.13 U93 < active 101.91/27.13 U11 < active 101.91/27.13 U21 < active 101.91/27.13 U31 < active 101.91/27.13 U41 < active 101.91/27.13 U51 < active 101.91/27.13 U61 < active 101.91/27.13 U71 < active 101.91/27.13 U81 < active 101.91/27.13 U91 < active 101.91/27.13 U101 < active 101.91/27.13 U111 < active 101.91/27.13 U121 < active 101.91/27.13 U131 < active 101.91/27.13 U141 < active 101.91/27.13 U151 < active 101.91/27.13 U161 < active 101.91/27.13 U171 < active 101.91/27.13 U181 < active 101.91/27.13 U191 < active 101.91/27.13 U201 < active 101.91/27.13 U211 < active 101.91/27.13 U221 < active 101.91/27.13 U231 < active 101.91/27.13 U241 < active 101.91/27.13 U251 < active 101.91/27.13 U261 < active 101.91/27.13 U271 < active 101.91/27.13 U281 < active 101.91/27.13 U291 < active 101.91/27.13 U301 < active 101.91/27.13 U311 < active 101.91/27.13 U321 < active 101.91/27.13 U331 < active 101.91/27.13 U341 < active 101.91/27.13 tail < active 101.91/27.13 take < active 101.91/27.13 sel < active 101.91/27.13 active < top 101.91/27.13 U204 < proper 101.91/27.13 U205 < proper 101.91/27.13 U206 < proper 101.91/27.13 U22 < proper 101.91/27.13 U23 < proper 101.91/27.13 U24 < proper 101.91/27.13 U232 < proper 101.91/27.13 U242 < proper 101.91/27.13 U243 < proper 101.91/27.13 U244 < proper 101.91/27.13 U245 < proper 101.91/27.13 U246 < proper 101.91/27.13 U252 < proper 101.91/27.13 U253 < proper 101.91/27.13 U254 < proper 101.91/27.13 U255 < proper 101.91/27.13 U256 < proper 101.91/27.13 U262 < proper 101.91/27.13 U272 < proper 101.91/27.13 U282 < proper 101.91/27.13 cons < proper 101.91/27.13 natsFrom < proper 101.91/27.13 s < proper 101.91/27.13 U292 < proper 101.91/27.13 U293 < proper 101.91/27.13 U294 < proper 101.91/27.13 head < proper 101.91/27.13 afterNth < proper 101.91/27.13 U302 < proper 101.91/27.13 U303 < proper 101.91/27.13 U304 < proper 101.91/27.13 U32 < proper 101.91/27.13 U312 < proper 101.91/27.13 pair < proper 101.91/27.13 U33 < proper 101.91/27.13 U322 < proper 101.91/27.13 U323 < proper 101.91/27.13 U324 < proper 101.91/27.13 U325 < proper 101.91/27.13 U326 < proper 101.91/27.13 U327 < proper 101.91/27.13 U34 < proper 101.91/27.13 U332 < proper 101.91/27.13 U333 < proper 101.91/27.13 U334 < proper 101.91/27.13 U342 < proper 101.91/27.13 U343 < proper 101.91/27.13 U344 < proper 101.91/27.13 fst < proper 101.91/27.13 U42 < proper 101.91/27.13 U43 < proper 101.91/27.13 U44 < proper 101.91/27.13 U45 < proper 101.91/27.13 U46 < proper 101.91/27.13 U52 < proper 101.91/27.13 U53 < proper 101.91/27.13 U54 < proper 101.91/27.13 U55 < proper 101.91/27.13 U56 < proper 101.91/27.13 U62 < proper 101.91/27.13 isPLNatKind < proper 101.91/27.13 U63 < proper 101.91/27.13 isPLNat < proper 101.91/27.13 U72 < proper 101.91/27.13 U73 < proper 101.91/27.13 U82 < proper 101.91/27.13 U83 < proper 101.91/27.13 U92 < proper 101.91/27.13 U93 < proper 101.91/27.13 U11 < proper 101.91/27.13 U21 < proper 101.91/27.13 U31 < proper 101.91/27.13 U41 < proper 101.91/27.13 U51 < proper 101.91/27.13 U61 < proper 101.91/27.13 U71 < proper 101.91/27.13 U81 < proper 101.91/27.13 U91 < proper 101.91/27.13 U101 < proper 101.91/27.13 U111 < proper 101.91/27.13 U121 < proper 101.91/27.13 U131 < proper 101.91/27.13 U141 < proper 101.91/27.13 U151 < proper 101.91/27.13 U161 < proper 101.91/27.13 U171 < proper 101.91/27.13 U181 < proper 101.91/27.13 U191 < proper 101.91/27.13 U201 < proper 101.91/27.13 U211 < proper 101.91/27.13 U221 < proper 101.91/27.13 U231 < proper 101.91/27.13 U241 < proper 101.91/27.13 U251 < proper 101.91/27.13 U261 < proper 101.91/27.13 U271 < proper 101.91/27.13 U281 < proper 101.91/27.13 U291 < proper 101.91/27.13 U301 < proper 101.91/27.13 U311 < proper 101.91/27.13 U321 < proper 101.91/27.13 U331 < proper 101.91/27.13 U341 < proper 101.91/27.13 tail < proper 101.91/27.13 take < proper 101.91/27.13 sel < proper 101.91/27.13 proper < top 101.91/27.13 101.91/27.13 ---------------------------------------- 101.91/27.13 101.91/27.13 (67) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.13 Proved the following rewrite lemma: 101.91/27.13 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.13 101.91/27.13 Induction Base: 101.91/27.13 U204(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.13 101.91/27.13 Induction Step: 101.91/27.13 U204(gen_tt:mark:nil:0':ok3_0(+(1, +(n246874_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.13 mark(U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.13 mark(*4_0) 101.91/27.13 101.91/27.13 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.13 ---------------------------------------- 101.91/27.13 101.91/27.13 (68) 101.91/27.13 Obligation: 101.91/27.13 TRS: 101.91/27.13 Rules: 101.91/27.13 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.13 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.13 active(U106(tt)) -> mark(tt) 101.91/27.13 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.13 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.13 active(U112(tt)) -> mark(tt) 101.91/27.13 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.13 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.13 active(U122(tt)) -> mark(tt) 101.91/27.13 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.13 active(U131(tt)) -> mark(tt) 101.91/27.13 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.13 active(U141(tt)) -> mark(tt) 101.91/27.13 active(U151(tt)) -> mark(tt) 101.91/27.13 active(U161(tt)) -> mark(tt) 101.91/27.13 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.13 active(U172(tt)) -> mark(tt) 101.91/27.13 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.13 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.13 active(U183(tt)) -> mark(tt) 101.91/27.13 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.13 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.13 active(U193(tt)) -> mark(tt) 101.91/27.13 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.13 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.13 active(U206(tt)) -> mark(tt) 101.91/27.13 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.13 active(U211(tt)) -> mark(tt) 101.91/27.13 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.13 active(U221(tt)) -> mark(tt) 101.91/27.13 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.13 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.13 active(U232(tt)) -> mark(tt) 101.91/27.13 active(U24(tt, X)) -> mark(X) 101.91/27.13 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.13 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.13 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.13 active(U246(tt)) -> mark(tt) 101.91/27.13 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.13 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.13 active(U256(tt)) -> mark(tt) 101.91/27.13 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.13 active(U262(tt)) -> mark(tt) 101.91/27.13 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.13 active(U272(tt)) -> mark(tt) 101.91/27.13 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.13 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.13 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.13 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.13 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.13 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.13 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.13 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.13 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.13 active(U304(tt, Y)) -> mark(Y) 101.91/27.13 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.13 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.13 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.13 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.13 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.13 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.13 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.13 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.13 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.13 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.13 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.13 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.13 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.13 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.13 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.13 active(U334(tt, XS)) -> mark(XS) 101.91/27.13 active(U34(tt, N)) -> mark(N) 101.91/27.13 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.13 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.13 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.13 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.13 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.13 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.13 active(U46(tt)) -> mark(tt) 101.91/27.13 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.13 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.13 active(U56(tt)) -> mark(tt) 101.91/27.13 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.13 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.13 active(U63(tt)) -> mark(tt) 101.91/27.13 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.13 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.13 active(U73(tt)) -> mark(tt) 101.91/27.13 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.13 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.13 active(U83(tt)) -> mark(tt) 101.91/27.13 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.13 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.13 active(U93(tt)) -> mark(tt) 101.91/27.13 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.13 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.13 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.13 active(isLNat(nil)) -> mark(tt) 101.91/27.13 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.13 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.13 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.13 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.13 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNatKind(nil)) -> mark(tt) 101.91/27.13 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.13 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.13 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.13 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.13 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.13 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.13 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.13 active(isNatural(0')) -> mark(tt) 101.91/27.13 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.13 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.13 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isNaturalKind(0')) -> mark(tt) 101.91/27.13 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.13 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.13 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.13 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.13 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.13 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.13 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.13 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.13 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.13 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.13 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.13 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.13 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.13 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.13 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.13 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.13 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.13 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.13 active(U106(X)) -> U106(active(X)) 101.91/27.13 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.13 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.13 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.13 active(U112(X)) -> U112(active(X)) 101.91/27.13 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.13 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.13 active(U122(X)) -> U122(active(X)) 101.91/27.13 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.13 active(U131(X)) -> U131(active(X)) 101.91/27.13 active(snd(X)) -> snd(active(X)) 101.91/27.13 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.13 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.13 active(U141(X)) -> U141(active(X)) 101.91/27.13 active(U151(X)) -> U151(active(X)) 101.91/27.13 active(U161(X)) -> U161(active(X)) 101.91/27.13 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.13 active(U172(X)) -> U172(active(X)) 101.91/27.13 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.13 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.13 active(U183(X)) -> U183(active(X)) 101.91/27.13 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.13 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.13 active(U193(X)) -> U193(active(X)) 101.91/27.13 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.13 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.13 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.13 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.13 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.13 active(U206(X)) -> U206(active(X)) 101.91/27.13 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.13 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.13 active(U211(X)) -> U211(active(X)) 101.91/27.13 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.13 active(U221(X)) -> U221(active(X)) 101.91/27.13 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.13 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.13 active(U232(X)) -> U232(active(X)) 101.91/27.13 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.13 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.13 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.13 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.13 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.13 active(U246(X)) -> U246(active(X)) 101.91/27.13 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.13 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.13 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.13 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.13 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.13 active(U256(X)) -> U256(active(X)) 101.91/27.13 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.13 active(U262(X)) -> U262(active(X)) 101.91/27.13 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.13 active(U272(X)) -> U272(active(X)) 101.91/27.13 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.13 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.13 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.13 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.13 active(s(X)) -> s(active(X)) 101.91/27.13 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.13 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.13 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.13 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.13 active(head(X)) -> head(active(X)) 101.91/27.13 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.13 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.13 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.13 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.13 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.13 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.13 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.13 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.13 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.13 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.13 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.13 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.13 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.13 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.13 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.13 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.13 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.13 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.13 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.13 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.13 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.13 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.13 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.13 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.13 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.13 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.13 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.13 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.13 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.13 active(fst(X)) -> fst(active(X)) 101.91/27.13 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.13 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.13 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.13 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.13 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.13 active(U46(X)) -> U46(active(X)) 101.91/27.13 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.13 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.13 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.13 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.13 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.13 active(U56(X)) -> U56(active(X)) 101.91/27.13 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.13 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.13 active(U63(X)) -> U63(active(X)) 101.91/27.13 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.13 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.13 active(U73(X)) -> U73(active(X)) 101.91/27.13 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.13 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.13 active(U83(X)) -> U83(active(X)) 101.91/27.13 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.13 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.13 active(U93(X)) -> U93(active(X)) 101.91/27.13 active(tail(X)) -> tail(active(X)) 101.91/27.13 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.13 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.13 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.13 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.13 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.13 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.13 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.13 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.13 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.13 U106(mark(X)) -> mark(U106(X)) 101.91/27.13 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.13 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.13 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.13 U112(mark(X)) -> mark(U112(X)) 101.91/27.13 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.13 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.13 U122(mark(X)) -> mark(U122(X)) 101.91/27.13 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.13 U131(mark(X)) -> mark(U131(X)) 101.91/27.13 snd(mark(X)) -> mark(snd(X)) 101.91/27.13 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.13 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.13 U141(mark(X)) -> mark(U141(X)) 101.91/27.13 U151(mark(X)) -> mark(U151(X)) 101.91/27.13 U161(mark(X)) -> mark(U161(X)) 101.91/27.13 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.13 U172(mark(X)) -> mark(U172(X)) 101.91/27.13 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.13 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.13 U183(mark(X)) -> mark(U183(X)) 101.91/27.13 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.13 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.13 U193(mark(X)) -> mark(U193(X)) 101.91/27.13 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.13 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.13 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.13 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.13 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.13 U206(mark(X)) -> mark(U206(X)) 101.91/27.13 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.13 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.13 U211(mark(X)) -> mark(U211(X)) 101.91/27.13 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.13 U221(mark(X)) -> mark(U221(X)) 101.91/27.13 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.13 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.13 U232(mark(X)) -> mark(U232(X)) 101.91/27.13 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.13 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.13 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.13 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.13 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.13 U246(mark(X)) -> mark(U246(X)) 101.91/27.13 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.13 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.13 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.13 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.13 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.13 U256(mark(X)) -> mark(U256(X)) 101.91/27.13 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.13 U262(mark(X)) -> mark(U262(X)) 101.91/27.13 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.13 U272(mark(X)) -> mark(U272(X)) 101.91/27.13 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.13 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.13 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.13 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.13 s(mark(X)) -> mark(s(X)) 101.91/27.13 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.13 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.13 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.13 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.13 head(mark(X)) -> mark(head(X)) 101.91/27.13 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.13 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.13 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.13 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.13 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.13 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.13 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.13 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.13 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.13 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.13 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.13 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.13 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.13 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.13 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.13 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.13 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.13 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.13 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.13 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.13 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.13 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.13 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.13 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.13 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.13 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.13 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.13 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.13 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.13 fst(mark(X)) -> mark(fst(X)) 101.91/27.13 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.13 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.13 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.13 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.13 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.13 U46(mark(X)) -> mark(U46(X)) 101.91/27.13 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.13 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.13 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.13 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.13 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.13 U56(mark(X)) -> mark(U56(X)) 101.91/27.13 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.13 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.13 U63(mark(X)) -> mark(U63(X)) 101.91/27.13 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.13 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.13 U73(mark(X)) -> mark(U73(X)) 101.91/27.13 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.13 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.13 U83(mark(X)) -> mark(U83(X)) 101.91/27.13 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.13 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.13 U93(mark(X)) -> mark(U93(X)) 101.91/27.13 tail(mark(X)) -> mark(tail(X)) 101.91/27.13 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.13 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.13 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.13 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.13 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(tt) -> ok(tt) 101.91/27.13 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.13 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.13 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.13 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.13 proper(U106(X)) -> U106(proper(X)) 101.91/27.13 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.13 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.13 proper(U112(X)) -> U112(proper(X)) 101.91/27.13 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.13 proper(U122(X)) -> U122(proper(X)) 101.91/27.13 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U131(X)) -> U131(proper(X)) 101.91/27.13 proper(snd(X)) -> snd(proper(X)) 101.91/27.13 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.13 proper(U141(X)) -> U141(proper(X)) 101.91/27.13 proper(U151(X)) -> U151(proper(X)) 101.91/27.13 proper(U161(X)) -> U161(proper(X)) 101.91/27.13 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.13 proper(U172(X)) -> U172(proper(X)) 101.91/27.13 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.13 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.13 proper(U183(X)) -> U183(proper(X)) 101.91/27.13 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.13 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.13 proper(U193(X)) -> U193(proper(X)) 101.91/27.13 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.13 proper(U206(X)) -> U206(proper(X)) 101.91/27.13 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U211(X)) -> U211(proper(X)) 101.91/27.13 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U221(X)) -> U221(proper(X)) 101.91/27.13 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.13 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.13 proper(U232(X)) -> U232(proper(X)) 101.91/27.13 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.13 proper(U246(X)) -> U246(proper(X)) 101.91/27.13 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.13 proper(U256(X)) -> U256(proper(X)) 101.91/27.13 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.13 proper(U262(X)) -> U262(proper(X)) 101.91/27.13 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.13 proper(U272(X)) -> U272(proper(X)) 101.91/27.13 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.13 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.13 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.13 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.13 proper(s(X)) -> s(proper(X)) 101.91/27.13 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(head(X)) -> head(proper(X)) 101.91/27.13 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.13 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.13 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.13 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.13 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.13 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.13 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.13 proper(nil) -> ok(nil) 101.91/27.13 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.13 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.13 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.13 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.13 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.13 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.13 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(fst(X)) -> fst(proper(X)) 101.91/27.13 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.13 proper(U46(X)) -> U46(proper(X)) 101.91/27.13 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.13 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.13 proper(U56(X)) -> U56(proper(X)) 101.91/27.13 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.13 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.13 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.13 proper(U63(X)) -> U63(proper(X)) 101.91/27.13 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.13 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.13 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.13 proper(U73(X)) -> U73(proper(X)) 101.91/27.13 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.13 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.13 proper(U83(X)) -> U83(proper(X)) 101.91/27.13 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.13 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.13 proper(U93(X)) -> U93(proper(X)) 101.91/27.13 proper(tail(X)) -> tail(proper(X)) 101.91/27.13 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.13 proper(0') -> ok(0') 101.91/27.13 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.13 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.13 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.13 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.13 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.13 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.13 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.13 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.13 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.13 U106(ok(X)) -> ok(U106(X)) 101.91/27.13 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.13 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.13 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.13 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.13 U112(ok(X)) -> ok(U112(X)) 101.91/27.13 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.13 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.13 U122(ok(X)) -> ok(U122(X)) 101.91/27.13 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.13 U131(ok(X)) -> ok(U131(X)) 101.91/27.13 snd(ok(X)) -> ok(snd(X)) 101.91/27.13 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.13 U141(ok(X)) -> ok(U141(X)) 101.91/27.13 U151(ok(X)) -> ok(U151(X)) 101.91/27.13 U161(ok(X)) -> ok(U161(X)) 101.91/27.13 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.13 U172(ok(X)) -> ok(U172(X)) 101.91/27.13 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.13 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.13 U183(ok(X)) -> ok(U183(X)) 101.91/27.13 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.13 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.13 U193(ok(X)) -> ok(U193(X)) 101.91/27.13 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.13 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.13 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.13 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.13 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.13 U206(ok(X)) -> ok(U206(X)) 101.91/27.13 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.13 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.13 U211(ok(X)) -> ok(U211(X)) 101.91/27.13 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.13 U221(ok(X)) -> ok(U221(X)) 101.91/27.13 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.13 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.13 U232(ok(X)) -> ok(U232(X)) 101.91/27.13 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.13 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.13 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.13 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.13 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.13 U246(ok(X)) -> ok(U246(X)) 101.91/27.13 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.13 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.13 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.13 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.13 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.13 U256(ok(X)) -> ok(U256(X)) 101.91/27.13 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.13 U262(ok(X)) -> ok(U262(X)) 101.91/27.13 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.13 U272(ok(X)) -> ok(U272(X)) 101.91/27.13 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.13 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.13 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.13 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.13 s(ok(X)) -> ok(s(X)) 101.91/27.13 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.13 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.13 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.13 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.13 head(ok(X)) -> ok(head(X)) 101.91/27.13 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.13 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.13 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.13 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.13 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.13 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.13 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.13 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.13 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.13 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.13 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.13 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.13 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.13 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.13 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.13 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.13 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.13 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.13 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.13 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.13 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.13 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.13 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.13 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.13 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.13 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.13 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.13 fst(ok(X)) -> ok(fst(X)) 101.91/27.13 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.13 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.13 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.13 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.13 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.13 U46(ok(X)) -> ok(U46(X)) 101.91/27.13 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.13 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.13 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.13 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.13 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.13 U56(ok(X)) -> ok(U56(X)) 101.91/27.13 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.13 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.13 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.13 U63(ok(X)) -> ok(U63(X)) 101.91/27.13 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.13 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.13 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.13 U73(ok(X)) -> ok(U73(X)) 101.91/27.13 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.13 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.13 U83(ok(X)) -> ok(U83(X)) 101.91/27.13 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.13 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.13 U93(ok(X)) -> ok(U93(X)) 101.91/27.13 tail(ok(X)) -> ok(tail(X)) 101.91/27.13 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.13 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.13 top(mark(X)) -> top(proper(X)) 101.91/27.13 top(ok(X)) -> top(active(X)) 101.91/27.13 101.91/27.13 Types: 101.91/27.13 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 tt :: tt:mark:nil:0':ok 101.91/27.13 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 nil :: tt:mark:nil:0':ok 101.91/27.13 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 0' :: tt:mark:nil:0':ok 101.91/27.13 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.13 top :: tt:mark:nil:0':ok -> top 101.91/27.13 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.13 hole_top2_0 :: top 101.91/27.13 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.13 101.91/27.13 101.91/27.13 Lemmas: 101.91/27.13 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.13 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.13 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.13 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.13 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.13 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.13 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.13 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.13 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.13 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.13 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.13 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.13 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.13 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.13 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.13 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.13 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.13 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.13 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.13 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.13 101.91/27.13 101.91/27.13 Generator Equations: 101.91/27.13 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.13 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.13 101.91/27.13 101.91/27.13 The following defined symbols remain to be analysed: 101.91/27.13 U205, active, U206, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.13 101.91/27.13 They will be analysed ascendingly in the following order: 101.91/27.13 U205 < active 101.91/27.13 U206 < active 101.91/27.13 U22 < active 101.91/27.13 U23 < active 101.91/27.13 U24 < active 101.91/27.13 U232 < active 101.91/27.13 U242 < active 101.91/27.13 U243 < active 101.91/27.13 U244 < active 101.91/27.13 U245 < active 101.91/27.13 U246 < active 101.91/27.13 U252 < active 101.91/27.13 U253 < active 101.91/27.13 U254 < active 101.91/27.13 U255 < active 101.91/27.13 U256 < active 101.91/27.13 U262 < active 101.91/27.13 U272 < active 101.91/27.13 U282 < active 101.91/27.13 cons < active 101.91/27.13 natsFrom < active 101.91/27.13 s < active 101.91/27.13 U292 < active 101.91/27.13 U293 < active 101.91/27.13 U294 < active 101.91/27.13 head < active 101.91/27.13 afterNth < active 101.91/27.13 U302 < active 101.91/27.13 U303 < active 101.91/27.13 U304 < active 101.91/27.13 U32 < active 101.91/27.13 U312 < active 101.91/27.13 pair < active 101.91/27.13 U33 < active 101.91/27.13 U322 < active 101.91/27.13 U323 < active 101.91/27.13 U324 < active 101.91/27.13 U325 < active 101.91/27.13 U326 < active 101.91/27.13 U327 < active 101.91/27.13 U34 < active 101.91/27.13 U332 < active 101.91/27.13 U333 < active 101.91/27.13 U334 < active 101.91/27.13 U342 < active 101.91/27.13 U343 < active 101.91/27.13 U344 < active 101.91/27.13 fst < active 101.91/27.13 U42 < active 101.91/27.13 U43 < active 101.91/27.13 U44 < active 101.91/27.13 U45 < active 101.91/27.13 U46 < active 101.91/27.13 U52 < active 101.91/27.13 U53 < active 101.91/27.13 U54 < active 101.91/27.13 U55 < active 101.91/27.13 U56 < active 101.91/27.13 U62 < active 101.91/27.13 isPLNatKind < active 101.91/27.13 U63 < active 101.91/27.13 isPLNat < active 101.91/27.13 U72 < active 101.91/27.13 U73 < active 101.91/27.13 U82 < active 101.91/27.13 U83 < active 101.91/27.13 U92 < active 101.91/27.13 U93 < active 101.91/27.13 U11 < active 101.91/27.13 U21 < active 101.91/27.13 U31 < active 101.91/27.13 U41 < active 101.91/27.13 U51 < active 101.91/27.13 U61 < active 101.91/27.13 U71 < active 101.91/27.13 U81 < active 101.91/27.13 U91 < active 101.91/27.13 U101 < active 101.91/27.13 U111 < active 101.91/27.13 U121 < active 101.91/27.13 U131 < active 101.91/27.13 U141 < active 101.91/27.13 U151 < active 101.91/27.13 U161 < active 101.91/27.13 U171 < active 101.91/27.13 U181 < active 101.91/27.13 U191 < active 101.91/27.13 U201 < active 101.91/27.13 U211 < active 101.91/27.13 U221 < active 101.91/27.13 U231 < active 101.91/27.13 U241 < active 101.91/27.13 U251 < active 101.91/27.13 U261 < active 101.91/27.13 U271 < active 101.91/27.13 U281 < active 101.91/27.13 U291 < active 101.91/27.13 U301 < active 101.91/27.13 U311 < active 101.91/27.13 U321 < active 101.91/27.13 U331 < active 101.91/27.13 U341 < active 101.91/27.13 tail < active 101.91/27.13 take < active 101.91/27.13 sel < active 101.91/27.13 active < top 101.91/27.13 U205 < proper 101.91/27.13 U206 < proper 101.91/27.13 U22 < proper 101.91/27.13 U23 < proper 101.91/27.13 U24 < proper 101.91/27.13 U232 < proper 101.91/27.13 U242 < proper 101.91/27.13 U243 < proper 101.91/27.13 U244 < proper 101.91/27.13 U245 < proper 101.91/27.13 U246 < proper 101.91/27.13 U252 < proper 101.91/27.13 U253 < proper 101.91/27.13 U254 < proper 101.91/27.13 U255 < proper 101.91/27.13 U256 < proper 101.91/27.13 U262 < proper 101.91/27.13 U272 < proper 101.91/27.13 U282 < proper 101.91/27.13 cons < proper 101.91/27.13 natsFrom < proper 101.91/27.13 s < proper 101.91/27.13 U292 < proper 101.91/27.13 U293 < proper 101.91/27.13 U294 < proper 101.91/27.13 head < proper 101.91/27.13 afterNth < proper 101.91/27.13 U302 < proper 101.91/27.13 U303 < proper 101.91/27.13 U304 < proper 101.91/27.13 U32 < proper 101.91/27.13 U312 < proper 101.91/27.13 pair < proper 101.91/27.13 U33 < proper 101.91/27.13 U322 < proper 101.91/27.13 U323 < proper 101.91/27.13 U324 < proper 101.91/27.13 U325 < proper 101.91/27.13 U326 < proper 101.91/27.13 U327 < proper 101.91/27.13 U34 < proper 101.91/27.13 U332 < proper 101.91/27.13 U333 < proper 101.91/27.13 U334 < proper 101.91/27.13 U342 < proper 101.91/27.13 U343 < proper 101.91/27.13 U344 < proper 101.91/27.13 fst < proper 101.91/27.13 U42 < proper 101.91/27.13 U43 < proper 101.91/27.13 U44 < proper 101.91/27.13 U45 < proper 101.91/27.13 U46 < proper 101.91/27.13 U52 < proper 101.91/27.13 U53 < proper 101.91/27.13 U54 < proper 101.91/27.13 U55 < proper 101.91/27.13 U56 < proper 101.91/27.13 U62 < proper 101.91/27.13 isPLNatKind < proper 101.91/27.13 U63 < proper 101.91/27.13 isPLNat < proper 101.91/27.13 U72 < proper 101.91/27.13 U73 < proper 101.91/27.13 U82 < proper 101.91/27.13 U83 < proper 101.91/27.13 U92 < proper 101.91/27.13 U93 < proper 101.91/27.13 U11 < proper 101.91/27.13 U21 < proper 101.91/27.13 U31 < proper 101.91/27.13 U41 < proper 101.91/27.13 U51 < proper 101.91/27.13 U61 < proper 101.91/27.13 U71 < proper 101.91/27.13 U81 < proper 101.91/27.13 U91 < proper 101.91/27.13 U101 < proper 101.91/27.13 U111 < proper 101.91/27.13 U121 < proper 101.91/27.13 U131 < proper 101.91/27.13 U141 < proper 101.91/27.13 U151 < proper 101.91/27.13 U161 < proper 101.91/27.13 U171 < proper 101.91/27.13 U181 < proper 101.91/27.13 U191 < proper 101.91/27.13 U201 < proper 101.91/27.13 U211 < proper 101.91/27.13 U221 < proper 101.91/27.13 U231 < proper 101.91/27.13 U241 < proper 101.91/27.13 U251 < proper 101.91/27.13 U261 < proper 101.91/27.13 U271 < proper 101.91/27.13 U281 < proper 101.91/27.13 U291 < proper 101.91/27.13 U301 < proper 101.91/27.13 U311 < proper 101.91/27.13 U321 < proper 101.91/27.13 U331 < proper 101.91/27.13 U341 < proper 101.91/27.13 tail < proper 101.91/27.13 take < proper 101.91/27.13 sel < proper 101.91/27.13 proper < top 101.91/27.13 101.91/27.13 ---------------------------------------- 101.91/27.13 101.91/27.13 (69) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.13 Proved the following rewrite lemma: 101.91/27.13 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.13 101.91/27.13 Induction Base: 101.91/27.13 U205(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.91/27.13 101.91/27.13 Induction Step: 101.91/27.13 U205(gen_tt:mark:nil:0':ok3_0(+(1, +(n273102_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.91/27.13 mark(U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.91/27.13 mark(*4_0) 101.91/27.13 101.91/27.13 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.13 ---------------------------------------- 101.91/27.13 101.91/27.13 (70) 101.91/27.13 Obligation: 101.91/27.13 TRS: 101.91/27.13 Rules: 101.91/27.13 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.13 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.13 active(U106(tt)) -> mark(tt) 101.91/27.13 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.13 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.13 active(U112(tt)) -> mark(tt) 101.91/27.13 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.13 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.13 active(U122(tt)) -> mark(tt) 101.91/27.13 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.13 active(U131(tt)) -> mark(tt) 101.91/27.13 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.13 active(U141(tt)) -> mark(tt) 101.91/27.13 active(U151(tt)) -> mark(tt) 101.91/27.13 active(U161(tt)) -> mark(tt) 101.91/27.13 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.13 active(U172(tt)) -> mark(tt) 101.91/27.13 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.13 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.13 active(U183(tt)) -> mark(tt) 101.91/27.13 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.13 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.13 active(U193(tt)) -> mark(tt) 101.91/27.13 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.13 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.13 active(U206(tt)) -> mark(tt) 101.91/27.13 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.13 active(U211(tt)) -> mark(tt) 101.91/27.13 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.13 active(U221(tt)) -> mark(tt) 101.91/27.13 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.13 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.13 active(U232(tt)) -> mark(tt) 101.91/27.13 active(U24(tt, X)) -> mark(X) 101.91/27.13 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.13 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.13 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.13 active(U246(tt)) -> mark(tt) 101.91/27.13 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.13 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.13 active(U256(tt)) -> mark(tt) 101.91/27.13 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.13 active(U262(tt)) -> mark(tt) 101.91/27.13 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.13 active(U272(tt)) -> mark(tt) 101.91/27.13 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.13 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.13 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.13 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.13 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.13 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.13 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.13 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.13 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.13 active(U304(tt, Y)) -> mark(Y) 101.91/27.13 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.13 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.13 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.13 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.13 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.13 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.13 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.13 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.13 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.13 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.13 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.13 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.13 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.13 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.13 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.13 active(U334(tt, XS)) -> mark(XS) 101.91/27.13 active(U34(tt, N)) -> mark(N) 101.91/27.13 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.13 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.13 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.13 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.13 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.13 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.13 active(U46(tt)) -> mark(tt) 101.91/27.13 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.13 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.13 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.13 active(U56(tt)) -> mark(tt) 101.91/27.13 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.13 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.13 active(U63(tt)) -> mark(tt) 101.91/27.13 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.13 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.13 active(U73(tt)) -> mark(tt) 101.91/27.13 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.13 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.13 active(U83(tt)) -> mark(tt) 101.91/27.13 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.13 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.13 active(U93(tt)) -> mark(tt) 101.91/27.13 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.13 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.13 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.13 active(isLNat(nil)) -> mark(tt) 101.91/27.13 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.13 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.13 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.13 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.13 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isLNatKind(nil)) -> mark(tt) 101.91/27.13 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.13 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.13 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.13 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.13 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.13 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.13 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.13 active(isNatural(0')) -> mark(tt) 101.91/27.13 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.13 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.13 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isNaturalKind(0')) -> mark(tt) 101.91/27.13 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.13 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.13 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.13 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.13 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.13 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.13 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.13 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.13 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.13 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.13 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.13 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.13 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.13 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.13 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.13 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.13 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.13 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.13 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.13 active(U106(X)) -> U106(active(X)) 101.91/27.13 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.13 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.13 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.13 active(U112(X)) -> U112(active(X)) 101.91/27.13 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.13 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.13 active(U122(X)) -> U122(active(X)) 101.91/27.13 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.13 active(U131(X)) -> U131(active(X)) 101.91/27.13 active(snd(X)) -> snd(active(X)) 101.91/27.13 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.13 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.13 active(U141(X)) -> U141(active(X)) 101.91/27.13 active(U151(X)) -> U151(active(X)) 101.91/27.13 active(U161(X)) -> U161(active(X)) 101.91/27.13 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.13 active(U172(X)) -> U172(active(X)) 101.91/27.13 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.13 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.13 active(U183(X)) -> U183(active(X)) 101.91/27.13 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.13 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.13 active(U193(X)) -> U193(active(X)) 101.91/27.13 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.13 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.13 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.13 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.13 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.13 active(U206(X)) -> U206(active(X)) 101.91/27.13 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.13 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.13 active(U211(X)) -> U211(active(X)) 101.91/27.13 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.13 active(U221(X)) -> U221(active(X)) 101.91/27.13 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.13 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.13 active(U232(X)) -> U232(active(X)) 101.91/27.13 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.13 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.13 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.13 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.13 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.13 active(U246(X)) -> U246(active(X)) 101.91/27.13 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.13 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.13 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.13 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.13 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.13 active(U256(X)) -> U256(active(X)) 101.91/27.13 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.13 active(U262(X)) -> U262(active(X)) 101.91/27.13 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.13 active(U272(X)) -> U272(active(X)) 101.91/27.13 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.13 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.13 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.13 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.13 active(s(X)) -> s(active(X)) 101.91/27.13 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.13 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.13 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.13 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.13 active(head(X)) -> head(active(X)) 101.91/27.13 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.13 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.13 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.13 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.13 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.13 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.13 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.13 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.13 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.13 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.13 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.13 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.13 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.13 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.13 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.13 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.13 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.13 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.13 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.13 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.13 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.13 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.13 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.13 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.13 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.13 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.13 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.13 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.13 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.13 active(fst(X)) -> fst(active(X)) 101.91/27.13 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.13 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.13 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.13 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.13 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.13 active(U46(X)) -> U46(active(X)) 101.91/27.13 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.13 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.13 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.13 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.13 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.13 active(U56(X)) -> U56(active(X)) 101.91/27.13 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.13 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.13 active(U63(X)) -> U63(active(X)) 101.91/27.13 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.13 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.13 active(U73(X)) -> U73(active(X)) 101.91/27.14 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.14 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.14 active(U83(X)) -> U83(active(X)) 101.91/27.14 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.14 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.14 active(U93(X)) -> U93(active(X)) 101.91/27.14 active(tail(X)) -> tail(active(X)) 101.91/27.14 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.14 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.14 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.14 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.14 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.14 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.14 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.14 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.14 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.14 U106(mark(X)) -> mark(U106(X)) 101.91/27.14 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.14 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.14 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.14 U112(mark(X)) -> mark(U112(X)) 101.91/27.14 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.14 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.14 U122(mark(X)) -> mark(U122(X)) 101.91/27.14 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.14 U131(mark(X)) -> mark(U131(X)) 101.91/27.14 snd(mark(X)) -> mark(snd(X)) 101.91/27.14 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.14 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.14 U141(mark(X)) -> mark(U141(X)) 101.91/27.14 U151(mark(X)) -> mark(U151(X)) 101.91/27.14 U161(mark(X)) -> mark(U161(X)) 101.91/27.14 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.14 U172(mark(X)) -> mark(U172(X)) 101.91/27.14 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.14 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.14 U183(mark(X)) -> mark(U183(X)) 101.91/27.14 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.14 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.14 U193(mark(X)) -> mark(U193(X)) 101.91/27.14 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.14 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.14 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.14 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.14 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.14 U206(mark(X)) -> mark(U206(X)) 101.91/27.14 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.14 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.14 U211(mark(X)) -> mark(U211(X)) 101.91/27.14 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.14 U221(mark(X)) -> mark(U221(X)) 101.91/27.14 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.14 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.14 U232(mark(X)) -> mark(U232(X)) 101.91/27.14 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.14 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.14 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.14 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.14 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.14 U246(mark(X)) -> mark(U246(X)) 101.91/27.14 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.14 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.14 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.14 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.14 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.14 U256(mark(X)) -> mark(U256(X)) 101.91/27.14 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.14 U262(mark(X)) -> mark(U262(X)) 101.91/27.14 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.14 U272(mark(X)) -> mark(U272(X)) 101.91/27.14 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.14 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.14 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.14 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.14 s(mark(X)) -> mark(s(X)) 101.91/27.14 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.14 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.14 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.14 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.14 head(mark(X)) -> mark(head(X)) 101.91/27.14 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.14 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.14 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.14 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.14 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.14 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.14 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.14 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.14 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.14 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.14 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.14 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.14 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.14 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.14 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.14 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.14 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.14 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.14 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.14 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.14 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.14 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.14 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.14 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.14 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.14 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.14 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.14 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.14 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.14 fst(mark(X)) -> mark(fst(X)) 101.91/27.14 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.14 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.14 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.14 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.14 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.14 U46(mark(X)) -> mark(U46(X)) 101.91/27.14 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.14 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.14 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.14 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.14 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.14 U56(mark(X)) -> mark(U56(X)) 101.91/27.14 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.14 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.14 U63(mark(X)) -> mark(U63(X)) 101.91/27.14 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.14 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.14 U73(mark(X)) -> mark(U73(X)) 101.91/27.14 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.14 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.14 U83(mark(X)) -> mark(U83(X)) 101.91/27.14 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.14 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.14 U93(mark(X)) -> mark(U93(X)) 101.91/27.14 tail(mark(X)) -> mark(tail(X)) 101.91/27.14 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.14 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.14 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.14 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.14 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(tt) -> ok(tt) 101.91/27.14 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.14 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.14 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.14 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.14 proper(U106(X)) -> U106(proper(X)) 101.91/27.14 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.14 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.14 proper(U112(X)) -> U112(proper(X)) 101.91/27.14 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.14 proper(U122(X)) -> U122(proper(X)) 101.91/27.14 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U131(X)) -> U131(proper(X)) 101.91/27.14 proper(snd(X)) -> snd(proper(X)) 101.91/27.14 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.14 proper(U141(X)) -> U141(proper(X)) 101.91/27.14 proper(U151(X)) -> U151(proper(X)) 101.91/27.14 proper(U161(X)) -> U161(proper(X)) 101.91/27.14 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.14 proper(U172(X)) -> U172(proper(X)) 101.91/27.14 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.14 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.14 proper(U183(X)) -> U183(proper(X)) 101.91/27.14 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.14 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.14 proper(U193(X)) -> U193(proper(X)) 101.91/27.14 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.14 proper(U206(X)) -> U206(proper(X)) 101.91/27.14 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U211(X)) -> U211(proper(X)) 101.91/27.14 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U221(X)) -> U221(proper(X)) 101.91/27.14 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.14 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.14 proper(U232(X)) -> U232(proper(X)) 101.91/27.14 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.14 proper(U246(X)) -> U246(proper(X)) 101.91/27.14 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.14 proper(U256(X)) -> U256(proper(X)) 101.91/27.14 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.14 proper(U262(X)) -> U262(proper(X)) 101.91/27.14 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.14 proper(U272(X)) -> U272(proper(X)) 101.91/27.14 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.14 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.14 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.14 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.14 proper(s(X)) -> s(proper(X)) 101.91/27.14 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(head(X)) -> head(proper(X)) 101.91/27.14 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.14 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.14 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.14 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.14 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.14 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.14 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.14 proper(nil) -> ok(nil) 101.91/27.14 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.14 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.14 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.14 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.14 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.14 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(fst(X)) -> fst(proper(X)) 101.91/27.14 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.14 proper(U46(X)) -> U46(proper(X)) 101.91/27.14 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.14 proper(U56(X)) -> U56(proper(X)) 101.91/27.14 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.14 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.14 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.14 proper(U63(X)) -> U63(proper(X)) 101.91/27.14 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.14 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.14 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.14 proper(U73(X)) -> U73(proper(X)) 101.91/27.14 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.14 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.14 proper(U83(X)) -> U83(proper(X)) 101.91/27.14 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.14 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.14 proper(U93(X)) -> U93(proper(X)) 101.91/27.14 proper(tail(X)) -> tail(proper(X)) 101.91/27.14 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.14 proper(0') -> ok(0') 101.91/27.14 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.14 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.14 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.14 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.14 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.14 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.14 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.14 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.14 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.14 U106(ok(X)) -> ok(U106(X)) 101.91/27.14 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.14 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.14 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.14 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.14 U112(ok(X)) -> ok(U112(X)) 101.91/27.14 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.14 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.14 U122(ok(X)) -> ok(U122(X)) 101.91/27.14 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.14 U131(ok(X)) -> ok(U131(X)) 101.91/27.14 snd(ok(X)) -> ok(snd(X)) 101.91/27.14 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.14 U141(ok(X)) -> ok(U141(X)) 101.91/27.14 U151(ok(X)) -> ok(U151(X)) 101.91/27.14 U161(ok(X)) -> ok(U161(X)) 101.91/27.14 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.14 U172(ok(X)) -> ok(U172(X)) 101.91/27.14 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.14 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.14 U183(ok(X)) -> ok(U183(X)) 101.91/27.14 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.14 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.14 U193(ok(X)) -> ok(U193(X)) 101.91/27.14 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.14 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.14 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.14 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.14 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.14 U206(ok(X)) -> ok(U206(X)) 101.91/27.14 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.14 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.14 U211(ok(X)) -> ok(U211(X)) 101.91/27.14 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.14 U221(ok(X)) -> ok(U221(X)) 101.91/27.14 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.14 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.14 U232(ok(X)) -> ok(U232(X)) 101.91/27.14 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.14 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.14 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.14 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.14 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.14 U246(ok(X)) -> ok(U246(X)) 101.91/27.14 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.14 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.14 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.14 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.14 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.14 U256(ok(X)) -> ok(U256(X)) 101.91/27.14 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.14 U262(ok(X)) -> ok(U262(X)) 101.91/27.14 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.14 U272(ok(X)) -> ok(U272(X)) 101.91/27.14 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.14 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.14 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.14 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.14 s(ok(X)) -> ok(s(X)) 101.91/27.14 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.14 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.14 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.14 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.14 head(ok(X)) -> ok(head(X)) 101.91/27.14 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.14 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.14 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.14 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.14 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.14 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.14 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.14 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.14 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.14 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.14 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.14 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.14 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.14 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.14 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.14 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.14 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.14 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.14 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.14 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.14 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.14 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.14 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.14 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.14 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.14 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.14 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.14 fst(ok(X)) -> ok(fst(X)) 101.91/27.14 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.14 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.14 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.14 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.14 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.14 U46(ok(X)) -> ok(U46(X)) 101.91/27.14 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.14 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.14 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.14 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.14 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.14 U56(ok(X)) -> ok(U56(X)) 101.91/27.14 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.14 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.14 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.14 U63(ok(X)) -> ok(U63(X)) 101.91/27.14 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.14 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.14 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.14 U73(ok(X)) -> ok(U73(X)) 101.91/27.14 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.14 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.14 U83(ok(X)) -> ok(U83(X)) 101.91/27.14 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.14 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.14 U93(ok(X)) -> ok(U93(X)) 101.91/27.14 tail(ok(X)) -> ok(tail(X)) 101.91/27.14 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.14 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.14 top(mark(X)) -> top(proper(X)) 101.91/27.14 top(ok(X)) -> top(active(X)) 101.91/27.14 101.91/27.14 Types: 101.91/27.14 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 tt :: tt:mark:nil:0':ok 101.91/27.14 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 nil :: tt:mark:nil:0':ok 101.91/27.14 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 0' :: tt:mark:nil:0':ok 101.91/27.14 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 top :: tt:mark:nil:0':ok -> top 101.91/27.14 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.14 hole_top2_0 :: top 101.91/27.14 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.14 101.91/27.14 101.91/27.14 Lemmas: 101.91/27.14 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.14 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.14 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.14 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.14 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.14 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.14 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.14 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.14 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.14 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.14 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.14 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.14 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.14 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.14 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.14 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.14 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.14 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.14 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.14 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.14 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.14 101.91/27.14 101.91/27.14 Generator Equations: 101.91/27.14 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.14 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.14 101.91/27.14 101.91/27.14 The following defined symbols remain to be analysed: 101.91/27.14 U206, active, U22, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.14 101.91/27.14 They will be analysed ascendingly in the following order: 101.91/27.14 U206 < active 101.91/27.14 U22 < active 101.91/27.14 U23 < active 101.91/27.14 U24 < active 101.91/27.14 U232 < active 101.91/27.14 U242 < active 101.91/27.14 U243 < active 101.91/27.14 U244 < active 101.91/27.14 U245 < active 101.91/27.14 U246 < active 101.91/27.14 U252 < active 101.91/27.14 U253 < active 101.91/27.14 U254 < active 101.91/27.14 U255 < active 101.91/27.14 U256 < active 101.91/27.14 U262 < active 101.91/27.14 U272 < active 101.91/27.14 U282 < active 101.91/27.14 cons < active 101.91/27.14 natsFrom < active 101.91/27.14 s < active 101.91/27.14 U292 < active 101.91/27.14 U293 < active 101.91/27.14 U294 < active 101.91/27.14 head < active 101.91/27.14 afterNth < active 101.91/27.14 U302 < active 101.91/27.14 U303 < active 101.91/27.14 U304 < active 101.91/27.14 U32 < active 101.91/27.14 U312 < active 101.91/27.14 pair < active 101.91/27.14 U33 < active 101.91/27.14 U322 < active 101.91/27.14 U323 < active 101.91/27.14 U324 < active 101.91/27.14 U325 < active 101.91/27.14 U326 < active 101.91/27.14 U327 < active 101.91/27.14 U34 < active 101.91/27.14 U332 < active 101.91/27.14 U333 < active 101.91/27.14 U334 < active 101.91/27.14 U342 < active 101.91/27.14 U343 < active 101.91/27.14 U344 < active 101.91/27.14 fst < active 101.91/27.14 U42 < active 101.91/27.14 U43 < active 101.91/27.14 U44 < active 101.91/27.14 U45 < active 101.91/27.14 U46 < active 101.91/27.14 U52 < active 101.91/27.14 U53 < active 101.91/27.14 U54 < active 101.91/27.14 U55 < active 101.91/27.14 U56 < active 101.91/27.14 U62 < active 101.91/27.14 isPLNatKind < active 101.91/27.14 U63 < active 101.91/27.14 isPLNat < active 101.91/27.14 U72 < active 101.91/27.14 U73 < active 101.91/27.14 U82 < active 101.91/27.14 U83 < active 101.91/27.14 U92 < active 101.91/27.14 U93 < active 101.91/27.14 U11 < active 101.91/27.14 U21 < active 101.91/27.14 U31 < active 101.91/27.14 U41 < active 101.91/27.14 U51 < active 101.91/27.14 U61 < active 101.91/27.14 U71 < active 101.91/27.14 U81 < active 101.91/27.14 U91 < active 101.91/27.14 U101 < active 101.91/27.14 U111 < active 101.91/27.14 U121 < active 101.91/27.14 U131 < active 101.91/27.14 U141 < active 101.91/27.14 U151 < active 101.91/27.14 U161 < active 101.91/27.14 U171 < active 101.91/27.14 U181 < active 101.91/27.14 U191 < active 101.91/27.14 U201 < active 101.91/27.14 U211 < active 101.91/27.14 U221 < active 101.91/27.14 U231 < active 101.91/27.14 U241 < active 101.91/27.14 U251 < active 101.91/27.14 U261 < active 101.91/27.14 U271 < active 101.91/27.14 U281 < active 101.91/27.14 U291 < active 101.91/27.14 U301 < active 101.91/27.14 U311 < active 101.91/27.14 U321 < active 101.91/27.14 U331 < active 101.91/27.14 U341 < active 101.91/27.14 tail < active 101.91/27.14 take < active 101.91/27.14 sel < active 101.91/27.14 active < top 101.91/27.14 U206 < proper 101.91/27.14 U22 < proper 101.91/27.14 U23 < proper 101.91/27.14 U24 < proper 101.91/27.14 U232 < proper 101.91/27.14 U242 < proper 101.91/27.14 U243 < proper 101.91/27.14 U244 < proper 101.91/27.14 U245 < proper 101.91/27.14 U246 < proper 101.91/27.14 U252 < proper 101.91/27.14 U253 < proper 101.91/27.14 U254 < proper 101.91/27.14 U255 < proper 101.91/27.14 U256 < proper 101.91/27.14 U262 < proper 101.91/27.14 U272 < proper 101.91/27.14 U282 < proper 101.91/27.14 cons < proper 101.91/27.14 natsFrom < proper 101.91/27.14 s < proper 101.91/27.14 U292 < proper 101.91/27.14 U293 < proper 101.91/27.14 U294 < proper 101.91/27.14 head < proper 101.91/27.14 afterNth < proper 101.91/27.14 U302 < proper 101.91/27.14 U303 < proper 101.91/27.14 U304 < proper 101.91/27.14 U32 < proper 101.91/27.14 U312 < proper 101.91/27.14 pair < proper 101.91/27.14 U33 < proper 101.91/27.14 U322 < proper 101.91/27.14 U323 < proper 101.91/27.14 U324 < proper 101.91/27.14 U325 < proper 101.91/27.14 U326 < proper 101.91/27.14 U327 < proper 101.91/27.14 U34 < proper 101.91/27.14 U332 < proper 101.91/27.14 U333 < proper 101.91/27.14 U334 < proper 101.91/27.14 U342 < proper 101.91/27.14 U343 < proper 101.91/27.14 U344 < proper 101.91/27.14 fst < proper 101.91/27.14 U42 < proper 101.91/27.14 U43 < proper 101.91/27.14 U44 < proper 101.91/27.14 U45 < proper 101.91/27.14 U46 < proper 101.91/27.14 U52 < proper 101.91/27.14 U53 < proper 101.91/27.14 U54 < proper 101.91/27.14 U55 < proper 101.91/27.14 U56 < proper 101.91/27.14 U62 < proper 101.91/27.14 isPLNatKind < proper 101.91/27.14 U63 < proper 101.91/27.14 isPLNat < proper 101.91/27.14 U72 < proper 101.91/27.14 U73 < proper 101.91/27.14 U82 < proper 101.91/27.14 U83 < proper 101.91/27.14 U92 < proper 101.91/27.14 U93 < proper 101.91/27.14 U11 < proper 101.91/27.14 U21 < proper 101.91/27.14 U31 < proper 101.91/27.14 U41 < proper 101.91/27.14 U51 < proper 101.91/27.14 U61 < proper 101.91/27.14 U71 < proper 101.91/27.14 U81 < proper 101.91/27.14 U91 < proper 101.91/27.14 U101 < proper 101.91/27.14 U111 < proper 101.91/27.14 U121 < proper 101.91/27.14 U131 < proper 101.91/27.14 U141 < proper 101.91/27.14 U151 < proper 101.91/27.14 U161 < proper 101.91/27.14 U171 < proper 101.91/27.14 U181 < proper 101.91/27.14 U191 < proper 101.91/27.14 U201 < proper 101.91/27.14 U211 < proper 101.91/27.14 U221 < proper 101.91/27.14 U231 < proper 101.91/27.14 U241 < proper 101.91/27.14 U251 < proper 101.91/27.14 U261 < proper 101.91/27.14 U271 < proper 101.91/27.14 U281 < proper 101.91/27.14 U291 < proper 101.91/27.14 U301 < proper 101.91/27.14 U311 < proper 101.91/27.14 U321 < proper 101.91/27.14 U331 < proper 101.91/27.14 U341 < proper 101.91/27.14 tail < proper 101.91/27.14 take < proper 101.91/27.14 sel < proper 101.91/27.14 proper < top 101.91/27.14 101.91/27.14 ---------------------------------------- 101.91/27.14 101.91/27.14 (71) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.14 Proved the following rewrite lemma: 101.91/27.14 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.14 101.91/27.14 Induction Base: 101.91/27.14 U206(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.91/27.14 101.91/27.14 Induction Step: 101.91/27.14 U206(gen_tt:mark:nil:0':ok3_0(+(1, +(n289205_0, 1)))) ->_R^Omega(1) 101.91/27.14 mark(U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0)))) ->_IH 101.91/27.14 mark(*4_0) 101.91/27.14 101.91/27.14 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.14 ---------------------------------------- 101.91/27.14 101.91/27.14 (72) 101.91/27.14 Obligation: 101.91/27.14 TRS: 101.91/27.14 Rules: 101.91/27.14 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.14 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.14 active(U106(tt)) -> mark(tt) 101.91/27.14 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.14 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.14 active(U112(tt)) -> mark(tt) 101.91/27.14 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.14 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.14 active(U122(tt)) -> mark(tt) 101.91/27.14 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.14 active(U131(tt)) -> mark(tt) 101.91/27.14 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.14 active(U141(tt)) -> mark(tt) 101.91/27.14 active(U151(tt)) -> mark(tt) 101.91/27.14 active(U161(tt)) -> mark(tt) 101.91/27.14 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.14 active(U172(tt)) -> mark(tt) 101.91/27.14 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.14 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.14 active(U183(tt)) -> mark(tt) 101.91/27.14 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.14 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.14 active(U193(tt)) -> mark(tt) 101.91/27.14 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.14 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.14 active(U206(tt)) -> mark(tt) 101.91/27.14 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.14 active(U211(tt)) -> mark(tt) 101.91/27.14 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.14 active(U221(tt)) -> mark(tt) 101.91/27.14 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.14 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.14 active(U232(tt)) -> mark(tt) 101.91/27.14 active(U24(tt, X)) -> mark(X) 101.91/27.14 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.14 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.14 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.14 active(U246(tt)) -> mark(tt) 101.91/27.14 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.14 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.14 active(U256(tt)) -> mark(tt) 101.91/27.14 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.14 active(U262(tt)) -> mark(tt) 101.91/27.14 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.14 active(U272(tt)) -> mark(tt) 101.91/27.14 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.14 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.14 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.14 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.14 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.14 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.14 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.14 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.14 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.14 active(U304(tt, Y)) -> mark(Y) 101.91/27.14 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.14 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.14 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.14 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.14 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.14 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.14 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.14 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.14 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.14 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.14 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.14 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.14 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.14 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.14 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.14 active(U334(tt, XS)) -> mark(XS) 101.91/27.14 active(U34(tt, N)) -> mark(N) 101.91/27.14 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.14 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.14 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.14 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.14 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.14 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.14 active(U46(tt)) -> mark(tt) 101.91/27.14 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.14 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.14 active(U56(tt)) -> mark(tt) 101.91/27.14 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.14 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.14 active(U63(tt)) -> mark(tt) 101.91/27.14 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.14 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.14 active(U73(tt)) -> mark(tt) 101.91/27.14 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.14 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.14 active(U83(tt)) -> mark(tt) 101.91/27.14 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.14 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.14 active(U93(tt)) -> mark(tt) 101.91/27.14 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.14 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.14 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.14 active(isLNat(nil)) -> mark(tt) 101.91/27.14 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.14 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.14 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.14 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.14 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNatKind(nil)) -> mark(tt) 101.91/27.14 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.14 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.14 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.14 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.14 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.14 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.14 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.14 active(isNatural(0')) -> mark(tt) 101.91/27.14 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.14 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.14 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isNaturalKind(0')) -> mark(tt) 101.91/27.14 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.14 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.14 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.14 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.14 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.14 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.14 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.14 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.14 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.14 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.14 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.14 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.14 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.14 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.14 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.14 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.14 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.14 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.14 active(U106(X)) -> U106(active(X)) 101.91/27.14 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.14 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.14 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.14 active(U112(X)) -> U112(active(X)) 101.91/27.14 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.14 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.14 active(U122(X)) -> U122(active(X)) 101.91/27.14 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.14 active(U131(X)) -> U131(active(X)) 101.91/27.14 active(snd(X)) -> snd(active(X)) 101.91/27.14 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.14 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.14 active(U141(X)) -> U141(active(X)) 101.91/27.14 active(U151(X)) -> U151(active(X)) 101.91/27.14 active(U161(X)) -> U161(active(X)) 101.91/27.14 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.14 active(U172(X)) -> U172(active(X)) 101.91/27.14 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.14 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.14 active(U183(X)) -> U183(active(X)) 101.91/27.14 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.14 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.14 active(U193(X)) -> U193(active(X)) 101.91/27.14 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.14 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.14 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.14 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.14 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.14 active(U206(X)) -> U206(active(X)) 101.91/27.14 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.14 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.14 active(U211(X)) -> U211(active(X)) 101.91/27.14 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.14 active(U221(X)) -> U221(active(X)) 101.91/27.14 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.14 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.14 active(U232(X)) -> U232(active(X)) 101.91/27.14 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.14 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.14 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.14 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.14 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.14 active(U246(X)) -> U246(active(X)) 101.91/27.14 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.14 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.14 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.14 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.14 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.14 active(U256(X)) -> U256(active(X)) 101.91/27.14 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.14 active(U262(X)) -> U262(active(X)) 101.91/27.14 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.14 active(U272(X)) -> U272(active(X)) 101.91/27.14 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.14 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.14 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.14 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.14 active(s(X)) -> s(active(X)) 101.91/27.14 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.14 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.14 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.14 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.14 active(head(X)) -> head(active(X)) 101.91/27.14 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.14 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.14 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.14 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.14 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.14 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.14 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.14 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.14 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.14 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.14 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.14 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.14 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.14 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.14 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.14 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.14 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.14 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.14 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.14 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.14 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.14 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.14 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.14 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.14 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.14 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.14 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.14 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.14 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.14 active(fst(X)) -> fst(active(X)) 101.91/27.14 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.14 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.14 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.14 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.14 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.14 active(U46(X)) -> U46(active(X)) 101.91/27.14 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.14 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.14 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.14 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.14 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.14 active(U56(X)) -> U56(active(X)) 101.91/27.14 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.14 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.14 active(U63(X)) -> U63(active(X)) 101.91/27.14 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.14 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.14 active(U73(X)) -> U73(active(X)) 101.91/27.14 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.14 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.14 active(U83(X)) -> U83(active(X)) 101.91/27.14 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.14 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.14 active(U93(X)) -> U93(active(X)) 101.91/27.14 active(tail(X)) -> tail(active(X)) 101.91/27.14 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.14 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.14 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.14 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.14 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.14 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.14 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.14 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.14 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.14 U106(mark(X)) -> mark(U106(X)) 101.91/27.14 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.14 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.14 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.14 U112(mark(X)) -> mark(U112(X)) 101.91/27.14 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.14 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.14 U122(mark(X)) -> mark(U122(X)) 101.91/27.14 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.14 U131(mark(X)) -> mark(U131(X)) 101.91/27.14 snd(mark(X)) -> mark(snd(X)) 101.91/27.14 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.14 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.14 U141(mark(X)) -> mark(U141(X)) 101.91/27.14 U151(mark(X)) -> mark(U151(X)) 101.91/27.14 U161(mark(X)) -> mark(U161(X)) 101.91/27.14 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.14 U172(mark(X)) -> mark(U172(X)) 101.91/27.14 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.14 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.14 U183(mark(X)) -> mark(U183(X)) 101.91/27.14 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.14 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.14 U193(mark(X)) -> mark(U193(X)) 101.91/27.14 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.14 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.14 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.14 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.14 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.14 U206(mark(X)) -> mark(U206(X)) 101.91/27.14 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.14 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.14 U211(mark(X)) -> mark(U211(X)) 101.91/27.14 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.14 U221(mark(X)) -> mark(U221(X)) 101.91/27.14 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.14 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.14 U232(mark(X)) -> mark(U232(X)) 101.91/27.14 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.14 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.14 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.14 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.14 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.14 U246(mark(X)) -> mark(U246(X)) 101.91/27.14 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.14 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.14 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.14 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.14 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.14 U256(mark(X)) -> mark(U256(X)) 101.91/27.14 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.14 U262(mark(X)) -> mark(U262(X)) 101.91/27.14 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.14 U272(mark(X)) -> mark(U272(X)) 101.91/27.14 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.14 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.14 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.14 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.14 s(mark(X)) -> mark(s(X)) 101.91/27.14 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.14 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.14 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.14 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.14 head(mark(X)) -> mark(head(X)) 101.91/27.14 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.14 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.14 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.14 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.14 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.14 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.14 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.14 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.14 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.14 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.14 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.14 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.14 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.14 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.14 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.14 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.14 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.14 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.14 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.14 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.14 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.14 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.14 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.14 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.14 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.14 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.14 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.14 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.14 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.14 fst(mark(X)) -> mark(fst(X)) 101.91/27.14 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.14 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.14 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.14 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.14 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.14 U46(mark(X)) -> mark(U46(X)) 101.91/27.14 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.14 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.14 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.14 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.14 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.14 U56(mark(X)) -> mark(U56(X)) 101.91/27.14 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.14 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.14 U63(mark(X)) -> mark(U63(X)) 101.91/27.14 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.14 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.14 U73(mark(X)) -> mark(U73(X)) 101.91/27.14 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.14 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.14 U83(mark(X)) -> mark(U83(X)) 101.91/27.14 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.14 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.14 U93(mark(X)) -> mark(U93(X)) 101.91/27.14 tail(mark(X)) -> mark(tail(X)) 101.91/27.14 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.14 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.14 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.14 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.14 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(tt) -> ok(tt) 101.91/27.14 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.14 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.14 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.14 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.14 proper(U106(X)) -> U106(proper(X)) 101.91/27.14 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.14 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.14 proper(U112(X)) -> U112(proper(X)) 101.91/27.14 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.14 proper(U122(X)) -> U122(proper(X)) 101.91/27.14 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U131(X)) -> U131(proper(X)) 101.91/27.14 proper(snd(X)) -> snd(proper(X)) 101.91/27.14 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.14 proper(U141(X)) -> U141(proper(X)) 101.91/27.14 proper(U151(X)) -> U151(proper(X)) 101.91/27.14 proper(U161(X)) -> U161(proper(X)) 101.91/27.14 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.14 proper(U172(X)) -> U172(proper(X)) 101.91/27.14 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.14 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.14 proper(U183(X)) -> U183(proper(X)) 101.91/27.14 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.14 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.14 proper(U193(X)) -> U193(proper(X)) 101.91/27.14 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.14 proper(U206(X)) -> U206(proper(X)) 101.91/27.14 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U211(X)) -> U211(proper(X)) 101.91/27.14 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U221(X)) -> U221(proper(X)) 101.91/27.14 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.14 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.14 proper(U232(X)) -> U232(proper(X)) 101.91/27.14 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.14 proper(U246(X)) -> U246(proper(X)) 101.91/27.14 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.14 proper(U256(X)) -> U256(proper(X)) 101.91/27.14 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.14 proper(U262(X)) -> U262(proper(X)) 101.91/27.14 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.14 proper(U272(X)) -> U272(proper(X)) 101.91/27.14 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.14 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.14 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.14 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.14 proper(s(X)) -> s(proper(X)) 101.91/27.14 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(head(X)) -> head(proper(X)) 101.91/27.14 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.14 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.14 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.14 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.14 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.14 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.14 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.14 proper(nil) -> ok(nil) 101.91/27.14 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.14 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.14 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.14 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.14 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.14 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.14 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(fst(X)) -> fst(proper(X)) 101.91/27.14 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.14 proper(U46(X)) -> U46(proper(X)) 101.91/27.14 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.14 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.14 proper(U56(X)) -> U56(proper(X)) 101.91/27.14 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.14 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.14 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.14 proper(U63(X)) -> U63(proper(X)) 101.91/27.14 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.14 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.14 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.14 proper(U73(X)) -> U73(proper(X)) 101.91/27.14 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.14 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.14 proper(U83(X)) -> U83(proper(X)) 101.91/27.14 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.14 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.14 proper(U93(X)) -> U93(proper(X)) 101.91/27.14 proper(tail(X)) -> tail(proper(X)) 101.91/27.14 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.14 proper(0') -> ok(0') 101.91/27.14 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.14 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.14 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.14 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.14 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.14 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.14 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.14 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.14 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.14 U106(ok(X)) -> ok(U106(X)) 101.91/27.14 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.14 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.14 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.14 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.14 U112(ok(X)) -> ok(U112(X)) 101.91/27.14 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.14 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.14 U122(ok(X)) -> ok(U122(X)) 101.91/27.14 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.14 U131(ok(X)) -> ok(U131(X)) 101.91/27.14 snd(ok(X)) -> ok(snd(X)) 101.91/27.14 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.14 U141(ok(X)) -> ok(U141(X)) 101.91/27.14 U151(ok(X)) -> ok(U151(X)) 101.91/27.14 U161(ok(X)) -> ok(U161(X)) 101.91/27.14 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.14 U172(ok(X)) -> ok(U172(X)) 101.91/27.14 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.14 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.14 U183(ok(X)) -> ok(U183(X)) 101.91/27.14 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.14 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.14 U193(ok(X)) -> ok(U193(X)) 101.91/27.14 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.14 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.14 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.14 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.14 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.14 U206(ok(X)) -> ok(U206(X)) 101.91/27.14 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.14 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.14 U211(ok(X)) -> ok(U211(X)) 101.91/27.14 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.14 U221(ok(X)) -> ok(U221(X)) 101.91/27.14 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.14 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.14 U232(ok(X)) -> ok(U232(X)) 101.91/27.14 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.14 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.14 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.14 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.14 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.14 U246(ok(X)) -> ok(U246(X)) 101.91/27.14 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.14 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.14 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.14 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.14 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.14 U256(ok(X)) -> ok(U256(X)) 101.91/27.14 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.14 U262(ok(X)) -> ok(U262(X)) 101.91/27.14 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.14 U272(ok(X)) -> ok(U272(X)) 101.91/27.14 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.14 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.14 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.14 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.14 s(ok(X)) -> ok(s(X)) 101.91/27.14 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.14 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.14 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.14 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.14 head(ok(X)) -> ok(head(X)) 101.91/27.14 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.14 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.14 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.14 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.14 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.14 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.14 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.14 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.14 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.14 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.14 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.14 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.14 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.14 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.14 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.14 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.14 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.14 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.14 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.14 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.14 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.14 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.14 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.14 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.14 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.14 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.14 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.14 fst(ok(X)) -> ok(fst(X)) 101.91/27.14 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.14 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.14 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.14 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.14 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.14 U46(ok(X)) -> ok(U46(X)) 101.91/27.14 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.14 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.14 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.14 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.14 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.14 U56(ok(X)) -> ok(U56(X)) 101.91/27.14 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.14 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.14 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.14 U63(ok(X)) -> ok(U63(X)) 101.91/27.14 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.14 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.14 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.14 U73(ok(X)) -> ok(U73(X)) 101.91/27.14 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.14 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.14 U83(ok(X)) -> ok(U83(X)) 101.91/27.14 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.14 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.14 U93(ok(X)) -> ok(U93(X)) 101.91/27.14 tail(ok(X)) -> ok(tail(X)) 101.91/27.14 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.14 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.14 top(mark(X)) -> top(proper(X)) 101.91/27.14 top(ok(X)) -> top(active(X)) 101.91/27.14 101.91/27.14 Types: 101.91/27.14 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 tt :: tt:mark:nil:0':ok 101.91/27.14 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 nil :: tt:mark:nil:0':ok 101.91/27.14 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 0' :: tt:mark:nil:0':ok 101.91/27.14 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.14 top :: tt:mark:nil:0':ok -> top 101.91/27.14 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.14 hole_top2_0 :: top 101.91/27.14 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.14 101.91/27.14 101.91/27.14 Lemmas: 101.91/27.14 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.14 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.14 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.14 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.14 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.14 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.14 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.14 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.14 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.14 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.14 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.14 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.14 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.14 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.14 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.14 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.14 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.14 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.14 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.14 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.14 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.14 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.14 101.91/27.14 101.91/27.14 Generator Equations: 101.91/27.14 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.14 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.14 101.91/27.14 101.91/27.14 The following defined symbols remain to be analysed: 101.91/27.14 U22, active, U23, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.14 101.91/27.14 They will be analysed ascendingly in the following order: 101.91/27.14 U22 < active 101.91/27.14 U23 < active 101.91/27.14 U24 < active 101.91/27.14 U232 < active 101.91/27.14 U242 < active 101.91/27.14 U243 < active 101.91/27.14 U244 < active 101.91/27.14 U245 < active 101.91/27.14 U246 < active 101.91/27.14 U252 < active 101.91/27.14 U253 < active 101.91/27.14 U254 < active 101.91/27.14 U255 < active 101.91/27.14 U256 < active 101.91/27.14 U262 < active 101.91/27.14 U272 < active 101.91/27.14 U282 < active 101.91/27.14 cons < active 101.91/27.14 natsFrom < active 101.91/27.14 s < active 101.91/27.14 U292 < active 101.91/27.14 U293 < active 101.91/27.14 U294 < active 101.91/27.14 head < active 101.91/27.14 afterNth < active 101.91/27.14 U302 < active 101.91/27.14 U303 < active 101.91/27.14 U304 < active 101.91/27.14 U32 < active 101.91/27.14 U312 < active 101.91/27.14 pair < active 101.91/27.14 U33 < active 101.91/27.14 U322 < active 101.91/27.14 U323 < active 101.91/27.14 U324 < active 101.91/27.14 U325 < active 101.91/27.14 U326 < active 101.91/27.14 U327 < active 101.91/27.14 U34 < active 101.91/27.14 U332 < active 101.91/27.14 U333 < active 101.91/27.14 U334 < active 101.91/27.14 U342 < active 101.91/27.14 U343 < active 101.91/27.14 U344 < active 101.91/27.14 fst < active 101.91/27.14 U42 < active 101.91/27.14 U43 < active 101.91/27.14 U44 < active 101.91/27.14 U45 < active 101.91/27.14 U46 < active 101.91/27.14 U52 < active 101.91/27.14 U53 < active 101.91/27.14 U54 < active 101.91/27.14 U55 < active 101.91/27.14 U56 < active 101.91/27.14 U62 < active 101.91/27.14 isPLNatKind < active 101.91/27.14 U63 < active 101.91/27.14 isPLNat < active 101.91/27.14 U72 < active 101.91/27.14 U73 < active 101.91/27.14 U82 < active 101.91/27.14 U83 < active 101.91/27.14 U92 < active 101.91/27.14 U93 < active 101.91/27.14 U11 < active 101.91/27.14 U21 < active 101.91/27.14 U31 < active 101.91/27.14 U41 < active 101.91/27.14 U51 < active 101.91/27.14 U61 < active 101.91/27.14 U71 < active 101.91/27.14 U81 < active 101.91/27.14 U91 < active 101.91/27.14 U101 < active 101.91/27.14 U111 < active 101.91/27.14 U121 < active 101.91/27.14 U131 < active 101.91/27.14 U141 < active 101.91/27.14 U151 < active 101.91/27.14 U161 < active 101.91/27.14 U171 < active 101.91/27.14 U181 < active 101.91/27.14 U191 < active 101.91/27.14 U201 < active 101.91/27.14 U211 < active 101.91/27.14 U221 < active 101.91/27.14 U231 < active 101.91/27.14 U241 < active 101.91/27.14 U251 < active 101.91/27.14 U261 < active 101.91/27.14 U271 < active 101.91/27.14 U281 < active 101.91/27.14 U291 < active 101.91/27.14 U301 < active 101.91/27.14 U311 < active 101.91/27.14 U321 < active 101.91/27.14 U331 < active 101.91/27.14 U341 < active 101.91/27.14 tail < active 101.91/27.14 take < active 101.91/27.14 sel < active 101.91/27.14 active < top 101.91/27.14 U22 < proper 101.91/27.14 U23 < proper 101.91/27.14 U24 < proper 101.91/27.14 U232 < proper 101.91/27.14 U242 < proper 101.91/27.14 U243 < proper 101.91/27.14 U244 < proper 101.91/27.14 U245 < proper 101.91/27.14 U246 < proper 101.91/27.14 U252 < proper 101.91/27.14 U253 < proper 101.91/27.14 U254 < proper 101.91/27.14 U255 < proper 101.91/27.14 U256 < proper 101.91/27.14 U262 < proper 101.91/27.14 U272 < proper 101.91/27.14 U282 < proper 101.91/27.14 cons < proper 101.91/27.14 natsFrom < proper 101.91/27.14 s < proper 101.91/27.14 U292 < proper 101.91/27.14 U293 < proper 101.91/27.14 U294 < proper 101.91/27.14 head < proper 101.91/27.14 afterNth < proper 101.91/27.14 U302 < proper 101.91/27.14 U303 < proper 101.91/27.14 U304 < proper 101.91/27.14 U32 < proper 101.91/27.14 U312 < proper 101.91/27.14 pair < proper 101.91/27.14 U33 < proper 101.91/27.14 U322 < proper 101.91/27.14 U323 < proper 101.91/27.14 U324 < proper 101.91/27.14 U325 < proper 101.91/27.14 U326 < proper 101.91/27.14 U327 < proper 101.91/27.14 U34 < proper 101.91/27.14 U332 < proper 101.91/27.14 U333 < proper 101.91/27.14 U334 < proper 101.91/27.14 U342 < proper 101.91/27.14 U343 < proper 101.91/27.14 U344 < proper 101.91/27.14 fst < proper 101.91/27.14 U42 < proper 101.91/27.14 U43 < proper 101.91/27.14 U44 < proper 101.91/27.14 U45 < proper 101.91/27.14 U46 < proper 101.91/27.14 U52 < proper 101.91/27.14 U53 < proper 101.91/27.14 U54 < proper 101.91/27.14 U55 < proper 101.91/27.14 U56 < proper 101.91/27.14 U62 < proper 101.91/27.14 isPLNatKind < proper 101.91/27.14 U63 < proper 101.91/27.14 isPLNat < proper 101.91/27.14 U72 < proper 101.91/27.14 U73 < proper 101.91/27.14 U82 < proper 101.91/27.14 U83 < proper 101.91/27.14 U92 < proper 101.91/27.14 U93 < proper 101.91/27.14 U11 < proper 101.91/27.14 U21 < proper 101.91/27.14 U31 < proper 101.91/27.14 U41 < proper 101.91/27.14 U51 < proper 101.91/27.14 U61 < proper 101.91/27.14 U71 < proper 101.91/27.14 U81 < proper 101.91/27.14 U91 < proper 101.91/27.14 U101 < proper 101.91/27.14 U111 < proper 101.91/27.14 U121 < proper 101.91/27.14 U131 < proper 101.91/27.14 U141 < proper 101.91/27.14 U151 < proper 101.91/27.14 U161 < proper 101.91/27.14 U171 < proper 101.91/27.14 U181 < proper 101.91/27.14 U191 < proper 101.91/27.14 U201 < proper 101.91/27.14 U211 < proper 101.91/27.14 U221 < proper 101.91/27.14 U231 < proper 101.91/27.14 U241 < proper 101.91/27.14 U251 < proper 101.91/27.14 U261 < proper 101.91/27.14 U271 < proper 101.91/27.14 U281 < proper 101.91/27.14 U291 < proper 101.91/27.14 U301 < proper 101.91/27.14 U311 < proper 101.91/27.14 U321 < proper 101.91/27.14 U331 < proper 101.91/27.14 U341 < proper 101.91/27.14 tail < proper 101.91/27.14 take < proper 101.91/27.14 sel < proper 101.91/27.14 proper < top 101.91/27.14 101.91/27.14 ---------------------------------------- 101.91/27.14 101.91/27.14 (73) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.14 Proved the following rewrite lemma: 101.91/27.14 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.14 101.91/27.14 Induction Base: 101.91/27.14 U22(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.14 101.91/27.14 Induction Step: 101.91/27.14 U22(gen_tt:mark:nil:0':ok3_0(+(1, +(n294724_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.14 mark(U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.14 mark(*4_0) 101.91/27.14 101.91/27.14 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.14 ---------------------------------------- 101.91/27.14 101.91/27.14 (74) 101.91/27.14 Obligation: 101.91/27.14 TRS: 101.91/27.14 Rules: 101.91/27.14 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.14 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.14 active(U106(tt)) -> mark(tt) 101.91/27.14 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.14 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.14 active(U112(tt)) -> mark(tt) 101.91/27.14 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.14 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.14 active(U122(tt)) -> mark(tt) 101.91/27.14 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.14 active(U131(tt)) -> mark(tt) 101.91/27.14 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.14 active(U141(tt)) -> mark(tt) 101.91/27.14 active(U151(tt)) -> mark(tt) 101.91/27.14 active(U161(tt)) -> mark(tt) 101.91/27.14 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.14 active(U172(tt)) -> mark(tt) 101.91/27.14 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.14 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.14 active(U183(tt)) -> mark(tt) 101.91/27.14 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.14 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.14 active(U193(tt)) -> mark(tt) 101.91/27.14 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.14 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.14 active(U206(tt)) -> mark(tt) 101.91/27.14 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.14 active(U211(tt)) -> mark(tt) 101.91/27.14 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.14 active(U221(tt)) -> mark(tt) 101.91/27.14 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.14 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.14 active(U232(tt)) -> mark(tt) 101.91/27.14 active(U24(tt, X)) -> mark(X) 101.91/27.14 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.14 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.14 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.14 active(U246(tt)) -> mark(tt) 101.91/27.14 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.14 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.14 active(U256(tt)) -> mark(tt) 101.91/27.14 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.14 active(U262(tt)) -> mark(tt) 101.91/27.14 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.14 active(U272(tt)) -> mark(tt) 101.91/27.14 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.14 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.14 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.14 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.14 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.14 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.14 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.14 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.14 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.14 active(U304(tt, Y)) -> mark(Y) 101.91/27.14 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.14 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.14 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.14 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.14 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.14 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.14 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.14 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.14 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.14 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.14 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.14 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.14 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.14 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.14 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.14 active(U334(tt, XS)) -> mark(XS) 101.91/27.14 active(U34(tt, N)) -> mark(N) 101.91/27.14 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.14 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.14 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.14 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.14 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.14 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.14 active(U46(tt)) -> mark(tt) 101.91/27.14 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.14 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.14 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.14 active(U56(tt)) -> mark(tt) 101.91/27.14 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.14 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.14 active(U63(tt)) -> mark(tt) 101.91/27.14 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.14 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.14 active(U73(tt)) -> mark(tt) 101.91/27.14 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.14 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.14 active(U83(tt)) -> mark(tt) 101.91/27.14 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.14 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.14 active(U93(tt)) -> mark(tt) 101.91/27.14 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.14 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.14 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.14 active(isLNat(nil)) -> mark(tt) 101.91/27.14 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.14 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.14 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.14 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.14 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isLNatKind(nil)) -> mark(tt) 101.91/27.14 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.14 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.14 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.14 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.14 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.14 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.14 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.14 active(isNatural(0')) -> mark(tt) 101.91/27.14 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.14 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.14 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isNaturalKind(0')) -> mark(tt) 101.91/27.14 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.14 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.14 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.14 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.14 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.14 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.14 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.14 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.14 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.14 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.14 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.14 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.14 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.14 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.14 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.14 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.14 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.14 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.14 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.14 active(U106(X)) -> U106(active(X)) 101.91/27.14 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.14 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.15 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.15 active(U112(X)) -> U112(active(X)) 101.91/27.15 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.15 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.15 active(U122(X)) -> U122(active(X)) 101.91/27.15 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.15 active(U131(X)) -> U131(active(X)) 101.91/27.15 active(snd(X)) -> snd(active(X)) 101.91/27.15 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.15 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.15 active(U141(X)) -> U141(active(X)) 101.91/27.15 active(U151(X)) -> U151(active(X)) 101.91/27.15 active(U161(X)) -> U161(active(X)) 101.91/27.15 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.15 active(U172(X)) -> U172(active(X)) 101.91/27.15 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.15 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.15 active(U183(X)) -> U183(active(X)) 101.91/27.15 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.15 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.15 active(U193(X)) -> U193(active(X)) 101.91/27.15 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.15 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.15 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.15 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.15 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.15 active(U206(X)) -> U206(active(X)) 101.91/27.15 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.15 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.15 active(U211(X)) -> U211(active(X)) 101.91/27.15 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.15 active(U221(X)) -> U221(active(X)) 101.91/27.15 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.15 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.15 active(U232(X)) -> U232(active(X)) 101.91/27.15 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.15 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.15 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.15 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.15 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.15 active(U246(X)) -> U246(active(X)) 101.91/27.15 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.15 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.15 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.15 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.15 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.15 active(U256(X)) -> U256(active(X)) 101.91/27.15 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.15 active(U262(X)) -> U262(active(X)) 101.91/27.15 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.15 active(U272(X)) -> U272(active(X)) 101.91/27.15 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.15 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.15 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.15 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.15 active(s(X)) -> s(active(X)) 101.91/27.15 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.15 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.15 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.15 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.15 active(head(X)) -> head(active(X)) 101.91/27.15 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.15 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.15 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.15 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.15 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.15 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.15 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.15 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.15 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.15 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.15 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.15 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.15 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.15 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.15 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.15 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.15 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.15 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.15 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.15 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.15 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.15 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.15 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.15 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.15 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.15 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.15 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.15 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.15 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.15 active(fst(X)) -> fst(active(X)) 101.91/27.15 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.15 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.15 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.15 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.15 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.15 active(U46(X)) -> U46(active(X)) 101.91/27.15 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.15 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.15 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.15 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.15 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.15 active(U56(X)) -> U56(active(X)) 101.91/27.15 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.15 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.15 active(U63(X)) -> U63(active(X)) 101.91/27.15 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.15 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.15 active(U73(X)) -> U73(active(X)) 101.91/27.15 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.15 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.15 active(U83(X)) -> U83(active(X)) 101.91/27.15 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.15 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.15 active(U93(X)) -> U93(active(X)) 101.91/27.15 active(tail(X)) -> tail(active(X)) 101.91/27.15 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.15 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.15 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.15 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.15 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.15 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.15 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.15 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.15 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.15 U106(mark(X)) -> mark(U106(X)) 101.91/27.15 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.15 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.15 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.15 U112(mark(X)) -> mark(U112(X)) 101.91/27.15 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.15 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.15 U122(mark(X)) -> mark(U122(X)) 101.91/27.15 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.15 U131(mark(X)) -> mark(U131(X)) 101.91/27.15 snd(mark(X)) -> mark(snd(X)) 101.91/27.15 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.15 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.15 U141(mark(X)) -> mark(U141(X)) 101.91/27.15 U151(mark(X)) -> mark(U151(X)) 101.91/27.15 U161(mark(X)) -> mark(U161(X)) 101.91/27.15 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.15 U172(mark(X)) -> mark(U172(X)) 101.91/27.15 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.15 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.15 U183(mark(X)) -> mark(U183(X)) 101.91/27.15 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.15 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.15 U193(mark(X)) -> mark(U193(X)) 101.91/27.15 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.15 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.15 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.15 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.15 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.15 U206(mark(X)) -> mark(U206(X)) 101.91/27.15 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.15 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.15 U211(mark(X)) -> mark(U211(X)) 101.91/27.15 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.15 U221(mark(X)) -> mark(U221(X)) 101.91/27.15 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.15 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.15 U232(mark(X)) -> mark(U232(X)) 101.91/27.15 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.15 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.15 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.15 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.15 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.15 U246(mark(X)) -> mark(U246(X)) 101.91/27.15 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.15 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.15 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.15 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.15 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.15 U256(mark(X)) -> mark(U256(X)) 101.91/27.15 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.15 U262(mark(X)) -> mark(U262(X)) 101.91/27.15 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.15 U272(mark(X)) -> mark(U272(X)) 101.91/27.15 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.15 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.15 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.15 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.15 s(mark(X)) -> mark(s(X)) 101.91/27.15 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.15 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.15 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.15 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.15 head(mark(X)) -> mark(head(X)) 101.91/27.15 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.15 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.15 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.15 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.15 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.15 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.15 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.15 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.15 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.15 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.15 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.15 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.15 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.15 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.15 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.15 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.15 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.15 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.15 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.15 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.15 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.15 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.15 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.15 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.15 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.15 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.15 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.15 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.15 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.15 fst(mark(X)) -> mark(fst(X)) 101.91/27.15 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.15 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.15 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.15 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.15 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.15 U46(mark(X)) -> mark(U46(X)) 101.91/27.15 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.15 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.15 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.15 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.15 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.15 U56(mark(X)) -> mark(U56(X)) 101.91/27.15 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.15 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.15 U63(mark(X)) -> mark(U63(X)) 101.91/27.15 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.15 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.15 U73(mark(X)) -> mark(U73(X)) 101.91/27.15 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.15 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.15 U83(mark(X)) -> mark(U83(X)) 101.91/27.15 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.15 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.15 U93(mark(X)) -> mark(U93(X)) 101.91/27.15 tail(mark(X)) -> mark(tail(X)) 101.91/27.15 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.15 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.15 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.15 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.15 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(tt) -> ok(tt) 101.91/27.15 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.15 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.15 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.15 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.15 proper(U106(X)) -> U106(proper(X)) 101.91/27.15 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.15 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.15 proper(U112(X)) -> U112(proper(X)) 101.91/27.15 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.15 proper(U122(X)) -> U122(proper(X)) 101.91/27.15 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U131(X)) -> U131(proper(X)) 101.91/27.15 proper(snd(X)) -> snd(proper(X)) 101.91/27.15 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.15 proper(U141(X)) -> U141(proper(X)) 101.91/27.15 proper(U151(X)) -> U151(proper(X)) 101.91/27.15 proper(U161(X)) -> U161(proper(X)) 101.91/27.15 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.15 proper(U172(X)) -> U172(proper(X)) 101.91/27.15 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.15 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.15 proper(U183(X)) -> U183(proper(X)) 101.91/27.15 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.15 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.15 proper(U193(X)) -> U193(proper(X)) 101.91/27.15 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.15 proper(U206(X)) -> U206(proper(X)) 101.91/27.15 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U211(X)) -> U211(proper(X)) 101.91/27.15 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U221(X)) -> U221(proper(X)) 101.91/27.15 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.15 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.15 proper(U232(X)) -> U232(proper(X)) 101.91/27.15 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.15 proper(U246(X)) -> U246(proper(X)) 101.91/27.15 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.15 proper(U256(X)) -> U256(proper(X)) 101.91/27.15 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.15 proper(U262(X)) -> U262(proper(X)) 101.91/27.15 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.15 proper(U272(X)) -> U272(proper(X)) 101.91/27.15 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.15 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.15 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.15 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.15 proper(s(X)) -> s(proper(X)) 101.91/27.15 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(head(X)) -> head(proper(X)) 101.91/27.15 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.15 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.15 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.15 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.15 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.15 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.15 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.15 proper(nil) -> ok(nil) 101.91/27.15 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.15 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.15 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.15 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.15 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.15 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(fst(X)) -> fst(proper(X)) 101.91/27.15 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.15 proper(U46(X)) -> U46(proper(X)) 101.91/27.15 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.15 proper(U56(X)) -> U56(proper(X)) 101.91/27.15 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.15 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.15 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.15 proper(U63(X)) -> U63(proper(X)) 101.91/27.15 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.15 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.15 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.15 proper(U73(X)) -> U73(proper(X)) 101.91/27.15 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.15 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.15 proper(U83(X)) -> U83(proper(X)) 101.91/27.15 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.15 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.15 proper(U93(X)) -> U93(proper(X)) 101.91/27.15 proper(tail(X)) -> tail(proper(X)) 101.91/27.15 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.15 proper(0') -> ok(0') 101.91/27.15 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.15 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.15 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.15 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.15 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.15 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.15 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.15 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.15 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.15 U106(ok(X)) -> ok(U106(X)) 101.91/27.15 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.15 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.15 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.15 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.15 U112(ok(X)) -> ok(U112(X)) 101.91/27.15 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.15 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.15 U122(ok(X)) -> ok(U122(X)) 101.91/27.15 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.15 U131(ok(X)) -> ok(U131(X)) 101.91/27.15 snd(ok(X)) -> ok(snd(X)) 101.91/27.15 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.15 U141(ok(X)) -> ok(U141(X)) 101.91/27.15 U151(ok(X)) -> ok(U151(X)) 101.91/27.15 U161(ok(X)) -> ok(U161(X)) 101.91/27.15 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.15 U172(ok(X)) -> ok(U172(X)) 101.91/27.15 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.15 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.15 U183(ok(X)) -> ok(U183(X)) 101.91/27.15 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.15 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.15 U193(ok(X)) -> ok(U193(X)) 101.91/27.15 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.15 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.15 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.15 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.15 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.15 U206(ok(X)) -> ok(U206(X)) 101.91/27.15 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.15 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.15 U211(ok(X)) -> ok(U211(X)) 101.91/27.15 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.15 U221(ok(X)) -> ok(U221(X)) 101.91/27.15 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.15 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.15 U232(ok(X)) -> ok(U232(X)) 101.91/27.15 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.15 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.15 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.15 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.15 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.15 U246(ok(X)) -> ok(U246(X)) 101.91/27.15 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.15 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.15 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.15 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.15 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.15 U256(ok(X)) -> ok(U256(X)) 101.91/27.15 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.15 U262(ok(X)) -> ok(U262(X)) 101.91/27.15 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.15 U272(ok(X)) -> ok(U272(X)) 101.91/27.15 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.15 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.15 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.15 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.15 s(ok(X)) -> ok(s(X)) 101.91/27.15 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.15 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.15 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.15 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.15 head(ok(X)) -> ok(head(X)) 101.91/27.15 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.15 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.15 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.15 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.15 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.15 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.15 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.15 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.15 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.15 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.15 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.15 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.15 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.15 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.15 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.15 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.15 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.15 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.15 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.15 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.15 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.15 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.15 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.15 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.15 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.15 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.15 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.15 fst(ok(X)) -> ok(fst(X)) 101.91/27.15 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.15 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.15 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.15 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.15 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.15 U46(ok(X)) -> ok(U46(X)) 101.91/27.15 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.15 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.15 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.15 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.15 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.15 U56(ok(X)) -> ok(U56(X)) 101.91/27.15 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.15 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.15 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.15 U63(ok(X)) -> ok(U63(X)) 101.91/27.15 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.15 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.15 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.15 U73(ok(X)) -> ok(U73(X)) 101.91/27.15 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.15 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.15 U83(ok(X)) -> ok(U83(X)) 101.91/27.15 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.15 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.15 U93(ok(X)) -> ok(U93(X)) 101.91/27.15 tail(ok(X)) -> ok(tail(X)) 101.91/27.15 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.15 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.15 top(mark(X)) -> top(proper(X)) 101.91/27.15 top(ok(X)) -> top(active(X)) 101.91/27.15 101.91/27.15 Types: 101.91/27.15 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 tt :: tt:mark:nil:0':ok 101.91/27.15 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 nil :: tt:mark:nil:0':ok 101.91/27.15 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 0' :: tt:mark:nil:0':ok 101.91/27.15 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 top :: tt:mark:nil:0':ok -> top 101.91/27.15 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.15 hole_top2_0 :: top 101.91/27.15 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.15 101.91/27.15 101.91/27.15 Lemmas: 101.91/27.15 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.15 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.15 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.15 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.15 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.15 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.15 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.15 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.15 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.15 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.15 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.15 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.15 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.15 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.15 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.15 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.15 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.15 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.15 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.15 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.15 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.15 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.15 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.15 101.91/27.15 101.91/27.15 Generator Equations: 101.91/27.15 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.15 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.15 101.91/27.15 101.91/27.15 The following defined symbols remain to be analysed: 101.91/27.15 U23, active, U24, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.15 101.91/27.15 They will be analysed ascendingly in the following order: 101.91/27.15 U23 < active 101.91/27.15 U24 < active 101.91/27.15 U232 < active 101.91/27.15 U242 < active 101.91/27.15 U243 < active 101.91/27.15 U244 < active 101.91/27.15 U245 < active 101.91/27.15 U246 < active 101.91/27.15 U252 < active 101.91/27.15 U253 < active 101.91/27.15 U254 < active 101.91/27.15 U255 < active 101.91/27.15 U256 < active 101.91/27.15 U262 < active 101.91/27.15 U272 < active 101.91/27.15 U282 < active 101.91/27.15 cons < active 101.91/27.15 natsFrom < active 101.91/27.15 s < active 101.91/27.15 U292 < active 101.91/27.15 U293 < active 101.91/27.15 U294 < active 101.91/27.15 head < active 101.91/27.15 afterNth < active 101.91/27.15 U302 < active 101.91/27.15 U303 < active 101.91/27.15 U304 < active 101.91/27.15 U32 < active 101.91/27.15 U312 < active 101.91/27.15 pair < active 101.91/27.15 U33 < active 101.91/27.15 U322 < active 101.91/27.15 U323 < active 101.91/27.15 U324 < active 101.91/27.15 U325 < active 101.91/27.15 U326 < active 101.91/27.15 U327 < active 101.91/27.15 U34 < active 101.91/27.15 U332 < active 101.91/27.15 U333 < active 101.91/27.15 U334 < active 101.91/27.15 U342 < active 101.91/27.15 U343 < active 101.91/27.15 U344 < active 101.91/27.15 fst < active 101.91/27.15 U42 < active 101.91/27.15 U43 < active 101.91/27.15 U44 < active 101.91/27.15 U45 < active 101.91/27.15 U46 < active 101.91/27.15 U52 < active 101.91/27.15 U53 < active 101.91/27.15 U54 < active 101.91/27.15 U55 < active 101.91/27.15 U56 < active 101.91/27.15 U62 < active 101.91/27.15 isPLNatKind < active 101.91/27.15 U63 < active 101.91/27.15 isPLNat < active 101.91/27.15 U72 < active 101.91/27.15 U73 < active 101.91/27.15 U82 < active 101.91/27.15 U83 < active 101.91/27.15 U92 < active 101.91/27.15 U93 < active 101.91/27.15 U11 < active 101.91/27.15 U21 < active 101.91/27.15 U31 < active 101.91/27.15 U41 < active 101.91/27.15 U51 < active 101.91/27.15 U61 < active 101.91/27.15 U71 < active 101.91/27.15 U81 < active 101.91/27.15 U91 < active 101.91/27.15 U101 < active 101.91/27.15 U111 < active 101.91/27.15 U121 < active 101.91/27.15 U131 < active 101.91/27.15 U141 < active 101.91/27.15 U151 < active 101.91/27.15 U161 < active 101.91/27.15 U171 < active 101.91/27.15 U181 < active 101.91/27.15 U191 < active 101.91/27.15 U201 < active 101.91/27.15 U211 < active 101.91/27.15 U221 < active 101.91/27.15 U231 < active 101.91/27.15 U241 < active 101.91/27.15 U251 < active 101.91/27.15 U261 < active 101.91/27.15 U271 < active 101.91/27.15 U281 < active 101.91/27.15 U291 < active 101.91/27.15 U301 < active 101.91/27.15 U311 < active 101.91/27.15 U321 < active 101.91/27.15 U331 < active 101.91/27.15 U341 < active 101.91/27.15 tail < active 101.91/27.15 take < active 101.91/27.15 sel < active 101.91/27.15 active < top 101.91/27.15 U23 < proper 101.91/27.15 U24 < proper 101.91/27.15 U232 < proper 101.91/27.15 U242 < proper 101.91/27.15 U243 < proper 101.91/27.15 U244 < proper 101.91/27.15 U245 < proper 101.91/27.15 U246 < proper 101.91/27.15 U252 < proper 101.91/27.15 U253 < proper 101.91/27.15 U254 < proper 101.91/27.15 U255 < proper 101.91/27.15 U256 < proper 101.91/27.15 U262 < proper 101.91/27.15 U272 < proper 101.91/27.15 U282 < proper 101.91/27.15 cons < proper 101.91/27.15 natsFrom < proper 101.91/27.15 s < proper 101.91/27.15 U292 < proper 101.91/27.15 U293 < proper 101.91/27.15 U294 < proper 101.91/27.15 head < proper 101.91/27.15 afterNth < proper 101.91/27.15 U302 < proper 101.91/27.15 U303 < proper 101.91/27.15 U304 < proper 101.91/27.15 U32 < proper 101.91/27.15 U312 < proper 101.91/27.15 pair < proper 101.91/27.15 U33 < proper 101.91/27.15 U322 < proper 101.91/27.15 U323 < proper 101.91/27.15 U324 < proper 101.91/27.15 U325 < proper 101.91/27.15 U326 < proper 101.91/27.15 U327 < proper 101.91/27.15 U34 < proper 101.91/27.15 U332 < proper 101.91/27.15 U333 < proper 101.91/27.15 U334 < proper 101.91/27.15 U342 < proper 101.91/27.15 U343 < proper 101.91/27.15 U344 < proper 101.91/27.15 fst < proper 101.91/27.15 U42 < proper 101.91/27.15 U43 < proper 101.91/27.15 U44 < proper 101.91/27.15 U45 < proper 101.91/27.15 U46 < proper 101.91/27.15 U52 < proper 101.91/27.15 U53 < proper 101.91/27.15 U54 < proper 101.91/27.15 U55 < proper 101.91/27.15 U56 < proper 101.91/27.15 U62 < proper 101.91/27.15 isPLNatKind < proper 101.91/27.15 U63 < proper 101.91/27.15 isPLNat < proper 101.91/27.15 U72 < proper 101.91/27.15 U73 < proper 101.91/27.15 U82 < proper 101.91/27.15 U83 < proper 101.91/27.15 U92 < proper 101.91/27.15 U93 < proper 101.91/27.15 U11 < proper 101.91/27.15 U21 < proper 101.91/27.15 U31 < proper 101.91/27.15 U41 < proper 101.91/27.15 U51 < proper 101.91/27.15 U61 < proper 101.91/27.15 U71 < proper 101.91/27.15 U81 < proper 101.91/27.15 U91 < proper 101.91/27.15 U101 < proper 101.91/27.15 U111 < proper 101.91/27.15 U121 < proper 101.91/27.15 U131 < proper 101.91/27.15 U141 < proper 101.91/27.15 U151 < proper 101.91/27.15 U161 < proper 101.91/27.15 U171 < proper 101.91/27.15 U181 < proper 101.91/27.15 U191 < proper 101.91/27.15 U201 < proper 101.91/27.15 U211 < proper 101.91/27.15 U221 < proper 101.91/27.15 U231 < proper 101.91/27.15 U241 < proper 101.91/27.15 U251 < proper 101.91/27.15 U261 < proper 101.91/27.15 U271 < proper 101.91/27.15 U281 < proper 101.91/27.15 U291 < proper 101.91/27.15 U301 < proper 101.91/27.15 U311 < proper 101.91/27.15 U321 < proper 101.91/27.15 U331 < proper 101.91/27.15 U341 < proper 101.91/27.15 tail < proper 101.91/27.15 take < proper 101.91/27.15 sel < proper 101.91/27.15 proper < top 101.91/27.15 101.91/27.15 ---------------------------------------- 101.91/27.15 101.91/27.15 (75) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.15 Proved the following rewrite lemma: 101.91/27.15 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.15 101.91/27.15 Induction Base: 101.91/27.15 U23(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.15 101.91/27.15 Induction Step: 101.91/27.15 U23(gen_tt:mark:nil:0':ok3_0(+(1, +(n322338_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.15 mark(U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.15 mark(*4_0) 101.91/27.15 101.91/27.15 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.15 ---------------------------------------- 101.91/27.15 101.91/27.15 (76) 101.91/27.15 Obligation: 101.91/27.15 TRS: 101.91/27.15 Rules: 101.91/27.15 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.15 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.15 active(U106(tt)) -> mark(tt) 101.91/27.15 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.15 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.15 active(U112(tt)) -> mark(tt) 101.91/27.15 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.15 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.15 active(U122(tt)) -> mark(tt) 101.91/27.15 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.15 active(U131(tt)) -> mark(tt) 101.91/27.15 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.15 active(U141(tt)) -> mark(tt) 101.91/27.15 active(U151(tt)) -> mark(tt) 101.91/27.15 active(U161(tt)) -> mark(tt) 101.91/27.15 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.15 active(U172(tt)) -> mark(tt) 101.91/27.15 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.15 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.15 active(U183(tt)) -> mark(tt) 101.91/27.15 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.15 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.15 active(U193(tt)) -> mark(tt) 101.91/27.15 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.15 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.15 active(U206(tt)) -> mark(tt) 101.91/27.15 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.15 active(U211(tt)) -> mark(tt) 101.91/27.15 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.15 active(U221(tt)) -> mark(tt) 101.91/27.15 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.15 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.15 active(U232(tt)) -> mark(tt) 101.91/27.15 active(U24(tt, X)) -> mark(X) 101.91/27.15 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.15 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.15 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.15 active(U246(tt)) -> mark(tt) 101.91/27.15 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.15 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.15 active(U256(tt)) -> mark(tt) 101.91/27.15 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.15 active(U262(tt)) -> mark(tt) 101.91/27.15 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.15 active(U272(tt)) -> mark(tt) 101.91/27.15 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.15 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.15 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.15 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.15 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.15 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.15 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.15 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.15 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.15 active(U304(tt, Y)) -> mark(Y) 101.91/27.15 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.15 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.15 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.15 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.15 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.15 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.15 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.15 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.15 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.15 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.15 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.15 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.15 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.15 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.15 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.15 active(U334(tt, XS)) -> mark(XS) 101.91/27.15 active(U34(tt, N)) -> mark(N) 101.91/27.15 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.15 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.15 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.15 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.15 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.15 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.15 active(U46(tt)) -> mark(tt) 101.91/27.15 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.15 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.15 active(U56(tt)) -> mark(tt) 101.91/27.15 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.15 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.15 active(U63(tt)) -> mark(tt) 101.91/27.15 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.15 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.15 active(U73(tt)) -> mark(tt) 101.91/27.15 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.15 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.15 active(U83(tt)) -> mark(tt) 101.91/27.15 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.15 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.15 active(U93(tt)) -> mark(tt) 101.91/27.15 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.15 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.15 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.15 active(isLNat(nil)) -> mark(tt) 101.91/27.15 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.15 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.15 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.15 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.15 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(isLNatKind(nil)) -> mark(tt) 101.91/27.15 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.15 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.15 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.15 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.15 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.15 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.15 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.15 active(isNatural(0')) -> mark(tt) 101.91/27.15 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.15 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.15 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(isNaturalKind(0')) -> mark(tt) 101.91/27.15 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.15 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.15 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.15 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.15 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.15 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.15 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.15 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.15 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.15 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.15 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.15 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.15 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.15 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.15 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.15 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.15 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.15 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.15 active(U106(X)) -> U106(active(X)) 101.91/27.15 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.15 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.15 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.15 active(U112(X)) -> U112(active(X)) 101.91/27.15 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.15 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.15 active(U122(X)) -> U122(active(X)) 101.91/27.15 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.15 active(U131(X)) -> U131(active(X)) 101.91/27.15 active(snd(X)) -> snd(active(X)) 101.91/27.15 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.15 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.15 active(U141(X)) -> U141(active(X)) 101.91/27.15 active(U151(X)) -> U151(active(X)) 101.91/27.15 active(U161(X)) -> U161(active(X)) 101.91/27.15 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.15 active(U172(X)) -> U172(active(X)) 101.91/27.15 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.15 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.15 active(U183(X)) -> U183(active(X)) 101.91/27.15 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.15 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.15 active(U193(X)) -> U193(active(X)) 101.91/27.15 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.15 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.15 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.15 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.15 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.15 active(U206(X)) -> U206(active(X)) 101.91/27.15 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.15 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.15 active(U211(X)) -> U211(active(X)) 101.91/27.15 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.15 active(U221(X)) -> U221(active(X)) 101.91/27.15 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.15 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.15 active(U232(X)) -> U232(active(X)) 101.91/27.15 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.15 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.15 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.15 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.15 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.15 active(U246(X)) -> U246(active(X)) 101.91/27.15 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.15 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.15 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.15 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.15 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.15 active(U256(X)) -> U256(active(X)) 101.91/27.15 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.15 active(U262(X)) -> U262(active(X)) 101.91/27.15 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.15 active(U272(X)) -> U272(active(X)) 101.91/27.15 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.15 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.15 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.15 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.15 active(s(X)) -> s(active(X)) 101.91/27.15 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.15 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.15 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.15 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.15 active(head(X)) -> head(active(X)) 101.91/27.15 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.15 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.15 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.15 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.15 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.15 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.15 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.15 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.15 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.15 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.15 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.15 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.15 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.15 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.15 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.15 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.15 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.15 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.15 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.15 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.15 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.15 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.15 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.15 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.15 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.15 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.15 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.15 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.15 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.15 active(fst(X)) -> fst(active(X)) 101.91/27.15 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.15 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.15 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.15 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.15 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.15 active(U46(X)) -> U46(active(X)) 101.91/27.15 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.15 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.15 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.15 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.15 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.15 active(U56(X)) -> U56(active(X)) 101.91/27.15 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.15 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.15 active(U63(X)) -> U63(active(X)) 101.91/27.15 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.15 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.15 active(U73(X)) -> U73(active(X)) 101.91/27.15 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.15 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.15 active(U83(X)) -> U83(active(X)) 101.91/27.15 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.15 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.15 active(U93(X)) -> U93(active(X)) 101.91/27.15 active(tail(X)) -> tail(active(X)) 101.91/27.15 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.15 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.15 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.15 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.15 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.15 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.15 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.15 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.15 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.15 U106(mark(X)) -> mark(U106(X)) 101.91/27.15 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.15 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.15 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.15 U112(mark(X)) -> mark(U112(X)) 101.91/27.15 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.15 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.15 U122(mark(X)) -> mark(U122(X)) 101.91/27.15 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.15 U131(mark(X)) -> mark(U131(X)) 101.91/27.15 snd(mark(X)) -> mark(snd(X)) 101.91/27.15 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.15 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.15 U141(mark(X)) -> mark(U141(X)) 101.91/27.15 U151(mark(X)) -> mark(U151(X)) 101.91/27.15 U161(mark(X)) -> mark(U161(X)) 101.91/27.15 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.15 U172(mark(X)) -> mark(U172(X)) 101.91/27.15 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.15 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.15 U183(mark(X)) -> mark(U183(X)) 101.91/27.15 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.15 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.15 U193(mark(X)) -> mark(U193(X)) 101.91/27.15 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.15 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.15 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.15 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.15 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.15 U206(mark(X)) -> mark(U206(X)) 101.91/27.15 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.15 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.15 U211(mark(X)) -> mark(U211(X)) 101.91/27.15 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.15 U221(mark(X)) -> mark(U221(X)) 101.91/27.15 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.15 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.15 U232(mark(X)) -> mark(U232(X)) 101.91/27.15 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.15 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.15 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.15 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.15 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.15 U246(mark(X)) -> mark(U246(X)) 101.91/27.15 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.15 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.15 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.15 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.15 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.15 U256(mark(X)) -> mark(U256(X)) 101.91/27.15 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.15 U262(mark(X)) -> mark(U262(X)) 101.91/27.15 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.15 U272(mark(X)) -> mark(U272(X)) 101.91/27.15 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.15 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.15 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.15 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.15 s(mark(X)) -> mark(s(X)) 101.91/27.15 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.15 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.15 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.15 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.15 head(mark(X)) -> mark(head(X)) 101.91/27.15 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.15 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.15 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.15 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.15 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.15 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.15 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.15 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.15 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.15 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.15 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.15 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.15 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.15 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.15 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.15 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.15 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.15 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.15 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.15 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.15 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.15 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.15 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.15 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.15 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.15 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.15 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.15 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.15 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.15 fst(mark(X)) -> mark(fst(X)) 101.91/27.15 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.15 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.15 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.15 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.15 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.15 U46(mark(X)) -> mark(U46(X)) 101.91/27.15 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.15 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.15 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.15 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.15 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.15 U56(mark(X)) -> mark(U56(X)) 101.91/27.15 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.15 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.15 U63(mark(X)) -> mark(U63(X)) 101.91/27.15 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.15 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.15 U73(mark(X)) -> mark(U73(X)) 101.91/27.15 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.15 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.15 U83(mark(X)) -> mark(U83(X)) 101.91/27.15 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.15 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.15 U93(mark(X)) -> mark(U93(X)) 101.91/27.15 tail(mark(X)) -> mark(tail(X)) 101.91/27.15 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.15 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.15 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.15 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.15 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(tt) -> ok(tt) 101.91/27.15 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.15 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.15 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.15 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.15 proper(U106(X)) -> U106(proper(X)) 101.91/27.15 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.15 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.15 proper(U112(X)) -> U112(proper(X)) 101.91/27.15 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.15 proper(U122(X)) -> U122(proper(X)) 101.91/27.15 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U131(X)) -> U131(proper(X)) 101.91/27.15 proper(snd(X)) -> snd(proper(X)) 101.91/27.15 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.15 proper(U141(X)) -> U141(proper(X)) 101.91/27.15 proper(U151(X)) -> U151(proper(X)) 101.91/27.15 proper(U161(X)) -> U161(proper(X)) 101.91/27.15 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.15 proper(U172(X)) -> U172(proper(X)) 101.91/27.15 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.15 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.15 proper(U183(X)) -> U183(proper(X)) 101.91/27.15 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.15 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.15 proper(U193(X)) -> U193(proper(X)) 101.91/27.15 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.15 proper(U206(X)) -> U206(proper(X)) 101.91/27.15 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U211(X)) -> U211(proper(X)) 101.91/27.15 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U221(X)) -> U221(proper(X)) 101.91/27.15 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.15 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.15 proper(U232(X)) -> U232(proper(X)) 101.91/27.15 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.15 proper(U246(X)) -> U246(proper(X)) 101.91/27.15 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.15 proper(U256(X)) -> U256(proper(X)) 101.91/27.15 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.15 proper(U262(X)) -> U262(proper(X)) 101.91/27.15 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.15 proper(U272(X)) -> U272(proper(X)) 101.91/27.15 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.15 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.15 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.15 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.15 proper(s(X)) -> s(proper(X)) 101.91/27.15 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(head(X)) -> head(proper(X)) 101.91/27.15 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.15 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.15 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.15 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.15 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.15 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.15 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.15 proper(nil) -> ok(nil) 101.91/27.15 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.15 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.15 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.15 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.15 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.15 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.15 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(fst(X)) -> fst(proper(X)) 101.91/27.15 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.15 proper(U46(X)) -> U46(proper(X)) 101.91/27.15 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.15 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.15 proper(U56(X)) -> U56(proper(X)) 101.91/27.15 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.15 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.15 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.15 proper(U63(X)) -> U63(proper(X)) 101.91/27.15 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.15 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.15 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.15 proper(U73(X)) -> U73(proper(X)) 101.91/27.15 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.15 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.15 proper(U83(X)) -> U83(proper(X)) 101.91/27.15 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.15 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.15 proper(U93(X)) -> U93(proper(X)) 101.91/27.15 proper(tail(X)) -> tail(proper(X)) 101.91/27.15 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.15 proper(0') -> ok(0') 101.91/27.15 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.15 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.15 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.15 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.15 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.15 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.15 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.15 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.15 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.15 U106(ok(X)) -> ok(U106(X)) 101.91/27.15 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.15 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.15 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.15 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.15 U112(ok(X)) -> ok(U112(X)) 101.91/27.15 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.15 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.15 U122(ok(X)) -> ok(U122(X)) 101.91/27.15 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.15 U131(ok(X)) -> ok(U131(X)) 101.91/27.15 snd(ok(X)) -> ok(snd(X)) 101.91/27.15 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.15 U141(ok(X)) -> ok(U141(X)) 101.91/27.15 U151(ok(X)) -> ok(U151(X)) 101.91/27.15 U161(ok(X)) -> ok(U161(X)) 101.91/27.15 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.15 U172(ok(X)) -> ok(U172(X)) 101.91/27.15 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.15 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.15 U183(ok(X)) -> ok(U183(X)) 101.91/27.15 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.15 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.15 U193(ok(X)) -> ok(U193(X)) 101.91/27.15 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.15 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.15 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.15 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.15 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.15 U206(ok(X)) -> ok(U206(X)) 101.91/27.15 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.15 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.15 U211(ok(X)) -> ok(U211(X)) 101.91/27.15 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.15 U221(ok(X)) -> ok(U221(X)) 101.91/27.15 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.15 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.15 U232(ok(X)) -> ok(U232(X)) 101.91/27.15 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.15 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.15 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.15 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.15 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.15 U246(ok(X)) -> ok(U246(X)) 101.91/27.15 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.15 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.15 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.15 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.15 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.15 U256(ok(X)) -> ok(U256(X)) 101.91/27.15 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.15 U262(ok(X)) -> ok(U262(X)) 101.91/27.15 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.15 U272(ok(X)) -> ok(U272(X)) 101.91/27.15 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.15 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.15 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.15 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.15 s(ok(X)) -> ok(s(X)) 101.91/27.15 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.15 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.15 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.15 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.15 head(ok(X)) -> ok(head(X)) 101.91/27.15 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.15 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.15 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.15 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.15 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.15 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.15 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.15 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.15 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.15 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.15 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.15 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.15 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.15 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.15 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.15 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.15 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.15 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.15 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.15 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.15 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.15 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.15 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.15 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.15 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.15 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.15 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.15 fst(ok(X)) -> ok(fst(X)) 101.91/27.15 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.15 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.15 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.15 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.15 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.15 U46(ok(X)) -> ok(U46(X)) 101.91/27.15 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.15 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.15 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.15 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.15 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.15 U56(ok(X)) -> ok(U56(X)) 101.91/27.15 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.15 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.15 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.15 U63(ok(X)) -> ok(U63(X)) 101.91/27.15 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.15 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.15 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.15 U73(ok(X)) -> ok(U73(X)) 101.91/27.15 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.15 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.15 U83(ok(X)) -> ok(U83(X)) 101.91/27.15 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.15 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.15 U93(ok(X)) -> ok(U93(X)) 101.91/27.15 tail(ok(X)) -> ok(tail(X)) 101.91/27.15 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.15 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.15 top(mark(X)) -> top(proper(X)) 101.91/27.15 top(ok(X)) -> top(active(X)) 101.91/27.15 101.91/27.15 Types: 101.91/27.15 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 tt :: tt:mark:nil:0':ok 101.91/27.15 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 nil :: tt:mark:nil:0':ok 101.91/27.15 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 0' :: tt:mark:nil:0':ok 101.91/27.15 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.15 top :: tt:mark:nil:0':ok -> top 101.91/27.15 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.15 hole_top2_0 :: top 101.91/27.15 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.15 101.91/27.15 101.91/27.15 Lemmas: 101.91/27.15 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.15 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.15 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.15 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.15 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.15 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.15 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.15 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.15 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.15 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.15 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.15 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.15 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.15 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.15 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.15 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.15 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.15 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.15 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.15 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.15 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.15 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.15 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.15 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.15 101.91/27.15 101.91/27.15 Generator Equations: 101.91/27.15 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.15 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.15 101.91/27.15 101.91/27.15 The following defined symbols remain to be analysed: 101.91/27.15 U24, active, U232, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.15 101.91/27.15 They will be analysed ascendingly in the following order: 101.91/27.15 U24 < active 101.91/27.15 U232 < active 101.91/27.15 U242 < active 101.91/27.15 U243 < active 101.91/27.15 U244 < active 101.91/27.15 U245 < active 101.91/27.15 U246 < active 101.91/27.15 U252 < active 101.91/27.15 U253 < active 101.91/27.15 U254 < active 101.91/27.15 U255 < active 101.91/27.15 U256 < active 101.91/27.15 U262 < active 101.91/27.15 U272 < active 101.91/27.15 U282 < active 101.91/27.15 cons < active 101.91/27.15 natsFrom < active 101.91/27.15 s < active 101.91/27.15 U292 < active 101.91/27.15 U293 < active 101.91/27.15 U294 < active 101.91/27.15 head < active 101.91/27.15 afterNth < active 101.91/27.15 U302 < active 101.91/27.15 U303 < active 101.91/27.15 U304 < active 101.91/27.15 U32 < active 101.91/27.15 U312 < active 101.91/27.15 pair < active 101.91/27.15 U33 < active 101.91/27.15 U322 < active 101.91/27.15 U323 < active 101.91/27.15 U324 < active 101.91/27.15 U325 < active 101.91/27.15 U326 < active 101.91/27.15 U327 < active 101.91/27.15 U34 < active 101.91/27.15 U332 < active 101.91/27.15 U333 < active 101.91/27.15 U334 < active 101.91/27.15 U342 < active 101.91/27.15 U343 < active 101.91/27.15 U344 < active 101.91/27.15 fst < active 101.91/27.15 U42 < active 101.91/27.15 U43 < active 101.91/27.15 U44 < active 101.91/27.15 U45 < active 101.91/27.15 U46 < active 101.91/27.15 U52 < active 101.91/27.15 U53 < active 101.91/27.15 U54 < active 101.91/27.15 U55 < active 101.91/27.15 U56 < active 101.91/27.15 U62 < active 101.91/27.15 isPLNatKind < active 101.91/27.15 U63 < active 101.91/27.15 isPLNat < active 101.91/27.15 U72 < active 101.91/27.15 U73 < active 101.91/27.15 U82 < active 101.91/27.15 U83 < active 101.91/27.15 U92 < active 101.91/27.15 U93 < active 101.91/27.15 U11 < active 101.91/27.15 U21 < active 101.91/27.15 U31 < active 101.91/27.15 U41 < active 101.91/27.15 U51 < active 101.91/27.15 U61 < active 101.91/27.15 U71 < active 101.91/27.15 U81 < active 101.91/27.15 U91 < active 101.91/27.15 U101 < active 101.91/27.15 U111 < active 101.91/27.15 U121 < active 101.91/27.15 U131 < active 101.91/27.15 U141 < active 101.91/27.15 U151 < active 101.91/27.15 U161 < active 101.91/27.15 U171 < active 101.91/27.15 U181 < active 101.91/27.15 U191 < active 101.91/27.15 U201 < active 101.91/27.15 U211 < active 101.91/27.15 U221 < active 101.91/27.15 U231 < active 101.91/27.15 U241 < active 101.91/27.15 U251 < active 101.91/27.15 U261 < active 101.91/27.15 U271 < active 101.91/27.15 U281 < active 101.91/27.15 U291 < active 101.91/27.15 U301 < active 101.91/27.15 U311 < active 101.91/27.15 U321 < active 101.91/27.15 U331 < active 101.91/27.15 U341 < active 101.91/27.15 tail < active 101.91/27.15 take < active 101.91/27.15 sel < active 101.91/27.15 active < top 101.91/27.15 U24 < proper 101.91/27.15 U232 < proper 101.91/27.15 U242 < proper 101.91/27.15 U243 < proper 101.91/27.15 U244 < proper 101.91/27.15 U245 < proper 101.91/27.15 U246 < proper 101.91/27.15 U252 < proper 101.91/27.15 U253 < proper 101.91/27.15 U254 < proper 101.91/27.15 U255 < proper 101.91/27.15 U256 < proper 101.91/27.15 U262 < proper 101.91/27.15 U272 < proper 101.91/27.15 U282 < proper 101.91/27.15 cons < proper 101.91/27.15 natsFrom < proper 101.91/27.15 s < proper 101.91/27.15 U292 < proper 101.91/27.15 U293 < proper 101.91/27.15 U294 < proper 101.91/27.15 head < proper 101.91/27.15 afterNth < proper 101.91/27.15 U302 < proper 101.91/27.15 U303 < proper 101.91/27.15 U304 < proper 101.91/27.15 U32 < proper 101.91/27.15 U312 < proper 101.91/27.15 pair < proper 101.91/27.15 U33 < proper 101.91/27.15 U322 < proper 101.91/27.15 U323 < proper 101.91/27.15 U324 < proper 101.91/27.15 U325 < proper 101.91/27.15 U326 < proper 101.91/27.15 U327 < proper 101.91/27.15 U34 < proper 101.91/27.15 U332 < proper 101.91/27.15 U333 < proper 101.91/27.15 U334 < proper 101.91/27.15 U342 < proper 101.91/27.15 U343 < proper 101.91/27.15 U344 < proper 101.91/27.15 fst < proper 101.91/27.15 U42 < proper 101.91/27.15 U43 < proper 101.91/27.15 U44 < proper 101.91/27.15 U45 < proper 101.91/27.15 U46 < proper 101.91/27.15 U52 < proper 101.91/27.15 U53 < proper 101.91/27.15 U54 < proper 101.91/27.15 U55 < proper 101.91/27.15 U56 < proper 101.91/27.15 U62 < proper 101.91/27.15 isPLNatKind < proper 101.91/27.15 U63 < proper 101.91/27.15 isPLNat < proper 101.91/27.15 U72 < proper 101.91/27.15 U73 < proper 101.91/27.15 U82 < proper 101.91/27.15 U83 < proper 101.91/27.15 U92 < proper 101.91/27.15 U93 < proper 101.91/27.15 U11 < proper 101.91/27.15 U21 < proper 101.91/27.15 U31 < proper 101.91/27.15 U41 < proper 101.91/27.15 U51 < proper 101.91/27.15 U61 < proper 101.91/27.15 U71 < proper 101.91/27.15 U81 < proper 101.91/27.15 U91 < proper 101.91/27.15 U101 < proper 101.91/27.15 U111 < proper 101.91/27.15 U121 < proper 101.91/27.15 U131 < proper 101.91/27.15 U141 < proper 101.91/27.15 U151 < proper 101.91/27.15 U161 < proper 101.91/27.15 U171 < proper 101.91/27.15 U181 < proper 101.91/27.15 U191 < proper 101.91/27.15 U201 < proper 101.91/27.15 U211 < proper 101.91/27.15 U221 < proper 101.91/27.15 U231 < proper 101.91/27.15 U241 < proper 101.91/27.15 U251 < proper 101.91/27.15 U261 < proper 101.91/27.15 U271 < proper 101.91/27.15 U281 < proper 101.91/27.15 U291 < proper 101.91/27.15 U301 < proper 101.91/27.15 U311 < proper 101.91/27.15 U321 < proper 101.91/27.15 U331 < proper 101.91/27.15 U341 < proper 101.91/27.15 tail < proper 101.91/27.15 take < proper 101.91/27.15 sel < proper 101.91/27.15 proper < top 101.91/27.15 101.91/27.15 ---------------------------------------- 101.91/27.15 101.91/27.15 (77) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.15 Proved the following rewrite lemma: 101.91/27.15 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.15 101.91/27.15 Induction Base: 101.91/27.15 U24(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.91/27.15 101.91/27.15 Induction Step: 101.91/27.15 U24(gen_tt:mark:nil:0':ok3_0(+(1, +(n350561_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.91/27.15 mark(U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.91/27.15 mark(*4_0) 101.91/27.15 101.91/27.15 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.15 ---------------------------------------- 101.91/27.15 101.91/27.15 (78) 101.91/27.15 Obligation: 101.91/27.15 TRS: 101.91/27.15 Rules: 101.91/27.15 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.15 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.15 active(U106(tt)) -> mark(tt) 101.91/27.15 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.15 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.15 active(U112(tt)) -> mark(tt) 101.91/27.15 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.15 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.15 active(U122(tt)) -> mark(tt) 101.91/27.15 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.15 active(U131(tt)) -> mark(tt) 101.91/27.15 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.15 active(U141(tt)) -> mark(tt) 101.91/27.15 active(U151(tt)) -> mark(tt) 101.91/27.15 active(U161(tt)) -> mark(tt) 101.91/27.15 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.15 active(U172(tt)) -> mark(tt) 101.91/27.15 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.15 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.15 active(U183(tt)) -> mark(tt) 101.91/27.15 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.15 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.15 active(U193(tt)) -> mark(tt) 101.91/27.15 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.15 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.15 active(U206(tt)) -> mark(tt) 101.91/27.15 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.15 active(U211(tt)) -> mark(tt) 101.91/27.15 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.15 active(U221(tt)) -> mark(tt) 101.91/27.15 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.15 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.15 active(U232(tt)) -> mark(tt) 101.91/27.15 active(U24(tt, X)) -> mark(X) 101.91/27.15 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.15 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.15 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.15 active(U246(tt)) -> mark(tt) 101.91/27.15 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.15 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.15 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.15 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.15 active(U256(tt)) -> mark(tt) 101.91/27.15 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.15 active(U262(tt)) -> mark(tt) 101.91/27.15 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.15 active(U272(tt)) -> mark(tt) 101.91/27.15 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.15 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.15 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.15 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.15 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.15 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.15 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.15 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.15 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.15 active(U304(tt, Y)) -> mark(Y) 101.91/27.15 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.15 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.15 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.15 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.15 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.15 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.15 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.15 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.15 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.16 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.16 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.16 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.16 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.16 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.16 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.16 active(U334(tt, XS)) -> mark(XS) 101.91/27.16 active(U34(tt, N)) -> mark(N) 101.91/27.16 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.16 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.16 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.16 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.16 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.16 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.16 active(U46(tt)) -> mark(tt) 101.91/27.16 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.16 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.16 active(U56(tt)) -> mark(tt) 101.91/27.16 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.16 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.16 active(U63(tt)) -> mark(tt) 101.91/27.16 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.16 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.16 active(U73(tt)) -> mark(tt) 101.91/27.16 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.16 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.16 active(U83(tt)) -> mark(tt) 101.91/27.16 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.16 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.16 active(U93(tt)) -> mark(tt) 101.91/27.16 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.16 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.16 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.16 active(isLNat(nil)) -> mark(tt) 101.91/27.16 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.16 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.16 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.16 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.16 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNatKind(nil)) -> mark(tt) 101.91/27.16 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.16 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.16 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.16 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.16 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.16 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.16 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.16 active(isNatural(0')) -> mark(tt) 101.91/27.16 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.16 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.16 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isNaturalKind(0')) -> mark(tt) 101.91/27.16 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.16 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.16 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.16 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.16 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.16 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.16 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.16 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.16 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.16 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.16 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.16 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.16 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.16 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.16 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.16 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.16 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.16 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.16 active(U106(X)) -> U106(active(X)) 101.91/27.16 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.16 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.16 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.16 active(U112(X)) -> U112(active(X)) 101.91/27.16 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.16 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.16 active(U122(X)) -> U122(active(X)) 101.91/27.16 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.16 active(U131(X)) -> U131(active(X)) 101.91/27.16 active(snd(X)) -> snd(active(X)) 101.91/27.16 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.16 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.16 active(U141(X)) -> U141(active(X)) 101.91/27.16 active(U151(X)) -> U151(active(X)) 101.91/27.16 active(U161(X)) -> U161(active(X)) 101.91/27.16 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.16 active(U172(X)) -> U172(active(X)) 101.91/27.16 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.16 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.16 active(U183(X)) -> U183(active(X)) 101.91/27.16 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.16 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.16 active(U193(X)) -> U193(active(X)) 101.91/27.16 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.16 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.16 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.16 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.16 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.16 active(U206(X)) -> U206(active(X)) 101.91/27.16 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.16 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.16 active(U211(X)) -> U211(active(X)) 101.91/27.16 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.16 active(U221(X)) -> U221(active(X)) 101.91/27.16 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.16 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.16 active(U232(X)) -> U232(active(X)) 101.91/27.16 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.16 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.16 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.16 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.16 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.16 active(U246(X)) -> U246(active(X)) 101.91/27.16 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.16 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.16 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.16 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.16 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.16 active(U256(X)) -> U256(active(X)) 101.91/27.16 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.16 active(U262(X)) -> U262(active(X)) 101.91/27.16 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.16 active(U272(X)) -> U272(active(X)) 101.91/27.16 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.16 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.16 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.16 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.16 active(s(X)) -> s(active(X)) 101.91/27.16 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.16 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.16 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.16 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.16 active(head(X)) -> head(active(X)) 101.91/27.16 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.16 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.16 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.16 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.16 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.16 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.16 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.16 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.16 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.16 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.16 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.16 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.16 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.16 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.16 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.16 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.16 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.16 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.16 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.16 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.16 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.16 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.16 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.16 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.16 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.16 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.16 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.16 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.16 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.16 active(fst(X)) -> fst(active(X)) 101.91/27.16 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.16 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.16 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.16 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.16 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.16 active(U46(X)) -> U46(active(X)) 101.91/27.16 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.16 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.16 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.16 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.16 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.16 active(U56(X)) -> U56(active(X)) 101.91/27.16 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.16 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.16 active(U63(X)) -> U63(active(X)) 101.91/27.16 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.16 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.16 active(U73(X)) -> U73(active(X)) 101.91/27.16 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.16 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.16 active(U83(X)) -> U83(active(X)) 101.91/27.16 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.16 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.16 active(U93(X)) -> U93(active(X)) 101.91/27.16 active(tail(X)) -> tail(active(X)) 101.91/27.16 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.16 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.16 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.16 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.16 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.16 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.16 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.16 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.16 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.16 U106(mark(X)) -> mark(U106(X)) 101.91/27.16 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.16 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.16 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.16 U112(mark(X)) -> mark(U112(X)) 101.91/27.16 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.16 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.16 U122(mark(X)) -> mark(U122(X)) 101.91/27.16 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.16 U131(mark(X)) -> mark(U131(X)) 101.91/27.16 snd(mark(X)) -> mark(snd(X)) 101.91/27.16 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.16 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.16 U141(mark(X)) -> mark(U141(X)) 101.91/27.16 U151(mark(X)) -> mark(U151(X)) 101.91/27.16 U161(mark(X)) -> mark(U161(X)) 101.91/27.16 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.16 U172(mark(X)) -> mark(U172(X)) 101.91/27.16 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.16 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.16 U183(mark(X)) -> mark(U183(X)) 101.91/27.16 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.16 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.16 U193(mark(X)) -> mark(U193(X)) 101.91/27.16 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.16 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.16 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.16 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.16 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.16 U206(mark(X)) -> mark(U206(X)) 101.91/27.16 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.16 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.16 U211(mark(X)) -> mark(U211(X)) 101.91/27.16 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.16 U221(mark(X)) -> mark(U221(X)) 101.91/27.16 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.16 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.16 U232(mark(X)) -> mark(U232(X)) 101.91/27.16 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.16 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.16 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.16 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.16 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.16 U246(mark(X)) -> mark(U246(X)) 101.91/27.16 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.16 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.16 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.16 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.16 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.16 U256(mark(X)) -> mark(U256(X)) 101.91/27.16 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.16 U262(mark(X)) -> mark(U262(X)) 101.91/27.16 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.16 U272(mark(X)) -> mark(U272(X)) 101.91/27.16 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.16 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.16 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.16 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.16 s(mark(X)) -> mark(s(X)) 101.91/27.16 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.16 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.16 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.16 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.16 head(mark(X)) -> mark(head(X)) 101.91/27.16 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.16 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.16 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.16 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.16 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.16 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.16 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.16 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.16 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.16 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.16 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.16 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.16 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.16 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.16 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.16 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.16 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.16 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.16 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.16 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.16 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.16 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.16 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.16 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.16 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.16 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.16 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.16 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.16 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.16 fst(mark(X)) -> mark(fst(X)) 101.91/27.16 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.16 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.16 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.16 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.16 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.16 U46(mark(X)) -> mark(U46(X)) 101.91/27.16 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.16 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.16 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.16 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.16 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.16 U56(mark(X)) -> mark(U56(X)) 101.91/27.16 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.16 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.16 U63(mark(X)) -> mark(U63(X)) 101.91/27.16 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.16 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.16 U73(mark(X)) -> mark(U73(X)) 101.91/27.16 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.16 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.16 U83(mark(X)) -> mark(U83(X)) 101.91/27.16 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.16 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.16 U93(mark(X)) -> mark(U93(X)) 101.91/27.16 tail(mark(X)) -> mark(tail(X)) 101.91/27.16 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.16 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.16 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.16 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.16 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(tt) -> ok(tt) 101.91/27.16 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.16 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.16 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.16 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.16 proper(U106(X)) -> U106(proper(X)) 101.91/27.16 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.16 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.16 proper(U112(X)) -> U112(proper(X)) 101.91/27.16 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.16 proper(U122(X)) -> U122(proper(X)) 101.91/27.16 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U131(X)) -> U131(proper(X)) 101.91/27.16 proper(snd(X)) -> snd(proper(X)) 101.91/27.16 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.16 proper(U141(X)) -> U141(proper(X)) 101.91/27.16 proper(U151(X)) -> U151(proper(X)) 101.91/27.16 proper(U161(X)) -> U161(proper(X)) 101.91/27.16 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.16 proper(U172(X)) -> U172(proper(X)) 101.91/27.16 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.16 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.16 proper(U183(X)) -> U183(proper(X)) 101.91/27.16 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.16 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.16 proper(U193(X)) -> U193(proper(X)) 101.91/27.16 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.16 proper(U206(X)) -> U206(proper(X)) 101.91/27.16 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U211(X)) -> U211(proper(X)) 101.91/27.16 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U221(X)) -> U221(proper(X)) 101.91/27.16 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.16 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.16 proper(U232(X)) -> U232(proper(X)) 101.91/27.16 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.16 proper(U246(X)) -> U246(proper(X)) 101.91/27.16 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.16 proper(U256(X)) -> U256(proper(X)) 101.91/27.16 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.16 proper(U262(X)) -> U262(proper(X)) 101.91/27.16 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.16 proper(U272(X)) -> U272(proper(X)) 101.91/27.16 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.16 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.16 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.16 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.16 proper(s(X)) -> s(proper(X)) 101.91/27.16 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(head(X)) -> head(proper(X)) 101.91/27.16 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.16 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.16 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.16 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.16 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.16 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.16 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.16 proper(nil) -> ok(nil) 101.91/27.16 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.16 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.16 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.16 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.16 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.16 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(fst(X)) -> fst(proper(X)) 101.91/27.16 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.16 proper(U46(X)) -> U46(proper(X)) 101.91/27.16 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.16 proper(U56(X)) -> U56(proper(X)) 101.91/27.16 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.16 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.16 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.16 proper(U63(X)) -> U63(proper(X)) 101.91/27.16 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.16 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.16 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.16 proper(U73(X)) -> U73(proper(X)) 101.91/27.16 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.16 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.16 proper(U83(X)) -> U83(proper(X)) 101.91/27.16 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.16 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.16 proper(U93(X)) -> U93(proper(X)) 101.91/27.16 proper(tail(X)) -> tail(proper(X)) 101.91/27.16 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.16 proper(0') -> ok(0') 101.91/27.16 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.16 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.16 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.16 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.16 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.16 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.16 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.16 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.16 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.16 U106(ok(X)) -> ok(U106(X)) 101.91/27.16 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.16 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.16 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.16 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.16 U112(ok(X)) -> ok(U112(X)) 101.91/27.16 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.16 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.16 U122(ok(X)) -> ok(U122(X)) 101.91/27.16 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.16 U131(ok(X)) -> ok(U131(X)) 101.91/27.16 snd(ok(X)) -> ok(snd(X)) 101.91/27.16 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.16 U141(ok(X)) -> ok(U141(X)) 101.91/27.16 U151(ok(X)) -> ok(U151(X)) 101.91/27.16 U161(ok(X)) -> ok(U161(X)) 101.91/27.16 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.16 U172(ok(X)) -> ok(U172(X)) 101.91/27.16 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.16 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.16 U183(ok(X)) -> ok(U183(X)) 101.91/27.16 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.16 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.16 U193(ok(X)) -> ok(U193(X)) 101.91/27.16 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.16 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.16 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.16 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.16 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.16 U206(ok(X)) -> ok(U206(X)) 101.91/27.16 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.16 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.16 U211(ok(X)) -> ok(U211(X)) 101.91/27.16 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.16 U221(ok(X)) -> ok(U221(X)) 101.91/27.16 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.16 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.16 U232(ok(X)) -> ok(U232(X)) 101.91/27.16 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.16 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.16 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.16 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.16 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.16 U246(ok(X)) -> ok(U246(X)) 101.91/27.16 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.16 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.16 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.16 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.16 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.16 U256(ok(X)) -> ok(U256(X)) 101.91/27.16 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.16 U262(ok(X)) -> ok(U262(X)) 101.91/27.16 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.16 U272(ok(X)) -> ok(U272(X)) 101.91/27.16 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.16 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.16 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.16 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.16 s(ok(X)) -> ok(s(X)) 101.91/27.16 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.16 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.16 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.16 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.16 head(ok(X)) -> ok(head(X)) 101.91/27.16 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.16 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.16 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.16 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.16 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.16 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.16 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.16 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.16 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.16 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.16 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.16 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.16 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.16 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.16 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.16 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.16 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.16 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.16 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.16 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.16 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.16 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.16 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.16 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.16 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.16 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.16 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.16 fst(ok(X)) -> ok(fst(X)) 101.91/27.16 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.16 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.16 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.16 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.16 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.16 U46(ok(X)) -> ok(U46(X)) 101.91/27.16 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.16 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.16 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.16 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.16 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.16 U56(ok(X)) -> ok(U56(X)) 101.91/27.16 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.16 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.16 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.16 U63(ok(X)) -> ok(U63(X)) 101.91/27.16 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.16 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.16 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.16 U73(ok(X)) -> ok(U73(X)) 101.91/27.16 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.16 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.16 U83(ok(X)) -> ok(U83(X)) 101.91/27.16 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.16 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.16 U93(ok(X)) -> ok(U93(X)) 101.91/27.16 tail(ok(X)) -> ok(tail(X)) 101.91/27.16 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.16 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.16 top(mark(X)) -> top(proper(X)) 101.91/27.16 top(ok(X)) -> top(active(X)) 101.91/27.16 101.91/27.16 Types: 101.91/27.16 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 tt :: tt:mark:nil:0':ok 101.91/27.16 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 nil :: tt:mark:nil:0':ok 101.91/27.16 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 0' :: tt:mark:nil:0':ok 101.91/27.16 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 top :: tt:mark:nil:0':ok -> top 101.91/27.16 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.16 hole_top2_0 :: top 101.91/27.16 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.16 101.91/27.16 101.91/27.16 Lemmas: 101.91/27.16 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.16 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.16 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.16 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.16 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.16 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.16 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.16 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.16 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.16 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.16 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.16 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.16 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.16 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.16 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.16 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.16 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.16 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.16 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.16 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.16 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.16 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.16 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.16 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.16 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.16 101.91/27.16 101.91/27.16 Generator Equations: 101.91/27.16 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.16 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.16 101.91/27.16 101.91/27.16 The following defined symbols remain to be analysed: 101.91/27.16 U232, active, U242, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.16 101.91/27.16 They will be analysed ascendingly in the following order: 101.91/27.16 U232 < active 101.91/27.16 U242 < active 101.91/27.16 U243 < active 101.91/27.16 U244 < active 101.91/27.16 U245 < active 101.91/27.16 U246 < active 101.91/27.16 U252 < active 101.91/27.16 U253 < active 101.91/27.16 U254 < active 101.91/27.16 U255 < active 101.91/27.16 U256 < active 101.91/27.16 U262 < active 101.91/27.16 U272 < active 101.91/27.16 U282 < active 101.91/27.16 cons < active 101.91/27.16 natsFrom < active 101.91/27.16 s < active 101.91/27.16 U292 < active 101.91/27.16 U293 < active 101.91/27.16 U294 < active 101.91/27.16 head < active 101.91/27.16 afterNth < active 101.91/27.16 U302 < active 101.91/27.16 U303 < active 101.91/27.16 U304 < active 101.91/27.16 U32 < active 101.91/27.16 U312 < active 101.91/27.16 pair < active 101.91/27.16 U33 < active 101.91/27.16 U322 < active 101.91/27.16 U323 < active 101.91/27.16 U324 < active 101.91/27.16 U325 < active 101.91/27.16 U326 < active 101.91/27.16 U327 < active 101.91/27.16 U34 < active 101.91/27.16 U332 < active 101.91/27.16 U333 < active 101.91/27.16 U334 < active 101.91/27.16 U342 < active 101.91/27.16 U343 < active 101.91/27.16 U344 < active 101.91/27.16 fst < active 101.91/27.16 U42 < active 101.91/27.16 U43 < active 101.91/27.16 U44 < active 101.91/27.16 U45 < active 101.91/27.16 U46 < active 101.91/27.16 U52 < active 101.91/27.16 U53 < active 101.91/27.16 U54 < active 101.91/27.16 U55 < active 101.91/27.16 U56 < active 101.91/27.16 U62 < active 101.91/27.16 isPLNatKind < active 101.91/27.16 U63 < active 101.91/27.16 isPLNat < active 101.91/27.16 U72 < active 101.91/27.16 U73 < active 101.91/27.16 U82 < active 101.91/27.16 U83 < active 101.91/27.16 U92 < active 101.91/27.16 U93 < active 101.91/27.16 U11 < active 101.91/27.16 U21 < active 101.91/27.16 U31 < active 101.91/27.16 U41 < active 101.91/27.16 U51 < active 101.91/27.16 U61 < active 101.91/27.16 U71 < active 101.91/27.16 U81 < active 101.91/27.16 U91 < active 101.91/27.16 U101 < active 101.91/27.16 U111 < active 101.91/27.16 U121 < active 101.91/27.16 U131 < active 101.91/27.16 U141 < active 101.91/27.16 U151 < active 101.91/27.16 U161 < active 101.91/27.16 U171 < active 101.91/27.16 U181 < active 101.91/27.16 U191 < active 101.91/27.16 U201 < active 101.91/27.16 U211 < active 101.91/27.16 U221 < active 101.91/27.16 U231 < active 101.91/27.16 U241 < active 101.91/27.16 U251 < active 101.91/27.16 U261 < active 101.91/27.16 U271 < active 101.91/27.16 U281 < active 101.91/27.16 U291 < active 101.91/27.16 U301 < active 101.91/27.16 U311 < active 101.91/27.16 U321 < active 101.91/27.16 U331 < active 101.91/27.16 U341 < active 101.91/27.16 tail < active 101.91/27.16 take < active 101.91/27.16 sel < active 101.91/27.16 active < top 101.91/27.16 U232 < proper 101.91/27.16 U242 < proper 101.91/27.16 U243 < proper 101.91/27.16 U244 < proper 101.91/27.16 U245 < proper 101.91/27.16 U246 < proper 101.91/27.16 U252 < proper 101.91/27.16 U253 < proper 101.91/27.16 U254 < proper 101.91/27.16 U255 < proper 101.91/27.16 U256 < proper 101.91/27.16 U262 < proper 101.91/27.16 U272 < proper 101.91/27.16 U282 < proper 101.91/27.16 cons < proper 101.91/27.16 natsFrom < proper 101.91/27.16 s < proper 101.91/27.16 U292 < proper 101.91/27.16 U293 < proper 101.91/27.16 U294 < proper 101.91/27.16 head < proper 101.91/27.16 afterNth < proper 101.91/27.16 U302 < proper 101.91/27.16 U303 < proper 101.91/27.16 U304 < proper 101.91/27.16 U32 < proper 101.91/27.16 U312 < proper 101.91/27.16 pair < proper 101.91/27.16 U33 < proper 101.91/27.16 U322 < proper 101.91/27.16 U323 < proper 101.91/27.16 U324 < proper 101.91/27.16 U325 < proper 101.91/27.16 U326 < proper 101.91/27.16 U327 < proper 101.91/27.16 U34 < proper 101.91/27.16 U332 < proper 101.91/27.16 U333 < proper 101.91/27.16 U334 < proper 101.91/27.16 U342 < proper 101.91/27.16 U343 < proper 101.91/27.16 U344 < proper 101.91/27.16 fst < proper 101.91/27.16 U42 < proper 101.91/27.16 U43 < proper 101.91/27.16 U44 < proper 101.91/27.16 U45 < proper 101.91/27.16 U46 < proper 101.91/27.16 U52 < proper 101.91/27.16 U53 < proper 101.91/27.16 U54 < proper 101.91/27.16 U55 < proper 101.91/27.16 U56 < proper 101.91/27.16 U62 < proper 101.91/27.16 isPLNatKind < proper 101.91/27.16 U63 < proper 101.91/27.16 isPLNat < proper 101.91/27.16 U72 < proper 101.91/27.16 U73 < proper 101.91/27.16 U82 < proper 101.91/27.16 U83 < proper 101.91/27.16 U92 < proper 101.91/27.16 U93 < proper 101.91/27.16 U11 < proper 101.91/27.16 U21 < proper 101.91/27.16 U31 < proper 101.91/27.16 U41 < proper 101.91/27.16 U51 < proper 101.91/27.16 U61 < proper 101.91/27.16 U71 < proper 101.91/27.16 U81 < proper 101.91/27.16 U91 < proper 101.91/27.16 U101 < proper 101.91/27.16 U111 < proper 101.91/27.16 U121 < proper 101.91/27.16 U131 < proper 101.91/27.16 U141 < proper 101.91/27.16 U151 < proper 101.91/27.16 U161 < proper 101.91/27.16 U171 < proper 101.91/27.16 U181 < proper 101.91/27.16 U191 < proper 101.91/27.16 U201 < proper 101.91/27.16 U211 < proper 101.91/27.16 U221 < proper 101.91/27.16 U231 < proper 101.91/27.16 U241 < proper 101.91/27.16 U251 < proper 101.91/27.16 U261 < proper 101.91/27.16 U271 < proper 101.91/27.16 U281 < proper 101.91/27.16 U291 < proper 101.91/27.16 U301 < proper 101.91/27.16 U311 < proper 101.91/27.16 U321 < proper 101.91/27.16 U331 < proper 101.91/27.16 U341 < proper 101.91/27.16 tail < proper 101.91/27.16 take < proper 101.91/27.16 sel < proper 101.91/27.16 proper < top 101.91/27.16 101.91/27.16 ---------------------------------------- 101.91/27.16 101.91/27.16 (79) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.16 Proved the following rewrite lemma: 101.91/27.16 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.16 101.91/27.16 Induction Base: 101.91/27.16 U232(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.91/27.16 101.91/27.16 Induction Step: 101.91/27.16 U232(gen_tt:mark:nil:0':ok3_0(+(1, +(n367986_0, 1)))) ->_R^Omega(1) 101.91/27.16 mark(U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0)))) ->_IH 101.91/27.16 mark(*4_0) 101.91/27.16 101.91/27.16 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.16 ---------------------------------------- 101.91/27.16 101.91/27.16 (80) 101.91/27.16 Obligation: 101.91/27.16 TRS: 101.91/27.16 Rules: 101.91/27.16 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.16 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.16 active(U106(tt)) -> mark(tt) 101.91/27.16 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.16 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.16 active(U112(tt)) -> mark(tt) 101.91/27.16 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.16 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.16 active(U122(tt)) -> mark(tt) 101.91/27.16 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.16 active(U131(tt)) -> mark(tt) 101.91/27.16 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.16 active(U141(tt)) -> mark(tt) 101.91/27.16 active(U151(tt)) -> mark(tt) 101.91/27.16 active(U161(tt)) -> mark(tt) 101.91/27.16 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.16 active(U172(tt)) -> mark(tt) 101.91/27.16 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.16 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.16 active(U183(tt)) -> mark(tt) 101.91/27.16 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.16 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.16 active(U193(tt)) -> mark(tt) 101.91/27.16 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.16 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.16 active(U206(tt)) -> mark(tt) 101.91/27.16 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.16 active(U211(tt)) -> mark(tt) 101.91/27.16 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.16 active(U221(tt)) -> mark(tt) 101.91/27.16 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.16 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.16 active(U232(tt)) -> mark(tt) 101.91/27.16 active(U24(tt, X)) -> mark(X) 101.91/27.16 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.16 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.16 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.16 active(U246(tt)) -> mark(tt) 101.91/27.16 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.16 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.16 active(U256(tt)) -> mark(tt) 101.91/27.16 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.16 active(U262(tt)) -> mark(tt) 101.91/27.16 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.16 active(U272(tt)) -> mark(tt) 101.91/27.16 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.16 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.16 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.16 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.16 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.16 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.16 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.16 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.16 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.16 active(U304(tt, Y)) -> mark(Y) 101.91/27.16 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.16 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.16 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.16 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.16 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.16 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.16 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.16 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.16 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.16 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.16 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.16 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.16 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.16 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.16 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.16 active(U334(tt, XS)) -> mark(XS) 101.91/27.16 active(U34(tt, N)) -> mark(N) 101.91/27.16 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.16 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.16 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.16 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.16 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.16 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.16 active(U46(tt)) -> mark(tt) 101.91/27.16 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.16 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.16 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.16 active(U56(tt)) -> mark(tt) 101.91/27.16 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.16 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.16 active(U63(tt)) -> mark(tt) 101.91/27.16 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.16 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.16 active(U73(tt)) -> mark(tt) 101.91/27.16 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.16 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.16 active(U83(tt)) -> mark(tt) 101.91/27.16 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.16 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.16 active(U93(tt)) -> mark(tt) 101.91/27.16 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.16 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.16 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.16 active(isLNat(nil)) -> mark(tt) 101.91/27.16 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.16 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.16 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.16 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.16 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isLNatKind(nil)) -> mark(tt) 101.91/27.16 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.16 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.16 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.16 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.16 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.16 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.16 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.16 active(isNatural(0')) -> mark(tt) 101.91/27.16 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.16 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.16 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isNaturalKind(0')) -> mark(tt) 101.91/27.16 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.16 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.16 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.16 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.16 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.16 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.16 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.16 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.16 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.16 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.16 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.16 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.16 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.16 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.16 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.16 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.16 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.16 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.16 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.16 active(U106(X)) -> U106(active(X)) 101.91/27.16 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.16 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.16 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.16 active(U112(X)) -> U112(active(X)) 101.91/27.16 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.16 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.16 active(U122(X)) -> U122(active(X)) 101.91/27.16 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.16 active(U131(X)) -> U131(active(X)) 101.91/27.16 active(snd(X)) -> snd(active(X)) 101.91/27.16 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.16 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.16 active(U141(X)) -> U141(active(X)) 101.91/27.16 active(U151(X)) -> U151(active(X)) 101.91/27.16 active(U161(X)) -> U161(active(X)) 101.91/27.16 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.16 active(U172(X)) -> U172(active(X)) 101.91/27.16 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.16 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.16 active(U183(X)) -> U183(active(X)) 101.91/27.16 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.16 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.16 active(U193(X)) -> U193(active(X)) 101.91/27.16 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.16 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.16 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.16 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.16 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.16 active(U206(X)) -> U206(active(X)) 101.91/27.16 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.16 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.16 active(U211(X)) -> U211(active(X)) 101.91/27.16 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.16 active(U221(X)) -> U221(active(X)) 101.91/27.16 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.16 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.16 active(U232(X)) -> U232(active(X)) 101.91/27.16 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.16 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.16 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.16 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.16 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.16 active(U246(X)) -> U246(active(X)) 101.91/27.16 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.16 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.16 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.16 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.16 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.16 active(U256(X)) -> U256(active(X)) 101.91/27.16 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.16 active(U262(X)) -> U262(active(X)) 101.91/27.16 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.16 active(U272(X)) -> U272(active(X)) 101.91/27.16 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.16 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.16 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.16 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.16 active(s(X)) -> s(active(X)) 101.91/27.16 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.16 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.16 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.16 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.16 active(head(X)) -> head(active(X)) 101.91/27.16 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.16 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.16 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.16 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.16 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.16 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.16 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.16 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.16 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.16 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.16 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.16 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.16 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.16 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.16 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.16 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.16 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.16 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.16 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.16 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.16 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.16 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.16 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.16 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.16 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.16 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.16 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.16 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.16 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.16 active(fst(X)) -> fst(active(X)) 101.91/27.16 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.16 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.16 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.16 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.16 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.16 active(U46(X)) -> U46(active(X)) 101.91/27.16 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.16 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.16 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.16 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.16 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.16 active(U56(X)) -> U56(active(X)) 101.91/27.16 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.16 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.16 active(U63(X)) -> U63(active(X)) 101.91/27.16 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.16 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.16 active(U73(X)) -> U73(active(X)) 101.91/27.16 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.16 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.16 active(U83(X)) -> U83(active(X)) 101.91/27.16 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.16 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.16 active(U93(X)) -> U93(active(X)) 101.91/27.16 active(tail(X)) -> tail(active(X)) 101.91/27.16 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.16 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.16 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.16 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.16 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.16 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.16 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.16 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.16 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.16 U106(mark(X)) -> mark(U106(X)) 101.91/27.16 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.16 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.16 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.16 U112(mark(X)) -> mark(U112(X)) 101.91/27.16 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.16 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.16 U122(mark(X)) -> mark(U122(X)) 101.91/27.16 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.16 U131(mark(X)) -> mark(U131(X)) 101.91/27.16 snd(mark(X)) -> mark(snd(X)) 101.91/27.16 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.16 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.16 U141(mark(X)) -> mark(U141(X)) 101.91/27.16 U151(mark(X)) -> mark(U151(X)) 101.91/27.16 U161(mark(X)) -> mark(U161(X)) 101.91/27.16 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.16 U172(mark(X)) -> mark(U172(X)) 101.91/27.16 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.16 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.16 U183(mark(X)) -> mark(U183(X)) 101.91/27.16 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.16 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.16 U193(mark(X)) -> mark(U193(X)) 101.91/27.16 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.16 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.16 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.16 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.16 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.16 U206(mark(X)) -> mark(U206(X)) 101.91/27.16 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.16 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.16 U211(mark(X)) -> mark(U211(X)) 101.91/27.16 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.16 U221(mark(X)) -> mark(U221(X)) 101.91/27.16 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.16 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.16 U232(mark(X)) -> mark(U232(X)) 101.91/27.16 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.16 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.16 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.16 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.16 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.16 U246(mark(X)) -> mark(U246(X)) 101.91/27.16 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.16 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.16 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.16 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.16 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.16 U256(mark(X)) -> mark(U256(X)) 101.91/27.16 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.16 U262(mark(X)) -> mark(U262(X)) 101.91/27.16 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.16 U272(mark(X)) -> mark(U272(X)) 101.91/27.16 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.16 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.16 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.16 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.16 s(mark(X)) -> mark(s(X)) 101.91/27.16 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.16 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.16 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.16 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.16 head(mark(X)) -> mark(head(X)) 101.91/27.16 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.16 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.16 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.16 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.16 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.16 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.16 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.16 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.16 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.16 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.16 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.16 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.16 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.16 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.16 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.16 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.16 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.16 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.16 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.16 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.16 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.16 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.16 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.16 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.16 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.16 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.16 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.16 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.16 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.16 fst(mark(X)) -> mark(fst(X)) 101.91/27.16 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.16 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.16 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.16 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.16 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.16 U46(mark(X)) -> mark(U46(X)) 101.91/27.16 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.16 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.16 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.16 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.16 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.16 U56(mark(X)) -> mark(U56(X)) 101.91/27.16 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.16 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.16 U63(mark(X)) -> mark(U63(X)) 101.91/27.16 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.16 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.16 U73(mark(X)) -> mark(U73(X)) 101.91/27.16 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.16 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.16 U83(mark(X)) -> mark(U83(X)) 101.91/27.16 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.16 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.16 U93(mark(X)) -> mark(U93(X)) 101.91/27.16 tail(mark(X)) -> mark(tail(X)) 101.91/27.16 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.16 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.16 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.16 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.16 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(tt) -> ok(tt) 101.91/27.16 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.16 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.16 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.16 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.16 proper(U106(X)) -> U106(proper(X)) 101.91/27.16 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.16 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.16 proper(U112(X)) -> U112(proper(X)) 101.91/27.16 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.16 proper(U122(X)) -> U122(proper(X)) 101.91/27.16 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U131(X)) -> U131(proper(X)) 101.91/27.16 proper(snd(X)) -> snd(proper(X)) 101.91/27.16 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.16 proper(U141(X)) -> U141(proper(X)) 101.91/27.16 proper(U151(X)) -> U151(proper(X)) 101.91/27.16 proper(U161(X)) -> U161(proper(X)) 101.91/27.16 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.16 proper(U172(X)) -> U172(proper(X)) 101.91/27.16 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.16 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.16 proper(U183(X)) -> U183(proper(X)) 101.91/27.16 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.16 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.16 proper(U193(X)) -> U193(proper(X)) 101.91/27.16 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.16 proper(U206(X)) -> U206(proper(X)) 101.91/27.16 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U211(X)) -> U211(proper(X)) 101.91/27.16 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U221(X)) -> U221(proper(X)) 101.91/27.16 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.16 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.16 proper(U232(X)) -> U232(proper(X)) 101.91/27.16 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.16 proper(U246(X)) -> U246(proper(X)) 101.91/27.16 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.16 proper(U256(X)) -> U256(proper(X)) 101.91/27.16 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.16 proper(U262(X)) -> U262(proper(X)) 101.91/27.16 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.16 proper(U272(X)) -> U272(proper(X)) 101.91/27.16 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.16 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.16 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.16 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.16 proper(s(X)) -> s(proper(X)) 101.91/27.16 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(head(X)) -> head(proper(X)) 101.91/27.16 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.16 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.16 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.16 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.16 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.16 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.16 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.16 proper(nil) -> ok(nil) 101.91/27.16 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.16 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.16 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.16 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.16 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.16 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.16 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(fst(X)) -> fst(proper(X)) 101.91/27.16 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.16 proper(U46(X)) -> U46(proper(X)) 101.91/27.16 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.16 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.16 proper(U56(X)) -> U56(proper(X)) 101.91/27.16 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.16 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.16 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.16 proper(U63(X)) -> U63(proper(X)) 101.91/27.16 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.16 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.16 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.16 proper(U73(X)) -> U73(proper(X)) 101.91/27.16 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.16 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.16 proper(U83(X)) -> U83(proper(X)) 101.91/27.16 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.16 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.16 proper(U93(X)) -> U93(proper(X)) 101.91/27.16 proper(tail(X)) -> tail(proper(X)) 101.91/27.16 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.16 proper(0') -> ok(0') 101.91/27.16 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.16 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.16 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.16 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.16 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.16 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.16 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.16 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.16 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.16 U106(ok(X)) -> ok(U106(X)) 101.91/27.16 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.16 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.16 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.16 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.16 U112(ok(X)) -> ok(U112(X)) 101.91/27.16 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.16 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.16 U122(ok(X)) -> ok(U122(X)) 101.91/27.16 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.16 U131(ok(X)) -> ok(U131(X)) 101.91/27.16 snd(ok(X)) -> ok(snd(X)) 101.91/27.16 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.16 U141(ok(X)) -> ok(U141(X)) 101.91/27.16 U151(ok(X)) -> ok(U151(X)) 101.91/27.16 U161(ok(X)) -> ok(U161(X)) 101.91/27.16 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.16 U172(ok(X)) -> ok(U172(X)) 101.91/27.16 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.16 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.16 U183(ok(X)) -> ok(U183(X)) 101.91/27.16 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.16 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.16 U193(ok(X)) -> ok(U193(X)) 101.91/27.16 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.16 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.16 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.16 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.16 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.16 U206(ok(X)) -> ok(U206(X)) 101.91/27.16 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.16 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.16 U211(ok(X)) -> ok(U211(X)) 101.91/27.16 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.16 U221(ok(X)) -> ok(U221(X)) 101.91/27.16 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.16 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.16 U232(ok(X)) -> ok(U232(X)) 101.91/27.16 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.16 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.16 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.16 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.16 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.16 U246(ok(X)) -> ok(U246(X)) 101.91/27.16 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.16 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.16 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.16 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.16 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.16 U256(ok(X)) -> ok(U256(X)) 101.91/27.16 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.16 U262(ok(X)) -> ok(U262(X)) 101.91/27.16 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.16 U272(ok(X)) -> ok(U272(X)) 101.91/27.16 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.16 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.16 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.16 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.16 s(ok(X)) -> ok(s(X)) 101.91/27.16 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.16 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.16 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.16 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.16 head(ok(X)) -> ok(head(X)) 101.91/27.16 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.16 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.16 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.16 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.16 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.16 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.16 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.16 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.16 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.16 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.16 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.16 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.16 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.16 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.16 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.16 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.16 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.16 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.16 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.16 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.16 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.16 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.16 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.16 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.16 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.16 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.16 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.16 fst(ok(X)) -> ok(fst(X)) 101.91/27.16 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.16 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.16 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.16 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.16 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.16 U46(ok(X)) -> ok(U46(X)) 101.91/27.16 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.16 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.16 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.16 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.16 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.16 U56(ok(X)) -> ok(U56(X)) 101.91/27.16 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.16 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.16 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.16 U63(ok(X)) -> ok(U63(X)) 101.91/27.16 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.16 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.16 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.16 U73(ok(X)) -> ok(U73(X)) 101.91/27.16 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.16 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.16 U83(ok(X)) -> ok(U83(X)) 101.91/27.16 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.16 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.16 U93(ok(X)) -> ok(U93(X)) 101.91/27.16 tail(ok(X)) -> ok(tail(X)) 101.91/27.16 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.16 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.16 top(mark(X)) -> top(proper(X)) 101.91/27.16 top(ok(X)) -> top(active(X)) 101.91/27.16 101.91/27.16 Types: 101.91/27.16 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 tt :: tt:mark:nil:0':ok 101.91/27.16 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 nil :: tt:mark:nil:0':ok 101.91/27.16 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 0' :: tt:mark:nil:0':ok 101.91/27.16 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.16 top :: tt:mark:nil:0':ok -> top 101.91/27.16 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.16 hole_top2_0 :: top 101.91/27.16 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.16 101.91/27.16 101.91/27.16 Lemmas: 101.91/27.16 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.16 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.16 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.16 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.16 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.16 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.16 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.16 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.16 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.16 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.16 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.16 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.16 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.16 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.16 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.16 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.16 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.16 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.16 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.16 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.16 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.16 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.16 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.16 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.16 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.16 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.16 101.91/27.16 101.91/27.16 Generator Equations: 101.91/27.16 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.16 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.16 101.91/27.16 101.91/27.16 The following defined symbols remain to be analysed: 101.91/27.16 U242, active, U243, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.16 101.91/27.16 They will be analysed ascendingly in the following order: 101.91/27.16 U242 < active 101.91/27.16 U243 < active 101.91/27.16 U244 < active 101.91/27.16 U245 < active 101.91/27.16 U246 < active 101.91/27.16 U252 < active 101.91/27.16 U253 < active 101.91/27.16 U254 < active 101.91/27.16 U255 < active 101.91/27.16 U256 < active 101.91/27.16 U262 < active 101.91/27.16 U272 < active 101.91/27.16 U282 < active 101.91/27.16 cons < active 101.91/27.16 natsFrom < active 101.91/27.16 s < active 101.91/27.16 U292 < active 101.91/27.16 U293 < active 101.91/27.16 U294 < active 101.91/27.16 head < active 101.91/27.16 afterNth < active 101.91/27.16 U302 < active 101.91/27.16 U303 < active 101.91/27.16 U304 < active 101.91/27.16 U32 < active 101.91/27.16 U312 < active 101.91/27.16 pair < active 101.91/27.16 U33 < active 101.91/27.16 U322 < active 101.91/27.16 U323 < active 101.91/27.16 U324 < active 101.91/27.16 U325 < active 101.91/27.16 U326 < active 101.91/27.16 U327 < active 101.91/27.16 U34 < active 101.91/27.16 U332 < active 101.91/27.16 U333 < active 101.91/27.16 U334 < active 101.91/27.16 U342 < active 101.91/27.16 U343 < active 101.91/27.16 U344 < active 101.91/27.16 fst < active 101.91/27.16 U42 < active 101.91/27.16 U43 < active 101.91/27.16 U44 < active 101.91/27.16 U45 < active 101.91/27.16 U46 < active 101.91/27.16 U52 < active 101.91/27.16 U53 < active 101.91/27.16 U54 < active 101.91/27.16 U55 < active 101.91/27.16 U56 < active 101.91/27.16 U62 < active 101.91/27.16 isPLNatKind < active 101.91/27.16 U63 < active 101.91/27.16 isPLNat < active 101.91/27.16 U72 < active 101.91/27.16 U73 < active 101.91/27.16 U82 < active 101.91/27.16 U83 < active 101.91/27.16 U92 < active 101.91/27.16 U93 < active 101.91/27.16 U11 < active 101.91/27.16 U21 < active 101.91/27.16 U31 < active 101.91/27.16 U41 < active 101.91/27.16 U51 < active 101.91/27.16 U61 < active 101.91/27.16 U71 < active 101.91/27.16 U81 < active 101.91/27.16 U91 < active 101.91/27.16 U101 < active 101.91/27.16 U111 < active 101.91/27.16 U121 < active 101.91/27.16 U131 < active 101.91/27.16 U141 < active 101.91/27.16 U151 < active 101.91/27.16 U161 < active 101.91/27.16 U171 < active 101.91/27.16 U181 < active 101.91/27.16 U191 < active 101.91/27.16 U201 < active 101.91/27.16 U211 < active 101.91/27.16 U221 < active 101.91/27.16 U231 < active 101.91/27.16 U241 < active 101.91/27.16 U251 < active 101.91/27.16 U261 < active 101.91/27.16 U271 < active 101.91/27.16 U281 < active 101.91/27.16 U291 < active 101.91/27.16 U301 < active 101.91/27.16 U311 < active 101.91/27.16 U321 < active 101.91/27.16 U331 < active 101.91/27.16 U341 < active 101.91/27.16 tail < active 101.91/27.16 take < active 101.91/27.16 sel < active 101.91/27.16 active < top 101.91/27.16 U242 < proper 101.91/27.16 U243 < proper 101.91/27.16 U244 < proper 101.91/27.16 U245 < proper 101.91/27.16 U246 < proper 101.91/27.16 U252 < proper 101.91/27.16 U253 < proper 101.91/27.16 U254 < proper 101.91/27.16 U255 < proper 101.91/27.16 U256 < proper 101.91/27.16 U262 < proper 101.91/27.16 U272 < proper 101.91/27.16 U282 < proper 101.91/27.16 cons < proper 101.91/27.16 natsFrom < proper 101.91/27.16 s < proper 101.91/27.16 U292 < proper 101.91/27.16 U293 < proper 101.91/27.16 U294 < proper 101.91/27.16 head < proper 101.91/27.16 afterNth < proper 101.91/27.16 U302 < proper 101.91/27.16 U303 < proper 101.91/27.16 U304 < proper 101.91/27.16 U32 < proper 101.91/27.16 U312 < proper 101.91/27.16 pair < proper 101.91/27.16 U33 < proper 101.91/27.16 U322 < proper 101.91/27.16 U323 < proper 101.91/27.16 U324 < proper 101.91/27.16 U325 < proper 101.91/27.16 U326 < proper 101.91/27.16 U327 < proper 101.91/27.16 U34 < proper 101.91/27.16 U332 < proper 101.91/27.16 U333 < proper 101.91/27.16 U334 < proper 101.91/27.16 U342 < proper 101.91/27.16 U343 < proper 101.91/27.16 U344 < proper 101.91/27.16 fst < proper 101.91/27.16 U42 < proper 101.91/27.16 U43 < proper 101.91/27.16 U44 < proper 101.91/27.16 U45 < proper 101.91/27.16 U46 < proper 101.91/27.16 U52 < proper 101.91/27.16 U53 < proper 101.91/27.16 U54 < proper 101.91/27.16 U55 < proper 101.91/27.16 U56 < proper 101.91/27.16 U62 < proper 101.91/27.16 isPLNatKind < proper 101.91/27.16 U63 < proper 101.91/27.16 isPLNat < proper 101.91/27.16 U72 < proper 101.91/27.16 U73 < proper 101.91/27.16 U82 < proper 101.91/27.16 U83 < proper 101.91/27.16 U92 < proper 101.91/27.16 U93 < proper 101.91/27.16 U11 < proper 101.91/27.16 U21 < proper 101.91/27.16 U31 < proper 101.91/27.16 U41 < proper 101.91/27.16 U51 < proper 101.91/27.16 U61 < proper 101.91/27.16 U71 < proper 101.91/27.16 U81 < proper 101.91/27.16 U91 < proper 101.91/27.16 U101 < proper 101.91/27.16 U111 < proper 101.91/27.16 U121 < proper 101.91/27.16 U131 < proper 101.91/27.16 U141 < proper 101.91/27.16 U151 < proper 101.91/27.16 U161 < proper 101.91/27.16 U171 < proper 101.91/27.16 U181 < proper 101.91/27.16 U191 < proper 101.91/27.16 U201 < proper 101.91/27.16 U211 < proper 101.91/27.16 U221 < proper 101.91/27.16 U231 < proper 101.91/27.16 U241 < proper 101.91/27.16 U251 < proper 101.91/27.16 U261 < proper 101.91/27.16 U271 < proper 101.91/27.16 U281 < proper 101.91/27.16 U291 < proper 101.91/27.16 U301 < proper 101.91/27.16 U311 < proper 101.91/27.16 U321 < proper 101.91/27.16 U331 < proper 101.91/27.16 U341 < proper 101.91/27.16 tail < proper 101.91/27.16 take < proper 101.91/27.16 sel < proper 101.91/27.16 proper < top 101.91/27.16 101.91/27.16 ---------------------------------------- 101.91/27.16 101.91/27.16 (81) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.16 Proved the following rewrite lemma: 101.91/27.16 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 101.91/27.16 101.91/27.16 Induction Base: 101.91/27.16 U242(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.16 101.91/27.16 Induction Step: 101.91/27.16 U242(gen_tt:mark:nil:0':ok3_0(+(1, +(n374154_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.16 mark(U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.16 mark(*4_0) 101.91/27.16 101.91/27.16 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.16 ---------------------------------------- 101.91/27.16 101.91/27.16 (82) 101.91/27.16 Obligation: 101.91/27.16 TRS: 101.91/27.16 Rules: 101.91/27.16 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.17 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.17 active(U106(tt)) -> mark(tt) 101.91/27.17 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.17 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.17 active(U112(tt)) -> mark(tt) 101.91/27.17 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.17 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.17 active(U122(tt)) -> mark(tt) 101.91/27.17 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.17 active(U131(tt)) -> mark(tt) 101.91/27.17 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.17 active(U141(tt)) -> mark(tt) 101.91/27.17 active(U151(tt)) -> mark(tt) 101.91/27.17 active(U161(tt)) -> mark(tt) 101.91/27.17 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.17 active(U172(tt)) -> mark(tt) 101.91/27.17 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.17 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.17 active(U183(tt)) -> mark(tt) 101.91/27.17 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.17 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.17 active(U193(tt)) -> mark(tt) 101.91/27.17 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.17 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.17 active(U206(tt)) -> mark(tt) 101.91/27.17 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.17 active(U211(tt)) -> mark(tt) 101.91/27.17 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.17 active(U221(tt)) -> mark(tt) 101.91/27.17 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.17 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.17 active(U232(tt)) -> mark(tt) 101.91/27.17 active(U24(tt, X)) -> mark(X) 101.91/27.17 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.17 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.17 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.17 active(U246(tt)) -> mark(tt) 101.91/27.17 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.17 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.17 active(U256(tt)) -> mark(tt) 101.91/27.17 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.17 active(U262(tt)) -> mark(tt) 101.91/27.17 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.17 active(U272(tt)) -> mark(tt) 101.91/27.17 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.17 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.17 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.17 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.17 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.17 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.17 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.17 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.17 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.17 active(U304(tt, Y)) -> mark(Y) 101.91/27.17 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.17 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.17 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.17 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.17 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.17 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.17 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.17 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.17 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.17 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.17 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.17 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.17 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.17 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.17 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.17 active(U334(tt, XS)) -> mark(XS) 101.91/27.17 active(U34(tt, N)) -> mark(N) 101.91/27.17 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.17 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.17 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.17 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.17 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.17 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.17 active(U46(tt)) -> mark(tt) 101.91/27.17 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.17 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.17 active(U56(tt)) -> mark(tt) 101.91/27.17 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.17 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.17 active(U63(tt)) -> mark(tt) 101.91/27.17 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.17 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.17 active(U73(tt)) -> mark(tt) 101.91/27.17 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.17 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.17 active(U83(tt)) -> mark(tt) 101.91/27.17 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.17 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.17 active(U93(tt)) -> mark(tt) 101.91/27.17 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.17 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.17 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.17 active(isLNat(nil)) -> mark(tt) 101.91/27.17 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.17 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.17 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.17 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.17 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNatKind(nil)) -> mark(tt) 101.91/27.17 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.17 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.17 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.17 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.17 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.17 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.17 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.17 active(isNatural(0')) -> mark(tt) 101.91/27.17 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.17 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.17 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isNaturalKind(0')) -> mark(tt) 101.91/27.17 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.17 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.17 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.17 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.17 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.17 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.17 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.17 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.17 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.17 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.17 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.17 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.17 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.17 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.17 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.17 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.17 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.17 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.17 active(U106(X)) -> U106(active(X)) 101.91/27.17 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.17 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.17 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.17 active(U112(X)) -> U112(active(X)) 101.91/27.17 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.17 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.17 active(U122(X)) -> U122(active(X)) 101.91/27.17 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.17 active(U131(X)) -> U131(active(X)) 101.91/27.17 active(snd(X)) -> snd(active(X)) 101.91/27.17 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.17 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.17 active(U141(X)) -> U141(active(X)) 101.91/27.17 active(U151(X)) -> U151(active(X)) 101.91/27.17 active(U161(X)) -> U161(active(X)) 101.91/27.17 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.17 active(U172(X)) -> U172(active(X)) 101.91/27.17 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.17 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.17 active(U183(X)) -> U183(active(X)) 101.91/27.17 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.17 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.17 active(U193(X)) -> U193(active(X)) 101.91/27.17 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.17 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.17 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.17 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.17 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.17 active(U206(X)) -> U206(active(X)) 101.91/27.17 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.17 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.17 active(U211(X)) -> U211(active(X)) 101.91/27.17 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.17 active(U221(X)) -> U221(active(X)) 101.91/27.17 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.17 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.17 active(U232(X)) -> U232(active(X)) 101.91/27.17 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.17 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.17 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.17 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.17 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.17 active(U246(X)) -> U246(active(X)) 101.91/27.17 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.17 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.17 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.17 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.17 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.17 active(U256(X)) -> U256(active(X)) 101.91/27.17 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.17 active(U262(X)) -> U262(active(X)) 101.91/27.17 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.17 active(U272(X)) -> U272(active(X)) 101.91/27.17 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.17 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.17 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.17 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.17 active(s(X)) -> s(active(X)) 101.91/27.17 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.17 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.17 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.17 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.17 active(head(X)) -> head(active(X)) 101.91/27.17 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.17 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.17 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.17 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.17 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.17 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.17 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.17 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.17 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.17 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.17 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.17 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.17 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.17 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.17 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.17 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.17 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.17 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.17 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.17 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.17 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.17 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.17 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.17 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.17 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.17 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.17 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.17 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.17 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.17 active(fst(X)) -> fst(active(X)) 101.91/27.17 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.17 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.17 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.17 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.17 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.17 active(U46(X)) -> U46(active(X)) 101.91/27.17 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.17 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.17 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.17 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.17 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.17 active(U56(X)) -> U56(active(X)) 101.91/27.17 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.17 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.17 active(U63(X)) -> U63(active(X)) 101.91/27.17 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.17 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.17 active(U73(X)) -> U73(active(X)) 101.91/27.17 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.17 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.17 active(U83(X)) -> U83(active(X)) 101.91/27.17 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.17 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.17 active(U93(X)) -> U93(active(X)) 101.91/27.17 active(tail(X)) -> tail(active(X)) 101.91/27.17 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.17 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.17 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.17 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.17 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.17 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.17 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.17 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.17 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.17 U106(mark(X)) -> mark(U106(X)) 101.91/27.17 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.17 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.17 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.17 U112(mark(X)) -> mark(U112(X)) 101.91/27.17 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.17 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.17 U122(mark(X)) -> mark(U122(X)) 101.91/27.17 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.17 U131(mark(X)) -> mark(U131(X)) 101.91/27.17 snd(mark(X)) -> mark(snd(X)) 101.91/27.17 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.17 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.17 U141(mark(X)) -> mark(U141(X)) 101.91/27.17 U151(mark(X)) -> mark(U151(X)) 101.91/27.17 U161(mark(X)) -> mark(U161(X)) 101.91/27.17 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.17 U172(mark(X)) -> mark(U172(X)) 101.91/27.17 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.17 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.17 U183(mark(X)) -> mark(U183(X)) 101.91/27.17 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.17 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.17 U193(mark(X)) -> mark(U193(X)) 101.91/27.17 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.17 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.17 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.17 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.17 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.17 U206(mark(X)) -> mark(U206(X)) 101.91/27.17 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.17 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.17 U211(mark(X)) -> mark(U211(X)) 101.91/27.17 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.17 U221(mark(X)) -> mark(U221(X)) 101.91/27.17 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.17 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.17 U232(mark(X)) -> mark(U232(X)) 101.91/27.17 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.17 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.17 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.17 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.17 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.17 U246(mark(X)) -> mark(U246(X)) 101.91/27.17 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.17 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.17 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.17 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.17 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.17 U256(mark(X)) -> mark(U256(X)) 101.91/27.17 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.17 U262(mark(X)) -> mark(U262(X)) 101.91/27.17 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.17 U272(mark(X)) -> mark(U272(X)) 101.91/27.17 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.17 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.17 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.17 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.17 s(mark(X)) -> mark(s(X)) 101.91/27.17 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.17 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.17 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.17 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.17 head(mark(X)) -> mark(head(X)) 101.91/27.17 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.17 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.17 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.17 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.17 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.17 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.17 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.17 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.17 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.17 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.17 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.17 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.17 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.17 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.17 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.17 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.17 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.17 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.17 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.17 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.17 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.17 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.17 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.17 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.17 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.17 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.17 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.17 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.17 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.17 fst(mark(X)) -> mark(fst(X)) 101.91/27.17 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.17 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.17 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.17 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.17 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.17 U46(mark(X)) -> mark(U46(X)) 101.91/27.17 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.17 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.17 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.17 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.17 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.17 U56(mark(X)) -> mark(U56(X)) 101.91/27.17 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.17 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.17 U63(mark(X)) -> mark(U63(X)) 101.91/27.17 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.17 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.17 U73(mark(X)) -> mark(U73(X)) 101.91/27.17 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.17 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.17 U83(mark(X)) -> mark(U83(X)) 101.91/27.17 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.17 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.17 U93(mark(X)) -> mark(U93(X)) 101.91/27.17 tail(mark(X)) -> mark(tail(X)) 101.91/27.17 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.17 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.17 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.17 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.17 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(tt) -> ok(tt) 101.91/27.17 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.17 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.17 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.17 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.17 proper(U106(X)) -> U106(proper(X)) 101.91/27.17 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.17 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.17 proper(U112(X)) -> U112(proper(X)) 101.91/27.17 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.17 proper(U122(X)) -> U122(proper(X)) 101.91/27.17 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U131(X)) -> U131(proper(X)) 101.91/27.17 proper(snd(X)) -> snd(proper(X)) 101.91/27.17 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.17 proper(U141(X)) -> U141(proper(X)) 101.91/27.17 proper(U151(X)) -> U151(proper(X)) 101.91/27.17 proper(U161(X)) -> U161(proper(X)) 101.91/27.17 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.17 proper(U172(X)) -> U172(proper(X)) 101.91/27.17 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.17 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.17 proper(U183(X)) -> U183(proper(X)) 101.91/27.17 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.17 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.17 proper(U193(X)) -> U193(proper(X)) 101.91/27.17 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.17 proper(U206(X)) -> U206(proper(X)) 101.91/27.17 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U211(X)) -> U211(proper(X)) 101.91/27.17 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U221(X)) -> U221(proper(X)) 101.91/27.17 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.17 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.17 proper(U232(X)) -> U232(proper(X)) 101.91/27.17 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.17 proper(U246(X)) -> U246(proper(X)) 101.91/27.17 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.17 proper(U256(X)) -> U256(proper(X)) 101.91/27.17 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.17 proper(U262(X)) -> U262(proper(X)) 101.91/27.17 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.17 proper(U272(X)) -> U272(proper(X)) 101.91/27.17 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.17 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.17 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.17 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.17 proper(s(X)) -> s(proper(X)) 101.91/27.17 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(head(X)) -> head(proper(X)) 101.91/27.17 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.17 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.17 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.17 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.17 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.17 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.17 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.17 proper(nil) -> ok(nil) 101.91/27.17 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.17 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.17 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.17 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.17 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.17 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(fst(X)) -> fst(proper(X)) 101.91/27.17 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.17 proper(U46(X)) -> U46(proper(X)) 101.91/27.17 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.17 proper(U56(X)) -> U56(proper(X)) 101.91/27.17 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.17 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.17 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.17 proper(U63(X)) -> U63(proper(X)) 101.91/27.17 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.17 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.17 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.17 proper(U73(X)) -> U73(proper(X)) 101.91/27.17 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.17 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.17 proper(U83(X)) -> U83(proper(X)) 101.91/27.17 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.17 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.17 proper(U93(X)) -> U93(proper(X)) 101.91/27.17 proper(tail(X)) -> tail(proper(X)) 101.91/27.17 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.17 proper(0') -> ok(0') 101.91/27.17 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.17 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.17 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.17 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.17 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.17 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.17 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.17 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.17 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.17 U106(ok(X)) -> ok(U106(X)) 101.91/27.17 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.17 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.17 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.17 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.17 U112(ok(X)) -> ok(U112(X)) 101.91/27.17 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.17 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.17 U122(ok(X)) -> ok(U122(X)) 101.91/27.17 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.17 U131(ok(X)) -> ok(U131(X)) 101.91/27.17 snd(ok(X)) -> ok(snd(X)) 101.91/27.17 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.17 U141(ok(X)) -> ok(U141(X)) 101.91/27.17 U151(ok(X)) -> ok(U151(X)) 101.91/27.17 U161(ok(X)) -> ok(U161(X)) 101.91/27.17 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.17 U172(ok(X)) -> ok(U172(X)) 101.91/27.17 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.17 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.17 U183(ok(X)) -> ok(U183(X)) 101.91/27.17 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.17 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.17 U193(ok(X)) -> ok(U193(X)) 101.91/27.17 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.17 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.17 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.17 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.17 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.17 U206(ok(X)) -> ok(U206(X)) 101.91/27.17 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.17 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.17 U211(ok(X)) -> ok(U211(X)) 101.91/27.17 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.17 U221(ok(X)) -> ok(U221(X)) 101.91/27.17 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.17 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.17 U232(ok(X)) -> ok(U232(X)) 101.91/27.17 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.17 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.17 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.17 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.17 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.17 U246(ok(X)) -> ok(U246(X)) 101.91/27.17 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.17 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.17 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.17 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.17 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.17 U256(ok(X)) -> ok(U256(X)) 101.91/27.17 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.17 U262(ok(X)) -> ok(U262(X)) 101.91/27.17 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.17 U272(ok(X)) -> ok(U272(X)) 101.91/27.17 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.17 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.17 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.17 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.17 s(ok(X)) -> ok(s(X)) 101.91/27.17 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.17 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.17 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.17 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.17 head(ok(X)) -> ok(head(X)) 101.91/27.17 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.17 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.17 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.17 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.17 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.17 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.17 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.17 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.17 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.17 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.17 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.17 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.17 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.17 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.17 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.17 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.17 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.17 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.17 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.17 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.17 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.17 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.17 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.17 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.17 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.17 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.17 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.17 fst(ok(X)) -> ok(fst(X)) 101.91/27.17 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.17 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.17 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.17 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.17 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.17 U46(ok(X)) -> ok(U46(X)) 101.91/27.17 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.17 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.17 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.17 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.17 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.17 U56(ok(X)) -> ok(U56(X)) 101.91/27.17 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.17 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.17 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.17 U63(ok(X)) -> ok(U63(X)) 101.91/27.17 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.17 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.17 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.17 U73(ok(X)) -> ok(U73(X)) 101.91/27.17 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.17 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.17 U83(ok(X)) -> ok(U83(X)) 101.91/27.17 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.17 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.17 U93(ok(X)) -> ok(U93(X)) 101.91/27.17 tail(ok(X)) -> ok(tail(X)) 101.91/27.17 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.17 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.17 top(mark(X)) -> top(proper(X)) 101.91/27.17 top(ok(X)) -> top(active(X)) 101.91/27.17 101.91/27.17 Types: 101.91/27.17 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 tt :: tt:mark:nil:0':ok 101.91/27.17 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 nil :: tt:mark:nil:0':ok 101.91/27.17 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 0' :: tt:mark:nil:0':ok 101.91/27.17 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 top :: tt:mark:nil:0':ok -> top 101.91/27.17 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.17 hole_top2_0 :: top 101.91/27.17 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.17 101.91/27.17 101.91/27.17 Lemmas: 101.91/27.17 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.17 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.17 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.17 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.17 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.17 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.17 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.17 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.17 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.17 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.17 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.17 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.17 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.17 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.17 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.17 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.17 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.17 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.17 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.17 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.17 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.17 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.17 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.17 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.17 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.17 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.17 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 101.91/27.17 101.91/27.17 101.91/27.17 Generator Equations: 101.91/27.17 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.17 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.17 101.91/27.17 101.91/27.17 The following defined symbols remain to be analysed: 101.91/27.17 U243, active, U244, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.17 101.91/27.17 They will be analysed ascendingly in the following order: 101.91/27.17 U243 < active 101.91/27.17 U244 < active 101.91/27.17 U245 < active 101.91/27.17 U246 < active 101.91/27.17 U252 < active 101.91/27.17 U253 < active 101.91/27.17 U254 < active 101.91/27.17 U255 < active 101.91/27.17 U256 < active 101.91/27.17 U262 < active 101.91/27.17 U272 < active 101.91/27.17 U282 < active 101.91/27.17 cons < active 101.91/27.17 natsFrom < active 101.91/27.17 s < active 101.91/27.17 U292 < active 101.91/27.17 U293 < active 101.91/27.17 U294 < active 101.91/27.17 head < active 101.91/27.17 afterNth < active 101.91/27.17 U302 < active 101.91/27.17 U303 < active 101.91/27.17 U304 < active 101.91/27.17 U32 < active 101.91/27.17 U312 < active 101.91/27.17 pair < active 101.91/27.17 U33 < active 101.91/27.17 U322 < active 101.91/27.17 U323 < active 101.91/27.17 U324 < active 101.91/27.17 U325 < active 101.91/27.17 U326 < active 101.91/27.17 U327 < active 101.91/27.17 U34 < active 101.91/27.17 U332 < active 101.91/27.17 U333 < active 101.91/27.17 U334 < active 101.91/27.17 U342 < active 101.91/27.17 U343 < active 101.91/27.17 U344 < active 101.91/27.17 fst < active 101.91/27.17 U42 < active 101.91/27.17 U43 < active 101.91/27.17 U44 < active 101.91/27.17 U45 < active 101.91/27.17 U46 < active 101.91/27.17 U52 < active 101.91/27.17 U53 < active 101.91/27.17 U54 < active 101.91/27.17 U55 < active 101.91/27.17 U56 < active 101.91/27.17 U62 < active 101.91/27.17 isPLNatKind < active 101.91/27.17 U63 < active 101.91/27.17 isPLNat < active 101.91/27.17 U72 < active 101.91/27.17 U73 < active 101.91/27.17 U82 < active 101.91/27.17 U83 < active 101.91/27.17 U92 < active 101.91/27.17 U93 < active 101.91/27.17 U11 < active 101.91/27.17 U21 < active 101.91/27.17 U31 < active 101.91/27.17 U41 < active 101.91/27.17 U51 < active 101.91/27.17 U61 < active 101.91/27.17 U71 < active 101.91/27.17 U81 < active 101.91/27.17 U91 < active 101.91/27.17 U101 < active 101.91/27.17 U111 < active 101.91/27.17 U121 < active 101.91/27.17 U131 < active 101.91/27.17 U141 < active 101.91/27.17 U151 < active 101.91/27.17 U161 < active 101.91/27.17 U171 < active 101.91/27.17 U181 < active 101.91/27.17 U191 < active 101.91/27.17 U201 < active 101.91/27.17 U211 < active 101.91/27.17 U221 < active 101.91/27.17 U231 < active 101.91/27.17 U241 < active 101.91/27.17 U251 < active 101.91/27.17 U261 < active 101.91/27.17 U271 < active 101.91/27.17 U281 < active 101.91/27.17 U291 < active 101.91/27.17 U301 < active 101.91/27.17 U311 < active 101.91/27.17 U321 < active 101.91/27.17 U331 < active 101.91/27.17 U341 < active 101.91/27.17 tail < active 101.91/27.17 take < active 101.91/27.17 sel < active 101.91/27.17 active < top 101.91/27.17 U243 < proper 101.91/27.17 U244 < proper 101.91/27.17 U245 < proper 101.91/27.17 U246 < proper 101.91/27.17 U252 < proper 101.91/27.17 U253 < proper 101.91/27.17 U254 < proper 101.91/27.17 U255 < proper 101.91/27.17 U256 < proper 101.91/27.17 U262 < proper 101.91/27.17 U272 < proper 101.91/27.17 U282 < proper 101.91/27.17 cons < proper 101.91/27.17 natsFrom < proper 101.91/27.17 s < proper 101.91/27.17 U292 < proper 101.91/27.17 U293 < proper 101.91/27.17 U294 < proper 101.91/27.17 head < proper 101.91/27.17 afterNth < proper 101.91/27.17 U302 < proper 101.91/27.17 U303 < proper 101.91/27.17 U304 < proper 101.91/27.17 U32 < proper 101.91/27.17 U312 < proper 101.91/27.17 pair < proper 101.91/27.17 U33 < proper 101.91/27.17 U322 < proper 101.91/27.17 U323 < proper 101.91/27.17 U324 < proper 101.91/27.17 U325 < proper 101.91/27.17 U326 < proper 101.91/27.17 U327 < proper 101.91/27.17 U34 < proper 101.91/27.17 U332 < proper 101.91/27.17 U333 < proper 101.91/27.17 U334 < proper 101.91/27.17 U342 < proper 101.91/27.17 U343 < proper 101.91/27.17 U344 < proper 101.91/27.17 fst < proper 101.91/27.17 U42 < proper 101.91/27.17 U43 < proper 101.91/27.17 U44 < proper 101.91/27.17 U45 < proper 101.91/27.17 U46 < proper 101.91/27.17 U52 < proper 101.91/27.17 U53 < proper 101.91/27.17 U54 < proper 101.91/27.17 U55 < proper 101.91/27.17 U56 < proper 101.91/27.17 U62 < proper 101.91/27.17 isPLNatKind < proper 101.91/27.17 U63 < proper 101.91/27.17 isPLNat < proper 101.91/27.17 U72 < proper 101.91/27.17 U73 < proper 101.91/27.17 U82 < proper 101.91/27.17 U83 < proper 101.91/27.17 U92 < proper 101.91/27.17 U93 < proper 101.91/27.17 U11 < proper 101.91/27.17 U21 < proper 101.91/27.17 U31 < proper 101.91/27.17 U41 < proper 101.91/27.17 U51 < proper 101.91/27.17 U61 < proper 101.91/27.17 U71 < proper 101.91/27.17 U81 < proper 101.91/27.17 U91 < proper 101.91/27.17 U101 < proper 101.91/27.17 U111 < proper 101.91/27.17 U121 < proper 101.91/27.17 U131 < proper 101.91/27.17 U141 < proper 101.91/27.17 U151 < proper 101.91/27.17 U161 < proper 101.91/27.17 U171 < proper 101.91/27.17 U181 < proper 101.91/27.17 U191 < proper 101.91/27.17 U201 < proper 101.91/27.17 U211 < proper 101.91/27.17 U221 < proper 101.91/27.17 U231 < proper 101.91/27.17 U241 < proper 101.91/27.17 U251 < proper 101.91/27.17 U261 < proper 101.91/27.17 U271 < proper 101.91/27.17 U281 < proper 101.91/27.17 U291 < proper 101.91/27.17 U301 < proper 101.91/27.17 U311 < proper 101.91/27.17 U321 < proper 101.91/27.17 U331 < proper 101.91/27.17 U341 < proper 101.91/27.17 tail < proper 101.91/27.17 take < proper 101.91/27.17 sel < proper 101.91/27.17 proper < top 101.91/27.17 101.91/27.17 ---------------------------------------- 101.91/27.17 101.91/27.17 (83) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.17 Proved the following rewrite lemma: 101.91/27.17 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 101.91/27.17 101.91/27.17 Induction Base: 101.91/27.17 U243(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.17 101.91/27.17 Induction Step: 101.91/27.17 U243(gen_tt:mark:nil:0':ok3_0(+(1, +(n403763_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.17 mark(U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.17 mark(*4_0) 101.91/27.17 101.91/27.17 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.17 ---------------------------------------- 101.91/27.17 101.91/27.17 (84) 101.91/27.17 Obligation: 101.91/27.17 TRS: 101.91/27.17 Rules: 101.91/27.17 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.17 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.17 active(U106(tt)) -> mark(tt) 101.91/27.17 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.17 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.17 active(U112(tt)) -> mark(tt) 101.91/27.17 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.17 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.17 active(U122(tt)) -> mark(tt) 101.91/27.17 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.17 active(U131(tt)) -> mark(tt) 101.91/27.17 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.17 active(U141(tt)) -> mark(tt) 101.91/27.17 active(U151(tt)) -> mark(tt) 101.91/27.17 active(U161(tt)) -> mark(tt) 101.91/27.17 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.17 active(U172(tt)) -> mark(tt) 101.91/27.17 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.17 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.17 active(U183(tt)) -> mark(tt) 101.91/27.17 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.17 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.17 active(U193(tt)) -> mark(tt) 101.91/27.17 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.17 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.17 active(U206(tt)) -> mark(tt) 101.91/27.17 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.17 active(U211(tt)) -> mark(tt) 101.91/27.17 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.17 active(U221(tt)) -> mark(tt) 101.91/27.17 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.17 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.17 active(U232(tt)) -> mark(tt) 101.91/27.17 active(U24(tt, X)) -> mark(X) 101.91/27.17 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.17 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.17 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.17 active(U246(tt)) -> mark(tt) 101.91/27.17 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.17 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.17 active(U256(tt)) -> mark(tt) 101.91/27.17 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.17 active(U262(tt)) -> mark(tt) 101.91/27.17 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.17 active(U272(tt)) -> mark(tt) 101.91/27.17 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.17 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.17 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.17 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.17 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.17 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.17 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.17 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.17 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.17 active(U304(tt, Y)) -> mark(Y) 101.91/27.17 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.17 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.17 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.17 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.17 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.17 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.17 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.17 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.17 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.17 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.17 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.17 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.17 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.17 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.17 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.17 active(U334(tt, XS)) -> mark(XS) 101.91/27.17 active(U34(tt, N)) -> mark(N) 101.91/27.17 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.17 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.17 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.17 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.17 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.17 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.17 active(U46(tt)) -> mark(tt) 101.91/27.17 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.17 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.17 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.17 active(U56(tt)) -> mark(tt) 101.91/27.17 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.17 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.17 active(U63(tt)) -> mark(tt) 101.91/27.17 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.17 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.17 active(U73(tt)) -> mark(tt) 101.91/27.17 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.17 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.17 active(U83(tt)) -> mark(tt) 101.91/27.17 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.17 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.17 active(U93(tt)) -> mark(tt) 101.91/27.17 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.17 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.17 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.17 active(isLNat(nil)) -> mark(tt) 101.91/27.17 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.17 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.17 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.17 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.17 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isLNatKind(nil)) -> mark(tt) 101.91/27.17 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.17 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.17 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.17 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.17 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.17 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.17 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.17 active(isNatural(0')) -> mark(tt) 101.91/27.17 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.17 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.17 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isNaturalKind(0')) -> mark(tt) 101.91/27.17 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.17 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.17 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.17 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.17 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.17 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.17 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.17 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.17 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.17 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.17 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.17 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.17 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.17 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.17 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.17 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.17 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.17 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.17 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.17 active(U106(X)) -> U106(active(X)) 101.91/27.17 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.17 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.17 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.17 active(U112(X)) -> U112(active(X)) 101.91/27.17 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.17 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.17 active(U122(X)) -> U122(active(X)) 101.91/27.17 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.17 active(U131(X)) -> U131(active(X)) 101.91/27.17 active(snd(X)) -> snd(active(X)) 101.91/27.17 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.17 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.17 active(U141(X)) -> U141(active(X)) 101.91/27.17 active(U151(X)) -> U151(active(X)) 101.91/27.17 active(U161(X)) -> U161(active(X)) 101.91/27.17 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.17 active(U172(X)) -> U172(active(X)) 101.91/27.17 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.17 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.17 active(U183(X)) -> U183(active(X)) 101.91/27.17 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.17 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.17 active(U193(X)) -> U193(active(X)) 101.91/27.17 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.17 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.17 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.17 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.17 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.17 active(U206(X)) -> U206(active(X)) 101.91/27.17 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.17 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.17 active(U211(X)) -> U211(active(X)) 101.91/27.17 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.17 active(U221(X)) -> U221(active(X)) 101.91/27.17 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.17 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.17 active(U232(X)) -> U232(active(X)) 101.91/27.17 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.17 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.17 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.17 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.17 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.17 active(U246(X)) -> U246(active(X)) 101.91/27.17 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.17 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.17 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.17 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.17 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.17 active(U256(X)) -> U256(active(X)) 101.91/27.17 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.17 active(U262(X)) -> U262(active(X)) 101.91/27.17 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.17 active(U272(X)) -> U272(active(X)) 101.91/27.17 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.17 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.17 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.17 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.17 active(s(X)) -> s(active(X)) 101.91/27.17 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.17 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.17 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.17 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.17 active(head(X)) -> head(active(X)) 101.91/27.17 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.17 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.17 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.17 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.17 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.17 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.17 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.17 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.17 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.17 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.17 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.17 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.17 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.17 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.17 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.17 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.17 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.17 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.17 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.17 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.17 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.17 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.17 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.17 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.17 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.17 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.17 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.17 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.17 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.17 active(fst(X)) -> fst(active(X)) 101.91/27.17 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.17 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.17 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.17 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.17 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.17 active(U46(X)) -> U46(active(X)) 101.91/27.17 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.17 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.17 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.17 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.17 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.17 active(U56(X)) -> U56(active(X)) 101.91/27.17 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.17 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.17 active(U63(X)) -> U63(active(X)) 101.91/27.17 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.17 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.17 active(U73(X)) -> U73(active(X)) 101.91/27.17 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.17 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.17 active(U83(X)) -> U83(active(X)) 101.91/27.17 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.17 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.17 active(U93(X)) -> U93(active(X)) 101.91/27.17 active(tail(X)) -> tail(active(X)) 101.91/27.17 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.17 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.17 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.17 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.17 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.17 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.17 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.17 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.17 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.17 U106(mark(X)) -> mark(U106(X)) 101.91/27.17 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.17 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.17 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.17 U112(mark(X)) -> mark(U112(X)) 101.91/27.17 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.17 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.17 U122(mark(X)) -> mark(U122(X)) 101.91/27.17 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.17 U131(mark(X)) -> mark(U131(X)) 101.91/27.17 snd(mark(X)) -> mark(snd(X)) 101.91/27.17 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.17 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.17 U141(mark(X)) -> mark(U141(X)) 101.91/27.17 U151(mark(X)) -> mark(U151(X)) 101.91/27.17 U161(mark(X)) -> mark(U161(X)) 101.91/27.17 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.17 U172(mark(X)) -> mark(U172(X)) 101.91/27.17 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.17 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.17 U183(mark(X)) -> mark(U183(X)) 101.91/27.17 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.17 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.17 U193(mark(X)) -> mark(U193(X)) 101.91/27.17 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.17 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.17 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.17 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.17 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.17 U206(mark(X)) -> mark(U206(X)) 101.91/27.17 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.17 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.17 U211(mark(X)) -> mark(U211(X)) 101.91/27.17 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.17 U221(mark(X)) -> mark(U221(X)) 101.91/27.17 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.17 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.17 U232(mark(X)) -> mark(U232(X)) 101.91/27.17 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.17 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.17 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.17 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.17 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.17 U246(mark(X)) -> mark(U246(X)) 101.91/27.17 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.17 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.17 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.17 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.17 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.17 U256(mark(X)) -> mark(U256(X)) 101.91/27.17 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.17 U262(mark(X)) -> mark(U262(X)) 101.91/27.17 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.17 U272(mark(X)) -> mark(U272(X)) 101.91/27.17 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.17 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.17 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.17 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.17 s(mark(X)) -> mark(s(X)) 101.91/27.17 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.17 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.17 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.17 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.17 head(mark(X)) -> mark(head(X)) 101.91/27.17 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.17 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.17 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.17 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.17 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.17 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.17 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.17 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.17 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.17 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.17 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.17 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.17 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.17 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.17 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.17 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.17 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.17 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.17 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.17 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.17 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.17 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.17 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.17 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.17 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.17 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.17 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.17 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.17 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.17 fst(mark(X)) -> mark(fst(X)) 101.91/27.17 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.17 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.17 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.17 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.17 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.17 U46(mark(X)) -> mark(U46(X)) 101.91/27.17 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.17 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.17 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.17 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.17 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.17 U56(mark(X)) -> mark(U56(X)) 101.91/27.17 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.17 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.17 U63(mark(X)) -> mark(U63(X)) 101.91/27.17 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.17 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.17 U73(mark(X)) -> mark(U73(X)) 101.91/27.17 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.17 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.17 U83(mark(X)) -> mark(U83(X)) 101.91/27.17 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.17 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.17 U93(mark(X)) -> mark(U93(X)) 101.91/27.17 tail(mark(X)) -> mark(tail(X)) 101.91/27.17 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.17 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.17 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.17 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.17 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(tt) -> ok(tt) 101.91/27.17 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.17 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.17 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.17 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.17 proper(U106(X)) -> U106(proper(X)) 101.91/27.17 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.17 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.17 proper(U112(X)) -> U112(proper(X)) 101.91/27.17 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.17 proper(U122(X)) -> U122(proper(X)) 101.91/27.17 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U131(X)) -> U131(proper(X)) 101.91/27.17 proper(snd(X)) -> snd(proper(X)) 101.91/27.17 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.17 proper(U141(X)) -> U141(proper(X)) 101.91/27.17 proper(U151(X)) -> U151(proper(X)) 101.91/27.17 proper(U161(X)) -> U161(proper(X)) 101.91/27.17 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.17 proper(U172(X)) -> U172(proper(X)) 101.91/27.17 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.17 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.17 proper(U183(X)) -> U183(proper(X)) 101.91/27.17 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.17 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.17 proper(U193(X)) -> U193(proper(X)) 101.91/27.17 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.17 proper(U206(X)) -> U206(proper(X)) 101.91/27.17 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U211(X)) -> U211(proper(X)) 101.91/27.17 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U221(X)) -> U221(proper(X)) 101.91/27.17 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.17 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.17 proper(U232(X)) -> U232(proper(X)) 101.91/27.17 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.17 proper(U246(X)) -> U246(proper(X)) 101.91/27.17 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.17 proper(U256(X)) -> U256(proper(X)) 101.91/27.17 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.17 proper(U262(X)) -> U262(proper(X)) 101.91/27.17 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.17 proper(U272(X)) -> U272(proper(X)) 101.91/27.17 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.17 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.17 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.17 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.17 proper(s(X)) -> s(proper(X)) 101.91/27.17 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(head(X)) -> head(proper(X)) 101.91/27.17 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.17 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.17 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.17 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.17 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.17 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.17 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.17 proper(nil) -> ok(nil) 101.91/27.17 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.17 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.17 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.17 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.17 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.17 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.17 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(fst(X)) -> fst(proper(X)) 101.91/27.17 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.17 proper(U46(X)) -> U46(proper(X)) 101.91/27.17 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.17 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.17 proper(U56(X)) -> U56(proper(X)) 101.91/27.17 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.17 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.17 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.17 proper(U63(X)) -> U63(proper(X)) 101.91/27.17 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.17 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.17 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.17 proper(U73(X)) -> U73(proper(X)) 101.91/27.17 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.17 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.17 proper(U83(X)) -> U83(proper(X)) 101.91/27.17 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.17 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.17 proper(U93(X)) -> U93(proper(X)) 101.91/27.17 proper(tail(X)) -> tail(proper(X)) 101.91/27.17 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.17 proper(0') -> ok(0') 101.91/27.17 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.17 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.17 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.17 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.17 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.17 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.17 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.17 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.17 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.17 U106(ok(X)) -> ok(U106(X)) 101.91/27.17 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.17 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.17 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.17 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.17 U112(ok(X)) -> ok(U112(X)) 101.91/27.17 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.17 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.17 U122(ok(X)) -> ok(U122(X)) 101.91/27.17 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.17 U131(ok(X)) -> ok(U131(X)) 101.91/27.17 snd(ok(X)) -> ok(snd(X)) 101.91/27.17 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.17 U141(ok(X)) -> ok(U141(X)) 101.91/27.17 U151(ok(X)) -> ok(U151(X)) 101.91/27.17 U161(ok(X)) -> ok(U161(X)) 101.91/27.17 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.17 U172(ok(X)) -> ok(U172(X)) 101.91/27.17 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.17 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.17 U183(ok(X)) -> ok(U183(X)) 101.91/27.17 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.17 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.17 U193(ok(X)) -> ok(U193(X)) 101.91/27.17 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.17 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.17 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.17 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.17 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.17 U206(ok(X)) -> ok(U206(X)) 101.91/27.17 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.17 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.17 U211(ok(X)) -> ok(U211(X)) 101.91/27.17 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.17 U221(ok(X)) -> ok(U221(X)) 101.91/27.17 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.17 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.17 U232(ok(X)) -> ok(U232(X)) 101.91/27.17 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.17 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.17 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.17 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.17 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.17 U246(ok(X)) -> ok(U246(X)) 101.91/27.17 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.17 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.17 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.17 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.17 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.17 U256(ok(X)) -> ok(U256(X)) 101.91/27.17 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.17 U262(ok(X)) -> ok(U262(X)) 101.91/27.17 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.17 U272(ok(X)) -> ok(U272(X)) 101.91/27.17 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.17 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.17 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.17 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.17 s(ok(X)) -> ok(s(X)) 101.91/27.17 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.17 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.17 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.17 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.17 head(ok(X)) -> ok(head(X)) 101.91/27.17 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.17 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.17 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.17 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.17 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.17 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.17 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.17 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.17 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.17 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.17 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.17 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.17 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.17 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.17 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.17 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.17 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.17 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.17 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.17 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.17 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.17 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.17 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.17 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.17 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.17 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.17 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.17 fst(ok(X)) -> ok(fst(X)) 101.91/27.17 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.17 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.17 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.17 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.17 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.17 U46(ok(X)) -> ok(U46(X)) 101.91/27.17 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.17 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.17 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.17 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.17 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.17 U56(ok(X)) -> ok(U56(X)) 101.91/27.17 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.17 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.17 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.17 U63(ok(X)) -> ok(U63(X)) 101.91/27.17 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.17 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.17 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.17 U73(ok(X)) -> ok(U73(X)) 101.91/27.17 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.17 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.17 U83(ok(X)) -> ok(U83(X)) 101.91/27.17 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.17 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.17 U93(ok(X)) -> ok(U93(X)) 101.91/27.17 tail(ok(X)) -> ok(tail(X)) 101.91/27.17 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.17 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.17 top(mark(X)) -> top(proper(X)) 101.91/27.17 top(ok(X)) -> top(active(X)) 101.91/27.17 101.91/27.17 Types: 101.91/27.17 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 tt :: tt:mark:nil:0':ok 101.91/27.17 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 nil :: tt:mark:nil:0':ok 101.91/27.17 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 0' :: tt:mark:nil:0':ok 101.91/27.17 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.17 top :: tt:mark:nil:0':ok -> top 101.91/27.17 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.17 hole_top2_0 :: top 101.91/27.17 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.17 101.91/27.17 101.91/27.17 Lemmas: 101.91/27.17 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.17 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.17 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.17 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.17 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.17 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.17 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.17 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.17 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.17 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.17 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.17 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.17 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.17 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.17 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.17 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.17 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.17 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.17 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.17 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.17 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.17 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.17 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.17 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.17 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.17 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.17 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 101.91/27.17 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 101.91/27.17 101.91/27.17 101.91/27.17 Generator Equations: 101.91/27.17 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.17 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.17 101.91/27.17 101.91/27.17 The following defined symbols remain to be analysed: 101.91/27.17 U244, active, U245, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.17 101.91/27.17 They will be analysed ascendingly in the following order: 101.91/27.17 U244 < active 101.91/27.17 U245 < active 101.91/27.17 U246 < active 101.91/27.17 U252 < active 101.91/27.17 U253 < active 101.91/27.17 U254 < active 101.91/27.17 U255 < active 101.91/27.17 U256 < active 101.91/27.17 U262 < active 101.91/27.17 U272 < active 101.91/27.17 U282 < active 101.91/27.17 cons < active 101.91/27.17 natsFrom < active 101.91/27.17 s < active 101.91/27.17 U292 < active 101.91/27.17 U293 < active 101.91/27.17 U294 < active 101.91/27.17 head < active 101.91/27.17 afterNth < active 101.91/27.17 U302 < active 101.91/27.17 U303 < active 101.91/27.17 U304 < active 101.91/27.17 U32 < active 101.91/27.17 U312 < active 101.91/27.17 pair < active 101.91/27.17 U33 < active 101.91/27.17 U322 < active 101.91/27.17 U323 < active 101.91/27.17 U324 < active 101.91/27.17 U325 < active 101.91/27.17 U326 < active 101.91/27.17 U327 < active 101.91/27.17 U34 < active 101.91/27.17 U332 < active 101.91/27.17 U333 < active 101.91/27.17 U334 < active 101.91/27.17 U342 < active 101.91/27.17 U343 < active 101.91/27.17 U344 < active 101.91/27.17 fst < active 101.91/27.17 U42 < active 101.91/27.17 U43 < active 101.91/27.17 U44 < active 101.91/27.17 U45 < active 101.91/27.17 U46 < active 101.91/27.17 U52 < active 101.91/27.17 U53 < active 101.91/27.17 U54 < active 101.91/27.17 U55 < active 101.91/27.17 U56 < active 101.91/27.17 U62 < active 101.91/27.17 isPLNatKind < active 101.91/27.17 U63 < active 101.91/27.17 isPLNat < active 101.91/27.17 U72 < active 101.91/27.17 U73 < active 101.91/27.17 U82 < active 101.91/27.17 U83 < active 101.91/27.17 U92 < active 101.91/27.17 U93 < active 101.91/27.17 U11 < active 101.91/27.17 U21 < active 101.91/27.17 U31 < active 101.91/27.17 U41 < active 101.91/27.17 U51 < active 101.91/27.17 U61 < active 101.91/27.17 U71 < active 101.91/27.17 U81 < active 101.91/27.17 U91 < active 101.91/27.17 U101 < active 101.91/27.17 U111 < active 101.91/27.17 U121 < active 101.91/27.17 U131 < active 101.91/27.17 U141 < active 101.91/27.17 U151 < active 101.91/27.17 U161 < active 101.91/27.17 U171 < active 101.91/27.17 U181 < active 101.91/27.17 U191 < active 101.91/27.17 U201 < active 101.91/27.17 U211 < active 101.91/27.17 U221 < active 101.91/27.17 U231 < active 101.91/27.17 U241 < active 101.91/27.17 U251 < active 101.91/27.17 U261 < active 101.91/27.17 U271 < active 101.91/27.17 U281 < active 101.91/27.17 U291 < active 101.91/27.17 U301 < active 101.91/27.17 U311 < active 101.91/27.17 U321 < active 101.91/27.17 U331 < active 101.91/27.17 U341 < active 101.91/27.17 tail < active 101.91/27.17 take < active 101.91/27.17 sel < active 101.91/27.17 active < top 101.91/27.17 U244 < proper 101.91/27.17 U245 < proper 101.91/27.17 U246 < proper 101.91/27.17 U252 < proper 101.91/27.17 U253 < proper 101.91/27.17 U254 < proper 101.91/27.17 U255 < proper 101.91/27.17 U256 < proper 101.91/27.17 U262 < proper 101.91/27.17 U272 < proper 101.91/27.17 U282 < proper 101.91/27.17 cons < proper 101.91/27.17 natsFrom < proper 101.91/27.17 s < proper 101.91/27.17 U292 < proper 101.91/27.17 U293 < proper 101.91/27.17 U294 < proper 101.91/27.17 head < proper 101.91/27.17 afterNth < proper 101.91/27.17 U302 < proper 101.91/27.17 U303 < proper 101.91/27.17 U304 < proper 101.91/27.17 U32 < proper 101.91/27.17 U312 < proper 101.91/27.17 pair < proper 101.91/27.17 U33 < proper 101.91/27.17 U322 < proper 101.91/27.17 U323 < proper 101.91/27.17 U324 < proper 101.91/27.17 U325 < proper 101.91/27.17 U326 < proper 101.91/27.17 U327 < proper 101.91/27.17 U34 < proper 101.91/27.17 U332 < proper 101.91/27.17 U333 < proper 101.91/27.17 U334 < proper 101.91/27.17 U342 < proper 101.91/27.17 U343 < proper 101.91/27.17 U344 < proper 101.91/27.17 fst < proper 101.91/27.17 U42 < proper 101.91/27.17 U43 < proper 101.91/27.17 U44 < proper 101.91/27.17 U45 < proper 101.91/27.17 U46 < proper 101.91/27.17 U52 < proper 101.91/27.17 U53 < proper 101.91/27.17 U54 < proper 101.91/27.17 U55 < proper 101.91/27.17 U56 < proper 101.91/27.17 U62 < proper 101.91/27.17 isPLNatKind < proper 101.91/27.17 U63 < proper 101.91/27.17 isPLNat < proper 101.91/27.17 U72 < proper 101.91/27.17 U73 < proper 101.91/27.17 U82 < proper 101.91/27.17 U83 < proper 101.91/27.17 U92 < proper 101.91/27.17 U93 < proper 101.91/27.17 U11 < proper 101.91/27.17 U21 < proper 101.91/27.17 U31 < proper 101.91/27.17 U41 < proper 101.91/27.17 U51 < proper 101.91/27.17 U61 < proper 101.91/27.17 U71 < proper 101.91/27.17 U81 < proper 101.91/27.17 U91 < proper 101.91/27.17 U101 < proper 101.91/27.17 U111 < proper 101.91/27.17 U121 < proper 101.91/27.17 U131 < proper 101.91/27.17 U141 < proper 101.91/27.18 U151 < proper 101.91/27.18 U161 < proper 101.91/27.18 U171 < proper 101.91/27.18 U181 < proper 101.91/27.18 U191 < proper 101.91/27.18 U201 < proper 101.91/27.18 U211 < proper 101.91/27.18 U221 < proper 101.91/27.18 U231 < proper 101.91/27.18 U241 < proper 101.91/27.18 U251 < proper 101.91/27.18 U261 < proper 101.91/27.18 U271 < proper 101.91/27.18 U281 < proper 101.91/27.18 U291 < proper 101.91/27.18 U301 < proper 101.91/27.18 U311 < proper 101.91/27.18 U321 < proper 101.91/27.18 U331 < proper 101.91/27.18 U341 < proper 101.91/27.18 tail < proper 101.91/27.18 take < proper 101.91/27.18 sel < proper 101.91/27.18 proper < top 101.91/27.18 101.91/27.18 ---------------------------------------- 101.91/27.18 101.91/27.18 (85) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.18 Proved the following rewrite lemma: 101.91/27.18 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 101.91/27.18 101.91/27.18 Induction Base: 101.91/27.18 U244(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 101.91/27.18 101.91/27.18 Induction Step: 101.91/27.18 U244(gen_tt:mark:nil:0':ok3_0(+(1, +(n433981_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 101.91/27.18 mark(U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 101.91/27.18 mark(*4_0) 101.91/27.18 101.91/27.18 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.18 ---------------------------------------- 101.91/27.18 101.91/27.18 (86) 101.91/27.18 Obligation: 101.91/27.18 TRS: 101.91/27.18 Rules: 101.91/27.18 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.18 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.18 active(U106(tt)) -> mark(tt) 101.91/27.18 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.18 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.18 active(U112(tt)) -> mark(tt) 101.91/27.18 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.18 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.18 active(U122(tt)) -> mark(tt) 101.91/27.18 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.18 active(U131(tt)) -> mark(tt) 101.91/27.18 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.18 active(U141(tt)) -> mark(tt) 101.91/27.18 active(U151(tt)) -> mark(tt) 101.91/27.18 active(U161(tt)) -> mark(tt) 101.91/27.18 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.18 active(U172(tt)) -> mark(tt) 101.91/27.18 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.18 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.18 active(U183(tt)) -> mark(tt) 101.91/27.18 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.18 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.18 active(U193(tt)) -> mark(tt) 101.91/27.18 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.18 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.18 active(U206(tt)) -> mark(tt) 101.91/27.18 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.18 active(U211(tt)) -> mark(tt) 101.91/27.18 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.18 active(U221(tt)) -> mark(tt) 101.91/27.18 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.18 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.18 active(U232(tt)) -> mark(tt) 101.91/27.18 active(U24(tt, X)) -> mark(X) 101.91/27.18 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.18 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.18 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.18 active(U246(tt)) -> mark(tt) 101.91/27.18 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.18 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.18 active(U256(tt)) -> mark(tt) 101.91/27.18 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.18 active(U262(tt)) -> mark(tt) 101.91/27.18 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.18 active(U272(tt)) -> mark(tt) 101.91/27.18 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.18 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.18 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.18 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.18 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.18 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.18 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.18 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.18 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.18 active(U304(tt, Y)) -> mark(Y) 101.91/27.18 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.18 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.18 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.18 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.18 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.18 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.18 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.18 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.18 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.18 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.18 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.18 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.18 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.18 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.18 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.18 active(U334(tt, XS)) -> mark(XS) 101.91/27.18 active(U34(tt, N)) -> mark(N) 101.91/27.18 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.18 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.18 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.18 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.18 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.18 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.18 active(U46(tt)) -> mark(tt) 101.91/27.18 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.18 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.18 active(U56(tt)) -> mark(tt) 101.91/27.18 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.18 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.18 active(U63(tt)) -> mark(tt) 101.91/27.18 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.18 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.18 active(U73(tt)) -> mark(tt) 101.91/27.18 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.18 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.18 active(U83(tt)) -> mark(tt) 101.91/27.18 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.18 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.18 active(U93(tt)) -> mark(tt) 101.91/27.18 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.18 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.18 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.18 active(isLNat(nil)) -> mark(tt) 101.91/27.18 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.18 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.18 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.18 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.18 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNatKind(nil)) -> mark(tt) 101.91/27.18 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.18 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.18 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.18 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.18 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.18 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.18 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.18 active(isNatural(0')) -> mark(tt) 101.91/27.18 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.18 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.18 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isNaturalKind(0')) -> mark(tt) 101.91/27.18 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.18 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.18 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.18 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.18 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.18 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.18 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.18 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.18 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.18 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.18 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.18 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.18 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.18 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.18 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.18 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.18 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.18 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.18 active(U106(X)) -> U106(active(X)) 101.91/27.18 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.18 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.18 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.18 active(U112(X)) -> U112(active(X)) 101.91/27.18 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.18 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.18 active(U122(X)) -> U122(active(X)) 101.91/27.18 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.18 active(U131(X)) -> U131(active(X)) 101.91/27.18 active(snd(X)) -> snd(active(X)) 101.91/27.18 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.18 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.18 active(U141(X)) -> U141(active(X)) 101.91/27.18 active(U151(X)) -> U151(active(X)) 101.91/27.18 active(U161(X)) -> U161(active(X)) 101.91/27.18 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.18 active(U172(X)) -> U172(active(X)) 101.91/27.18 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.18 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.18 active(U183(X)) -> U183(active(X)) 101.91/27.18 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.18 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.18 active(U193(X)) -> U193(active(X)) 101.91/27.18 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.18 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.18 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.18 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.18 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.18 active(U206(X)) -> U206(active(X)) 101.91/27.18 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.18 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.18 active(U211(X)) -> U211(active(X)) 101.91/27.18 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.18 active(U221(X)) -> U221(active(X)) 101.91/27.18 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.18 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.18 active(U232(X)) -> U232(active(X)) 101.91/27.18 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.18 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.18 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.18 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.18 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.18 active(U246(X)) -> U246(active(X)) 101.91/27.18 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.18 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.18 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.18 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.18 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.18 active(U256(X)) -> U256(active(X)) 101.91/27.18 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.18 active(U262(X)) -> U262(active(X)) 101.91/27.18 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.18 active(U272(X)) -> U272(active(X)) 101.91/27.18 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.18 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.18 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.18 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.18 active(s(X)) -> s(active(X)) 101.91/27.18 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.18 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.18 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.18 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.18 active(head(X)) -> head(active(X)) 101.91/27.18 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.18 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.18 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.18 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.18 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.18 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.18 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.18 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.18 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.18 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.18 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.18 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.18 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.18 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.18 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.18 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.18 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.18 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.18 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.18 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.18 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.18 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.18 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.18 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.18 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.18 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.18 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.18 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.18 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.18 active(fst(X)) -> fst(active(X)) 101.91/27.18 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.18 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.18 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.18 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.18 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.18 active(U46(X)) -> U46(active(X)) 101.91/27.18 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.18 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.18 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.18 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.18 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.18 active(U56(X)) -> U56(active(X)) 101.91/27.18 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.18 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.18 active(U63(X)) -> U63(active(X)) 101.91/27.18 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.18 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.18 active(U73(X)) -> U73(active(X)) 101.91/27.18 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.18 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.18 active(U83(X)) -> U83(active(X)) 101.91/27.18 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.18 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.18 active(U93(X)) -> U93(active(X)) 101.91/27.18 active(tail(X)) -> tail(active(X)) 101.91/27.18 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.18 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.18 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.18 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.18 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.18 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.18 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.18 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.18 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.18 U106(mark(X)) -> mark(U106(X)) 101.91/27.18 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.18 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.18 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.18 U112(mark(X)) -> mark(U112(X)) 101.91/27.18 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.18 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.18 U122(mark(X)) -> mark(U122(X)) 101.91/27.18 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.18 U131(mark(X)) -> mark(U131(X)) 101.91/27.18 snd(mark(X)) -> mark(snd(X)) 101.91/27.18 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.18 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.18 U141(mark(X)) -> mark(U141(X)) 101.91/27.18 U151(mark(X)) -> mark(U151(X)) 101.91/27.18 U161(mark(X)) -> mark(U161(X)) 101.91/27.18 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.18 U172(mark(X)) -> mark(U172(X)) 101.91/27.18 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.18 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.18 U183(mark(X)) -> mark(U183(X)) 101.91/27.18 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.18 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.18 U193(mark(X)) -> mark(U193(X)) 101.91/27.18 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.18 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.18 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.18 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.18 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.18 U206(mark(X)) -> mark(U206(X)) 101.91/27.18 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.18 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.18 U211(mark(X)) -> mark(U211(X)) 101.91/27.18 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.18 U221(mark(X)) -> mark(U221(X)) 101.91/27.18 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.18 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.18 U232(mark(X)) -> mark(U232(X)) 101.91/27.18 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.18 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.18 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.18 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.18 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.18 U246(mark(X)) -> mark(U246(X)) 101.91/27.18 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.18 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.18 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.18 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.18 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.18 U256(mark(X)) -> mark(U256(X)) 101.91/27.18 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.18 U262(mark(X)) -> mark(U262(X)) 101.91/27.18 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.18 U272(mark(X)) -> mark(U272(X)) 101.91/27.18 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.18 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.18 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.18 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.18 s(mark(X)) -> mark(s(X)) 101.91/27.18 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.18 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.18 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.18 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.18 head(mark(X)) -> mark(head(X)) 101.91/27.18 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.18 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.18 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.18 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.18 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.18 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.18 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.18 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.18 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.18 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.18 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.18 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.18 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.18 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.18 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.18 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.18 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.18 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.18 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.18 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.18 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.18 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.18 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.18 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.18 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.18 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.18 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.18 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.18 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.18 fst(mark(X)) -> mark(fst(X)) 101.91/27.18 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.18 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.18 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.18 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.18 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.18 U46(mark(X)) -> mark(U46(X)) 101.91/27.18 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.18 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.18 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.18 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.18 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.18 U56(mark(X)) -> mark(U56(X)) 101.91/27.18 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.18 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.18 U63(mark(X)) -> mark(U63(X)) 101.91/27.18 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.18 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.18 U73(mark(X)) -> mark(U73(X)) 101.91/27.18 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.18 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.18 U83(mark(X)) -> mark(U83(X)) 101.91/27.18 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.18 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.18 U93(mark(X)) -> mark(U93(X)) 101.91/27.18 tail(mark(X)) -> mark(tail(X)) 101.91/27.18 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.18 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.18 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.18 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.18 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(tt) -> ok(tt) 101.91/27.18 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.18 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.18 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.18 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.18 proper(U106(X)) -> U106(proper(X)) 101.91/27.18 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.18 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.18 proper(U112(X)) -> U112(proper(X)) 101.91/27.18 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.18 proper(U122(X)) -> U122(proper(X)) 101.91/27.18 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U131(X)) -> U131(proper(X)) 101.91/27.18 proper(snd(X)) -> snd(proper(X)) 101.91/27.18 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.18 proper(U141(X)) -> U141(proper(X)) 101.91/27.18 proper(U151(X)) -> U151(proper(X)) 101.91/27.18 proper(U161(X)) -> U161(proper(X)) 101.91/27.18 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.18 proper(U172(X)) -> U172(proper(X)) 101.91/27.18 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.18 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.18 proper(U183(X)) -> U183(proper(X)) 101.91/27.18 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.18 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.18 proper(U193(X)) -> U193(proper(X)) 101.91/27.18 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.18 proper(U206(X)) -> U206(proper(X)) 101.91/27.18 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U211(X)) -> U211(proper(X)) 101.91/27.18 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U221(X)) -> U221(proper(X)) 101.91/27.18 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.18 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.18 proper(U232(X)) -> U232(proper(X)) 101.91/27.18 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.18 proper(U246(X)) -> U246(proper(X)) 101.91/27.18 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.18 proper(U256(X)) -> U256(proper(X)) 101.91/27.18 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.18 proper(U262(X)) -> U262(proper(X)) 101.91/27.18 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.18 proper(U272(X)) -> U272(proper(X)) 101.91/27.18 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.18 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.18 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.18 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.18 proper(s(X)) -> s(proper(X)) 101.91/27.18 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(head(X)) -> head(proper(X)) 101.91/27.18 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.18 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.18 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.18 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.18 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.18 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.18 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.18 proper(nil) -> ok(nil) 101.91/27.18 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.18 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.18 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.18 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.18 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.18 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(fst(X)) -> fst(proper(X)) 101.91/27.18 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.18 proper(U46(X)) -> U46(proper(X)) 101.91/27.18 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.18 proper(U56(X)) -> U56(proper(X)) 101.91/27.18 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.18 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.18 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.18 proper(U63(X)) -> U63(proper(X)) 101.91/27.18 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.18 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.18 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.18 proper(U73(X)) -> U73(proper(X)) 101.91/27.18 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.18 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.18 proper(U83(X)) -> U83(proper(X)) 101.91/27.18 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.18 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.18 proper(U93(X)) -> U93(proper(X)) 101.91/27.18 proper(tail(X)) -> tail(proper(X)) 101.91/27.18 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.18 proper(0') -> ok(0') 101.91/27.18 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.18 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.18 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.18 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.18 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.18 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.18 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.18 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.18 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.18 U106(ok(X)) -> ok(U106(X)) 101.91/27.18 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.18 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.18 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.18 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.18 U112(ok(X)) -> ok(U112(X)) 101.91/27.18 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.18 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.18 U122(ok(X)) -> ok(U122(X)) 101.91/27.18 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.18 U131(ok(X)) -> ok(U131(X)) 101.91/27.18 snd(ok(X)) -> ok(snd(X)) 101.91/27.18 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.18 U141(ok(X)) -> ok(U141(X)) 101.91/27.18 U151(ok(X)) -> ok(U151(X)) 101.91/27.18 U161(ok(X)) -> ok(U161(X)) 101.91/27.18 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.18 U172(ok(X)) -> ok(U172(X)) 101.91/27.18 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.18 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.18 U183(ok(X)) -> ok(U183(X)) 101.91/27.18 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.18 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.18 U193(ok(X)) -> ok(U193(X)) 101.91/27.18 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.18 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.18 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.18 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.18 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.18 U206(ok(X)) -> ok(U206(X)) 101.91/27.18 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.18 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.18 U211(ok(X)) -> ok(U211(X)) 101.91/27.18 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.18 U221(ok(X)) -> ok(U221(X)) 101.91/27.18 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.18 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.18 U232(ok(X)) -> ok(U232(X)) 101.91/27.18 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.18 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.18 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.18 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.18 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.18 U246(ok(X)) -> ok(U246(X)) 101.91/27.18 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.18 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.18 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.18 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.18 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.18 U256(ok(X)) -> ok(U256(X)) 101.91/27.18 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.18 U262(ok(X)) -> ok(U262(X)) 101.91/27.18 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.18 U272(ok(X)) -> ok(U272(X)) 101.91/27.18 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.18 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.18 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.18 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.18 s(ok(X)) -> ok(s(X)) 101.91/27.18 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.18 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.18 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.18 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.18 head(ok(X)) -> ok(head(X)) 101.91/27.18 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.18 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.18 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.18 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.18 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.18 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.18 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.18 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.18 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.18 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.18 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.18 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.18 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.18 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.18 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.18 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.18 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.18 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.18 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.18 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.18 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.18 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.18 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.18 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.18 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.18 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.18 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.18 fst(ok(X)) -> ok(fst(X)) 101.91/27.18 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.18 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.18 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.18 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.18 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.18 U46(ok(X)) -> ok(U46(X)) 101.91/27.18 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.18 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.18 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.18 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.18 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.18 U56(ok(X)) -> ok(U56(X)) 101.91/27.18 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.18 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.18 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.18 U63(ok(X)) -> ok(U63(X)) 101.91/27.18 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.18 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.18 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.18 U73(ok(X)) -> ok(U73(X)) 101.91/27.18 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.18 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.18 U83(ok(X)) -> ok(U83(X)) 101.91/27.18 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.18 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.18 U93(ok(X)) -> ok(U93(X)) 101.91/27.18 tail(ok(X)) -> ok(tail(X)) 101.91/27.18 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.18 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.18 top(mark(X)) -> top(proper(X)) 101.91/27.18 top(ok(X)) -> top(active(X)) 101.91/27.18 101.91/27.18 Types: 101.91/27.18 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 tt :: tt:mark:nil:0':ok 101.91/27.18 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 nil :: tt:mark:nil:0':ok 101.91/27.18 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 0' :: tt:mark:nil:0':ok 101.91/27.18 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 top :: tt:mark:nil:0':ok -> top 101.91/27.18 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.18 hole_top2_0 :: top 101.91/27.18 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.18 101.91/27.18 101.91/27.18 Lemmas: 101.91/27.18 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.18 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.18 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.18 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.18 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.18 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.18 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.18 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.18 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.18 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.18 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.18 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.18 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.18 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.18 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.18 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.18 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.18 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.18 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.18 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.18 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.18 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.18 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.18 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.18 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.18 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.18 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 101.91/27.18 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 101.91/27.18 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 101.91/27.18 101.91/27.18 101.91/27.18 Generator Equations: 101.91/27.18 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.18 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.18 101.91/27.18 101.91/27.18 The following defined symbols remain to be analysed: 101.91/27.18 U245, active, U246, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.18 101.91/27.18 They will be analysed ascendingly in the following order: 101.91/27.18 U245 < active 101.91/27.18 U246 < active 101.91/27.18 U252 < active 101.91/27.18 U253 < active 101.91/27.18 U254 < active 101.91/27.18 U255 < active 101.91/27.18 U256 < active 101.91/27.18 U262 < active 101.91/27.18 U272 < active 101.91/27.18 U282 < active 101.91/27.18 cons < active 101.91/27.18 natsFrom < active 101.91/27.18 s < active 101.91/27.18 U292 < active 101.91/27.18 U293 < active 101.91/27.18 U294 < active 101.91/27.18 head < active 101.91/27.18 afterNth < active 101.91/27.18 U302 < active 101.91/27.18 U303 < active 101.91/27.18 U304 < active 101.91/27.18 U32 < active 101.91/27.18 U312 < active 101.91/27.18 pair < active 101.91/27.18 U33 < active 101.91/27.18 U322 < active 101.91/27.18 U323 < active 101.91/27.18 U324 < active 101.91/27.18 U325 < active 101.91/27.18 U326 < active 101.91/27.18 U327 < active 101.91/27.18 U34 < active 101.91/27.18 U332 < active 101.91/27.18 U333 < active 101.91/27.18 U334 < active 101.91/27.18 U342 < active 101.91/27.18 U343 < active 101.91/27.18 U344 < active 101.91/27.18 fst < active 101.91/27.18 U42 < active 101.91/27.18 U43 < active 101.91/27.18 U44 < active 101.91/27.18 U45 < active 101.91/27.18 U46 < active 101.91/27.18 U52 < active 101.91/27.18 U53 < active 101.91/27.18 U54 < active 101.91/27.18 U55 < active 101.91/27.18 U56 < active 101.91/27.18 U62 < active 101.91/27.18 isPLNatKind < active 101.91/27.18 U63 < active 101.91/27.18 isPLNat < active 101.91/27.18 U72 < active 101.91/27.18 U73 < active 101.91/27.18 U82 < active 101.91/27.18 U83 < active 101.91/27.18 U92 < active 101.91/27.18 U93 < active 101.91/27.18 U11 < active 101.91/27.18 U21 < active 101.91/27.18 U31 < active 101.91/27.18 U41 < active 101.91/27.18 U51 < active 101.91/27.18 U61 < active 101.91/27.18 U71 < active 101.91/27.18 U81 < active 101.91/27.18 U91 < active 101.91/27.18 U101 < active 101.91/27.18 U111 < active 101.91/27.18 U121 < active 101.91/27.18 U131 < active 101.91/27.18 U141 < active 101.91/27.18 U151 < active 101.91/27.18 U161 < active 101.91/27.18 U171 < active 101.91/27.18 U181 < active 101.91/27.18 U191 < active 101.91/27.18 U201 < active 101.91/27.18 U211 < active 101.91/27.18 U221 < active 101.91/27.18 U231 < active 101.91/27.18 U241 < active 101.91/27.18 U251 < active 101.91/27.18 U261 < active 101.91/27.18 U271 < active 101.91/27.18 U281 < active 101.91/27.18 U291 < active 101.91/27.18 U301 < active 101.91/27.18 U311 < active 101.91/27.18 U321 < active 101.91/27.18 U331 < active 101.91/27.18 U341 < active 101.91/27.18 tail < active 101.91/27.18 take < active 101.91/27.18 sel < active 101.91/27.18 active < top 101.91/27.18 U245 < proper 101.91/27.18 U246 < proper 101.91/27.18 U252 < proper 101.91/27.18 U253 < proper 101.91/27.18 U254 < proper 101.91/27.18 U255 < proper 101.91/27.18 U256 < proper 101.91/27.18 U262 < proper 101.91/27.18 U272 < proper 101.91/27.18 U282 < proper 101.91/27.18 cons < proper 101.91/27.18 natsFrom < proper 101.91/27.18 s < proper 101.91/27.18 U292 < proper 101.91/27.18 U293 < proper 101.91/27.18 U294 < proper 101.91/27.18 head < proper 101.91/27.18 afterNth < proper 101.91/27.18 U302 < proper 101.91/27.18 U303 < proper 101.91/27.18 U304 < proper 101.91/27.18 U32 < proper 101.91/27.18 U312 < proper 101.91/27.18 pair < proper 101.91/27.18 U33 < proper 101.91/27.18 U322 < proper 101.91/27.18 U323 < proper 101.91/27.18 U324 < proper 101.91/27.18 U325 < proper 101.91/27.18 U326 < proper 101.91/27.18 U327 < proper 101.91/27.18 U34 < proper 101.91/27.18 U332 < proper 101.91/27.18 U333 < proper 101.91/27.18 U334 < proper 101.91/27.18 U342 < proper 101.91/27.18 U343 < proper 101.91/27.18 U344 < proper 101.91/27.18 fst < proper 101.91/27.18 U42 < proper 101.91/27.18 U43 < proper 101.91/27.18 U44 < proper 101.91/27.18 U45 < proper 101.91/27.18 U46 < proper 101.91/27.18 U52 < proper 101.91/27.18 U53 < proper 101.91/27.18 U54 < proper 101.91/27.18 U55 < proper 101.91/27.18 U56 < proper 101.91/27.18 U62 < proper 101.91/27.18 isPLNatKind < proper 101.91/27.18 U63 < proper 101.91/27.18 isPLNat < proper 101.91/27.18 U72 < proper 101.91/27.18 U73 < proper 101.91/27.18 U82 < proper 101.91/27.18 U83 < proper 101.91/27.18 U92 < proper 101.91/27.18 U93 < proper 101.91/27.18 U11 < proper 101.91/27.18 U21 < proper 101.91/27.18 U31 < proper 101.91/27.18 U41 < proper 101.91/27.18 U51 < proper 101.91/27.18 U61 < proper 101.91/27.18 U71 < proper 101.91/27.18 U81 < proper 101.91/27.18 U91 < proper 101.91/27.18 U101 < proper 101.91/27.18 U111 < proper 101.91/27.18 U121 < proper 101.91/27.18 U131 < proper 101.91/27.18 U141 < proper 101.91/27.18 U151 < proper 101.91/27.18 U161 < proper 101.91/27.18 U171 < proper 101.91/27.18 U181 < proper 101.91/27.18 U191 < proper 101.91/27.18 U201 < proper 101.91/27.18 U211 < proper 101.91/27.18 U221 < proper 101.91/27.18 U231 < proper 101.91/27.18 U241 < proper 101.91/27.18 U251 < proper 101.91/27.18 U261 < proper 101.91/27.18 U271 < proper 101.91/27.18 U281 < proper 101.91/27.18 U291 < proper 101.91/27.18 U301 < proper 101.91/27.18 U311 < proper 101.91/27.18 U321 < proper 101.91/27.18 U331 < proper 101.91/27.18 U341 < proper 101.91/27.18 tail < proper 101.91/27.18 take < proper 101.91/27.18 sel < proper 101.91/27.18 proper < top 101.91/27.18 101.91/27.18 ---------------------------------------- 101.91/27.18 101.91/27.18 (87) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.18 Proved the following rewrite lemma: 101.91/27.18 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 101.91/27.18 101.91/27.18 Induction Base: 101.91/27.18 U245(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 101.91/27.18 101.91/27.18 Induction Step: 101.91/27.18 U245(gen_tt:mark:nil:0':ok3_0(+(1, +(n464808_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 101.91/27.18 mark(U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 101.91/27.18 mark(*4_0) 101.91/27.18 101.91/27.18 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.18 ---------------------------------------- 101.91/27.18 101.91/27.18 (88) 101.91/27.18 Obligation: 101.91/27.18 TRS: 101.91/27.18 Rules: 101.91/27.18 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.18 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.18 active(U106(tt)) -> mark(tt) 101.91/27.18 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.18 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.18 active(U112(tt)) -> mark(tt) 101.91/27.18 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.18 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.18 active(U122(tt)) -> mark(tt) 101.91/27.18 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.18 active(U131(tt)) -> mark(tt) 101.91/27.18 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.18 active(U141(tt)) -> mark(tt) 101.91/27.18 active(U151(tt)) -> mark(tt) 101.91/27.18 active(U161(tt)) -> mark(tt) 101.91/27.18 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.18 active(U172(tt)) -> mark(tt) 101.91/27.18 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.18 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.18 active(U183(tt)) -> mark(tt) 101.91/27.18 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.18 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.18 active(U193(tt)) -> mark(tt) 101.91/27.18 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.18 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.18 active(U206(tt)) -> mark(tt) 101.91/27.18 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.18 active(U211(tt)) -> mark(tt) 101.91/27.18 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.18 active(U221(tt)) -> mark(tt) 101.91/27.18 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.18 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.18 active(U232(tt)) -> mark(tt) 101.91/27.18 active(U24(tt, X)) -> mark(X) 101.91/27.18 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.18 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.18 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.18 active(U246(tt)) -> mark(tt) 101.91/27.18 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.18 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.18 active(U256(tt)) -> mark(tt) 101.91/27.18 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.18 active(U262(tt)) -> mark(tt) 101.91/27.18 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.18 active(U272(tt)) -> mark(tt) 101.91/27.18 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.18 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.18 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.18 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.18 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.18 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.18 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.18 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.18 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.18 active(U304(tt, Y)) -> mark(Y) 101.91/27.18 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.18 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.18 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.18 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.18 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.18 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.18 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.18 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.18 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.18 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.18 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.18 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.18 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.18 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.18 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.18 active(U334(tt, XS)) -> mark(XS) 101.91/27.18 active(U34(tt, N)) -> mark(N) 101.91/27.18 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.18 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.18 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.18 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.18 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.18 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.18 active(U46(tt)) -> mark(tt) 101.91/27.18 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.18 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.18 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.18 active(U56(tt)) -> mark(tt) 101.91/27.18 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.18 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.18 active(U63(tt)) -> mark(tt) 101.91/27.18 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.18 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.18 active(U73(tt)) -> mark(tt) 101.91/27.18 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.18 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.18 active(U83(tt)) -> mark(tt) 101.91/27.18 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.18 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.18 active(U93(tt)) -> mark(tt) 101.91/27.18 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.18 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.18 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.18 active(isLNat(nil)) -> mark(tt) 101.91/27.18 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.18 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.18 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.18 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.18 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isLNatKind(nil)) -> mark(tt) 101.91/27.18 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.18 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.18 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.18 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.18 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.18 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.18 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.18 active(isNatural(0')) -> mark(tt) 101.91/27.18 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.18 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.18 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isNaturalKind(0')) -> mark(tt) 101.91/27.18 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.18 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.18 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.18 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.18 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.18 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.18 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.18 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.18 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.18 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.18 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.18 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.18 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.18 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.18 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.18 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.18 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.18 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.18 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.18 active(U106(X)) -> U106(active(X)) 101.91/27.18 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.18 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.18 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.18 active(U112(X)) -> U112(active(X)) 101.91/27.18 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.18 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.18 active(U122(X)) -> U122(active(X)) 101.91/27.18 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.18 active(U131(X)) -> U131(active(X)) 101.91/27.18 active(snd(X)) -> snd(active(X)) 101.91/27.18 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.18 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.18 active(U141(X)) -> U141(active(X)) 101.91/27.18 active(U151(X)) -> U151(active(X)) 101.91/27.18 active(U161(X)) -> U161(active(X)) 101.91/27.18 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.18 active(U172(X)) -> U172(active(X)) 101.91/27.18 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.18 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.18 active(U183(X)) -> U183(active(X)) 101.91/27.18 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.18 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.18 active(U193(X)) -> U193(active(X)) 101.91/27.18 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.18 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.18 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.18 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.18 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.18 active(U206(X)) -> U206(active(X)) 101.91/27.18 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.18 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.18 active(U211(X)) -> U211(active(X)) 101.91/27.18 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.18 active(U221(X)) -> U221(active(X)) 101.91/27.18 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.18 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.18 active(U232(X)) -> U232(active(X)) 101.91/27.18 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.18 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.18 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.18 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.18 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.18 active(U246(X)) -> U246(active(X)) 101.91/27.18 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.18 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.18 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.18 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.18 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.18 active(U256(X)) -> U256(active(X)) 101.91/27.18 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.18 active(U262(X)) -> U262(active(X)) 101.91/27.18 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.18 active(U272(X)) -> U272(active(X)) 101.91/27.18 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.18 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.18 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.18 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.18 active(s(X)) -> s(active(X)) 101.91/27.18 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.18 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.18 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.18 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.18 active(head(X)) -> head(active(X)) 101.91/27.18 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.18 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.18 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.18 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.18 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.18 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.18 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.18 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.18 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.18 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.18 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.18 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.18 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.18 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.18 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.18 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.18 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.18 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.18 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.18 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.18 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.18 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.18 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.18 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.18 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.18 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.18 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.18 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.18 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.18 active(fst(X)) -> fst(active(X)) 101.91/27.18 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.18 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.18 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.18 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.18 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.18 active(U46(X)) -> U46(active(X)) 101.91/27.18 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.18 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.18 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.18 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.18 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.18 active(U56(X)) -> U56(active(X)) 101.91/27.18 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.18 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.18 active(U63(X)) -> U63(active(X)) 101.91/27.18 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.18 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.18 active(U73(X)) -> U73(active(X)) 101.91/27.18 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.18 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.18 active(U83(X)) -> U83(active(X)) 101.91/27.18 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.18 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.18 active(U93(X)) -> U93(active(X)) 101.91/27.18 active(tail(X)) -> tail(active(X)) 101.91/27.18 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.18 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.18 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.18 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.18 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.18 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.18 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.18 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.18 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.18 U106(mark(X)) -> mark(U106(X)) 101.91/27.18 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.18 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.18 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.18 U112(mark(X)) -> mark(U112(X)) 101.91/27.18 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.18 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.18 U122(mark(X)) -> mark(U122(X)) 101.91/27.18 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.18 U131(mark(X)) -> mark(U131(X)) 101.91/27.18 snd(mark(X)) -> mark(snd(X)) 101.91/27.18 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.18 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.18 U141(mark(X)) -> mark(U141(X)) 101.91/27.18 U151(mark(X)) -> mark(U151(X)) 101.91/27.18 U161(mark(X)) -> mark(U161(X)) 101.91/27.18 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.18 U172(mark(X)) -> mark(U172(X)) 101.91/27.18 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.18 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.18 U183(mark(X)) -> mark(U183(X)) 101.91/27.18 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.18 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.18 U193(mark(X)) -> mark(U193(X)) 101.91/27.18 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.18 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.18 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.18 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.18 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.18 U206(mark(X)) -> mark(U206(X)) 101.91/27.18 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.18 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.18 U211(mark(X)) -> mark(U211(X)) 101.91/27.18 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.18 U221(mark(X)) -> mark(U221(X)) 101.91/27.18 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.18 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.18 U232(mark(X)) -> mark(U232(X)) 101.91/27.18 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.18 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.18 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.18 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.18 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.18 U246(mark(X)) -> mark(U246(X)) 101.91/27.18 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.18 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.18 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.18 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.18 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.18 U256(mark(X)) -> mark(U256(X)) 101.91/27.18 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.18 U262(mark(X)) -> mark(U262(X)) 101.91/27.18 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.18 U272(mark(X)) -> mark(U272(X)) 101.91/27.18 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.18 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.18 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.18 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.18 s(mark(X)) -> mark(s(X)) 101.91/27.18 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.18 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.18 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.18 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.18 head(mark(X)) -> mark(head(X)) 101.91/27.18 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.18 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.18 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.18 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.18 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.18 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.18 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.18 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.18 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.18 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.18 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.18 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.18 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.18 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.18 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.18 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.18 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.18 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.18 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.18 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.18 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.18 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.18 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.18 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.18 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.18 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.18 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.18 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.18 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.18 fst(mark(X)) -> mark(fst(X)) 101.91/27.18 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.18 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.18 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.18 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.18 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.18 U46(mark(X)) -> mark(U46(X)) 101.91/27.18 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.18 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.18 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.18 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.18 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.18 U56(mark(X)) -> mark(U56(X)) 101.91/27.18 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.18 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.18 U63(mark(X)) -> mark(U63(X)) 101.91/27.18 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.18 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.18 U73(mark(X)) -> mark(U73(X)) 101.91/27.18 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.18 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.18 U83(mark(X)) -> mark(U83(X)) 101.91/27.18 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.18 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.18 U93(mark(X)) -> mark(U93(X)) 101.91/27.18 tail(mark(X)) -> mark(tail(X)) 101.91/27.18 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.18 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.18 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.18 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.18 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(tt) -> ok(tt) 101.91/27.18 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.18 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.18 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.18 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.18 proper(U106(X)) -> U106(proper(X)) 101.91/27.18 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.18 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.18 proper(U112(X)) -> U112(proper(X)) 101.91/27.18 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.18 proper(U122(X)) -> U122(proper(X)) 101.91/27.18 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U131(X)) -> U131(proper(X)) 101.91/27.18 proper(snd(X)) -> snd(proper(X)) 101.91/27.18 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.18 proper(U141(X)) -> U141(proper(X)) 101.91/27.18 proper(U151(X)) -> U151(proper(X)) 101.91/27.18 proper(U161(X)) -> U161(proper(X)) 101.91/27.18 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.18 proper(U172(X)) -> U172(proper(X)) 101.91/27.18 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.18 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.18 proper(U183(X)) -> U183(proper(X)) 101.91/27.18 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.18 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.18 proper(U193(X)) -> U193(proper(X)) 101.91/27.18 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.18 proper(U206(X)) -> U206(proper(X)) 101.91/27.18 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U211(X)) -> U211(proper(X)) 101.91/27.18 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U221(X)) -> U221(proper(X)) 101.91/27.18 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.18 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.18 proper(U232(X)) -> U232(proper(X)) 101.91/27.18 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.18 proper(U246(X)) -> U246(proper(X)) 101.91/27.18 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.18 proper(U256(X)) -> U256(proper(X)) 101.91/27.18 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.18 proper(U262(X)) -> U262(proper(X)) 101.91/27.18 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.18 proper(U272(X)) -> U272(proper(X)) 101.91/27.18 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.18 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.18 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.18 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.18 proper(s(X)) -> s(proper(X)) 101.91/27.18 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(head(X)) -> head(proper(X)) 101.91/27.18 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.18 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.18 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.18 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.18 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.18 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.18 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.18 proper(nil) -> ok(nil) 101.91/27.18 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.18 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.18 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.18 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.18 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.18 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.18 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(fst(X)) -> fst(proper(X)) 101.91/27.18 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.18 proper(U46(X)) -> U46(proper(X)) 101.91/27.18 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.18 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.18 proper(U56(X)) -> U56(proper(X)) 101.91/27.18 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.18 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.18 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.18 proper(U63(X)) -> U63(proper(X)) 101.91/27.18 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.18 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.18 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.18 proper(U73(X)) -> U73(proper(X)) 101.91/27.18 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.18 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.18 proper(U83(X)) -> U83(proper(X)) 101.91/27.18 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.18 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.18 proper(U93(X)) -> U93(proper(X)) 101.91/27.18 proper(tail(X)) -> tail(proper(X)) 101.91/27.18 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.18 proper(0') -> ok(0') 101.91/27.18 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.18 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.18 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.18 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.18 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.18 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.18 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.18 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.18 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.18 U106(ok(X)) -> ok(U106(X)) 101.91/27.18 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.18 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.18 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.18 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.18 U112(ok(X)) -> ok(U112(X)) 101.91/27.18 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.18 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.18 U122(ok(X)) -> ok(U122(X)) 101.91/27.18 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.18 U131(ok(X)) -> ok(U131(X)) 101.91/27.18 snd(ok(X)) -> ok(snd(X)) 101.91/27.18 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.18 U141(ok(X)) -> ok(U141(X)) 101.91/27.18 U151(ok(X)) -> ok(U151(X)) 101.91/27.18 U161(ok(X)) -> ok(U161(X)) 101.91/27.18 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.18 U172(ok(X)) -> ok(U172(X)) 101.91/27.18 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.18 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.18 U183(ok(X)) -> ok(U183(X)) 101.91/27.18 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.18 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.18 U193(ok(X)) -> ok(U193(X)) 101.91/27.18 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.18 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.18 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.18 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.18 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.18 U206(ok(X)) -> ok(U206(X)) 101.91/27.18 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.18 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.18 U211(ok(X)) -> ok(U211(X)) 101.91/27.18 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.18 U221(ok(X)) -> ok(U221(X)) 101.91/27.18 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.18 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.18 U232(ok(X)) -> ok(U232(X)) 101.91/27.18 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.18 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.18 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.18 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.18 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.18 U246(ok(X)) -> ok(U246(X)) 101.91/27.18 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.18 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.18 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.18 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.18 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.18 U256(ok(X)) -> ok(U256(X)) 101.91/27.18 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.18 U262(ok(X)) -> ok(U262(X)) 101.91/27.18 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.18 U272(ok(X)) -> ok(U272(X)) 101.91/27.18 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.18 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.18 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.18 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.18 s(ok(X)) -> ok(s(X)) 101.91/27.18 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.18 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.18 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.18 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.18 head(ok(X)) -> ok(head(X)) 101.91/27.18 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.18 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.18 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.18 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.18 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.18 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.18 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 101.91/27.18 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 101.91/27.18 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 101.91/27.18 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 101.91/27.18 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 101.91/27.18 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 101.91/27.18 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 101.91/27.18 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 101.91/27.18 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 101.91/27.18 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 101.91/27.18 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 101.91/27.18 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 101.91/27.18 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 101.91/27.18 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 101.91/27.18 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 101.91/27.18 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 101.91/27.18 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 101.91/27.18 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 101.91/27.18 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 101.91/27.18 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 101.91/27.18 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 101.91/27.18 fst(ok(X)) -> ok(fst(X)) 101.91/27.18 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 101.91/27.18 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 101.91/27.18 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 101.91/27.18 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 101.91/27.18 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 101.91/27.18 U46(ok(X)) -> ok(U46(X)) 101.91/27.18 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 101.91/27.18 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 101.91/27.18 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 101.91/27.18 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 101.91/27.18 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 101.91/27.18 U56(ok(X)) -> ok(U56(X)) 101.91/27.18 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 101.91/27.18 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 101.91/27.18 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 101.91/27.18 U63(ok(X)) -> ok(U63(X)) 101.91/27.18 isPLNat(ok(X)) -> ok(isPLNat(X)) 101.91/27.18 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 101.91/27.18 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 101.91/27.18 U73(ok(X)) -> ok(U73(X)) 101.91/27.18 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 101.91/27.18 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 101.91/27.18 U83(ok(X)) -> ok(U83(X)) 101.91/27.18 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 101.91/27.18 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 101.91/27.18 U93(ok(X)) -> ok(U93(X)) 101.91/27.18 tail(ok(X)) -> ok(tail(X)) 101.91/27.18 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 101.91/27.18 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 101.91/27.18 top(mark(X)) -> top(proper(X)) 101.91/27.18 top(ok(X)) -> top(active(X)) 101.91/27.18 101.91/27.18 Types: 101.91/27.18 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 tt :: tt:mark:nil:0':ok 101.91/27.18 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 nil :: tt:mark:nil:0':ok 101.91/27.18 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 0' :: tt:mark:nil:0':ok 101.91/27.18 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 101.91/27.18 top :: tt:mark:nil:0':ok -> top 101.91/27.18 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 101.91/27.18 hole_top2_0 :: top 101.91/27.18 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 101.91/27.18 101.91/27.18 101.91/27.18 Lemmas: 101.91/27.18 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 101.91/27.18 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 101.91/27.18 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 101.91/27.18 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 101.91/27.18 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 101.91/27.18 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 101.91/27.18 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 101.91/27.18 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 101.91/27.18 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 101.91/27.18 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 101.91/27.18 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 101.91/27.18 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 101.91/27.18 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 101.91/27.18 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 101.91/27.18 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 101.91/27.18 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 101.91/27.18 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 101.91/27.18 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 101.91/27.18 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 101.91/27.18 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 101.91/27.18 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 101.91/27.18 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 101.91/27.18 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 101.91/27.18 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 101.91/27.18 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 101.91/27.18 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 101.91/27.18 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 101.91/27.18 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 101.91/27.18 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 101.91/27.18 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 101.91/27.18 101.91/27.18 101.91/27.18 Generator Equations: 101.91/27.18 gen_tt:mark:nil:0':ok3_0(0) <=> tt 101.91/27.18 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 101.91/27.18 101.91/27.18 101.91/27.18 The following defined symbols remain to be analysed: 101.91/27.18 U246, active, U252, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 101.91/27.18 101.91/27.18 They will be analysed ascendingly in the following order: 101.91/27.18 U246 < active 101.91/27.18 U252 < active 101.91/27.18 U253 < active 101.91/27.18 U254 < active 101.91/27.18 U255 < active 101.91/27.18 U256 < active 101.91/27.18 U262 < active 101.91/27.18 U272 < active 101.91/27.18 U282 < active 101.91/27.18 cons < active 101.91/27.18 natsFrom < active 101.91/27.18 s < active 101.91/27.18 U292 < active 101.91/27.18 U293 < active 101.91/27.18 U294 < active 101.91/27.18 head < active 101.91/27.18 afterNth < active 101.91/27.18 U302 < active 101.91/27.18 U303 < active 101.91/27.18 U304 < active 101.91/27.18 U32 < active 101.91/27.18 U312 < active 101.91/27.18 pair < active 101.91/27.18 U33 < active 101.91/27.18 U322 < active 101.91/27.18 U323 < active 101.91/27.18 U324 < active 101.91/27.18 U325 < active 101.91/27.18 U326 < active 101.91/27.18 U327 < active 101.91/27.18 U34 < active 101.91/27.18 U332 < active 101.91/27.18 U333 < active 101.91/27.18 U334 < active 101.91/27.18 U342 < active 101.91/27.18 U343 < active 101.91/27.18 U344 < active 101.91/27.18 fst < active 101.91/27.18 U42 < active 101.91/27.18 U43 < active 101.91/27.18 U44 < active 101.91/27.18 U45 < active 101.91/27.18 U46 < active 101.91/27.18 U52 < active 101.91/27.18 U53 < active 101.91/27.18 U54 < active 101.91/27.18 U55 < active 101.91/27.18 U56 < active 101.91/27.18 U62 < active 101.91/27.18 isPLNatKind < active 101.91/27.18 U63 < active 101.91/27.18 isPLNat < active 101.91/27.18 U72 < active 101.91/27.18 U73 < active 101.91/27.18 U82 < active 101.91/27.18 U83 < active 101.91/27.18 U92 < active 101.91/27.18 U93 < active 101.91/27.18 U11 < active 101.91/27.18 U21 < active 101.91/27.18 U31 < active 101.91/27.18 U41 < active 101.91/27.18 U51 < active 101.91/27.19 U61 < active 101.91/27.19 U71 < active 101.91/27.19 U81 < active 101.91/27.19 U91 < active 101.91/27.19 U101 < active 101.91/27.19 U111 < active 101.91/27.19 U121 < active 101.91/27.19 U131 < active 101.91/27.19 U141 < active 101.91/27.19 U151 < active 101.91/27.19 U161 < active 101.91/27.19 U171 < active 101.91/27.19 U181 < active 101.91/27.19 U191 < active 101.91/27.19 U201 < active 101.91/27.19 U211 < active 101.91/27.19 U221 < active 101.91/27.19 U231 < active 101.91/27.19 U241 < active 101.91/27.19 U251 < active 101.91/27.19 U261 < active 101.91/27.19 U271 < active 101.91/27.19 U281 < active 101.91/27.19 U291 < active 101.91/27.19 U301 < active 101.91/27.19 U311 < active 101.91/27.19 U321 < active 101.91/27.19 U331 < active 101.91/27.19 U341 < active 101.91/27.19 tail < active 101.91/27.19 take < active 101.91/27.19 sel < active 101.91/27.19 active < top 101.91/27.19 U246 < proper 101.91/27.19 U252 < proper 101.91/27.19 U253 < proper 101.91/27.19 U254 < proper 101.91/27.19 U255 < proper 101.91/27.19 U256 < proper 101.91/27.19 U262 < proper 101.91/27.19 U272 < proper 101.91/27.19 U282 < proper 101.91/27.19 cons < proper 101.91/27.19 natsFrom < proper 101.91/27.19 s < proper 101.91/27.19 U292 < proper 101.91/27.19 U293 < proper 101.91/27.19 U294 < proper 101.91/27.19 head < proper 101.91/27.19 afterNth < proper 101.91/27.19 U302 < proper 101.91/27.19 U303 < proper 101.91/27.19 U304 < proper 101.91/27.19 U32 < proper 101.91/27.19 U312 < proper 101.91/27.19 pair < proper 101.91/27.19 U33 < proper 101.91/27.19 U322 < proper 101.91/27.19 U323 < proper 101.91/27.19 U324 < proper 101.91/27.19 U325 < proper 101.91/27.19 U326 < proper 101.91/27.19 U327 < proper 101.91/27.19 U34 < proper 101.91/27.19 U332 < proper 101.91/27.19 U333 < proper 101.91/27.19 U334 < proper 101.91/27.19 U342 < proper 101.91/27.19 U343 < proper 101.91/27.19 U344 < proper 101.91/27.19 fst < proper 101.91/27.19 U42 < proper 101.91/27.19 U43 < proper 101.91/27.19 U44 < proper 101.91/27.19 U45 < proper 101.91/27.19 U46 < proper 101.91/27.19 U52 < proper 101.91/27.19 U53 < proper 101.91/27.19 U54 < proper 101.91/27.19 U55 < proper 101.91/27.19 U56 < proper 101.91/27.19 U62 < proper 101.91/27.19 isPLNatKind < proper 101.91/27.19 U63 < proper 101.91/27.19 isPLNat < proper 101.91/27.19 U72 < proper 101.91/27.19 U73 < proper 101.91/27.19 U82 < proper 101.91/27.19 U83 < proper 101.91/27.19 U92 < proper 101.91/27.19 U93 < proper 101.91/27.19 U11 < proper 101.91/27.19 U21 < proper 101.91/27.19 U31 < proper 101.91/27.19 U41 < proper 101.91/27.19 U51 < proper 101.91/27.19 U61 < proper 101.91/27.19 U71 < proper 101.91/27.19 U81 < proper 101.91/27.19 U91 < proper 101.91/27.19 U101 < proper 101.91/27.19 U111 < proper 101.91/27.19 U121 < proper 101.91/27.19 U131 < proper 101.91/27.19 U141 < proper 101.91/27.19 U151 < proper 101.91/27.19 U161 < proper 101.91/27.19 U171 < proper 101.91/27.19 U181 < proper 101.91/27.19 U191 < proper 101.91/27.19 U201 < proper 101.91/27.19 U211 < proper 101.91/27.19 U221 < proper 101.91/27.19 U231 < proper 101.91/27.19 U241 < proper 101.91/27.19 U251 < proper 101.91/27.19 U261 < proper 101.91/27.19 U271 < proper 101.91/27.19 U281 < proper 101.91/27.19 U291 < proper 101.91/27.19 U301 < proper 101.91/27.19 U311 < proper 101.91/27.19 U321 < proper 101.91/27.19 U331 < proper 101.91/27.19 U341 < proper 101.91/27.19 tail < proper 101.91/27.19 take < proper 101.91/27.19 sel < proper 101.91/27.19 proper < top 101.91/27.19 101.91/27.19 ---------------------------------------- 101.91/27.19 101.91/27.19 (89) RewriteLemmaProof (LOWER BOUND(ID)) 101.91/27.19 Proved the following rewrite lemma: 101.91/27.19 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 101.91/27.19 101.91/27.19 Induction Base: 101.91/27.19 U246(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 101.91/27.19 101.91/27.19 Induction Step: 101.91/27.19 U246(gen_tt:mark:nil:0':ok3_0(+(1, +(n483959_0, 1)))) ->_R^Omega(1) 101.91/27.19 mark(U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0)))) ->_IH 101.91/27.19 mark(*4_0) 101.91/27.19 101.91/27.19 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 101.91/27.19 ---------------------------------------- 101.91/27.19 101.91/27.19 (90) 101.91/27.19 Obligation: 101.91/27.19 TRS: 101.91/27.19 Rules: 101.91/27.19 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 101.91/27.19 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 101.91/27.19 active(U106(tt)) -> mark(tt) 101.91/27.19 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 101.91/27.19 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 101.91/27.19 active(U112(tt)) -> mark(tt) 101.91/27.19 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 101.91/27.19 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 101.91/27.19 active(U122(tt)) -> mark(tt) 101.91/27.19 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 101.91/27.19 active(U131(tt)) -> mark(tt) 101.91/27.19 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 101.91/27.19 active(U141(tt)) -> mark(tt) 101.91/27.19 active(U151(tt)) -> mark(tt) 101.91/27.19 active(U161(tt)) -> mark(tt) 101.91/27.19 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 101.91/27.19 active(U172(tt)) -> mark(tt) 101.91/27.19 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 101.91/27.19 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 101.91/27.19 active(U183(tt)) -> mark(tt) 101.91/27.19 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 101.91/27.19 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 101.91/27.19 active(U193(tt)) -> mark(tt) 101.91/27.19 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 101.91/27.19 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 101.91/27.19 active(U206(tt)) -> mark(tt) 101.91/27.19 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 101.91/27.19 active(U211(tt)) -> mark(tt) 101.91/27.19 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 101.91/27.19 active(U221(tt)) -> mark(tt) 101.91/27.19 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 101.91/27.19 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 101.91/27.19 active(U232(tt)) -> mark(tt) 101.91/27.19 active(U24(tt, X)) -> mark(X) 101.91/27.19 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 101.91/27.19 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 101.91/27.19 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 101.91/27.19 active(U246(tt)) -> mark(tt) 101.91/27.19 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 101.91/27.19 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 101.91/27.19 active(U256(tt)) -> mark(tt) 101.91/27.19 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 101.91/27.19 active(U262(tt)) -> mark(tt) 101.91/27.19 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 101.91/27.19 active(U272(tt)) -> mark(tt) 101.91/27.19 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 101.91/27.19 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 101.91/27.19 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 101.91/27.19 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 101.91/27.19 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 101.91/27.19 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 101.91/27.19 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 101.91/27.19 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 101.91/27.19 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 101.91/27.19 active(U304(tt, Y)) -> mark(Y) 101.91/27.19 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 101.91/27.19 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 101.91/27.19 active(U312(tt, XS)) -> mark(pair(nil, XS)) 101.91/27.19 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 101.91/27.19 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 101.91/27.19 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 101.91/27.19 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 101.91/27.19 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 101.91/27.19 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 101.91/27.19 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 101.91/27.19 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 101.91/27.19 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 101.91/27.19 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 101.91/27.19 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 101.91/27.19 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 101.91/27.19 active(U334(tt, XS)) -> mark(XS) 101.91/27.19 active(U34(tt, N)) -> mark(N) 101.91/27.19 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 101.91/27.19 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 101.91/27.19 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 101.91/27.19 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 101.91/27.19 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 101.91/27.19 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 101.91/27.19 active(U46(tt)) -> mark(tt) 101.91/27.19 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 101.91/27.19 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 101.91/27.19 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 101.91/27.19 active(U56(tt)) -> mark(tt) 101.91/27.19 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 101.91/27.19 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 101.91/27.19 active(U63(tt)) -> mark(tt) 101.91/27.19 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 101.91/27.19 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 101.91/27.19 active(U73(tt)) -> mark(tt) 101.91/27.19 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 101.91/27.19 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 101.91/27.19 active(U83(tt)) -> mark(tt) 101.91/27.19 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 101.91/27.19 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 101.91/27.19 active(U93(tt)) -> mark(tt) 101.91/27.19 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 101.91/27.19 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 101.91/27.19 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 101.91/27.19 active(isLNat(nil)) -> mark(tt) 101.91/27.19 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 101.91/27.19 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 101.91/27.19 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 101.91/27.19 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 101.91/27.19 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(isLNatKind(nil)) -> mark(tt) 101.91/27.19 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 101.91/27.19 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 101.91/27.19 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 101.91/27.19 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 101.91/27.19 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 101.91/27.19 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 101.91/27.19 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 101.91/27.19 active(isNatural(0')) -> mark(tt) 101.91/27.19 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 101.91/27.19 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 101.91/27.19 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(isNaturalKind(0')) -> mark(tt) 101.91/27.19 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 101.91/27.19 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 101.91/27.19 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 101.91/27.19 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 101.91/27.19 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 101.91/27.19 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 101.91/27.19 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 101.91/27.19 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 101.91/27.19 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 101.91/27.19 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 101.91/27.19 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 101.91/27.19 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 101.91/27.19 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 101.91/27.19 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 101.91/27.19 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 101.91/27.19 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 101.91/27.19 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 101.91/27.19 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 101.91/27.19 active(U105(X1, X2)) -> U105(active(X1), X2) 101.91/27.19 active(U106(X)) -> U106(active(X)) 101.91/27.19 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 101.91/27.19 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 101.91/27.19 active(U111(X1, X2)) -> U111(active(X1), X2) 101.91/27.19 active(U112(X)) -> U112(active(X)) 101.91/27.19 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 101.91/27.19 active(U121(X1, X2)) -> U121(active(X1), X2) 101.91/27.19 active(U122(X)) -> U122(active(X)) 101.91/27.19 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 101.91/27.19 active(U131(X)) -> U131(active(X)) 101.91/27.19 active(snd(X)) -> snd(active(X)) 101.91/27.19 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 101.91/27.19 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 101.91/27.19 active(U141(X)) -> U141(active(X)) 101.91/27.19 active(U151(X)) -> U151(active(X)) 101.91/27.19 active(U161(X)) -> U161(active(X)) 101.91/27.19 active(U171(X1, X2)) -> U171(active(X1), X2) 101.91/27.19 active(U172(X)) -> U172(active(X)) 101.91/27.19 active(U181(X1, X2)) -> U181(active(X1), X2) 101.91/27.19 active(U182(X1, X2)) -> U182(active(X1), X2) 101.91/27.19 active(U183(X)) -> U183(active(X)) 101.91/27.19 active(U191(X1, X2)) -> U191(active(X1), X2) 101.91/27.19 active(U192(X1, X2)) -> U192(active(X1), X2) 101.91/27.19 active(U193(X)) -> U193(active(X)) 101.91/27.19 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 101.91/27.19 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 101.91/27.19 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 101.91/27.19 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 101.91/27.19 active(U205(X1, X2)) -> U205(active(X1), X2) 101.91/27.19 active(U206(X)) -> U206(active(X)) 101.91/27.19 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 101.91/27.19 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 101.91/27.19 active(U211(X)) -> U211(active(X)) 101.91/27.19 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 101.91/27.19 active(U221(X)) -> U221(active(X)) 101.91/27.19 active(U24(X1, X2)) -> U24(active(X1), X2) 101.91/27.19 active(U231(X1, X2)) -> U231(active(X1), X2) 101.91/27.19 active(U232(X)) -> U232(active(X)) 101.91/27.19 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 101.91/27.19 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 101.91/27.19 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 101.91/27.19 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 101.91/27.19 active(U245(X1, X2)) -> U245(active(X1), X2) 101.91/27.19 active(U246(X)) -> U246(active(X)) 101.91/27.19 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 101.91/27.19 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 101.91/27.19 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 101.91/27.19 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 101.91/27.19 active(U255(X1, X2)) -> U255(active(X1), X2) 101.91/27.19 active(U256(X)) -> U256(active(X)) 101.91/27.19 active(U261(X1, X2)) -> U261(active(X1), X2) 101.91/27.19 active(U262(X)) -> U262(active(X)) 101.91/27.19 active(U271(X1, X2)) -> U271(active(X1), X2) 101.91/27.19 active(U272(X)) -> U272(active(X)) 101.91/27.19 active(U281(X1, X2)) -> U281(active(X1), X2) 101.91/27.19 active(U282(X1, X2)) -> U282(active(X1), X2) 101.91/27.19 active(cons(X1, X2)) -> cons(active(X1), X2) 101.91/27.19 active(natsFrom(X)) -> natsFrom(active(X)) 101.91/27.19 active(s(X)) -> s(active(X)) 101.91/27.19 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 101.91/27.19 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 101.91/27.19 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 101.91/27.19 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 101.91/27.19 active(head(X)) -> head(active(X)) 101.91/27.19 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 101.91/27.19 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 101.91/27.19 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 101.91/27.19 active(U302(X1, X2)) -> U302(active(X1), X2) 101.91/27.19 active(U303(X1, X2)) -> U303(active(X1), X2) 101.91/27.19 active(U304(X1, X2)) -> U304(active(X1), X2) 101.91/27.19 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 101.91/27.19 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 101.91/27.19 active(U311(X1, X2)) -> U311(active(X1), X2) 101.91/27.19 active(U312(X1, X2)) -> U312(active(X1), X2) 101.91/27.19 active(pair(X1, X2)) -> pair(active(X1), X2) 101.91/27.19 active(pair(X1, X2)) -> pair(X1, active(X2)) 101.91/27.19 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 101.91/27.19 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 101.91/27.19 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 101.91/27.19 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 101.91/27.19 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 101.91/27.19 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 101.91/27.19 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 101.91/27.19 active(U327(X1, X2)) -> U327(active(X1), X2) 101.91/27.19 active(U34(X1, X2)) -> U34(active(X1), X2) 101.91/27.19 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 101.91/27.19 active(U332(X1, X2)) -> U332(active(X1), X2) 101.91/27.19 active(U333(X1, X2)) -> U333(active(X1), X2) 101.91/27.19 active(U334(X1, X2)) -> U334(active(X1), X2) 101.91/27.19 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 101.91/27.19 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 101.91/27.19 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 101.91/27.19 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 101.91/27.19 active(fst(X)) -> fst(active(X)) 101.91/27.19 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 101.91/27.19 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 101.91/27.19 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 101.91/27.19 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 101.91/27.19 active(U45(X1, X2)) -> U45(active(X1), X2) 101.91/27.19 active(U46(X)) -> U46(active(X)) 101.91/27.19 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 101.91/27.19 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 101.91/27.19 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 101.91/27.19 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 101.91/27.19 active(U55(X1, X2)) -> U55(active(X1), X2) 101.91/27.19 active(U56(X)) -> U56(active(X)) 101.91/27.19 active(U61(X1, X2)) -> U61(active(X1), X2) 101.91/27.19 active(U62(X1, X2)) -> U62(active(X1), X2) 101.91/27.19 active(U63(X)) -> U63(active(X)) 101.91/27.19 active(U71(X1, X2)) -> U71(active(X1), X2) 101.91/27.19 active(U72(X1, X2)) -> U72(active(X1), X2) 101.91/27.19 active(U73(X)) -> U73(active(X)) 101.91/27.19 active(U81(X1, X2)) -> U81(active(X1), X2) 101.91/27.19 active(U82(X1, X2)) -> U82(active(X1), X2) 101.91/27.19 active(U83(X)) -> U83(active(X)) 101.91/27.19 active(U91(X1, X2)) -> U91(active(X1), X2) 101.91/27.19 active(U92(X1, X2)) -> U92(active(X1), X2) 101.91/27.19 active(U93(X)) -> U93(active(X)) 101.91/27.19 active(tail(X)) -> tail(active(X)) 101.91/27.19 active(take(X1, X2)) -> take(active(X1), X2) 101.91/27.19 active(take(X1, X2)) -> take(X1, active(X2)) 101.91/27.19 active(sel(X1, X2)) -> sel(active(X1), X2) 101.91/27.19 active(sel(X1, X2)) -> sel(X1, active(X2)) 101.91/27.19 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 101.91/27.19 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 101.91/27.19 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 101.91/27.19 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 101.91/27.19 U105(mark(X1), X2) -> mark(U105(X1, X2)) 101.91/27.19 U106(mark(X)) -> mark(U106(X)) 101.91/27.19 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 101.91/27.19 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 101.91/27.19 U111(mark(X1), X2) -> mark(U111(X1, X2)) 101.91/27.19 U112(mark(X)) -> mark(U112(X)) 101.91/27.19 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 101.91/27.19 U121(mark(X1), X2) -> mark(U121(X1, X2)) 101.91/27.19 U122(mark(X)) -> mark(U122(X)) 101.91/27.19 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 101.91/27.19 U131(mark(X)) -> mark(U131(X)) 101.91/27.19 snd(mark(X)) -> mark(snd(X)) 101.91/27.19 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 101.91/27.19 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 101.91/27.19 U141(mark(X)) -> mark(U141(X)) 101.91/27.19 U151(mark(X)) -> mark(U151(X)) 101.91/27.19 U161(mark(X)) -> mark(U161(X)) 101.91/27.19 U171(mark(X1), X2) -> mark(U171(X1, X2)) 101.91/27.19 U172(mark(X)) -> mark(U172(X)) 101.91/27.19 U181(mark(X1), X2) -> mark(U181(X1, X2)) 101.91/27.19 U182(mark(X1), X2) -> mark(U182(X1, X2)) 101.91/27.19 U183(mark(X)) -> mark(U183(X)) 101.91/27.19 U191(mark(X1), X2) -> mark(U191(X1, X2)) 101.91/27.19 U192(mark(X1), X2) -> mark(U192(X1, X2)) 101.91/27.19 U193(mark(X)) -> mark(U193(X)) 101.91/27.19 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 101.91/27.19 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 101.91/27.19 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 101.91/27.19 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 101.91/27.19 U205(mark(X1), X2) -> mark(U205(X1, X2)) 101.91/27.19 U206(mark(X)) -> mark(U206(X)) 101.91/27.19 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 101.91/27.19 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 101.91/27.19 U211(mark(X)) -> mark(U211(X)) 101.91/27.19 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 101.91/27.19 U221(mark(X)) -> mark(U221(X)) 101.91/27.19 U24(mark(X1), X2) -> mark(U24(X1, X2)) 101.91/27.19 U231(mark(X1), X2) -> mark(U231(X1, X2)) 101.91/27.19 U232(mark(X)) -> mark(U232(X)) 101.91/27.19 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 101.91/27.19 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 101.91/27.19 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 101.91/27.19 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 101.91/27.19 U245(mark(X1), X2) -> mark(U245(X1, X2)) 101.91/27.19 U246(mark(X)) -> mark(U246(X)) 101.91/27.19 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 101.91/27.19 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 101.91/27.19 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 101.91/27.19 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 101.91/27.19 U255(mark(X1), X2) -> mark(U255(X1, X2)) 101.91/27.19 U256(mark(X)) -> mark(U256(X)) 101.91/27.19 U261(mark(X1), X2) -> mark(U261(X1, X2)) 101.91/27.19 U262(mark(X)) -> mark(U262(X)) 101.91/27.19 U271(mark(X1), X2) -> mark(U271(X1, X2)) 101.91/27.19 U272(mark(X)) -> mark(U272(X)) 101.91/27.19 U281(mark(X1), X2) -> mark(U281(X1, X2)) 101.91/27.19 U282(mark(X1), X2) -> mark(U282(X1, X2)) 101.91/27.19 cons(mark(X1), X2) -> mark(cons(X1, X2)) 101.91/27.19 natsFrom(mark(X)) -> mark(natsFrom(X)) 101.91/27.19 s(mark(X)) -> mark(s(X)) 101.91/27.19 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 101.91/27.19 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 101.91/27.19 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 101.91/27.19 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 101.91/27.19 head(mark(X)) -> mark(head(X)) 101.91/27.19 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 101.91/27.19 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 101.91/27.19 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 101.91/27.19 U302(mark(X1), X2) -> mark(U302(X1, X2)) 101.91/27.19 U303(mark(X1), X2) -> mark(U303(X1, X2)) 101.91/27.19 U304(mark(X1), X2) -> mark(U304(X1, X2)) 101.91/27.19 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 101.91/27.19 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 101.91/27.19 U311(mark(X1), X2) -> mark(U311(X1, X2)) 101.91/27.19 U312(mark(X1), X2) -> mark(U312(X1, X2)) 101.91/27.19 pair(mark(X1), X2) -> mark(pair(X1, X2)) 101.91/27.19 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 101.91/27.19 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 101.91/27.19 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 101.91/27.19 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 101.91/27.19 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 101.91/27.19 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 101.91/27.19 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 101.91/27.19 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 101.91/27.19 U327(mark(X1), X2) -> mark(U327(X1, X2)) 101.91/27.19 U34(mark(X1), X2) -> mark(U34(X1, X2)) 101.91/27.19 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 101.91/27.19 U332(mark(X1), X2) -> mark(U332(X1, X2)) 101.91/27.19 U333(mark(X1), X2) -> mark(U333(X1, X2)) 101.91/27.19 U334(mark(X1), X2) -> mark(U334(X1, X2)) 101.91/27.19 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 101.91/27.19 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 101.91/27.19 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 101.91/27.19 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 101.91/27.19 fst(mark(X)) -> mark(fst(X)) 101.91/27.19 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 101.91/27.19 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 101.91/27.19 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 101.91/27.19 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 101.91/27.19 U45(mark(X1), X2) -> mark(U45(X1, X2)) 101.91/27.19 U46(mark(X)) -> mark(U46(X)) 101.91/27.19 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 101.91/27.19 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 101.91/27.19 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 101.91/27.19 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 101.91/27.19 U55(mark(X1), X2) -> mark(U55(X1, X2)) 101.91/27.19 U56(mark(X)) -> mark(U56(X)) 101.91/27.19 U61(mark(X1), X2) -> mark(U61(X1, X2)) 101.91/27.19 U62(mark(X1), X2) -> mark(U62(X1, X2)) 101.91/27.19 U63(mark(X)) -> mark(U63(X)) 101.91/27.19 U71(mark(X1), X2) -> mark(U71(X1, X2)) 101.91/27.19 U72(mark(X1), X2) -> mark(U72(X1, X2)) 101.91/27.19 U73(mark(X)) -> mark(U73(X)) 101.91/27.19 U81(mark(X1), X2) -> mark(U81(X1, X2)) 101.91/27.19 U82(mark(X1), X2) -> mark(U82(X1, X2)) 101.91/27.19 U83(mark(X)) -> mark(U83(X)) 101.91/27.19 U91(mark(X1), X2) -> mark(U91(X1, X2)) 101.91/27.19 U92(mark(X1), X2) -> mark(U92(X1, X2)) 101.91/27.19 U93(mark(X)) -> mark(U93(X)) 101.91/27.19 tail(mark(X)) -> mark(tail(X)) 101.91/27.19 take(mark(X1), X2) -> mark(take(X1, X2)) 101.91/27.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 101.91/27.19 sel(mark(X1), X2) -> mark(sel(X1, X2)) 101.91/27.19 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 101.91/27.19 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(tt) -> ok(tt) 101.91/27.19 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 101.91/27.19 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 101.91/27.19 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 101.91/27.19 proper(isNatural(X)) -> isNatural(proper(X)) 101.91/27.19 proper(U106(X)) -> U106(proper(X)) 101.91/27.19 proper(isLNat(X)) -> isLNat(proper(X)) 101.91/27.19 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 101.91/27.19 proper(U112(X)) -> U112(proper(X)) 101.91/27.19 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 101.91/27.19 proper(U122(X)) -> U122(proper(X)) 101.91/27.19 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U131(X)) -> U131(proper(X)) 101.91/27.19 proper(snd(X)) -> snd(proper(X)) 101.91/27.19 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 101.91/27.19 proper(U141(X)) -> U141(proper(X)) 101.91/27.19 proper(U151(X)) -> U151(proper(X)) 101.91/27.19 proper(U161(X)) -> U161(proper(X)) 101.91/27.19 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 101.91/27.19 proper(U172(X)) -> U172(proper(X)) 101.91/27.19 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 101.91/27.19 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 101.91/27.19 proper(U183(X)) -> U183(proper(X)) 101.91/27.19 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 101.91/27.19 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 101.91/27.19 proper(U193(X)) -> U193(proper(X)) 101.91/27.19 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 101.91/27.19 proper(U206(X)) -> U206(proper(X)) 101.91/27.19 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U211(X)) -> U211(proper(X)) 101.91/27.19 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U221(X)) -> U221(proper(X)) 101.91/27.19 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 101.91/27.19 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 101.91/27.19 proper(U232(X)) -> U232(proper(X)) 101.91/27.19 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 101.91/27.19 proper(U246(X)) -> U246(proper(X)) 101.91/27.19 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 101.91/27.19 proper(U256(X)) -> U256(proper(X)) 101.91/27.19 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 101.91/27.19 proper(U262(X)) -> U262(proper(X)) 101.91/27.19 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 101.91/27.19 proper(U272(X)) -> U272(proper(X)) 101.91/27.19 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 101.91/27.19 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 101.91/27.19 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 101.91/27.19 proper(natsFrom(X)) -> natsFrom(proper(X)) 101.91/27.19 proper(s(X)) -> s(proper(X)) 101.91/27.19 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(head(X)) -> head(proper(X)) 101.91/27.19 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 101.91/27.19 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 101.91/27.19 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 101.91/27.19 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 101.91/27.19 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 101.91/27.19 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 101.91/27.19 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 101.91/27.19 proper(nil) -> ok(nil) 101.91/27.19 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 101.91/27.19 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 101.91/27.19 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 101.91/27.19 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 101.91/27.19 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 101.91/27.19 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 101.91/27.19 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(fst(X)) -> fst(proper(X)) 101.91/27.19 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 101.91/27.19 proper(U46(X)) -> U46(proper(X)) 101.91/27.19 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 101.91/27.19 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 101.91/27.19 proper(U56(X)) -> U56(proper(X)) 101.91/27.19 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 101.91/27.19 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 101.91/27.19 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 101.91/27.19 proper(U63(X)) -> U63(proper(X)) 101.91/27.19 proper(isPLNat(X)) -> isPLNat(proper(X)) 101.91/27.19 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 101.91/27.19 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 101.91/27.19 proper(U73(X)) -> U73(proper(X)) 101.91/27.19 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 101.91/27.19 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 101.91/27.19 proper(U83(X)) -> U83(proper(X)) 101.91/27.19 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 101.91/27.19 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 101.91/27.19 proper(U93(X)) -> U93(proper(X)) 101.91/27.19 proper(tail(X)) -> tail(proper(X)) 101.91/27.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 101.91/27.19 proper(0') -> ok(0') 101.91/27.19 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 101.91/27.19 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 101.91/27.19 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 101.91/27.19 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 101.91/27.19 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 101.91/27.19 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 101.91/27.19 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 101.91/27.19 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 101.91/27.19 isNatural(ok(X)) -> ok(isNatural(X)) 101.91/27.19 U106(ok(X)) -> ok(U106(X)) 101.91/27.19 isLNat(ok(X)) -> ok(isLNat(X)) 101.91/27.19 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 101.91/27.19 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 101.91/27.19 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 101.91/27.19 U112(ok(X)) -> ok(U112(X)) 101.91/27.19 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 101.91/27.19 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 101.91/27.19 U122(ok(X)) -> ok(U122(X)) 101.91/27.19 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 101.91/27.19 U131(ok(X)) -> ok(U131(X)) 101.91/27.19 snd(ok(X)) -> ok(snd(X)) 101.91/27.19 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 101.91/27.19 U141(ok(X)) -> ok(U141(X)) 101.91/27.19 U151(ok(X)) -> ok(U151(X)) 101.91/27.19 U161(ok(X)) -> ok(U161(X)) 101.91/27.19 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 101.91/27.19 U172(ok(X)) -> ok(U172(X)) 101.91/27.19 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 101.91/27.19 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 101.91/27.19 U183(ok(X)) -> ok(U183(X)) 101.91/27.19 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 101.91/27.19 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 101.91/27.19 U193(ok(X)) -> ok(U193(X)) 101.91/27.19 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 101.91/27.19 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 101.91/27.19 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 101.91/27.19 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 101.91/27.19 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 101.91/27.19 U206(ok(X)) -> ok(U206(X)) 101.91/27.19 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 101.91/27.19 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 101.91/27.19 U211(ok(X)) -> ok(U211(X)) 101.91/27.19 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 101.91/27.19 U221(ok(X)) -> ok(U221(X)) 101.91/27.19 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 101.91/27.19 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 101.91/27.19 U232(ok(X)) -> ok(U232(X)) 101.91/27.19 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 101.91/27.19 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 101.91/27.19 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 101.91/27.19 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 101.91/27.19 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 101.91/27.19 U246(ok(X)) -> ok(U246(X)) 101.91/27.19 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 101.91/27.19 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 101.91/27.19 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 101.91/27.19 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 101.91/27.19 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 101.91/27.19 U256(ok(X)) -> ok(U256(X)) 101.91/27.19 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 101.91/27.19 U262(ok(X)) -> ok(U262(X)) 101.91/27.19 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 101.91/27.19 U272(ok(X)) -> ok(U272(X)) 101.91/27.19 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 101.91/27.19 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 101.91/27.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 101.91/27.19 natsFrom(ok(X)) -> ok(natsFrom(X)) 101.91/27.19 s(ok(X)) -> ok(s(X)) 101.91/27.19 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 101.91/27.19 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 101.91/27.19 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 101.91/27.19 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 101.91/27.19 head(ok(X)) -> ok(head(X)) 101.91/27.19 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 101.91/27.19 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 101.91/27.19 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 101.91/27.19 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 101.91/27.19 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 101.91/27.19 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 101.91/27.19 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.19 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.19 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.19 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.19 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.19 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.19 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.19 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.19 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.19 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.19 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.19 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.19 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.19 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.19 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.19 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.19 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.19 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.19 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.19 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.19 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.19 fst(ok(X)) -> ok(fst(X)) 102.08/27.19 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.19 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.19 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.19 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.19 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.19 U46(ok(X)) -> ok(U46(X)) 102.08/27.19 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.19 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.19 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.19 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.19 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.19 U56(ok(X)) -> ok(U56(X)) 102.08/27.19 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.19 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.19 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.19 U63(ok(X)) -> ok(U63(X)) 102.08/27.19 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.19 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.19 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.19 U73(ok(X)) -> ok(U73(X)) 102.08/27.19 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.19 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.19 U83(ok(X)) -> ok(U83(X)) 102.08/27.19 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.19 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.19 U93(ok(X)) -> ok(U93(X)) 102.08/27.19 tail(ok(X)) -> ok(tail(X)) 102.08/27.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.19 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.19 top(mark(X)) -> top(proper(X)) 102.08/27.19 top(ok(X)) -> top(active(X)) 102.08/27.19 102.08/27.19 Types: 102.08/27.19 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 tt :: tt:mark:nil:0':ok 102.08/27.19 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 nil :: tt:mark:nil:0':ok 102.08/27.19 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 0' :: tt:mark:nil:0':ok 102.08/27.19 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 top :: tt:mark:nil:0':ok -> top 102.08/27.19 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.19 hole_top2_0 :: top 102.08/27.19 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.19 102.08/27.19 102.08/27.19 Lemmas: 102.08/27.19 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.19 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.19 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.19 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.19 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.19 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.19 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.19 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.19 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.19 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.19 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.19 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.19 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.19 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.19 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.19 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.19 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.19 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.19 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.19 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.19 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.19 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.19 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.19 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.19 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.19 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.19 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.19 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.19 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.19 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.19 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.19 102.08/27.19 102.08/27.19 Generator Equations: 102.08/27.19 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.19 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.19 102.08/27.19 102.08/27.19 The following defined symbols remain to be analysed: 102.08/27.19 U252, active, U253, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.19 102.08/27.19 They will be analysed ascendingly in the following order: 102.08/27.19 U252 < active 102.08/27.19 U253 < active 102.08/27.19 U254 < active 102.08/27.19 U255 < active 102.08/27.19 U256 < active 102.08/27.19 U262 < active 102.08/27.19 U272 < active 102.08/27.19 U282 < active 102.08/27.19 cons < active 102.08/27.19 natsFrom < active 102.08/27.19 s < active 102.08/27.19 U292 < active 102.08/27.19 U293 < active 102.08/27.19 U294 < active 102.08/27.19 head < active 102.08/27.19 afterNth < active 102.08/27.19 U302 < active 102.08/27.19 U303 < active 102.08/27.19 U304 < active 102.08/27.19 U32 < active 102.08/27.19 U312 < active 102.08/27.19 pair < active 102.08/27.19 U33 < active 102.08/27.19 U322 < active 102.08/27.19 U323 < active 102.08/27.19 U324 < active 102.08/27.19 U325 < active 102.08/27.19 U326 < active 102.08/27.19 U327 < active 102.08/27.19 U34 < active 102.08/27.19 U332 < active 102.08/27.19 U333 < active 102.08/27.19 U334 < active 102.08/27.19 U342 < active 102.08/27.19 U343 < active 102.08/27.19 U344 < active 102.08/27.19 fst < active 102.08/27.19 U42 < active 102.08/27.19 U43 < active 102.08/27.19 U44 < active 102.08/27.19 U45 < active 102.08/27.19 U46 < active 102.08/27.19 U52 < active 102.08/27.19 U53 < active 102.08/27.19 U54 < active 102.08/27.19 U55 < active 102.08/27.19 U56 < active 102.08/27.19 U62 < active 102.08/27.19 isPLNatKind < active 102.08/27.19 U63 < active 102.08/27.19 isPLNat < active 102.08/27.19 U72 < active 102.08/27.19 U73 < active 102.08/27.19 U82 < active 102.08/27.19 U83 < active 102.08/27.19 U92 < active 102.08/27.19 U93 < active 102.08/27.19 U11 < active 102.08/27.19 U21 < active 102.08/27.19 U31 < active 102.08/27.19 U41 < active 102.08/27.19 U51 < active 102.08/27.19 U61 < active 102.08/27.19 U71 < active 102.08/27.19 U81 < active 102.08/27.19 U91 < active 102.08/27.19 U101 < active 102.08/27.19 U111 < active 102.08/27.19 U121 < active 102.08/27.19 U131 < active 102.08/27.19 U141 < active 102.08/27.19 U151 < active 102.08/27.19 U161 < active 102.08/27.19 U171 < active 102.08/27.19 U181 < active 102.08/27.19 U191 < active 102.08/27.19 U201 < active 102.08/27.19 U211 < active 102.08/27.19 U221 < active 102.08/27.19 U231 < active 102.08/27.19 U241 < active 102.08/27.19 U251 < active 102.08/27.19 U261 < active 102.08/27.19 U271 < active 102.08/27.19 U281 < active 102.08/27.19 U291 < active 102.08/27.19 U301 < active 102.08/27.19 U311 < active 102.08/27.19 U321 < active 102.08/27.19 U331 < active 102.08/27.19 U341 < active 102.08/27.19 tail < active 102.08/27.19 take < active 102.08/27.19 sel < active 102.08/27.19 active < top 102.08/27.19 U252 < proper 102.08/27.19 U253 < proper 102.08/27.19 U254 < proper 102.08/27.19 U255 < proper 102.08/27.19 U256 < proper 102.08/27.19 U262 < proper 102.08/27.19 U272 < proper 102.08/27.19 U282 < proper 102.08/27.19 cons < proper 102.08/27.19 natsFrom < proper 102.08/27.19 s < proper 102.08/27.19 U292 < proper 102.08/27.19 U293 < proper 102.08/27.19 U294 < proper 102.08/27.19 head < proper 102.08/27.19 afterNth < proper 102.08/27.19 U302 < proper 102.08/27.19 U303 < proper 102.08/27.19 U304 < proper 102.08/27.19 U32 < proper 102.08/27.19 U312 < proper 102.08/27.19 pair < proper 102.08/27.19 U33 < proper 102.08/27.19 U322 < proper 102.08/27.19 U323 < proper 102.08/27.19 U324 < proper 102.08/27.19 U325 < proper 102.08/27.19 U326 < proper 102.08/27.19 U327 < proper 102.08/27.19 U34 < proper 102.08/27.19 U332 < proper 102.08/27.19 U333 < proper 102.08/27.19 U334 < proper 102.08/27.19 U342 < proper 102.08/27.19 U343 < proper 102.08/27.19 U344 < proper 102.08/27.19 fst < proper 102.08/27.19 U42 < proper 102.08/27.19 U43 < proper 102.08/27.19 U44 < proper 102.08/27.19 U45 < proper 102.08/27.19 U46 < proper 102.08/27.19 U52 < proper 102.08/27.19 U53 < proper 102.08/27.19 U54 < proper 102.08/27.19 U55 < proper 102.08/27.19 U56 < proper 102.08/27.19 U62 < proper 102.08/27.19 isPLNatKind < proper 102.08/27.19 U63 < proper 102.08/27.19 isPLNat < proper 102.08/27.19 U72 < proper 102.08/27.19 U73 < proper 102.08/27.19 U82 < proper 102.08/27.19 U83 < proper 102.08/27.19 U92 < proper 102.08/27.19 U93 < proper 102.08/27.19 U11 < proper 102.08/27.19 U21 < proper 102.08/27.19 U31 < proper 102.08/27.19 U41 < proper 102.08/27.19 U51 < proper 102.08/27.19 U61 < proper 102.08/27.19 U71 < proper 102.08/27.19 U81 < proper 102.08/27.19 U91 < proper 102.08/27.19 U101 < proper 102.08/27.19 U111 < proper 102.08/27.19 U121 < proper 102.08/27.19 U131 < proper 102.08/27.19 U141 < proper 102.08/27.19 U151 < proper 102.08/27.19 U161 < proper 102.08/27.19 U171 < proper 102.08/27.19 U181 < proper 102.08/27.19 U191 < proper 102.08/27.19 U201 < proper 102.08/27.19 U211 < proper 102.08/27.19 U221 < proper 102.08/27.19 U231 < proper 102.08/27.19 U241 < proper 102.08/27.19 U251 < proper 102.08/27.19 U261 < proper 102.08/27.19 U271 < proper 102.08/27.19 U281 < proper 102.08/27.19 U291 < proper 102.08/27.19 U301 < proper 102.08/27.19 U311 < proper 102.08/27.19 U321 < proper 102.08/27.19 U331 < proper 102.08/27.19 U341 < proper 102.08/27.19 tail < proper 102.08/27.19 take < proper 102.08/27.19 sel < proper 102.08/27.19 proper < top 102.08/27.19 102.08/27.19 ---------------------------------------- 102.08/27.19 102.08/27.19 (91) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.19 Proved the following rewrite lemma: 102.08/27.19 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.19 102.08/27.19 Induction Base: 102.08/27.19 U252(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 102.08/27.19 102.08/27.19 Induction Step: 102.08/27.19 U252(gen_tt:mark:nil:0':ok3_0(+(1, +(n490975_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 102.08/27.19 mark(U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 102.08/27.19 mark(*4_0) 102.08/27.19 102.08/27.19 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.19 ---------------------------------------- 102.08/27.19 102.08/27.19 (92) 102.08/27.19 Obligation: 102.08/27.19 TRS: 102.08/27.19 Rules: 102.08/27.19 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.19 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.19 active(U106(tt)) -> mark(tt) 102.08/27.19 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.19 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.19 active(U112(tt)) -> mark(tt) 102.08/27.19 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.19 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.19 active(U122(tt)) -> mark(tt) 102.08/27.19 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.19 active(U131(tt)) -> mark(tt) 102.08/27.19 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.19 active(U141(tt)) -> mark(tt) 102.08/27.19 active(U151(tt)) -> mark(tt) 102.08/27.19 active(U161(tt)) -> mark(tt) 102.08/27.19 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.19 active(U172(tt)) -> mark(tt) 102.08/27.19 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.19 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.19 active(U183(tt)) -> mark(tt) 102.08/27.19 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.19 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.19 active(U193(tt)) -> mark(tt) 102.08/27.19 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.19 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.19 active(U206(tt)) -> mark(tt) 102.08/27.19 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.19 active(U211(tt)) -> mark(tt) 102.08/27.19 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.19 active(U221(tt)) -> mark(tt) 102.08/27.19 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.19 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.19 active(U232(tt)) -> mark(tt) 102.08/27.19 active(U24(tt, X)) -> mark(X) 102.08/27.19 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.19 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.19 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.19 active(U246(tt)) -> mark(tt) 102.08/27.19 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.19 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.19 active(U256(tt)) -> mark(tt) 102.08/27.19 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.19 active(U262(tt)) -> mark(tt) 102.08/27.19 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.19 active(U272(tt)) -> mark(tt) 102.08/27.19 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.19 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.19 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.19 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.19 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.19 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.19 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.19 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.19 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.19 active(U304(tt, Y)) -> mark(Y) 102.08/27.19 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.19 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.19 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.19 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.19 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.19 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.19 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.19 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.19 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.19 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.19 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.19 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.19 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.19 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.19 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.19 active(U334(tt, XS)) -> mark(XS) 102.08/27.19 active(U34(tt, N)) -> mark(N) 102.08/27.19 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.19 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.19 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.19 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.19 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.19 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.19 active(U46(tt)) -> mark(tt) 102.08/27.19 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.19 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.19 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.19 active(U56(tt)) -> mark(tt) 102.08/27.19 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.19 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.19 active(U63(tt)) -> mark(tt) 102.08/27.19 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.19 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.19 active(U73(tt)) -> mark(tt) 102.08/27.19 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.19 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.19 active(U83(tt)) -> mark(tt) 102.08/27.19 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.19 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.19 active(U93(tt)) -> mark(tt) 102.08/27.19 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.19 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.19 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.19 active(isLNat(nil)) -> mark(tt) 102.08/27.19 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.19 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.19 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.19 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.19 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(isLNatKind(nil)) -> mark(tt) 102.08/27.19 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.19 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.19 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.19 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.19 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.19 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.19 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.19 active(isNatural(0')) -> mark(tt) 102.08/27.19 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.19 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.19 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(isNaturalKind(0')) -> mark(tt) 102.08/27.19 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.19 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.19 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.19 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.19 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.19 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.19 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.19 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.19 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.19 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.19 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.19 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.19 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.19 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.19 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.19 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.19 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.19 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.19 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.19 active(U106(X)) -> U106(active(X)) 102.08/27.19 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.19 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.19 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.19 active(U112(X)) -> U112(active(X)) 102.08/27.19 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.19 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.19 active(U122(X)) -> U122(active(X)) 102.08/27.19 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.19 active(U131(X)) -> U131(active(X)) 102.08/27.19 active(snd(X)) -> snd(active(X)) 102.08/27.19 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.19 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.19 active(U141(X)) -> U141(active(X)) 102.08/27.19 active(U151(X)) -> U151(active(X)) 102.08/27.19 active(U161(X)) -> U161(active(X)) 102.08/27.19 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.19 active(U172(X)) -> U172(active(X)) 102.08/27.19 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.19 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.19 active(U183(X)) -> U183(active(X)) 102.08/27.19 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.19 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.19 active(U193(X)) -> U193(active(X)) 102.08/27.19 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.19 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.19 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.19 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.19 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.19 active(U206(X)) -> U206(active(X)) 102.08/27.19 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.19 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.19 active(U211(X)) -> U211(active(X)) 102.08/27.19 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.19 active(U221(X)) -> U221(active(X)) 102.08/27.19 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.19 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.19 active(U232(X)) -> U232(active(X)) 102.08/27.19 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.19 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.19 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.19 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.19 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.19 active(U246(X)) -> U246(active(X)) 102.08/27.19 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.19 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.19 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.19 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.19 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.19 active(U256(X)) -> U256(active(X)) 102.08/27.19 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.19 active(U262(X)) -> U262(active(X)) 102.08/27.19 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.19 active(U272(X)) -> U272(active(X)) 102.08/27.19 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.19 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.19 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.19 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.19 active(s(X)) -> s(active(X)) 102.08/27.19 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.19 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.19 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.19 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.19 active(head(X)) -> head(active(X)) 102.08/27.19 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.19 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.19 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.19 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.19 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.19 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.19 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.19 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.19 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.19 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.19 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.19 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.19 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.19 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.19 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.19 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.19 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.19 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.19 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.19 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.19 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.19 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.19 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.19 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.19 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.19 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.19 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.19 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.19 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.19 active(fst(X)) -> fst(active(X)) 102.08/27.19 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.19 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.19 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.19 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.19 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.19 active(U46(X)) -> U46(active(X)) 102.08/27.19 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.19 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.19 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.19 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.19 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.19 active(U56(X)) -> U56(active(X)) 102.08/27.19 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.19 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.19 active(U63(X)) -> U63(active(X)) 102.08/27.19 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.19 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.19 active(U73(X)) -> U73(active(X)) 102.08/27.19 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.19 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.19 active(U83(X)) -> U83(active(X)) 102.08/27.19 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.19 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.19 active(U93(X)) -> U93(active(X)) 102.08/27.19 active(tail(X)) -> tail(active(X)) 102.08/27.19 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.19 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.19 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.19 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.19 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.19 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.19 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.19 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.19 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.19 U106(mark(X)) -> mark(U106(X)) 102.08/27.19 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.19 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.19 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.19 U112(mark(X)) -> mark(U112(X)) 102.08/27.19 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.19 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.19 U122(mark(X)) -> mark(U122(X)) 102.08/27.19 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.19 U131(mark(X)) -> mark(U131(X)) 102.08/27.19 snd(mark(X)) -> mark(snd(X)) 102.08/27.19 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.19 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.19 U141(mark(X)) -> mark(U141(X)) 102.08/27.19 U151(mark(X)) -> mark(U151(X)) 102.08/27.19 U161(mark(X)) -> mark(U161(X)) 102.08/27.19 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.19 U172(mark(X)) -> mark(U172(X)) 102.08/27.19 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.19 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.19 U183(mark(X)) -> mark(U183(X)) 102.08/27.19 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.19 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.19 U193(mark(X)) -> mark(U193(X)) 102.08/27.19 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.19 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.19 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.19 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.19 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.19 U206(mark(X)) -> mark(U206(X)) 102.08/27.19 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.19 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.19 U211(mark(X)) -> mark(U211(X)) 102.08/27.19 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.19 U221(mark(X)) -> mark(U221(X)) 102.08/27.19 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.19 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.19 U232(mark(X)) -> mark(U232(X)) 102.08/27.19 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.19 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.19 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.19 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.19 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.19 U246(mark(X)) -> mark(U246(X)) 102.08/27.19 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.19 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.19 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.19 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.19 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.19 U256(mark(X)) -> mark(U256(X)) 102.08/27.19 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.19 U262(mark(X)) -> mark(U262(X)) 102.08/27.19 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.19 U272(mark(X)) -> mark(U272(X)) 102.08/27.19 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.19 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.19 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.19 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.19 s(mark(X)) -> mark(s(X)) 102.08/27.19 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.19 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.19 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.19 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.19 head(mark(X)) -> mark(head(X)) 102.08/27.19 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.19 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.19 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.19 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.19 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.19 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.19 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.19 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.19 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.19 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.19 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.19 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.19 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.19 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.19 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.19 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.19 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.19 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.19 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.19 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.19 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.19 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.19 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.19 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.19 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.19 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.19 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.19 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.19 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.19 fst(mark(X)) -> mark(fst(X)) 102.08/27.19 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.19 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.19 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.19 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.19 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.19 U46(mark(X)) -> mark(U46(X)) 102.08/27.19 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.19 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.19 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.19 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.19 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.19 U56(mark(X)) -> mark(U56(X)) 102.08/27.19 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.19 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.19 U63(mark(X)) -> mark(U63(X)) 102.08/27.19 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.19 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.19 U73(mark(X)) -> mark(U73(X)) 102.08/27.19 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.19 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.19 U83(mark(X)) -> mark(U83(X)) 102.08/27.19 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.19 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.19 U93(mark(X)) -> mark(U93(X)) 102.08/27.19 tail(mark(X)) -> mark(tail(X)) 102.08/27.19 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.19 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.19 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.19 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.19 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(tt) -> ok(tt) 102.08/27.19 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.19 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.19 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.19 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.19 proper(U106(X)) -> U106(proper(X)) 102.08/27.19 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.19 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.19 proper(U112(X)) -> U112(proper(X)) 102.08/27.19 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.19 proper(U122(X)) -> U122(proper(X)) 102.08/27.19 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U131(X)) -> U131(proper(X)) 102.08/27.19 proper(snd(X)) -> snd(proper(X)) 102.08/27.19 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.19 proper(U141(X)) -> U141(proper(X)) 102.08/27.19 proper(U151(X)) -> U151(proper(X)) 102.08/27.19 proper(U161(X)) -> U161(proper(X)) 102.08/27.19 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.19 proper(U172(X)) -> U172(proper(X)) 102.08/27.19 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.19 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.19 proper(U183(X)) -> U183(proper(X)) 102.08/27.19 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.19 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.19 proper(U193(X)) -> U193(proper(X)) 102.08/27.19 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.19 proper(U206(X)) -> U206(proper(X)) 102.08/27.19 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U211(X)) -> U211(proper(X)) 102.08/27.19 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U221(X)) -> U221(proper(X)) 102.08/27.19 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.19 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.19 proper(U232(X)) -> U232(proper(X)) 102.08/27.19 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.19 proper(U246(X)) -> U246(proper(X)) 102.08/27.19 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.19 proper(U256(X)) -> U256(proper(X)) 102.08/27.19 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.19 proper(U262(X)) -> U262(proper(X)) 102.08/27.19 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.19 proper(U272(X)) -> U272(proper(X)) 102.08/27.19 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.19 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.19 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.19 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.19 proper(s(X)) -> s(proper(X)) 102.08/27.19 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(head(X)) -> head(proper(X)) 102.08/27.19 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.19 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.19 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.19 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.19 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.19 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.19 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.19 proper(nil) -> ok(nil) 102.08/27.19 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.19 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.19 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.19 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.19 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.19 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.19 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(fst(X)) -> fst(proper(X)) 102.08/27.19 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.19 proper(U46(X)) -> U46(proper(X)) 102.08/27.19 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.19 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.19 proper(U56(X)) -> U56(proper(X)) 102.08/27.19 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.19 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.19 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.19 proper(U63(X)) -> U63(proper(X)) 102.08/27.19 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.19 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.19 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.19 proper(U73(X)) -> U73(proper(X)) 102.08/27.19 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.19 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.19 proper(U83(X)) -> U83(proper(X)) 102.08/27.19 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.19 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.19 proper(U93(X)) -> U93(proper(X)) 102.08/27.19 proper(tail(X)) -> tail(proper(X)) 102.08/27.19 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.19 proper(0') -> ok(0') 102.08/27.19 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.19 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.19 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.19 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.19 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.19 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.19 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.19 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.19 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.19 U106(ok(X)) -> ok(U106(X)) 102.08/27.19 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.19 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.19 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.19 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.19 U112(ok(X)) -> ok(U112(X)) 102.08/27.19 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.19 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.19 U122(ok(X)) -> ok(U122(X)) 102.08/27.19 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.19 U131(ok(X)) -> ok(U131(X)) 102.08/27.19 snd(ok(X)) -> ok(snd(X)) 102.08/27.19 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.19 U141(ok(X)) -> ok(U141(X)) 102.08/27.19 U151(ok(X)) -> ok(U151(X)) 102.08/27.19 U161(ok(X)) -> ok(U161(X)) 102.08/27.19 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.19 U172(ok(X)) -> ok(U172(X)) 102.08/27.19 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.19 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.19 U183(ok(X)) -> ok(U183(X)) 102.08/27.19 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.19 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.19 U193(ok(X)) -> ok(U193(X)) 102.08/27.19 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.19 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.19 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.19 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.19 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.19 U206(ok(X)) -> ok(U206(X)) 102.08/27.19 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.19 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.19 U211(ok(X)) -> ok(U211(X)) 102.08/27.19 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.19 U221(ok(X)) -> ok(U221(X)) 102.08/27.19 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.19 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.19 U232(ok(X)) -> ok(U232(X)) 102.08/27.19 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.19 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.19 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.19 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.19 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.19 U246(ok(X)) -> ok(U246(X)) 102.08/27.19 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.19 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.19 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.19 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.19 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.19 U256(ok(X)) -> ok(U256(X)) 102.08/27.19 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.19 U262(ok(X)) -> ok(U262(X)) 102.08/27.19 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.19 U272(ok(X)) -> ok(U272(X)) 102.08/27.19 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.19 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.19 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.19 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.19 s(ok(X)) -> ok(s(X)) 102.08/27.19 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.19 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.19 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.19 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.19 head(ok(X)) -> ok(head(X)) 102.08/27.19 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.19 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.19 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.19 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.19 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.19 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.19 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.19 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.19 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.19 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.19 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.19 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.19 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.19 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.19 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.19 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.19 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.19 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.19 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.19 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.19 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.19 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.19 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.19 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.19 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.19 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.19 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.19 fst(ok(X)) -> ok(fst(X)) 102.08/27.19 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.19 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.19 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.19 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.19 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.19 U46(ok(X)) -> ok(U46(X)) 102.08/27.19 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.19 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.19 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.19 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.19 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.19 U56(ok(X)) -> ok(U56(X)) 102.08/27.19 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.19 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.19 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.19 U63(ok(X)) -> ok(U63(X)) 102.08/27.19 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.19 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.19 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.19 U73(ok(X)) -> ok(U73(X)) 102.08/27.19 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.19 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.19 U83(ok(X)) -> ok(U83(X)) 102.08/27.19 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.19 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.19 U93(ok(X)) -> ok(U93(X)) 102.08/27.19 tail(ok(X)) -> ok(tail(X)) 102.08/27.19 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.19 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.19 top(mark(X)) -> top(proper(X)) 102.08/27.19 top(ok(X)) -> top(active(X)) 102.08/27.19 102.08/27.19 Types: 102.08/27.19 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 tt :: tt:mark:nil:0':ok 102.08/27.19 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 nil :: tt:mark:nil:0':ok 102.08/27.19 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.19 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 0' :: tt:mark:nil:0':ok 102.08/27.20 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 top :: tt:mark:nil:0':ok -> top 102.08/27.20 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.20 hole_top2_0 :: top 102.08/27.20 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.20 102.08/27.20 102.08/27.20 Lemmas: 102.08/27.20 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.20 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.20 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.20 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.20 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.20 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.20 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.20 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.20 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.20 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.20 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.20 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.20 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.20 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.20 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.20 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.20 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.20 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.20 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.20 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.20 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.20 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.20 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.20 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.20 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.20 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.20 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.20 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.20 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.20 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.20 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.20 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.20 102.08/27.20 102.08/27.20 Generator Equations: 102.08/27.20 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.20 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.20 102.08/27.20 102.08/27.20 The following defined symbols remain to be analysed: 102.08/27.20 U253, active, U254, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.20 102.08/27.20 They will be analysed ascendingly in the following order: 102.08/27.20 U253 < active 102.08/27.20 U254 < active 102.08/27.20 U255 < active 102.08/27.20 U256 < active 102.08/27.20 U262 < active 102.08/27.20 U272 < active 102.08/27.20 U282 < active 102.08/27.20 cons < active 102.08/27.20 natsFrom < active 102.08/27.20 s < active 102.08/27.20 U292 < active 102.08/27.20 U293 < active 102.08/27.20 U294 < active 102.08/27.20 head < active 102.08/27.20 afterNth < active 102.08/27.20 U302 < active 102.08/27.20 U303 < active 102.08/27.20 U304 < active 102.08/27.20 U32 < active 102.08/27.20 U312 < active 102.08/27.20 pair < active 102.08/27.20 U33 < active 102.08/27.20 U322 < active 102.08/27.20 U323 < active 102.08/27.20 U324 < active 102.08/27.20 U325 < active 102.08/27.20 U326 < active 102.08/27.20 U327 < active 102.08/27.20 U34 < active 102.08/27.20 U332 < active 102.08/27.20 U333 < active 102.08/27.20 U334 < active 102.08/27.20 U342 < active 102.08/27.20 U343 < active 102.08/27.20 U344 < active 102.08/27.20 fst < active 102.08/27.20 U42 < active 102.08/27.20 U43 < active 102.08/27.20 U44 < active 102.08/27.20 U45 < active 102.08/27.20 U46 < active 102.08/27.20 U52 < active 102.08/27.20 U53 < active 102.08/27.20 U54 < active 102.08/27.20 U55 < active 102.08/27.20 U56 < active 102.08/27.20 U62 < active 102.08/27.20 isPLNatKind < active 102.08/27.20 U63 < active 102.08/27.20 isPLNat < active 102.08/27.20 U72 < active 102.08/27.20 U73 < active 102.08/27.20 U82 < active 102.08/27.20 U83 < active 102.08/27.20 U92 < active 102.08/27.20 U93 < active 102.08/27.20 U11 < active 102.08/27.20 U21 < active 102.08/27.20 U31 < active 102.08/27.20 U41 < active 102.08/27.20 U51 < active 102.08/27.20 U61 < active 102.08/27.20 U71 < active 102.08/27.20 U81 < active 102.08/27.20 U91 < active 102.08/27.20 U101 < active 102.08/27.20 U111 < active 102.08/27.20 U121 < active 102.08/27.20 U131 < active 102.08/27.20 U141 < active 102.08/27.20 U151 < active 102.08/27.20 U161 < active 102.08/27.20 U171 < active 102.08/27.20 U181 < active 102.08/27.20 U191 < active 102.08/27.20 U201 < active 102.08/27.20 U211 < active 102.08/27.20 U221 < active 102.08/27.20 U231 < active 102.08/27.20 U241 < active 102.08/27.20 U251 < active 102.08/27.20 U261 < active 102.08/27.20 U271 < active 102.08/27.20 U281 < active 102.08/27.20 U291 < active 102.08/27.20 U301 < active 102.08/27.20 U311 < active 102.08/27.20 U321 < active 102.08/27.20 U331 < active 102.08/27.20 U341 < active 102.08/27.20 tail < active 102.08/27.20 take < active 102.08/27.20 sel < active 102.08/27.20 active < top 102.08/27.20 U253 < proper 102.08/27.20 U254 < proper 102.08/27.20 U255 < proper 102.08/27.20 U256 < proper 102.08/27.20 U262 < proper 102.08/27.20 U272 < proper 102.08/27.20 U282 < proper 102.08/27.20 cons < proper 102.08/27.20 natsFrom < proper 102.08/27.20 s < proper 102.08/27.20 U292 < proper 102.08/27.20 U293 < proper 102.08/27.20 U294 < proper 102.08/27.20 head < proper 102.08/27.20 afterNth < proper 102.08/27.20 U302 < proper 102.08/27.20 U303 < proper 102.08/27.20 U304 < proper 102.08/27.20 U32 < proper 102.08/27.20 U312 < proper 102.08/27.20 pair < proper 102.08/27.20 U33 < proper 102.08/27.20 U322 < proper 102.08/27.20 U323 < proper 102.08/27.20 U324 < proper 102.08/27.20 U325 < proper 102.08/27.20 U326 < proper 102.08/27.20 U327 < proper 102.08/27.20 U34 < proper 102.08/27.20 U332 < proper 102.08/27.20 U333 < proper 102.08/27.20 U334 < proper 102.08/27.20 U342 < proper 102.08/27.20 U343 < proper 102.08/27.20 U344 < proper 102.08/27.20 fst < proper 102.08/27.20 U42 < proper 102.08/27.20 U43 < proper 102.08/27.20 U44 < proper 102.08/27.20 U45 < proper 102.08/27.20 U46 < proper 102.08/27.20 U52 < proper 102.08/27.20 U53 < proper 102.08/27.20 U54 < proper 102.08/27.20 U55 < proper 102.08/27.20 U56 < proper 102.08/27.20 U62 < proper 102.08/27.20 isPLNatKind < proper 102.08/27.20 U63 < proper 102.08/27.20 isPLNat < proper 102.08/27.20 U72 < proper 102.08/27.20 U73 < proper 102.08/27.20 U82 < proper 102.08/27.20 U83 < proper 102.08/27.20 U92 < proper 102.08/27.20 U93 < proper 102.08/27.20 U11 < proper 102.08/27.20 U21 < proper 102.08/27.20 U31 < proper 102.08/27.20 U41 < proper 102.08/27.20 U51 < proper 102.08/27.20 U61 < proper 102.08/27.20 U71 < proper 102.08/27.20 U81 < proper 102.08/27.20 U91 < proper 102.08/27.20 U101 < proper 102.08/27.20 U111 < proper 102.08/27.20 U121 < proper 102.08/27.20 U131 < proper 102.08/27.20 U141 < proper 102.08/27.20 U151 < proper 102.08/27.20 U161 < proper 102.08/27.20 U171 < proper 102.08/27.20 U181 < proper 102.08/27.20 U191 < proper 102.08/27.20 U201 < proper 102.08/27.20 U211 < proper 102.08/27.20 U221 < proper 102.08/27.20 U231 < proper 102.08/27.20 U241 < proper 102.08/27.20 U251 < proper 102.08/27.20 U261 < proper 102.08/27.20 U271 < proper 102.08/27.20 U281 < proper 102.08/27.20 U291 < proper 102.08/27.20 U301 < proper 102.08/27.20 U311 < proper 102.08/27.20 U321 < proper 102.08/27.20 U331 < proper 102.08/27.20 U341 < proper 102.08/27.20 tail < proper 102.08/27.20 take < proper 102.08/27.20 sel < proper 102.08/27.20 proper < top 102.08/27.20 102.08/27.20 ---------------------------------------- 102.08/27.20 102.08/27.20 (93) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.20 Proved the following rewrite lemma: 102.08/27.20 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.20 102.08/27.20 Induction Base: 102.08/27.20 U253(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 102.08/27.20 102.08/27.20 Induction Step: 102.08/27.20 U253(gen_tt:mark:nil:0':ok3_0(+(1, +(n523188_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 102.08/27.20 mark(U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 102.08/27.20 mark(*4_0) 102.08/27.20 102.08/27.20 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.20 ---------------------------------------- 102.08/27.20 102.08/27.20 (94) 102.08/27.20 Obligation: 102.08/27.20 TRS: 102.08/27.20 Rules: 102.08/27.20 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.20 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.20 active(U106(tt)) -> mark(tt) 102.08/27.20 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.20 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.20 active(U112(tt)) -> mark(tt) 102.08/27.20 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.20 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.20 active(U122(tt)) -> mark(tt) 102.08/27.20 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.20 active(U131(tt)) -> mark(tt) 102.08/27.20 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.20 active(U141(tt)) -> mark(tt) 102.08/27.20 active(U151(tt)) -> mark(tt) 102.08/27.20 active(U161(tt)) -> mark(tt) 102.08/27.20 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.20 active(U172(tt)) -> mark(tt) 102.08/27.20 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.20 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.20 active(U183(tt)) -> mark(tt) 102.08/27.20 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.20 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.20 active(U193(tt)) -> mark(tt) 102.08/27.20 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.20 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.20 active(U206(tt)) -> mark(tt) 102.08/27.20 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.20 active(U211(tt)) -> mark(tt) 102.08/27.20 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.20 active(U221(tt)) -> mark(tt) 102.08/27.20 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.20 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.20 active(U232(tt)) -> mark(tt) 102.08/27.20 active(U24(tt, X)) -> mark(X) 102.08/27.20 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.20 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.20 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.20 active(U246(tt)) -> mark(tt) 102.08/27.20 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.20 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.20 active(U256(tt)) -> mark(tt) 102.08/27.20 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.20 active(U262(tt)) -> mark(tt) 102.08/27.20 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.20 active(U272(tt)) -> mark(tt) 102.08/27.20 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.20 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.20 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.20 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.20 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.20 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.20 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.20 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.20 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.20 active(U304(tt, Y)) -> mark(Y) 102.08/27.20 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.20 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.20 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.20 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.20 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.20 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.20 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.20 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.20 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.20 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.20 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.20 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.20 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.20 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.20 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.20 active(U334(tt, XS)) -> mark(XS) 102.08/27.20 active(U34(tt, N)) -> mark(N) 102.08/27.20 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.20 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.20 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.20 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.20 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.20 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.20 active(U46(tt)) -> mark(tt) 102.08/27.20 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.20 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.20 active(U56(tt)) -> mark(tt) 102.08/27.20 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.20 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.20 active(U63(tt)) -> mark(tt) 102.08/27.20 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.20 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.20 active(U73(tt)) -> mark(tt) 102.08/27.20 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.20 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.20 active(U83(tt)) -> mark(tt) 102.08/27.20 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.20 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.20 active(U93(tt)) -> mark(tt) 102.08/27.20 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.20 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.20 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.20 active(isLNat(nil)) -> mark(tt) 102.08/27.20 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.20 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.20 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.20 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.20 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNatKind(nil)) -> mark(tt) 102.08/27.20 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.20 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.20 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.20 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.20 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.20 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.20 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.20 active(isNatural(0')) -> mark(tt) 102.08/27.20 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.20 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.20 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isNaturalKind(0')) -> mark(tt) 102.08/27.20 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.20 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.20 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.20 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.20 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.20 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.20 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.20 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.20 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.20 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.20 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.20 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.20 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.20 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.20 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.20 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.20 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.20 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.20 active(U106(X)) -> U106(active(X)) 102.08/27.20 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.20 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.20 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.20 active(U112(X)) -> U112(active(X)) 102.08/27.20 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.20 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.20 active(U122(X)) -> U122(active(X)) 102.08/27.20 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.20 active(U131(X)) -> U131(active(X)) 102.08/27.20 active(snd(X)) -> snd(active(X)) 102.08/27.20 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.20 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.20 active(U141(X)) -> U141(active(X)) 102.08/27.20 active(U151(X)) -> U151(active(X)) 102.08/27.20 active(U161(X)) -> U161(active(X)) 102.08/27.20 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.20 active(U172(X)) -> U172(active(X)) 102.08/27.20 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.20 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.20 active(U183(X)) -> U183(active(X)) 102.08/27.20 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.20 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.20 active(U193(X)) -> U193(active(X)) 102.08/27.20 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.20 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.20 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.20 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.20 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.20 active(U206(X)) -> U206(active(X)) 102.08/27.20 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.20 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.20 active(U211(X)) -> U211(active(X)) 102.08/27.20 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.20 active(U221(X)) -> U221(active(X)) 102.08/27.20 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.20 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.20 active(U232(X)) -> U232(active(X)) 102.08/27.20 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.20 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.20 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.20 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.20 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.20 active(U246(X)) -> U246(active(X)) 102.08/27.20 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.20 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.20 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.20 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.20 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.20 active(U256(X)) -> U256(active(X)) 102.08/27.20 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.20 active(U262(X)) -> U262(active(X)) 102.08/27.20 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.20 active(U272(X)) -> U272(active(X)) 102.08/27.20 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.20 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.20 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.20 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.20 active(s(X)) -> s(active(X)) 102.08/27.20 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.20 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.20 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.20 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.20 active(head(X)) -> head(active(X)) 102.08/27.20 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.20 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.20 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.20 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.20 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.20 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.20 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.20 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.20 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.20 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.20 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.20 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.20 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.20 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.20 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.20 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.20 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.20 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.20 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.20 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.20 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.20 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.20 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.20 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.20 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.20 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.20 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.20 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.20 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.20 active(fst(X)) -> fst(active(X)) 102.08/27.20 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.20 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.20 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.20 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.20 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.20 active(U46(X)) -> U46(active(X)) 102.08/27.20 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.20 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.20 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.20 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.20 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.20 active(U56(X)) -> U56(active(X)) 102.08/27.20 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.20 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.20 active(U63(X)) -> U63(active(X)) 102.08/27.20 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.20 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.20 active(U73(X)) -> U73(active(X)) 102.08/27.20 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.20 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.20 active(U83(X)) -> U83(active(X)) 102.08/27.20 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.20 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.20 active(U93(X)) -> U93(active(X)) 102.08/27.20 active(tail(X)) -> tail(active(X)) 102.08/27.20 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.20 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.20 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.20 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.20 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.20 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.20 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.20 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.20 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.20 U106(mark(X)) -> mark(U106(X)) 102.08/27.20 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.20 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.20 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.20 U112(mark(X)) -> mark(U112(X)) 102.08/27.20 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.20 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.20 U122(mark(X)) -> mark(U122(X)) 102.08/27.20 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.20 U131(mark(X)) -> mark(U131(X)) 102.08/27.20 snd(mark(X)) -> mark(snd(X)) 102.08/27.20 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.20 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.20 U141(mark(X)) -> mark(U141(X)) 102.08/27.20 U151(mark(X)) -> mark(U151(X)) 102.08/27.20 U161(mark(X)) -> mark(U161(X)) 102.08/27.20 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.20 U172(mark(X)) -> mark(U172(X)) 102.08/27.20 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.20 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.20 U183(mark(X)) -> mark(U183(X)) 102.08/27.20 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.20 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.20 U193(mark(X)) -> mark(U193(X)) 102.08/27.20 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.20 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.20 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.20 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.20 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.20 U206(mark(X)) -> mark(U206(X)) 102.08/27.20 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.20 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.20 U211(mark(X)) -> mark(U211(X)) 102.08/27.20 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.20 U221(mark(X)) -> mark(U221(X)) 102.08/27.20 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.20 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.20 U232(mark(X)) -> mark(U232(X)) 102.08/27.20 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.20 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.20 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.20 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.20 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.20 U246(mark(X)) -> mark(U246(X)) 102.08/27.20 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.20 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.20 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.20 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.20 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.20 U256(mark(X)) -> mark(U256(X)) 102.08/27.20 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.20 U262(mark(X)) -> mark(U262(X)) 102.08/27.20 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.20 U272(mark(X)) -> mark(U272(X)) 102.08/27.20 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.20 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.20 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.20 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.20 s(mark(X)) -> mark(s(X)) 102.08/27.20 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.20 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.20 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.20 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.20 head(mark(X)) -> mark(head(X)) 102.08/27.20 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.20 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.20 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.20 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.20 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.20 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.20 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.20 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.20 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.20 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.20 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.20 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.20 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.20 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.20 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.20 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.20 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.20 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.20 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.20 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.20 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.20 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.20 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.20 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.20 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.20 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.20 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.20 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.20 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.20 fst(mark(X)) -> mark(fst(X)) 102.08/27.20 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.20 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.20 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.20 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.20 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.20 U46(mark(X)) -> mark(U46(X)) 102.08/27.20 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.20 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.20 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.20 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.20 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.20 U56(mark(X)) -> mark(U56(X)) 102.08/27.20 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.20 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.20 U63(mark(X)) -> mark(U63(X)) 102.08/27.20 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.20 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.20 U73(mark(X)) -> mark(U73(X)) 102.08/27.20 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.20 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.20 U83(mark(X)) -> mark(U83(X)) 102.08/27.20 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.20 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.20 U93(mark(X)) -> mark(U93(X)) 102.08/27.20 tail(mark(X)) -> mark(tail(X)) 102.08/27.20 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.20 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.20 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.20 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.20 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(tt) -> ok(tt) 102.08/27.20 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.20 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.20 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.20 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.20 proper(U106(X)) -> U106(proper(X)) 102.08/27.20 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.20 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.20 proper(U112(X)) -> U112(proper(X)) 102.08/27.20 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.20 proper(U122(X)) -> U122(proper(X)) 102.08/27.20 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U131(X)) -> U131(proper(X)) 102.08/27.20 proper(snd(X)) -> snd(proper(X)) 102.08/27.20 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.20 proper(U141(X)) -> U141(proper(X)) 102.08/27.20 proper(U151(X)) -> U151(proper(X)) 102.08/27.20 proper(U161(X)) -> U161(proper(X)) 102.08/27.20 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.20 proper(U172(X)) -> U172(proper(X)) 102.08/27.20 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.20 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.20 proper(U183(X)) -> U183(proper(X)) 102.08/27.20 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.20 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.20 proper(U193(X)) -> U193(proper(X)) 102.08/27.20 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.20 proper(U206(X)) -> U206(proper(X)) 102.08/27.20 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U211(X)) -> U211(proper(X)) 102.08/27.20 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U221(X)) -> U221(proper(X)) 102.08/27.20 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.20 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.20 proper(U232(X)) -> U232(proper(X)) 102.08/27.20 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.20 proper(U246(X)) -> U246(proper(X)) 102.08/27.20 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.20 proper(U256(X)) -> U256(proper(X)) 102.08/27.20 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.20 proper(U262(X)) -> U262(proper(X)) 102.08/27.20 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.20 proper(U272(X)) -> U272(proper(X)) 102.08/27.20 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.20 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.20 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.20 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.20 proper(s(X)) -> s(proper(X)) 102.08/27.20 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(head(X)) -> head(proper(X)) 102.08/27.20 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.20 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.20 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.20 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.20 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.20 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.20 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.20 proper(nil) -> ok(nil) 102.08/27.20 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.20 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.20 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.20 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.20 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.20 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(fst(X)) -> fst(proper(X)) 102.08/27.20 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.20 proper(U46(X)) -> U46(proper(X)) 102.08/27.20 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.20 proper(U56(X)) -> U56(proper(X)) 102.08/27.20 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.20 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.20 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.20 proper(U63(X)) -> U63(proper(X)) 102.08/27.20 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.20 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.20 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.20 proper(U73(X)) -> U73(proper(X)) 102.08/27.20 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.20 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.20 proper(U83(X)) -> U83(proper(X)) 102.08/27.20 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.20 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.20 proper(U93(X)) -> U93(proper(X)) 102.08/27.20 proper(tail(X)) -> tail(proper(X)) 102.08/27.20 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.20 proper(0') -> ok(0') 102.08/27.20 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.20 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.20 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.20 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.20 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.20 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.20 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.20 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.20 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.20 U106(ok(X)) -> ok(U106(X)) 102.08/27.20 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.20 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.20 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.20 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.20 U112(ok(X)) -> ok(U112(X)) 102.08/27.20 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.20 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.20 U122(ok(X)) -> ok(U122(X)) 102.08/27.20 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.20 U131(ok(X)) -> ok(U131(X)) 102.08/27.20 snd(ok(X)) -> ok(snd(X)) 102.08/27.20 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.20 U141(ok(X)) -> ok(U141(X)) 102.08/27.20 U151(ok(X)) -> ok(U151(X)) 102.08/27.20 U161(ok(X)) -> ok(U161(X)) 102.08/27.20 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.20 U172(ok(X)) -> ok(U172(X)) 102.08/27.20 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.20 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.20 U183(ok(X)) -> ok(U183(X)) 102.08/27.20 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.20 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.20 U193(ok(X)) -> ok(U193(X)) 102.08/27.20 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.20 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.20 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.20 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.20 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.20 U206(ok(X)) -> ok(U206(X)) 102.08/27.20 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.20 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.20 U211(ok(X)) -> ok(U211(X)) 102.08/27.20 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.20 U221(ok(X)) -> ok(U221(X)) 102.08/27.20 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.20 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.20 U232(ok(X)) -> ok(U232(X)) 102.08/27.20 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.20 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.20 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.20 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.20 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.20 U246(ok(X)) -> ok(U246(X)) 102.08/27.20 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.20 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.20 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.20 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.20 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.20 U256(ok(X)) -> ok(U256(X)) 102.08/27.20 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.20 U262(ok(X)) -> ok(U262(X)) 102.08/27.20 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.20 U272(ok(X)) -> ok(U272(X)) 102.08/27.20 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.20 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.20 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.20 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.20 s(ok(X)) -> ok(s(X)) 102.08/27.20 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.20 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.20 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.20 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.20 head(ok(X)) -> ok(head(X)) 102.08/27.20 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.20 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.20 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.20 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.20 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.20 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.20 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.20 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.20 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.20 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.20 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.20 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.20 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.20 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.20 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.20 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.20 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.20 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.20 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.20 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.20 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.20 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.20 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.20 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.20 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.20 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.20 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.20 fst(ok(X)) -> ok(fst(X)) 102.08/27.20 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.20 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.20 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.20 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.20 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.20 U46(ok(X)) -> ok(U46(X)) 102.08/27.20 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.20 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.20 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.20 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.20 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.20 U56(ok(X)) -> ok(U56(X)) 102.08/27.20 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.20 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.20 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.20 U63(ok(X)) -> ok(U63(X)) 102.08/27.20 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.20 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.20 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.20 U73(ok(X)) -> ok(U73(X)) 102.08/27.20 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.20 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.20 U83(ok(X)) -> ok(U83(X)) 102.08/27.20 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.20 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.20 U93(ok(X)) -> ok(U93(X)) 102.08/27.20 tail(ok(X)) -> ok(tail(X)) 102.08/27.20 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.20 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.20 top(mark(X)) -> top(proper(X)) 102.08/27.20 top(ok(X)) -> top(active(X)) 102.08/27.20 102.08/27.20 Types: 102.08/27.20 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 tt :: tt:mark:nil:0':ok 102.08/27.20 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 nil :: tt:mark:nil:0':ok 102.08/27.20 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 0' :: tt:mark:nil:0':ok 102.08/27.20 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 top :: tt:mark:nil:0':ok -> top 102.08/27.20 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.20 hole_top2_0 :: top 102.08/27.20 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.20 102.08/27.20 102.08/27.20 Lemmas: 102.08/27.20 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.20 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.20 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.20 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.20 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.20 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.20 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.20 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.20 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.20 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.20 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.20 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.20 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.20 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.20 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.20 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.20 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.20 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.20 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.20 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.20 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.20 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.20 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.20 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.20 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.20 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.20 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.20 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.20 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.20 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.20 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.20 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.20 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.20 102.08/27.20 102.08/27.20 Generator Equations: 102.08/27.20 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.20 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.20 102.08/27.20 102.08/27.20 The following defined symbols remain to be analysed: 102.08/27.20 U254, active, U255, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.20 102.08/27.20 They will be analysed ascendingly in the following order: 102.08/27.20 U254 < active 102.08/27.20 U255 < active 102.08/27.20 U256 < active 102.08/27.20 U262 < active 102.08/27.20 U272 < active 102.08/27.20 U282 < active 102.08/27.20 cons < active 102.08/27.20 natsFrom < active 102.08/27.20 s < active 102.08/27.20 U292 < active 102.08/27.20 U293 < active 102.08/27.20 U294 < active 102.08/27.20 head < active 102.08/27.20 afterNth < active 102.08/27.20 U302 < active 102.08/27.20 U303 < active 102.08/27.20 U304 < active 102.08/27.20 U32 < active 102.08/27.20 U312 < active 102.08/27.20 pair < active 102.08/27.20 U33 < active 102.08/27.20 U322 < active 102.08/27.20 U323 < active 102.08/27.20 U324 < active 102.08/27.20 U325 < active 102.08/27.20 U326 < active 102.08/27.20 U327 < active 102.08/27.20 U34 < active 102.08/27.20 U332 < active 102.08/27.20 U333 < active 102.08/27.20 U334 < active 102.08/27.20 U342 < active 102.08/27.20 U343 < active 102.08/27.20 U344 < active 102.08/27.20 fst < active 102.08/27.20 U42 < active 102.08/27.20 U43 < active 102.08/27.20 U44 < active 102.08/27.20 U45 < active 102.08/27.20 U46 < active 102.08/27.20 U52 < active 102.08/27.20 U53 < active 102.08/27.20 U54 < active 102.08/27.20 U55 < active 102.08/27.20 U56 < active 102.08/27.20 U62 < active 102.08/27.20 isPLNatKind < active 102.08/27.20 U63 < active 102.08/27.20 isPLNat < active 102.08/27.20 U72 < active 102.08/27.20 U73 < active 102.08/27.20 U82 < active 102.08/27.20 U83 < active 102.08/27.20 U92 < active 102.08/27.20 U93 < active 102.08/27.20 U11 < active 102.08/27.20 U21 < active 102.08/27.20 U31 < active 102.08/27.20 U41 < active 102.08/27.20 U51 < active 102.08/27.20 U61 < active 102.08/27.20 U71 < active 102.08/27.20 U81 < active 102.08/27.20 U91 < active 102.08/27.20 U101 < active 102.08/27.20 U111 < active 102.08/27.20 U121 < active 102.08/27.20 U131 < active 102.08/27.20 U141 < active 102.08/27.20 U151 < active 102.08/27.20 U161 < active 102.08/27.20 U171 < active 102.08/27.20 U181 < active 102.08/27.20 U191 < active 102.08/27.20 U201 < active 102.08/27.20 U211 < active 102.08/27.20 U221 < active 102.08/27.20 U231 < active 102.08/27.20 U241 < active 102.08/27.20 U251 < active 102.08/27.20 U261 < active 102.08/27.20 U271 < active 102.08/27.20 U281 < active 102.08/27.20 U291 < active 102.08/27.20 U301 < active 102.08/27.20 U311 < active 102.08/27.20 U321 < active 102.08/27.20 U331 < active 102.08/27.20 U341 < active 102.08/27.20 tail < active 102.08/27.20 take < active 102.08/27.20 sel < active 102.08/27.20 active < top 102.08/27.20 U254 < proper 102.08/27.20 U255 < proper 102.08/27.20 U256 < proper 102.08/27.20 U262 < proper 102.08/27.20 U272 < proper 102.08/27.20 U282 < proper 102.08/27.20 cons < proper 102.08/27.20 natsFrom < proper 102.08/27.20 s < proper 102.08/27.20 U292 < proper 102.08/27.20 U293 < proper 102.08/27.20 U294 < proper 102.08/27.20 head < proper 102.08/27.20 afterNth < proper 102.08/27.20 U302 < proper 102.08/27.20 U303 < proper 102.08/27.20 U304 < proper 102.08/27.20 U32 < proper 102.08/27.20 U312 < proper 102.08/27.20 pair < proper 102.08/27.20 U33 < proper 102.08/27.20 U322 < proper 102.08/27.20 U323 < proper 102.08/27.20 U324 < proper 102.08/27.20 U325 < proper 102.08/27.20 U326 < proper 102.08/27.20 U327 < proper 102.08/27.20 U34 < proper 102.08/27.20 U332 < proper 102.08/27.20 U333 < proper 102.08/27.20 U334 < proper 102.08/27.20 U342 < proper 102.08/27.20 U343 < proper 102.08/27.20 U344 < proper 102.08/27.20 fst < proper 102.08/27.20 U42 < proper 102.08/27.20 U43 < proper 102.08/27.20 U44 < proper 102.08/27.20 U45 < proper 102.08/27.20 U46 < proper 102.08/27.20 U52 < proper 102.08/27.20 U53 < proper 102.08/27.20 U54 < proper 102.08/27.20 U55 < proper 102.08/27.20 U56 < proper 102.08/27.20 U62 < proper 102.08/27.20 isPLNatKind < proper 102.08/27.20 U63 < proper 102.08/27.20 isPLNat < proper 102.08/27.20 U72 < proper 102.08/27.20 U73 < proper 102.08/27.20 U82 < proper 102.08/27.20 U83 < proper 102.08/27.20 U92 < proper 102.08/27.20 U93 < proper 102.08/27.20 U11 < proper 102.08/27.20 U21 < proper 102.08/27.20 U31 < proper 102.08/27.20 U41 < proper 102.08/27.20 U51 < proper 102.08/27.20 U61 < proper 102.08/27.20 U71 < proper 102.08/27.20 U81 < proper 102.08/27.20 U91 < proper 102.08/27.20 U101 < proper 102.08/27.20 U111 < proper 102.08/27.20 U121 < proper 102.08/27.20 U131 < proper 102.08/27.20 U141 < proper 102.08/27.20 U151 < proper 102.08/27.20 U161 < proper 102.08/27.20 U171 < proper 102.08/27.20 U181 < proper 102.08/27.20 U191 < proper 102.08/27.20 U201 < proper 102.08/27.20 U211 < proper 102.08/27.20 U221 < proper 102.08/27.20 U231 < proper 102.08/27.20 U241 < proper 102.08/27.20 U251 < proper 102.08/27.20 U261 < proper 102.08/27.20 U271 < proper 102.08/27.20 U281 < proper 102.08/27.20 U291 < proper 102.08/27.20 U301 < proper 102.08/27.20 U311 < proper 102.08/27.20 U321 < proper 102.08/27.20 U331 < proper 102.08/27.20 U341 < proper 102.08/27.20 tail < proper 102.08/27.20 take < proper 102.08/27.20 sel < proper 102.08/27.20 proper < top 102.08/27.20 102.08/27.20 ---------------------------------------- 102.08/27.20 102.08/27.20 (95) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.20 Proved the following rewrite lemma: 102.08/27.20 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.20 102.08/27.20 Induction Base: 102.08/27.20 U254(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) 102.08/27.20 102.08/27.20 Induction Step: 102.08/27.20 U254(gen_tt:mark:nil:0':ok3_0(+(1, +(n556010_0, 1))), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) ->_R^Omega(1) 102.08/27.20 mark(U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c))) ->_IH 102.08/27.20 mark(*4_0) 102.08/27.20 102.08/27.20 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.20 ---------------------------------------- 102.08/27.20 102.08/27.20 (96) 102.08/27.20 Obligation: 102.08/27.20 TRS: 102.08/27.20 Rules: 102.08/27.20 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.20 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.20 active(U106(tt)) -> mark(tt) 102.08/27.20 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.20 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.20 active(U112(tt)) -> mark(tt) 102.08/27.20 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.20 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.20 active(U122(tt)) -> mark(tt) 102.08/27.20 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.20 active(U131(tt)) -> mark(tt) 102.08/27.20 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.20 active(U141(tt)) -> mark(tt) 102.08/27.20 active(U151(tt)) -> mark(tt) 102.08/27.20 active(U161(tt)) -> mark(tt) 102.08/27.20 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.20 active(U172(tt)) -> mark(tt) 102.08/27.20 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.20 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.20 active(U183(tt)) -> mark(tt) 102.08/27.20 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.20 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.20 active(U193(tt)) -> mark(tt) 102.08/27.20 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.20 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.20 active(U206(tt)) -> mark(tt) 102.08/27.20 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.20 active(U211(tt)) -> mark(tt) 102.08/27.20 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.20 active(U221(tt)) -> mark(tt) 102.08/27.20 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.20 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.20 active(U232(tt)) -> mark(tt) 102.08/27.20 active(U24(tt, X)) -> mark(X) 102.08/27.20 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.20 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.20 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.20 active(U246(tt)) -> mark(tt) 102.08/27.20 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.20 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.20 active(U256(tt)) -> mark(tt) 102.08/27.20 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.20 active(U262(tt)) -> mark(tt) 102.08/27.20 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.20 active(U272(tt)) -> mark(tt) 102.08/27.20 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.20 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.20 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.20 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.20 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.20 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.20 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.20 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.20 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.20 active(U304(tt, Y)) -> mark(Y) 102.08/27.20 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.20 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.20 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.20 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.20 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.20 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.20 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.20 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.20 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.20 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.20 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.20 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.20 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.20 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.20 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.20 active(U334(tt, XS)) -> mark(XS) 102.08/27.20 active(U34(tt, N)) -> mark(N) 102.08/27.20 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.20 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.20 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.20 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.20 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.20 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.20 active(U46(tt)) -> mark(tt) 102.08/27.20 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.20 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.20 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.20 active(U56(tt)) -> mark(tt) 102.08/27.20 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.20 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.20 active(U63(tt)) -> mark(tt) 102.08/27.20 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.20 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.20 active(U73(tt)) -> mark(tt) 102.08/27.20 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.20 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.20 active(U83(tt)) -> mark(tt) 102.08/27.20 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.20 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.20 active(U93(tt)) -> mark(tt) 102.08/27.20 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.20 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.20 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.20 active(isLNat(nil)) -> mark(tt) 102.08/27.20 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.20 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.20 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.20 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.20 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isLNatKind(nil)) -> mark(tt) 102.08/27.20 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.20 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.20 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.20 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.20 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.20 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.20 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.20 active(isNatural(0')) -> mark(tt) 102.08/27.20 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.20 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.20 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isNaturalKind(0')) -> mark(tt) 102.08/27.20 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.20 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.20 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.20 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.20 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.20 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.20 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.20 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.20 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.20 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.20 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.20 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.20 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.20 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.20 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.20 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.20 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.20 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.20 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.20 active(U106(X)) -> U106(active(X)) 102.08/27.20 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.20 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.20 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.20 active(U112(X)) -> U112(active(X)) 102.08/27.20 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.20 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.20 active(U122(X)) -> U122(active(X)) 102.08/27.20 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.20 active(U131(X)) -> U131(active(X)) 102.08/27.20 active(snd(X)) -> snd(active(X)) 102.08/27.20 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.20 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.20 active(U141(X)) -> U141(active(X)) 102.08/27.20 active(U151(X)) -> U151(active(X)) 102.08/27.20 active(U161(X)) -> U161(active(X)) 102.08/27.20 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.20 active(U172(X)) -> U172(active(X)) 102.08/27.20 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.20 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.20 active(U183(X)) -> U183(active(X)) 102.08/27.20 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.20 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.20 active(U193(X)) -> U193(active(X)) 102.08/27.20 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.20 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.20 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.20 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.20 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.20 active(U206(X)) -> U206(active(X)) 102.08/27.20 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.20 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.20 active(U211(X)) -> U211(active(X)) 102.08/27.20 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.20 active(U221(X)) -> U221(active(X)) 102.08/27.20 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.20 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.20 active(U232(X)) -> U232(active(X)) 102.08/27.20 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.20 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.20 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.20 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.20 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.20 active(U246(X)) -> U246(active(X)) 102.08/27.20 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.20 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.20 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.20 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.20 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.20 active(U256(X)) -> U256(active(X)) 102.08/27.20 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.20 active(U262(X)) -> U262(active(X)) 102.08/27.20 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.20 active(U272(X)) -> U272(active(X)) 102.08/27.20 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.20 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.20 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.20 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.20 active(s(X)) -> s(active(X)) 102.08/27.20 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.20 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.20 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.20 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.20 active(head(X)) -> head(active(X)) 102.08/27.20 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.20 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.20 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.20 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.20 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.20 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.20 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.20 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.20 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.20 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.20 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.20 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.20 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.20 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.20 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.20 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.20 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.20 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.20 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.20 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.20 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.20 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.20 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.20 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.20 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.20 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.20 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.20 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.20 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.20 active(fst(X)) -> fst(active(X)) 102.08/27.20 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.20 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.20 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.20 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.20 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.20 active(U46(X)) -> U46(active(X)) 102.08/27.20 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.20 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.20 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.20 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.20 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.20 active(U56(X)) -> U56(active(X)) 102.08/27.20 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.20 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.20 active(U63(X)) -> U63(active(X)) 102.08/27.20 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.20 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.20 active(U73(X)) -> U73(active(X)) 102.08/27.20 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.20 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.20 active(U83(X)) -> U83(active(X)) 102.08/27.20 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.20 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.20 active(U93(X)) -> U93(active(X)) 102.08/27.20 active(tail(X)) -> tail(active(X)) 102.08/27.20 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.20 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.20 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.20 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.20 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.20 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.20 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.20 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.20 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.20 U106(mark(X)) -> mark(U106(X)) 102.08/27.20 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.20 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.20 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.20 U112(mark(X)) -> mark(U112(X)) 102.08/27.20 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.20 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.20 U122(mark(X)) -> mark(U122(X)) 102.08/27.20 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.20 U131(mark(X)) -> mark(U131(X)) 102.08/27.20 snd(mark(X)) -> mark(snd(X)) 102.08/27.20 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.20 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.20 U141(mark(X)) -> mark(U141(X)) 102.08/27.20 U151(mark(X)) -> mark(U151(X)) 102.08/27.20 U161(mark(X)) -> mark(U161(X)) 102.08/27.20 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.20 U172(mark(X)) -> mark(U172(X)) 102.08/27.20 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.20 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.20 U183(mark(X)) -> mark(U183(X)) 102.08/27.20 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.20 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.20 U193(mark(X)) -> mark(U193(X)) 102.08/27.20 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.20 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.20 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.20 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.20 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.20 U206(mark(X)) -> mark(U206(X)) 102.08/27.20 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.20 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.20 U211(mark(X)) -> mark(U211(X)) 102.08/27.20 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.20 U221(mark(X)) -> mark(U221(X)) 102.08/27.20 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.20 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.20 U232(mark(X)) -> mark(U232(X)) 102.08/27.20 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.20 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.20 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.20 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.20 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.20 U246(mark(X)) -> mark(U246(X)) 102.08/27.20 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.20 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.20 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.20 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.20 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.20 U256(mark(X)) -> mark(U256(X)) 102.08/27.20 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.20 U262(mark(X)) -> mark(U262(X)) 102.08/27.20 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.20 U272(mark(X)) -> mark(U272(X)) 102.08/27.20 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.20 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.20 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.20 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.20 s(mark(X)) -> mark(s(X)) 102.08/27.20 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.20 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.20 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.20 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.20 head(mark(X)) -> mark(head(X)) 102.08/27.20 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.20 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.20 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.20 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.20 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.20 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.20 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.20 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.20 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.20 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.20 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.20 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.20 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.20 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.20 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.20 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.20 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.20 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.20 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.20 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.20 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.20 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.20 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.20 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.20 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.20 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.20 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.20 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.20 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.20 fst(mark(X)) -> mark(fst(X)) 102.08/27.20 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.20 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.20 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.20 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.20 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.20 U46(mark(X)) -> mark(U46(X)) 102.08/27.20 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.20 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.20 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.20 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.20 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.20 U56(mark(X)) -> mark(U56(X)) 102.08/27.20 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.20 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.20 U63(mark(X)) -> mark(U63(X)) 102.08/27.20 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.20 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.20 U73(mark(X)) -> mark(U73(X)) 102.08/27.20 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.20 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.20 U83(mark(X)) -> mark(U83(X)) 102.08/27.20 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.20 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.20 U93(mark(X)) -> mark(U93(X)) 102.08/27.20 tail(mark(X)) -> mark(tail(X)) 102.08/27.20 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.20 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.20 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.20 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.20 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(tt) -> ok(tt) 102.08/27.20 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.20 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.20 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.20 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.20 proper(U106(X)) -> U106(proper(X)) 102.08/27.20 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.20 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.20 proper(U112(X)) -> U112(proper(X)) 102.08/27.20 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.20 proper(U122(X)) -> U122(proper(X)) 102.08/27.20 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U131(X)) -> U131(proper(X)) 102.08/27.20 proper(snd(X)) -> snd(proper(X)) 102.08/27.20 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.20 proper(U141(X)) -> U141(proper(X)) 102.08/27.20 proper(U151(X)) -> U151(proper(X)) 102.08/27.20 proper(U161(X)) -> U161(proper(X)) 102.08/27.20 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.20 proper(U172(X)) -> U172(proper(X)) 102.08/27.20 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.20 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.20 proper(U183(X)) -> U183(proper(X)) 102.08/27.20 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.20 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.20 proper(U193(X)) -> U193(proper(X)) 102.08/27.20 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.20 proper(U206(X)) -> U206(proper(X)) 102.08/27.20 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U211(X)) -> U211(proper(X)) 102.08/27.20 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U221(X)) -> U221(proper(X)) 102.08/27.20 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.20 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.20 proper(U232(X)) -> U232(proper(X)) 102.08/27.20 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.20 proper(U246(X)) -> U246(proper(X)) 102.08/27.20 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.20 proper(U256(X)) -> U256(proper(X)) 102.08/27.20 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.20 proper(U262(X)) -> U262(proper(X)) 102.08/27.20 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.20 proper(U272(X)) -> U272(proper(X)) 102.08/27.20 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.20 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.20 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.20 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.20 proper(s(X)) -> s(proper(X)) 102.08/27.20 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(head(X)) -> head(proper(X)) 102.08/27.20 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.20 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.20 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.20 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.20 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.20 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.20 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.20 proper(nil) -> ok(nil) 102.08/27.20 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.20 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.20 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.20 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.20 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.20 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.20 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(fst(X)) -> fst(proper(X)) 102.08/27.20 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.20 proper(U46(X)) -> U46(proper(X)) 102.08/27.20 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.20 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.20 proper(U56(X)) -> U56(proper(X)) 102.08/27.20 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.20 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.20 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.20 proper(U63(X)) -> U63(proper(X)) 102.08/27.20 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.20 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.20 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.20 proper(U73(X)) -> U73(proper(X)) 102.08/27.20 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.20 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.20 proper(U83(X)) -> U83(proper(X)) 102.08/27.20 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.20 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.20 proper(U93(X)) -> U93(proper(X)) 102.08/27.20 proper(tail(X)) -> tail(proper(X)) 102.08/27.20 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.20 proper(0') -> ok(0') 102.08/27.20 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.20 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.20 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.20 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.20 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.20 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.20 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.20 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.20 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.20 U106(ok(X)) -> ok(U106(X)) 102.08/27.20 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.20 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.20 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.20 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.20 U112(ok(X)) -> ok(U112(X)) 102.08/27.20 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.20 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.20 U122(ok(X)) -> ok(U122(X)) 102.08/27.20 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.20 U131(ok(X)) -> ok(U131(X)) 102.08/27.20 snd(ok(X)) -> ok(snd(X)) 102.08/27.20 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.20 U141(ok(X)) -> ok(U141(X)) 102.08/27.20 U151(ok(X)) -> ok(U151(X)) 102.08/27.20 U161(ok(X)) -> ok(U161(X)) 102.08/27.20 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.20 U172(ok(X)) -> ok(U172(X)) 102.08/27.20 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.20 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.20 U183(ok(X)) -> ok(U183(X)) 102.08/27.20 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.20 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.20 U193(ok(X)) -> ok(U193(X)) 102.08/27.20 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.20 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.20 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.20 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.20 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.20 U206(ok(X)) -> ok(U206(X)) 102.08/27.20 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.20 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.20 U211(ok(X)) -> ok(U211(X)) 102.08/27.20 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.20 U221(ok(X)) -> ok(U221(X)) 102.08/27.20 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.20 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.20 U232(ok(X)) -> ok(U232(X)) 102.08/27.20 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.20 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.20 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.20 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.20 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.20 U246(ok(X)) -> ok(U246(X)) 102.08/27.20 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.20 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.20 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.20 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.20 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.20 U256(ok(X)) -> ok(U256(X)) 102.08/27.20 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.20 U262(ok(X)) -> ok(U262(X)) 102.08/27.20 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.20 U272(ok(X)) -> ok(U272(X)) 102.08/27.20 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.20 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.20 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.20 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.20 s(ok(X)) -> ok(s(X)) 102.08/27.20 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.20 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.20 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.20 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.20 head(ok(X)) -> ok(head(X)) 102.08/27.20 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.20 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.20 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.20 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.20 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.20 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.20 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.20 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.20 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.20 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.20 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.20 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.20 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.20 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.20 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.20 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.20 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.20 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.20 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.20 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.20 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.20 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.20 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.20 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.20 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.20 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.20 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.20 fst(ok(X)) -> ok(fst(X)) 102.08/27.20 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.20 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.20 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.20 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.20 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.20 U46(ok(X)) -> ok(U46(X)) 102.08/27.20 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.20 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.20 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.20 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.20 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.20 U56(ok(X)) -> ok(U56(X)) 102.08/27.20 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.20 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.20 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.20 U63(ok(X)) -> ok(U63(X)) 102.08/27.20 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.20 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.20 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.20 U73(ok(X)) -> ok(U73(X)) 102.08/27.20 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.20 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.20 U83(ok(X)) -> ok(U83(X)) 102.08/27.20 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.20 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.20 U93(ok(X)) -> ok(U93(X)) 102.08/27.20 tail(ok(X)) -> ok(tail(X)) 102.08/27.20 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.20 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.20 top(mark(X)) -> top(proper(X)) 102.08/27.20 top(ok(X)) -> top(active(X)) 102.08/27.20 102.08/27.20 Types: 102.08/27.20 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 tt :: tt:mark:nil:0':ok 102.08/27.20 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.20 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 nil :: tt:mark:nil:0':ok 102.08/27.21 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 0' :: tt:mark:nil:0':ok 102.08/27.21 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 top :: tt:mark:nil:0':ok -> top 102.08/27.21 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.21 hole_top2_0 :: top 102.08/27.21 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.21 102.08/27.21 102.08/27.21 Lemmas: 102.08/27.21 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.21 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.21 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.21 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.21 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.21 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.21 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.21 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.21 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.21 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.21 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.21 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.21 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.21 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.21 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.21 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.21 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.21 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.21 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.21 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.21 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.21 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.21 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.21 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.21 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.21 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.21 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.21 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.21 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.21 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.21 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.21 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.21 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.21 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.21 102.08/27.21 102.08/27.21 Generator Equations: 102.08/27.21 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.21 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.21 102.08/27.21 102.08/27.21 The following defined symbols remain to be analysed: 102.08/27.21 U255, active, U256, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.21 102.08/27.21 They will be analysed ascendingly in the following order: 102.08/27.21 U255 < active 102.08/27.21 U256 < active 102.08/27.21 U262 < active 102.08/27.21 U272 < active 102.08/27.21 U282 < active 102.08/27.21 cons < active 102.08/27.21 natsFrom < active 102.08/27.21 s < active 102.08/27.21 U292 < active 102.08/27.21 U293 < active 102.08/27.21 U294 < active 102.08/27.21 head < active 102.08/27.21 afterNth < active 102.08/27.21 U302 < active 102.08/27.21 U303 < active 102.08/27.21 U304 < active 102.08/27.21 U32 < active 102.08/27.21 U312 < active 102.08/27.21 pair < active 102.08/27.21 U33 < active 102.08/27.21 U322 < active 102.08/27.21 U323 < active 102.08/27.21 U324 < active 102.08/27.21 U325 < active 102.08/27.21 U326 < active 102.08/27.21 U327 < active 102.08/27.21 U34 < active 102.08/27.21 U332 < active 102.08/27.21 U333 < active 102.08/27.21 U334 < active 102.08/27.21 U342 < active 102.08/27.21 U343 < active 102.08/27.21 U344 < active 102.08/27.21 fst < active 102.08/27.21 U42 < active 102.08/27.21 U43 < active 102.08/27.21 U44 < active 102.08/27.21 U45 < active 102.08/27.21 U46 < active 102.08/27.21 U52 < active 102.08/27.21 U53 < active 102.08/27.21 U54 < active 102.08/27.21 U55 < active 102.08/27.21 U56 < active 102.08/27.21 U62 < active 102.08/27.21 isPLNatKind < active 102.08/27.21 U63 < active 102.08/27.21 isPLNat < active 102.08/27.21 U72 < active 102.08/27.21 U73 < active 102.08/27.21 U82 < active 102.08/27.21 U83 < active 102.08/27.21 U92 < active 102.08/27.21 U93 < active 102.08/27.21 U11 < active 102.08/27.21 U21 < active 102.08/27.21 U31 < active 102.08/27.21 U41 < active 102.08/27.21 U51 < active 102.08/27.21 U61 < active 102.08/27.21 U71 < active 102.08/27.21 U81 < active 102.08/27.21 U91 < active 102.08/27.21 U101 < active 102.08/27.21 U111 < active 102.08/27.21 U121 < active 102.08/27.21 U131 < active 102.08/27.21 U141 < active 102.08/27.21 U151 < active 102.08/27.21 U161 < active 102.08/27.21 U171 < active 102.08/27.21 U181 < active 102.08/27.21 U191 < active 102.08/27.21 U201 < active 102.08/27.21 U211 < active 102.08/27.21 U221 < active 102.08/27.21 U231 < active 102.08/27.21 U241 < active 102.08/27.21 U251 < active 102.08/27.21 U261 < active 102.08/27.21 U271 < active 102.08/27.21 U281 < active 102.08/27.21 U291 < active 102.08/27.21 U301 < active 102.08/27.21 U311 < active 102.08/27.21 U321 < active 102.08/27.21 U331 < active 102.08/27.21 U341 < active 102.08/27.21 tail < active 102.08/27.21 take < active 102.08/27.21 sel < active 102.08/27.21 active < top 102.08/27.21 U255 < proper 102.08/27.21 U256 < proper 102.08/27.21 U262 < proper 102.08/27.21 U272 < proper 102.08/27.21 U282 < proper 102.08/27.21 cons < proper 102.08/27.21 natsFrom < proper 102.08/27.21 s < proper 102.08/27.21 U292 < proper 102.08/27.21 U293 < proper 102.08/27.21 U294 < proper 102.08/27.21 head < proper 102.08/27.21 afterNth < proper 102.08/27.21 U302 < proper 102.08/27.21 U303 < proper 102.08/27.21 U304 < proper 102.08/27.21 U32 < proper 102.08/27.21 U312 < proper 102.08/27.21 pair < proper 102.08/27.21 U33 < proper 102.08/27.21 U322 < proper 102.08/27.21 U323 < proper 102.08/27.21 U324 < proper 102.08/27.21 U325 < proper 102.08/27.21 U326 < proper 102.08/27.21 U327 < proper 102.08/27.21 U34 < proper 102.08/27.21 U332 < proper 102.08/27.21 U333 < proper 102.08/27.21 U334 < proper 102.08/27.21 U342 < proper 102.08/27.21 U343 < proper 102.08/27.21 U344 < proper 102.08/27.21 fst < proper 102.08/27.21 U42 < proper 102.08/27.21 U43 < proper 102.08/27.21 U44 < proper 102.08/27.21 U45 < proper 102.08/27.21 U46 < proper 102.08/27.21 U52 < proper 102.08/27.21 U53 < proper 102.08/27.21 U54 < proper 102.08/27.21 U55 < proper 102.08/27.21 U56 < proper 102.08/27.21 U62 < proper 102.08/27.21 isPLNatKind < proper 102.08/27.21 U63 < proper 102.08/27.21 isPLNat < proper 102.08/27.21 U72 < proper 102.08/27.21 U73 < proper 102.08/27.21 U82 < proper 102.08/27.21 U83 < proper 102.08/27.21 U92 < proper 102.08/27.21 U93 < proper 102.08/27.21 U11 < proper 102.08/27.21 U21 < proper 102.08/27.21 U31 < proper 102.08/27.21 U41 < proper 102.08/27.21 U51 < proper 102.08/27.21 U61 < proper 102.08/27.21 U71 < proper 102.08/27.21 U81 < proper 102.08/27.21 U91 < proper 102.08/27.21 U101 < proper 102.08/27.21 U111 < proper 102.08/27.21 U121 < proper 102.08/27.21 U131 < proper 102.08/27.21 U141 < proper 102.08/27.21 U151 < proper 102.08/27.21 U161 < proper 102.08/27.21 U171 < proper 102.08/27.21 U181 < proper 102.08/27.21 U191 < proper 102.08/27.21 U201 < proper 102.08/27.21 U211 < proper 102.08/27.21 U221 < proper 102.08/27.21 U231 < proper 102.08/27.21 U241 < proper 102.08/27.21 U251 < proper 102.08/27.21 U261 < proper 102.08/27.21 U271 < proper 102.08/27.21 U281 < proper 102.08/27.21 U291 < proper 102.08/27.21 U301 < proper 102.08/27.21 U311 < proper 102.08/27.21 U321 < proper 102.08/27.21 U331 < proper 102.08/27.21 U341 < proper 102.08/27.21 tail < proper 102.08/27.21 take < proper 102.08/27.21 sel < proper 102.08/27.21 proper < top 102.08/27.21 102.08/27.21 ---------------------------------------- 102.08/27.21 102.08/27.21 (97) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.21 Proved the following rewrite lemma: 102.08/27.21 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.21 102.08/27.21 Induction Base: 102.08/27.21 U255(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 102.08/27.21 102.08/27.21 Induction Step: 102.08/27.21 U255(gen_tt:mark:nil:0':ok3_0(+(1, +(n589441_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 102.08/27.21 mark(U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 102.08/27.21 mark(*4_0) 102.08/27.21 102.08/27.21 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.21 ---------------------------------------- 102.08/27.21 102.08/27.21 (98) 102.08/27.21 Obligation: 102.08/27.21 TRS: 102.08/27.21 Rules: 102.08/27.21 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.21 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.21 active(U106(tt)) -> mark(tt) 102.08/27.21 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.21 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.21 active(U112(tt)) -> mark(tt) 102.08/27.21 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.21 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.21 active(U122(tt)) -> mark(tt) 102.08/27.21 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.21 active(U131(tt)) -> mark(tt) 102.08/27.21 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.21 active(U141(tt)) -> mark(tt) 102.08/27.21 active(U151(tt)) -> mark(tt) 102.08/27.21 active(U161(tt)) -> mark(tt) 102.08/27.21 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.21 active(U172(tt)) -> mark(tt) 102.08/27.21 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.21 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.21 active(U183(tt)) -> mark(tt) 102.08/27.21 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.21 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.21 active(U193(tt)) -> mark(tt) 102.08/27.21 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.21 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.21 active(U206(tt)) -> mark(tt) 102.08/27.21 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.21 active(U211(tt)) -> mark(tt) 102.08/27.21 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.21 active(U221(tt)) -> mark(tt) 102.08/27.21 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.21 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.21 active(U232(tt)) -> mark(tt) 102.08/27.21 active(U24(tt, X)) -> mark(X) 102.08/27.21 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.21 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.21 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.21 active(U246(tt)) -> mark(tt) 102.08/27.21 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.21 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.21 active(U256(tt)) -> mark(tt) 102.08/27.21 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.21 active(U262(tt)) -> mark(tt) 102.08/27.21 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.21 active(U272(tt)) -> mark(tt) 102.08/27.21 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.21 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.21 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.21 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.21 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.21 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.21 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.21 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.21 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.21 active(U304(tt, Y)) -> mark(Y) 102.08/27.21 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.21 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.21 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.21 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.21 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.21 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.21 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.21 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.21 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.21 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.21 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.21 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.21 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.21 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.21 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.21 active(U334(tt, XS)) -> mark(XS) 102.08/27.21 active(U34(tt, N)) -> mark(N) 102.08/27.21 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.21 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.21 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.21 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.21 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.21 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.21 active(U46(tt)) -> mark(tt) 102.08/27.21 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.21 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.21 active(U56(tt)) -> mark(tt) 102.08/27.21 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.21 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.21 active(U63(tt)) -> mark(tt) 102.08/27.21 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.21 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.21 active(U73(tt)) -> mark(tt) 102.08/27.21 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.21 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.21 active(U83(tt)) -> mark(tt) 102.08/27.21 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.21 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.21 active(U93(tt)) -> mark(tt) 102.08/27.21 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.21 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.21 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.21 active(isLNat(nil)) -> mark(tt) 102.08/27.21 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.21 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.21 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.21 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.21 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNatKind(nil)) -> mark(tt) 102.08/27.21 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.21 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.21 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.21 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.21 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.21 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.21 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.21 active(isNatural(0')) -> mark(tt) 102.08/27.21 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.21 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.21 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isNaturalKind(0')) -> mark(tt) 102.08/27.21 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.21 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.21 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.21 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.21 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.21 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.21 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.21 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.21 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.21 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.21 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.21 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.21 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.21 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.21 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.21 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.21 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.21 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.21 active(U106(X)) -> U106(active(X)) 102.08/27.21 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.21 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.21 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.21 active(U112(X)) -> U112(active(X)) 102.08/27.21 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.21 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.21 active(U122(X)) -> U122(active(X)) 102.08/27.21 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.21 active(U131(X)) -> U131(active(X)) 102.08/27.21 active(snd(X)) -> snd(active(X)) 102.08/27.21 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.21 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.21 active(U141(X)) -> U141(active(X)) 102.08/27.21 active(U151(X)) -> U151(active(X)) 102.08/27.21 active(U161(X)) -> U161(active(X)) 102.08/27.21 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.21 active(U172(X)) -> U172(active(X)) 102.08/27.21 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.21 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.21 active(U183(X)) -> U183(active(X)) 102.08/27.21 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.21 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.21 active(U193(X)) -> U193(active(X)) 102.08/27.21 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.21 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.21 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.21 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.21 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.21 active(U206(X)) -> U206(active(X)) 102.08/27.21 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.21 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.21 active(U211(X)) -> U211(active(X)) 102.08/27.21 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.21 active(U221(X)) -> U221(active(X)) 102.08/27.21 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.21 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.21 active(U232(X)) -> U232(active(X)) 102.08/27.21 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.21 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.21 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.21 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.21 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.21 active(U246(X)) -> U246(active(X)) 102.08/27.21 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.21 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.21 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.21 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.21 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.21 active(U256(X)) -> U256(active(X)) 102.08/27.21 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.21 active(U262(X)) -> U262(active(X)) 102.08/27.21 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.21 active(U272(X)) -> U272(active(X)) 102.08/27.21 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.21 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.21 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.21 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.21 active(s(X)) -> s(active(X)) 102.08/27.21 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.21 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.21 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.21 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.21 active(head(X)) -> head(active(X)) 102.08/27.21 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.21 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.21 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.21 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.21 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.21 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.21 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.21 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.21 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.21 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.21 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.21 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.21 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.21 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.21 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.21 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.21 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.21 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.21 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.21 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.21 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.21 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.21 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.21 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.21 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.21 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.21 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.21 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.21 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.21 active(fst(X)) -> fst(active(X)) 102.08/27.21 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.21 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.21 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.21 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.21 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.21 active(U46(X)) -> U46(active(X)) 102.08/27.21 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.21 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.21 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.21 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.21 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.21 active(U56(X)) -> U56(active(X)) 102.08/27.21 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.21 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.21 active(U63(X)) -> U63(active(X)) 102.08/27.21 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.21 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.21 active(U73(X)) -> U73(active(X)) 102.08/27.21 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.21 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.21 active(U83(X)) -> U83(active(X)) 102.08/27.21 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.21 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.21 active(U93(X)) -> U93(active(X)) 102.08/27.21 active(tail(X)) -> tail(active(X)) 102.08/27.21 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.21 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.21 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.21 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.21 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.21 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.21 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.21 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.21 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.21 U106(mark(X)) -> mark(U106(X)) 102.08/27.21 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.21 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.21 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.21 U112(mark(X)) -> mark(U112(X)) 102.08/27.21 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.21 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.21 U122(mark(X)) -> mark(U122(X)) 102.08/27.21 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.21 U131(mark(X)) -> mark(U131(X)) 102.08/27.21 snd(mark(X)) -> mark(snd(X)) 102.08/27.21 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.21 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.21 U141(mark(X)) -> mark(U141(X)) 102.08/27.21 U151(mark(X)) -> mark(U151(X)) 102.08/27.21 U161(mark(X)) -> mark(U161(X)) 102.08/27.21 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.21 U172(mark(X)) -> mark(U172(X)) 102.08/27.21 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.21 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.21 U183(mark(X)) -> mark(U183(X)) 102.08/27.21 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.21 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.21 U193(mark(X)) -> mark(U193(X)) 102.08/27.21 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.21 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.21 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.21 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.21 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.21 U206(mark(X)) -> mark(U206(X)) 102.08/27.21 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.21 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.21 U211(mark(X)) -> mark(U211(X)) 102.08/27.21 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.21 U221(mark(X)) -> mark(U221(X)) 102.08/27.21 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.21 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.21 U232(mark(X)) -> mark(U232(X)) 102.08/27.21 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.21 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.21 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.21 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.21 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.21 U246(mark(X)) -> mark(U246(X)) 102.08/27.21 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.21 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.21 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.21 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.21 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.21 U256(mark(X)) -> mark(U256(X)) 102.08/27.21 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.21 U262(mark(X)) -> mark(U262(X)) 102.08/27.21 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.21 U272(mark(X)) -> mark(U272(X)) 102.08/27.21 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.21 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.21 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.21 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.21 s(mark(X)) -> mark(s(X)) 102.08/27.21 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.21 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.21 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.21 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.21 head(mark(X)) -> mark(head(X)) 102.08/27.21 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.21 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.21 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.21 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.21 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.21 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.21 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.21 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.21 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.21 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.21 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.21 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.21 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.21 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.21 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.21 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.21 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.21 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.21 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.21 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.21 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.21 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.21 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.21 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.21 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.21 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.21 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.21 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.21 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.21 fst(mark(X)) -> mark(fst(X)) 102.08/27.21 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.21 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.21 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.21 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.21 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.21 U46(mark(X)) -> mark(U46(X)) 102.08/27.21 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.21 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.21 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.21 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.21 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.21 U56(mark(X)) -> mark(U56(X)) 102.08/27.21 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.21 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.21 U63(mark(X)) -> mark(U63(X)) 102.08/27.21 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.21 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.21 U73(mark(X)) -> mark(U73(X)) 102.08/27.21 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.21 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.21 U83(mark(X)) -> mark(U83(X)) 102.08/27.21 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.21 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.21 U93(mark(X)) -> mark(U93(X)) 102.08/27.21 tail(mark(X)) -> mark(tail(X)) 102.08/27.21 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.21 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.21 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.21 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.21 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(tt) -> ok(tt) 102.08/27.21 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.21 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.21 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.21 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.21 proper(U106(X)) -> U106(proper(X)) 102.08/27.21 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.21 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.21 proper(U112(X)) -> U112(proper(X)) 102.08/27.21 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.21 proper(U122(X)) -> U122(proper(X)) 102.08/27.21 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U131(X)) -> U131(proper(X)) 102.08/27.21 proper(snd(X)) -> snd(proper(X)) 102.08/27.21 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.21 proper(U141(X)) -> U141(proper(X)) 102.08/27.21 proper(U151(X)) -> U151(proper(X)) 102.08/27.21 proper(U161(X)) -> U161(proper(X)) 102.08/27.21 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.21 proper(U172(X)) -> U172(proper(X)) 102.08/27.21 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.21 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.21 proper(U183(X)) -> U183(proper(X)) 102.08/27.21 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.21 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.21 proper(U193(X)) -> U193(proper(X)) 102.08/27.21 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.21 proper(U206(X)) -> U206(proper(X)) 102.08/27.21 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U211(X)) -> U211(proper(X)) 102.08/27.21 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U221(X)) -> U221(proper(X)) 102.08/27.21 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.21 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.21 proper(U232(X)) -> U232(proper(X)) 102.08/27.21 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.21 proper(U246(X)) -> U246(proper(X)) 102.08/27.21 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.21 proper(U256(X)) -> U256(proper(X)) 102.08/27.21 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.21 proper(U262(X)) -> U262(proper(X)) 102.08/27.21 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.21 proper(U272(X)) -> U272(proper(X)) 102.08/27.21 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.21 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.21 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.21 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.21 proper(s(X)) -> s(proper(X)) 102.08/27.21 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(head(X)) -> head(proper(X)) 102.08/27.21 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.21 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.21 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.21 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.21 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.21 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.21 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.21 proper(nil) -> ok(nil) 102.08/27.21 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.21 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.21 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.21 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.21 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.21 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(fst(X)) -> fst(proper(X)) 102.08/27.21 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.21 proper(U46(X)) -> U46(proper(X)) 102.08/27.21 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.21 proper(U56(X)) -> U56(proper(X)) 102.08/27.21 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.21 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.21 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.21 proper(U63(X)) -> U63(proper(X)) 102.08/27.21 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.21 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.21 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.21 proper(U73(X)) -> U73(proper(X)) 102.08/27.21 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.21 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.21 proper(U83(X)) -> U83(proper(X)) 102.08/27.21 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.21 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.21 proper(U93(X)) -> U93(proper(X)) 102.08/27.21 proper(tail(X)) -> tail(proper(X)) 102.08/27.21 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.21 proper(0') -> ok(0') 102.08/27.21 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.21 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.21 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.21 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.21 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.21 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.21 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.21 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.21 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.21 U106(ok(X)) -> ok(U106(X)) 102.08/27.21 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.21 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.21 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.21 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.21 U112(ok(X)) -> ok(U112(X)) 102.08/27.21 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.21 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.21 U122(ok(X)) -> ok(U122(X)) 102.08/27.21 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.21 U131(ok(X)) -> ok(U131(X)) 102.08/27.21 snd(ok(X)) -> ok(snd(X)) 102.08/27.21 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.21 U141(ok(X)) -> ok(U141(X)) 102.08/27.21 U151(ok(X)) -> ok(U151(X)) 102.08/27.21 U161(ok(X)) -> ok(U161(X)) 102.08/27.21 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.21 U172(ok(X)) -> ok(U172(X)) 102.08/27.21 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.21 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.21 U183(ok(X)) -> ok(U183(X)) 102.08/27.21 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.21 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.21 U193(ok(X)) -> ok(U193(X)) 102.08/27.21 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.21 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.21 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.21 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.21 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.21 U206(ok(X)) -> ok(U206(X)) 102.08/27.21 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.21 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.21 U211(ok(X)) -> ok(U211(X)) 102.08/27.21 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.21 U221(ok(X)) -> ok(U221(X)) 102.08/27.21 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.21 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.21 U232(ok(X)) -> ok(U232(X)) 102.08/27.21 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.21 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.21 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.21 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.21 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.21 U246(ok(X)) -> ok(U246(X)) 102.08/27.21 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.21 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.21 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.21 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.21 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.21 U256(ok(X)) -> ok(U256(X)) 102.08/27.21 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.21 U262(ok(X)) -> ok(U262(X)) 102.08/27.21 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.21 U272(ok(X)) -> ok(U272(X)) 102.08/27.21 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.21 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.21 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.21 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.21 s(ok(X)) -> ok(s(X)) 102.08/27.21 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.21 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.21 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.21 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.21 head(ok(X)) -> ok(head(X)) 102.08/27.21 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.21 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.21 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.21 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.21 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.21 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.21 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.21 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.21 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.21 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.21 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.21 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.21 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.21 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.21 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.21 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.21 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.21 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.21 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.21 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.21 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.21 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.21 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.21 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.21 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.21 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.21 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.21 fst(ok(X)) -> ok(fst(X)) 102.08/27.21 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.21 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.21 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.21 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.21 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.21 U46(ok(X)) -> ok(U46(X)) 102.08/27.21 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.21 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.21 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.21 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.21 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.21 U56(ok(X)) -> ok(U56(X)) 102.08/27.21 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.21 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.21 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.21 U63(ok(X)) -> ok(U63(X)) 102.08/27.21 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.21 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.21 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.21 U73(ok(X)) -> ok(U73(X)) 102.08/27.21 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.21 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.21 U83(ok(X)) -> ok(U83(X)) 102.08/27.21 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.21 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.21 U93(ok(X)) -> ok(U93(X)) 102.08/27.21 tail(ok(X)) -> ok(tail(X)) 102.08/27.21 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.21 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.21 top(mark(X)) -> top(proper(X)) 102.08/27.21 top(ok(X)) -> top(active(X)) 102.08/27.21 102.08/27.21 Types: 102.08/27.21 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 tt :: tt:mark:nil:0':ok 102.08/27.21 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 nil :: tt:mark:nil:0':ok 102.08/27.21 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 0' :: tt:mark:nil:0':ok 102.08/27.21 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.21 top :: tt:mark:nil:0':ok -> top 102.08/27.21 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.21 hole_top2_0 :: top 102.08/27.21 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.21 102.08/27.21 102.08/27.21 Lemmas: 102.08/27.21 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.21 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.21 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.21 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.21 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.21 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.21 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.21 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.21 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.21 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.21 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.21 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.21 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.21 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.21 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.21 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.21 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.21 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.21 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.21 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.21 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.21 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.21 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.21 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.21 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.21 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.21 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.21 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.21 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.21 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.21 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.21 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.21 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.21 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.21 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.21 102.08/27.21 102.08/27.21 Generator Equations: 102.08/27.21 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.21 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.21 102.08/27.21 102.08/27.21 The following defined symbols remain to be analysed: 102.08/27.21 U256, active, U262, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.21 102.08/27.21 They will be analysed ascendingly in the following order: 102.08/27.21 U256 < active 102.08/27.21 U262 < active 102.08/27.21 U272 < active 102.08/27.21 U282 < active 102.08/27.21 cons < active 102.08/27.21 natsFrom < active 102.08/27.21 s < active 102.08/27.21 U292 < active 102.08/27.21 U293 < active 102.08/27.21 U294 < active 102.08/27.21 head < active 102.08/27.21 afterNth < active 102.08/27.21 U302 < active 102.08/27.21 U303 < active 102.08/27.21 U304 < active 102.08/27.21 U32 < active 102.08/27.21 U312 < active 102.08/27.21 pair < active 102.08/27.21 U33 < active 102.08/27.21 U322 < active 102.08/27.21 U323 < active 102.08/27.21 U324 < active 102.08/27.21 U325 < active 102.08/27.21 U326 < active 102.08/27.21 U327 < active 102.08/27.21 U34 < active 102.08/27.21 U332 < active 102.08/27.21 U333 < active 102.08/27.21 U334 < active 102.08/27.21 U342 < active 102.08/27.21 U343 < active 102.08/27.21 U344 < active 102.08/27.21 fst < active 102.08/27.21 U42 < active 102.08/27.21 U43 < active 102.08/27.21 U44 < active 102.08/27.21 U45 < active 102.08/27.21 U46 < active 102.08/27.21 U52 < active 102.08/27.21 U53 < active 102.08/27.21 U54 < active 102.08/27.21 U55 < active 102.08/27.21 U56 < active 102.08/27.21 U62 < active 102.08/27.21 isPLNatKind < active 102.08/27.21 U63 < active 102.08/27.21 isPLNat < active 102.08/27.21 U72 < active 102.08/27.21 U73 < active 102.08/27.21 U82 < active 102.08/27.21 U83 < active 102.08/27.21 U92 < active 102.08/27.21 U93 < active 102.08/27.21 U11 < active 102.08/27.21 U21 < active 102.08/27.21 U31 < active 102.08/27.21 U41 < active 102.08/27.21 U51 < active 102.08/27.21 U61 < active 102.08/27.21 U71 < active 102.08/27.21 U81 < active 102.08/27.21 U91 < active 102.08/27.21 U101 < active 102.08/27.21 U111 < active 102.08/27.21 U121 < active 102.08/27.21 U131 < active 102.08/27.21 U141 < active 102.08/27.21 U151 < active 102.08/27.21 U161 < active 102.08/27.21 U171 < active 102.08/27.21 U181 < active 102.08/27.21 U191 < active 102.08/27.21 U201 < active 102.08/27.21 U211 < active 102.08/27.21 U221 < active 102.08/27.21 U231 < active 102.08/27.21 U241 < active 102.08/27.21 U251 < active 102.08/27.21 U261 < active 102.08/27.21 U271 < active 102.08/27.21 U281 < active 102.08/27.21 U291 < active 102.08/27.21 U301 < active 102.08/27.21 U311 < active 102.08/27.21 U321 < active 102.08/27.21 U331 < active 102.08/27.21 U341 < active 102.08/27.21 tail < active 102.08/27.21 take < active 102.08/27.21 sel < active 102.08/27.21 active < top 102.08/27.21 U256 < proper 102.08/27.21 U262 < proper 102.08/27.21 U272 < proper 102.08/27.21 U282 < proper 102.08/27.21 cons < proper 102.08/27.21 natsFrom < proper 102.08/27.21 s < proper 102.08/27.21 U292 < proper 102.08/27.21 U293 < proper 102.08/27.21 U294 < proper 102.08/27.21 head < proper 102.08/27.21 afterNth < proper 102.08/27.21 U302 < proper 102.08/27.21 U303 < proper 102.08/27.21 U304 < proper 102.08/27.21 U32 < proper 102.08/27.21 U312 < proper 102.08/27.21 pair < proper 102.08/27.21 U33 < proper 102.08/27.21 U322 < proper 102.08/27.21 U323 < proper 102.08/27.21 U324 < proper 102.08/27.21 U325 < proper 102.08/27.21 U326 < proper 102.08/27.21 U327 < proper 102.08/27.21 U34 < proper 102.08/27.21 U332 < proper 102.08/27.21 U333 < proper 102.08/27.21 U334 < proper 102.08/27.21 U342 < proper 102.08/27.21 U343 < proper 102.08/27.21 U344 < proper 102.08/27.21 fst < proper 102.08/27.21 U42 < proper 102.08/27.21 U43 < proper 102.08/27.21 U44 < proper 102.08/27.21 U45 < proper 102.08/27.21 U46 < proper 102.08/27.21 U52 < proper 102.08/27.21 U53 < proper 102.08/27.21 U54 < proper 102.08/27.21 U55 < proper 102.08/27.21 U56 < proper 102.08/27.21 U62 < proper 102.08/27.21 isPLNatKind < proper 102.08/27.21 U63 < proper 102.08/27.21 isPLNat < proper 102.08/27.21 U72 < proper 102.08/27.21 U73 < proper 102.08/27.21 U82 < proper 102.08/27.21 U83 < proper 102.08/27.21 U92 < proper 102.08/27.21 U93 < proper 102.08/27.21 U11 < proper 102.08/27.21 U21 < proper 102.08/27.21 U31 < proper 102.08/27.21 U41 < proper 102.08/27.21 U51 < proper 102.08/27.21 U61 < proper 102.08/27.21 U71 < proper 102.08/27.21 U81 < proper 102.08/27.21 U91 < proper 102.08/27.21 U101 < proper 102.08/27.21 U111 < proper 102.08/27.21 U121 < proper 102.08/27.21 U131 < proper 102.08/27.21 U141 < proper 102.08/27.21 U151 < proper 102.08/27.21 U161 < proper 102.08/27.21 U171 < proper 102.08/27.21 U181 < proper 102.08/27.21 U191 < proper 102.08/27.21 U201 < proper 102.08/27.21 U211 < proper 102.08/27.21 U221 < proper 102.08/27.21 U231 < proper 102.08/27.21 U241 < proper 102.08/27.21 U251 < proper 102.08/27.21 U261 < proper 102.08/27.21 U271 < proper 102.08/27.21 U281 < proper 102.08/27.21 U291 < proper 102.08/27.21 U301 < proper 102.08/27.21 U311 < proper 102.08/27.21 U321 < proper 102.08/27.21 U331 < proper 102.08/27.21 U341 < proper 102.08/27.21 tail < proper 102.08/27.21 take < proper 102.08/27.21 sel < proper 102.08/27.21 proper < top 102.08/27.21 102.08/27.21 ---------------------------------------- 102.08/27.21 102.08/27.21 (99) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.21 Proved the following rewrite lemma: 102.08/27.21 U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0))) -> *4_0, rt in Omega(n610318_0) 102.08/27.21 102.08/27.21 Induction Base: 102.08/27.21 U256(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 102.08/27.21 102.08/27.21 Induction Step: 102.08/27.21 U256(gen_tt:mark:nil:0':ok3_0(+(1, +(n610318_0, 1)))) ->_R^Omega(1) 102.08/27.21 mark(U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0)))) ->_IH 102.08/27.21 mark(*4_0) 102.08/27.21 102.08/27.21 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.21 ---------------------------------------- 102.08/27.21 102.08/27.21 (100) 102.08/27.21 Obligation: 102.08/27.21 TRS: 102.08/27.21 Rules: 102.08/27.21 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.21 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.21 active(U106(tt)) -> mark(tt) 102.08/27.21 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.21 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.21 active(U112(tt)) -> mark(tt) 102.08/27.21 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.21 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.21 active(U122(tt)) -> mark(tt) 102.08/27.21 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.21 active(U131(tt)) -> mark(tt) 102.08/27.21 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.21 active(U141(tt)) -> mark(tt) 102.08/27.21 active(U151(tt)) -> mark(tt) 102.08/27.21 active(U161(tt)) -> mark(tt) 102.08/27.21 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.21 active(U172(tt)) -> mark(tt) 102.08/27.21 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.21 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.21 active(U183(tt)) -> mark(tt) 102.08/27.21 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.21 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.21 active(U193(tt)) -> mark(tt) 102.08/27.21 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.21 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.21 active(U206(tt)) -> mark(tt) 102.08/27.21 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.21 active(U211(tt)) -> mark(tt) 102.08/27.21 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.21 active(U221(tt)) -> mark(tt) 102.08/27.21 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.21 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.21 active(U232(tt)) -> mark(tt) 102.08/27.21 active(U24(tt, X)) -> mark(X) 102.08/27.21 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.21 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.21 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.21 active(U246(tt)) -> mark(tt) 102.08/27.21 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.21 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.21 active(U256(tt)) -> mark(tt) 102.08/27.21 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.21 active(U262(tt)) -> mark(tt) 102.08/27.21 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.21 active(U272(tt)) -> mark(tt) 102.08/27.21 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.21 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.21 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.21 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.21 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.21 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.21 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.21 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.21 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.21 active(U304(tt, Y)) -> mark(Y) 102.08/27.21 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.21 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.21 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.21 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.21 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.21 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.21 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.21 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.21 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.21 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.21 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.21 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.21 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.21 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.21 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.21 active(U334(tt, XS)) -> mark(XS) 102.08/27.21 active(U34(tt, N)) -> mark(N) 102.08/27.21 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.21 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.21 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.21 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.21 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.21 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.21 active(U46(tt)) -> mark(tt) 102.08/27.21 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.21 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.21 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.21 active(U56(tt)) -> mark(tt) 102.08/27.21 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.21 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.21 active(U63(tt)) -> mark(tt) 102.08/27.21 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.21 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.21 active(U73(tt)) -> mark(tt) 102.08/27.21 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.21 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.21 active(U83(tt)) -> mark(tt) 102.08/27.21 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.21 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.21 active(U93(tt)) -> mark(tt) 102.08/27.21 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.21 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.21 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.21 active(isLNat(nil)) -> mark(tt) 102.08/27.21 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.21 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.21 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.21 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.21 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isLNatKind(nil)) -> mark(tt) 102.08/27.21 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.21 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.21 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.21 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.21 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.21 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.21 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.21 active(isNatural(0')) -> mark(tt) 102.08/27.21 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.21 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.21 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isNaturalKind(0')) -> mark(tt) 102.08/27.21 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.21 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.21 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.21 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.21 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.21 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.21 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.21 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.21 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.21 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.21 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.21 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.21 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.21 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.21 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.21 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.21 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.21 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.21 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.21 active(U106(X)) -> U106(active(X)) 102.08/27.21 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.21 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.21 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.21 active(U112(X)) -> U112(active(X)) 102.08/27.21 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.21 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.21 active(U122(X)) -> U122(active(X)) 102.08/27.21 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.21 active(U131(X)) -> U131(active(X)) 102.08/27.21 active(snd(X)) -> snd(active(X)) 102.08/27.21 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.21 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.21 active(U141(X)) -> U141(active(X)) 102.08/27.21 active(U151(X)) -> U151(active(X)) 102.08/27.21 active(U161(X)) -> U161(active(X)) 102.08/27.21 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.21 active(U172(X)) -> U172(active(X)) 102.08/27.21 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.21 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.21 active(U183(X)) -> U183(active(X)) 102.08/27.21 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.21 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.21 active(U193(X)) -> U193(active(X)) 102.08/27.21 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.21 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.21 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.21 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.21 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.21 active(U206(X)) -> U206(active(X)) 102.08/27.21 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.21 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.21 active(U211(X)) -> U211(active(X)) 102.08/27.21 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.21 active(U221(X)) -> U221(active(X)) 102.08/27.21 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.21 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.21 active(U232(X)) -> U232(active(X)) 102.08/27.21 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.21 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.21 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.21 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.21 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.21 active(U246(X)) -> U246(active(X)) 102.08/27.21 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.21 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.21 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.21 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.21 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.21 active(U256(X)) -> U256(active(X)) 102.08/27.21 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.21 active(U262(X)) -> U262(active(X)) 102.08/27.21 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.21 active(U272(X)) -> U272(active(X)) 102.08/27.21 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.21 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.21 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.21 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.21 active(s(X)) -> s(active(X)) 102.08/27.21 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.21 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.21 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.21 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.21 active(head(X)) -> head(active(X)) 102.08/27.21 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.21 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.21 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.21 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.21 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.21 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.21 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.21 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.21 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.21 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.21 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.21 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.21 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.21 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.21 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.21 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.21 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.21 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.21 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.21 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.21 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.21 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.21 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.21 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.21 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.21 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.21 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.21 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.21 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.21 active(fst(X)) -> fst(active(X)) 102.08/27.21 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.21 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.21 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.21 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.21 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.21 active(U46(X)) -> U46(active(X)) 102.08/27.21 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.21 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.21 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.21 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.21 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.21 active(U56(X)) -> U56(active(X)) 102.08/27.21 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.21 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.21 active(U63(X)) -> U63(active(X)) 102.08/27.21 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.21 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.21 active(U73(X)) -> U73(active(X)) 102.08/27.21 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.21 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.21 active(U83(X)) -> U83(active(X)) 102.08/27.21 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.21 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.21 active(U93(X)) -> U93(active(X)) 102.08/27.21 active(tail(X)) -> tail(active(X)) 102.08/27.21 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.21 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.21 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.21 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.21 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.21 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.21 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.21 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.21 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.21 U106(mark(X)) -> mark(U106(X)) 102.08/27.21 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.21 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.21 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.21 U112(mark(X)) -> mark(U112(X)) 102.08/27.21 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.21 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.21 U122(mark(X)) -> mark(U122(X)) 102.08/27.21 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.21 U131(mark(X)) -> mark(U131(X)) 102.08/27.21 snd(mark(X)) -> mark(snd(X)) 102.08/27.21 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.21 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.21 U141(mark(X)) -> mark(U141(X)) 102.08/27.21 U151(mark(X)) -> mark(U151(X)) 102.08/27.21 U161(mark(X)) -> mark(U161(X)) 102.08/27.21 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.21 U172(mark(X)) -> mark(U172(X)) 102.08/27.21 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.21 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.21 U183(mark(X)) -> mark(U183(X)) 102.08/27.21 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.21 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.21 U193(mark(X)) -> mark(U193(X)) 102.08/27.21 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.21 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.21 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.21 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.21 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.21 U206(mark(X)) -> mark(U206(X)) 102.08/27.21 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.21 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.21 U211(mark(X)) -> mark(U211(X)) 102.08/27.21 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.21 U221(mark(X)) -> mark(U221(X)) 102.08/27.21 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.21 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.21 U232(mark(X)) -> mark(U232(X)) 102.08/27.21 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.21 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.21 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.21 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.21 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.21 U246(mark(X)) -> mark(U246(X)) 102.08/27.21 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.21 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.21 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.21 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.21 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.21 U256(mark(X)) -> mark(U256(X)) 102.08/27.21 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.21 U262(mark(X)) -> mark(U262(X)) 102.08/27.21 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.21 U272(mark(X)) -> mark(U272(X)) 102.08/27.21 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.21 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.21 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.21 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.21 s(mark(X)) -> mark(s(X)) 102.08/27.21 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.21 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.21 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.21 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.21 head(mark(X)) -> mark(head(X)) 102.08/27.21 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.21 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.21 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.21 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.21 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.21 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.21 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.21 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.21 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.21 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.21 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.21 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.21 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.21 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.21 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.21 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.21 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.21 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.21 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.21 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.21 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.21 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.21 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.21 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.21 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.21 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.21 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.21 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.21 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.21 fst(mark(X)) -> mark(fst(X)) 102.08/27.21 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.21 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.21 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.21 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.21 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.21 U46(mark(X)) -> mark(U46(X)) 102.08/27.21 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.21 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.21 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.21 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.21 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.21 U56(mark(X)) -> mark(U56(X)) 102.08/27.21 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.21 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.21 U63(mark(X)) -> mark(U63(X)) 102.08/27.21 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.21 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.21 U73(mark(X)) -> mark(U73(X)) 102.08/27.21 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.21 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.21 U83(mark(X)) -> mark(U83(X)) 102.08/27.21 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.21 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.21 U93(mark(X)) -> mark(U93(X)) 102.08/27.21 tail(mark(X)) -> mark(tail(X)) 102.08/27.21 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.21 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.21 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.21 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.21 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(tt) -> ok(tt) 102.08/27.21 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.21 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.21 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.21 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.21 proper(U106(X)) -> U106(proper(X)) 102.08/27.21 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.21 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.21 proper(U112(X)) -> U112(proper(X)) 102.08/27.21 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.21 proper(U122(X)) -> U122(proper(X)) 102.08/27.21 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U131(X)) -> U131(proper(X)) 102.08/27.21 proper(snd(X)) -> snd(proper(X)) 102.08/27.21 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.21 proper(U141(X)) -> U141(proper(X)) 102.08/27.21 proper(U151(X)) -> U151(proper(X)) 102.08/27.21 proper(U161(X)) -> U161(proper(X)) 102.08/27.21 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.21 proper(U172(X)) -> U172(proper(X)) 102.08/27.21 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.21 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.21 proper(U183(X)) -> U183(proper(X)) 102.08/27.21 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.21 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.21 proper(U193(X)) -> U193(proper(X)) 102.08/27.21 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.21 proper(U206(X)) -> U206(proper(X)) 102.08/27.21 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U211(X)) -> U211(proper(X)) 102.08/27.21 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U221(X)) -> U221(proper(X)) 102.08/27.21 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.21 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.21 proper(U232(X)) -> U232(proper(X)) 102.08/27.21 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.21 proper(U246(X)) -> U246(proper(X)) 102.08/27.21 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.21 proper(U256(X)) -> U256(proper(X)) 102.08/27.21 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.21 proper(U262(X)) -> U262(proper(X)) 102.08/27.21 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.21 proper(U272(X)) -> U272(proper(X)) 102.08/27.21 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.21 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.21 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.21 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.21 proper(s(X)) -> s(proper(X)) 102.08/27.21 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(head(X)) -> head(proper(X)) 102.08/27.21 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.21 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.21 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.21 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.21 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.21 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.21 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.21 proper(nil) -> ok(nil) 102.08/27.21 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.21 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.21 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.21 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.21 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.21 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.21 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(fst(X)) -> fst(proper(X)) 102.08/27.21 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.21 proper(U46(X)) -> U46(proper(X)) 102.08/27.21 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.21 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.21 proper(U56(X)) -> U56(proper(X)) 102.08/27.21 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.21 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.21 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.21 proper(U63(X)) -> U63(proper(X)) 102.08/27.21 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.21 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.21 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.21 proper(U73(X)) -> U73(proper(X)) 102.08/27.21 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.21 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.21 proper(U83(X)) -> U83(proper(X)) 102.08/27.21 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.21 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.21 proper(U93(X)) -> U93(proper(X)) 102.08/27.21 proper(tail(X)) -> tail(proper(X)) 102.08/27.21 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.21 proper(0') -> ok(0') 102.08/27.21 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.21 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.21 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.21 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.21 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.21 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.21 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.21 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.21 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.21 U106(ok(X)) -> ok(U106(X)) 102.08/27.21 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.21 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.21 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.21 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.21 U112(ok(X)) -> ok(U112(X)) 102.08/27.21 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.21 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.21 U122(ok(X)) -> ok(U122(X)) 102.08/27.21 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.21 U131(ok(X)) -> ok(U131(X)) 102.08/27.21 snd(ok(X)) -> ok(snd(X)) 102.08/27.21 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.21 U141(ok(X)) -> ok(U141(X)) 102.08/27.21 U151(ok(X)) -> ok(U151(X)) 102.08/27.21 U161(ok(X)) -> ok(U161(X)) 102.08/27.21 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.21 U172(ok(X)) -> ok(U172(X)) 102.08/27.21 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.21 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.21 U183(ok(X)) -> ok(U183(X)) 102.08/27.21 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.21 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.21 U193(ok(X)) -> ok(U193(X)) 102.08/27.21 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.21 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.21 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.21 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.21 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.21 U206(ok(X)) -> ok(U206(X)) 102.08/27.21 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.21 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.21 U211(ok(X)) -> ok(U211(X)) 102.08/27.21 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.21 U221(ok(X)) -> ok(U221(X)) 102.08/27.21 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.21 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.21 U232(ok(X)) -> ok(U232(X)) 102.08/27.21 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.21 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.21 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.21 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.21 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.21 U246(ok(X)) -> ok(U246(X)) 102.08/27.21 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.21 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.21 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.21 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.21 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.21 U256(ok(X)) -> ok(U256(X)) 102.08/27.21 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.21 U262(ok(X)) -> ok(U262(X)) 102.08/27.21 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.21 U272(ok(X)) -> ok(U272(X)) 102.08/27.21 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.21 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.21 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.21 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.21 s(ok(X)) -> ok(s(X)) 102.08/27.21 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.21 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.21 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.21 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.21 head(ok(X)) -> ok(head(X)) 102.08/27.21 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.21 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.21 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.21 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.21 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.21 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.21 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.21 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.21 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.21 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.21 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.21 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.21 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.21 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.21 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.21 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.21 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.21 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.21 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.21 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.21 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.21 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.21 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.21 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.21 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.21 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.21 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.21 fst(ok(X)) -> ok(fst(X)) 102.08/27.21 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.21 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.21 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.21 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.21 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.21 U46(ok(X)) -> ok(U46(X)) 102.08/27.21 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.21 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.21 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.21 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.21 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.21 U56(ok(X)) -> ok(U56(X)) 102.08/27.21 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.21 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.21 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.21 U63(ok(X)) -> ok(U63(X)) 102.08/27.21 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.21 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.21 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.21 U73(ok(X)) -> ok(U73(X)) 102.08/27.21 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.21 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.21 U83(ok(X)) -> ok(U83(X)) 102.08/27.21 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.21 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.21 U93(ok(X)) -> ok(U93(X)) 102.08/27.21 tail(ok(X)) -> ok(tail(X)) 102.08/27.21 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.21 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.22 top(mark(X)) -> top(proper(X)) 102.08/27.22 top(ok(X)) -> top(active(X)) 102.08/27.22 102.08/27.22 Types: 102.08/27.22 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 tt :: tt:mark:nil:0':ok 102.08/27.22 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 nil :: tt:mark:nil:0':ok 102.08/27.22 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 0' :: tt:mark:nil:0':ok 102.08/27.22 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 top :: tt:mark:nil:0':ok -> top 102.08/27.22 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.22 hole_top2_0 :: top 102.08/27.22 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.22 102.08/27.22 102.08/27.22 Lemmas: 102.08/27.22 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.22 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.22 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.22 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.22 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.22 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.22 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.22 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.22 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.22 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.22 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.22 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.22 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.22 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.22 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.22 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.22 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.22 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.22 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.22 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.22 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.22 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.22 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.22 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.22 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.22 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.22 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.22 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.22 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.22 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.22 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.22 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.22 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.22 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.22 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.22 U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0))) -> *4_0, rt in Omega(n610318_0) 102.08/27.22 102.08/27.22 102.08/27.22 Generator Equations: 102.08/27.22 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.22 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.22 102.08/27.22 102.08/27.22 The following defined symbols remain to be analysed: 102.08/27.22 U262, active, U272, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.22 102.08/27.22 They will be analysed ascendingly in the following order: 102.08/27.22 U262 < active 102.08/27.22 U272 < active 102.08/27.22 U282 < active 102.08/27.22 cons < active 102.08/27.22 natsFrom < active 102.08/27.22 s < active 102.08/27.22 U292 < active 102.08/27.22 U293 < active 102.08/27.22 U294 < active 102.08/27.22 head < active 102.08/27.22 afterNth < active 102.08/27.22 U302 < active 102.08/27.22 U303 < active 102.08/27.22 U304 < active 102.08/27.22 U32 < active 102.08/27.22 U312 < active 102.08/27.22 pair < active 102.08/27.22 U33 < active 102.08/27.22 U322 < active 102.08/27.22 U323 < active 102.08/27.22 U324 < active 102.08/27.22 U325 < active 102.08/27.22 U326 < active 102.08/27.22 U327 < active 102.08/27.22 U34 < active 102.08/27.22 U332 < active 102.08/27.22 U333 < active 102.08/27.22 U334 < active 102.08/27.22 U342 < active 102.08/27.22 U343 < active 102.08/27.22 U344 < active 102.08/27.22 fst < active 102.08/27.22 U42 < active 102.08/27.22 U43 < active 102.08/27.22 U44 < active 102.08/27.22 U45 < active 102.08/27.22 U46 < active 102.08/27.22 U52 < active 102.08/27.22 U53 < active 102.08/27.22 U54 < active 102.08/27.22 U55 < active 102.08/27.22 U56 < active 102.08/27.22 U62 < active 102.08/27.22 isPLNatKind < active 102.08/27.22 U63 < active 102.08/27.22 isPLNat < active 102.08/27.22 U72 < active 102.08/27.22 U73 < active 102.08/27.22 U82 < active 102.08/27.22 U83 < active 102.08/27.22 U92 < active 102.08/27.22 U93 < active 102.08/27.22 U11 < active 102.08/27.22 U21 < active 102.08/27.22 U31 < active 102.08/27.22 U41 < active 102.08/27.22 U51 < active 102.08/27.22 U61 < active 102.08/27.22 U71 < active 102.08/27.22 U81 < active 102.08/27.22 U91 < active 102.08/27.22 U101 < active 102.08/27.22 U111 < active 102.08/27.22 U121 < active 102.08/27.22 U131 < active 102.08/27.22 U141 < active 102.08/27.22 U151 < active 102.08/27.22 U161 < active 102.08/27.22 U171 < active 102.08/27.22 U181 < active 102.08/27.22 U191 < active 102.08/27.22 U201 < active 102.08/27.22 U211 < active 102.08/27.22 U221 < active 102.08/27.22 U231 < active 102.08/27.22 U241 < active 102.08/27.22 U251 < active 102.08/27.22 U261 < active 102.08/27.22 U271 < active 102.08/27.22 U281 < active 102.08/27.22 U291 < active 102.08/27.22 U301 < active 102.08/27.22 U311 < active 102.08/27.22 U321 < active 102.08/27.22 U331 < active 102.08/27.22 U341 < active 102.08/27.22 tail < active 102.08/27.22 take < active 102.08/27.22 sel < active 102.08/27.22 active < top 102.08/27.22 U262 < proper 102.08/27.22 U272 < proper 102.08/27.22 U282 < proper 102.08/27.22 cons < proper 102.08/27.22 natsFrom < proper 102.08/27.22 s < proper 102.08/27.22 U292 < proper 102.08/27.22 U293 < proper 102.08/27.22 U294 < proper 102.08/27.22 head < proper 102.08/27.22 afterNth < proper 102.08/27.22 U302 < proper 102.08/27.22 U303 < proper 102.08/27.22 U304 < proper 102.08/27.22 U32 < proper 102.08/27.22 U312 < proper 102.08/27.22 pair < proper 102.08/27.22 U33 < proper 102.08/27.22 U322 < proper 102.08/27.22 U323 < proper 102.08/27.22 U324 < proper 102.08/27.22 U325 < proper 102.08/27.22 U326 < proper 102.08/27.22 U327 < proper 102.08/27.22 U34 < proper 102.08/27.22 U332 < proper 102.08/27.22 U333 < proper 102.08/27.22 U334 < proper 102.08/27.22 U342 < proper 102.08/27.22 U343 < proper 102.08/27.22 U344 < proper 102.08/27.22 fst < proper 102.08/27.22 U42 < proper 102.08/27.22 U43 < proper 102.08/27.22 U44 < proper 102.08/27.22 U45 < proper 102.08/27.22 U46 < proper 102.08/27.22 U52 < proper 102.08/27.22 U53 < proper 102.08/27.22 U54 < proper 102.08/27.22 U55 < proper 102.08/27.22 U56 < proper 102.08/27.22 U62 < proper 102.08/27.22 isPLNatKind < proper 102.08/27.22 U63 < proper 102.08/27.22 isPLNat < proper 102.08/27.22 U72 < proper 102.08/27.22 U73 < proper 102.08/27.22 U82 < proper 102.08/27.22 U83 < proper 102.08/27.22 U92 < proper 102.08/27.22 U93 < proper 102.08/27.22 U11 < proper 102.08/27.22 U21 < proper 102.08/27.22 U31 < proper 102.08/27.22 U41 < proper 102.08/27.22 U51 < proper 102.08/27.22 U61 < proper 102.08/27.22 U71 < proper 102.08/27.22 U81 < proper 102.08/27.22 U91 < proper 102.08/27.22 U101 < proper 102.08/27.22 U111 < proper 102.08/27.22 U121 < proper 102.08/27.22 U131 < proper 102.08/27.22 U141 < proper 102.08/27.22 U151 < proper 102.08/27.22 U161 < proper 102.08/27.22 U171 < proper 102.08/27.22 U181 < proper 102.08/27.22 U191 < proper 102.08/27.22 U201 < proper 102.08/27.22 U211 < proper 102.08/27.22 U221 < proper 102.08/27.22 U231 < proper 102.08/27.22 U241 < proper 102.08/27.22 U251 < proper 102.08/27.22 U261 < proper 102.08/27.22 U271 < proper 102.08/27.22 U281 < proper 102.08/27.22 U291 < proper 102.08/27.22 U301 < proper 102.08/27.22 U311 < proper 102.08/27.22 U321 < proper 102.08/27.22 U331 < proper 102.08/27.22 U341 < proper 102.08/27.22 tail < proper 102.08/27.22 take < proper 102.08/27.22 sel < proper 102.08/27.22 proper < top 102.08/27.22 102.08/27.22 ---------------------------------------- 102.08/27.22 102.08/27.22 (101) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.22 Proved the following rewrite lemma: 102.08/27.22 U262(gen_tt:mark:nil:0':ok3_0(+(1, n618182_0))) -> *4_0, rt in Omega(n618182_0) 102.08/27.22 102.08/27.22 Induction Base: 102.08/27.22 U262(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 102.08/27.22 102.08/27.22 Induction Step: 102.08/27.22 U262(gen_tt:mark:nil:0':ok3_0(+(1, +(n618182_0, 1)))) ->_R^Omega(1) 102.08/27.22 mark(U262(gen_tt:mark:nil:0':ok3_0(+(1, n618182_0)))) ->_IH 102.08/27.22 mark(*4_0) 102.08/27.22 102.08/27.22 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.22 ---------------------------------------- 102.08/27.22 102.08/27.22 (102) 102.08/27.22 Obligation: 102.08/27.22 TRS: 102.08/27.22 Rules: 102.08/27.22 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.22 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.22 active(U106(tt)) -> mark(tt) 102.08/27.22 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.22 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.22 active(U112(tt)) -> mark(tt) 102.08/27.22 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.22 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.22 active(U122(tt)) -> mark(tt) 102.08/27.22 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.22 active(U131(tt)) -> mark(tt) 102.08/27.22 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.22 active(U141(tt)) -> mark(tt) 102.08/27.22 active(U151(tt)) -> mark(tt) 102.08/27.22 active(U161(tt)) -> mark(tt) 102.08/27.22 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.22 active(U172(tt)) -> mark(tt) 102.08/27.22 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.22 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.22 active(U183(tt)) -> mark(tt) 102.08/27.22 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.22 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.22 active(U193(tt)) -> mark(tt) 102.08/27.22 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.22 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.22 active(U206(tt)) -> mark(tt) 102.08/27.22 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.22 active(U211(tt)) -> mark(tt) 102.08/27.22 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.22 active(U221(tt)) -> mark(tt) 102.08/27.22 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.22 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.22 active(U232(tt)) -> mark(tt) 102.08/27.22 active(U24(tt, X)) -> mark(X) 102.08/27.22 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.22 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.22 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.22 active(U246(tt)) -> mark(tt) 102.08/27.22 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.22 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.22 active(U256(tt)) -> mark(tt) 102.08/27.22 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.22 active(U262(tt)) -> mark(tt) 102.08/27.22 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.22 active(U272(tt)) -> mark(tt) 102.08/27.22 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.22 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.22 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.22 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.22 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.22 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.22 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.22 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.22 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.22 active(U304(tt, Y)) -> mark(Y) 102.08/27.22 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.22 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.22 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.22 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.22 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.22 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.22 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.22 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.22 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.22 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.22 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.22 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.22 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.22 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.22 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.22 active(U334(tt, XS)) -> mark(XS) 102.08/27.22 active(U34(tt, N)) -> mark(N) 102.08/27.22 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.22 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.22 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.22 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.22 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.22 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.22 active(U46(tt)) -> mark(tt) 102.08/27.22 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.22 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.22 active(U56(tt)) -> mark(tt) 102.08/27.22 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.22 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.22 active(U63(tt)) -> mark(tt) 102.08/27.22 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.22 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.22 active(U73(tt)) -> mark(tt) 102.08/27.22 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.22 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.22 active(U83(tt)) -> mark(tt) 102.08/27.22 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.22 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.22 active(U93(tt)) -> mark(tt) 102.08/27.22 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.22 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.22 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.22 active(isLNat(nil)) -> mark(tt) 102.08/27.22 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.22 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.22 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.22 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.22 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNatKind(nil)) -> mark(tt) 102.08/27.22 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.22 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.22 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.22 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.22 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.22 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.22 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.22 active(isNatural(0')) -> mark(tt) 102.08/27.22 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.22 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.22 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isNaturalKind(0')) -> mark(tt) 102.08/27.22 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.22 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.22 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.22 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.22 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.22 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.22 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.22 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.22 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.22 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.22 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.22 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.22 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.22 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.22 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.22 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.22 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.22 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.22 active(U106(X)) -> U106(active(X)) 102.08/27.22 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.22 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.22 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.22 active(U112(X)) -> U112(active(X)) 102.08/27.22 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.22 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.22 active(U122(X)) -> U122(active(X)) 102.08/27.22 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.22 active(U131(X)) -> U131(active(X)) 102.08/27.22 active(snd(X)) -> snd(active(X)) 102.08/27.22 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.22 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.22 active(U141(X)) -> U141(active(X)) 102.08/27.22 active(U151(X)) -> U151(active(X)) 102.08/27.22 active(U161(X)) -> U161(active(X)) 102.08/27.22 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.22 active(U172(X)) -> U172(active(X)) 102.08/27.22 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.22 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.22 active(U183(X)) -> U183(active(X)) 102.08/27.22 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.22 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.22 active(U193(X)) -> U193(active(X)) 102.08/27.22 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.22 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.22 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.22 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.22 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.22 active(U206(X)) -> U206(active(X)) 102.08/27.22 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.22 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.22 active(U211(X)) -> U211(active(X)) 102.08/27.22 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.22 active(U221(X)) -> U221(active(X)) 102.08/27.22 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.22 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.22 active(U232(X)) -> U232(active(X)) 102.08/27.22 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.22 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.22 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.22 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.22 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.22 active(U246(X)) -> U246(active(X)) 102.08/27.22 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.22 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.22 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.22 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.22 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.22 active(U256(X)) -> U256(active(X)) 102.08/27.22 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.22 active(U262(X)) -> U262(active(X)) 102.08/27.22 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.22 active(U272(X)) -> U272(active(X)) 102.08/27.22 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.22 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.22 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.22 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.22 active(s(X)) -> s(active(X)) 102.08/27.22 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.22 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.22 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.22 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.22 active(head(X)) -> head(active(X)) 102.08/27.22 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.22 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.22 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.22 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.22 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.22 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.22 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.22 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.22 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.22 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.22 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.22 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.22 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.22 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.22 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.22 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.22 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.22 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.22 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.22 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.22 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.22 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.22 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.22 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.22 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.22 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.22 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.22 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.22 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.22 active(fst(X)) -> fst(active(X)) 102.08/27.22 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.22 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.22 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.22 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.22 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.22 active(U46(X)) -> U46(active(X)) 102.08/27.22 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.22 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.22 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.22 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.22 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.22 active(U56(X)) -> U56(active(X)) 102.08/27.22 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.22 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.22 active(U63(X)) -> U63(active(X)) 102.08/27.22 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.22 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.22 active(U73(X)) -> U73(active(X)) 102.08/27.22 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.22 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.22 active(U83(X)) -> U83(active(X)) 102.08/27.22 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.22 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.22 active(U93(X)) -> U93(active(X)) 102.08/27.22 active(tail(X)) -> tail(active(X)) 102.08/27.22 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.22 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.22 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.22 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.22 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.22 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.22 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.22 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.22 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.22 U106(mark(X)) -> mark(U106(X)) 102.08/27.22 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.22 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.22 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.22 U112(mark(X)) -> mark(U112(X)) 102.08/27.22 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.22 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.22 U122(mark(X)) -> mark(U122(X)) 102.08/27.22 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.22 U131(mark(X)) -> mark(U131(X)) 102.08/27.22 snd(mark(X)) -> mark(snd(X)) 102.08/27.22 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.22 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.22 U141(mark(X)) -> mark(U141(X)) 102.08/27.22 U151(mark(X)) -> mark(U151(X)) 102.08/27.22 U161(mark(X)) -> mark(U161(X)) 102.08/27.22 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.22 U172(mark(X)) -> mark(U172(X)) 102.08/27.22 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.22 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.22 U183(mark(X)) -> mark(U183(X)) 102.08/27.22 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.22 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.22 U193(mark(X)) -> mark(U193(X)) 102.08/27.22 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.22 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.22 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.22 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.22 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.22 U206(mark(X)) -> mark(U206(X)) 102.08/27.22 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.22 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.22 U211(mark(X)) -> mark(U211(X)) 102.08/27.22 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.22 U221(mark(X)) -> mark(U221(X)) 102.08/27.22 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.22 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.22 U232(mark(X)) -> mark(U232(X)) 102.08/27.22 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.22 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.22 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.22 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.22 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.22 U246(mark(X)) -> mark(U246(X)) 102.08/27.22 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.22 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.22 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.22 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.22 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.22 U256(mark(X)) -> mark(U256(X)) 102.08/27.22 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.22 U262(mark(X)) -> mark(U262(X)) 102.08/27.22 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.22 U272(mark(X)) -> mark(U272(X)) 102.08/27.22 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.22 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.22 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.22 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.22 s(mark(X)) -> mark(s(X)) 102.08/27.22 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.22 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.22 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.22 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.22 head(mark(X)) -> mark(head(X)) 102.08/27.22 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.22 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.22 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.22 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.22 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.22 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.22 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.22 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.22 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.22 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.22 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.22 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.22 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.22 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.22 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.22 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.22 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.22 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.22 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.22 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.22 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.22 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.22 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.22 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.22 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.22 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.22 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.22 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.22 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.22 fst(mark(X)) -> mark(fst(X)) 102.08/27.22 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.22 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.22 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.22 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.22 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.22 U46(mark(X)) -> mark(U46(X)) 102.08/27.22 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.22 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.22 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.22 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.22 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.22 U56(mark(X)) -> mark(U56(X)) 102.08/27.22 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.22 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.22 U63(mark(X)) -> mark(U63(X)) 102.08/27.22 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.22 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.22 U73(mark(X)) -> mark(U73(X)) 102.08/27.22 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.22 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.22 U83(mark(X)) -> mark(U83(X)) 102.08/27.22 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.22 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.22 U93(mark(X)) -> mark(U93(X)) 102.08/27.22 tail(mark(X)) -> mark(tail(X)) 102.08/27.22 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.22 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.22 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.22 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.22 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(tt) -> ok(tt) 102.08/27.22 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.22 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.22 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.22 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.22 proper(U106(X)) -> U106(proper(X)) 102.08/27.22 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.22 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.22 proper(U112(X)) -> U112(proper(X)) 102.08/27.22 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.22 proper(U122(X)) -> U122(proper(X)) 102.08/27.22 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U131(X)) -> U131(proper(X)) 102.08/27.22 proper(snd(X)) -> snd(proper(X)) 102.08/27.22 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.22 proper(U141(X)) -> U141(proper(X)) 102.08/27.22 proper(U151(X)) -> U151(proper(X)) 102.08/27.22 proper(U161(X)) -> U161(proper(X)) 102.08/27.22 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.22 proper(U172(X)) -> U172(proper(X)) 102.08/27.22 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.22 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.22 proper(U183(X)) -> U183(proper(X)) 102.08/27.22 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.22 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.22 proper(U193(X)) -> U193(proper(X)) 102.08/27.22 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.22 proper(U206(X)) -> U206(proper(X)) 102.08/27.22 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U211(X)) -> U211(proper(X)) 102.08/27.22 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U221(X)) -> U221(proper(X)) 102.08/27.22 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.22 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.22 proper(U232(X)) -> U232(proper(X)) 102.08/27.22 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.22 proper(U246(X)) -> U246(proper(X)) 102.08/27.22 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.22 proper(U256(X)) -> U256(proper(X)) 102.08/27.22 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.22 proper(U262(X)) -> U262(proper(X)) 102.08/27.22 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.22 proper(U272(X)) -> U272(proper(X)) 102.08/27.22 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.22 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.22 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.22 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.22 proper(s(X)) -> s(proper(X)) 102.08/27.22 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(head(X)) -> head(proper(X)) 102.08/27.22 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.22 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.22 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.22 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.22 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.22 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.22 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.22 proper(nil) -> ok(nil) 102.08/27.22 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.22 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.22 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.22 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.22 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.22 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(fst(X)) -> fst(proper(X)) 102.08/27.22 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.22 proper(U46(X)) -> U46(proper(X)) 102.08/27.22 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.22 proper(U56(X)) -> U56(proper(X)) 102.08/27.22 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.22 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.22 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.22 proper(U63(X)) -> U63(proper(X)) 102.08/27.22 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.22 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.22 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.22 proper(U73(X)) -> U73(proper(X)) 102.08/27.22 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.22 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.22 proper(U83(X)) -> U83(proper(X)) 102.08/27.22 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.22 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.22 proper(U93(X)) -> U93(proper(X)) 102.08/27.22 proper(tail(X)) -> tail(proper(X)) 102.08/27.22 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.22 proper(0') -> ok(0') 102.08/27.22 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.22 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.22 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.22 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.22 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.22 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.22 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.22 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.22 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.22 U106(ok(X)) -> ok(U106(X)) 102.08/27.22 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.22 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.22 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.22 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.22 U112(ok(X)) -> ok(U112(X)) 102.08/27.22 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.22 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.22 U122(ok(X)) -> ok(U122(X)) 102.08/27.22 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.22 U131(ok(X)) -> ok(U131(X)) 102.08/27.22 snd(ok(X)) -> ok(snd(X)) 102.08/27.22 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.22 U141(ok(X)) -> ok(U141(X)) 102.08/27.22 U151(ok(X)) -> ok(U151(X)) 102.08/27.22 U161(ok(X)) -> ok(U161(X)) 102.08/27.22 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.22 U172(ok(X)) -> ok(U172(X)) 102.08/27.22 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.22 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.22 U183(ok(X)) -> ok(U183(X)) 102.08/27.22 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.22 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.22 U193(ok(X)) -> ok(U193(X)) 102.08/27.22 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.22 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.22 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.22 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.22 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.22 U206(ok(X)) -> ok(U206(X)) 102.08/27.22 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.22 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.22 U211(ok(X)) -> ok(U211(X)) 102.08/27.22 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.22 U221(ok(X)) -> ok(U221(X)) 102.08/27.22 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.22 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.22 U232(ok(X)) -> ok(U232(X)) 102.08/27.22 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.22 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.22 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.22 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.22 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.22 U246(ok(X)) -> ok(U246(X)) 102.08/27.22 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.22 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.22 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.22 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.22 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.22 U256(ok(X)) -> ok(U256(X)) 102.08/27.22 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.22 U262(ok(X)) -> ok(U262(X)) 102.08/27.22 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.22 U272(ok(X)) -> ok(U272(X)) 102.08/27.22 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.22 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.22 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.22 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.22 s(ok(X)) -> ok(s(X)) 102.08/27.22 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.22 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.22 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.22 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.22 head(ok(X)) -> ok(head(X)) 102.08/27.22 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.22 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.22 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.22 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.22 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.22 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.22 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.22 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.22 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.22 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.22 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.22 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.22 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.22 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.22 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.22 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.22 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.22 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.22 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.22 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.22 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.22 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.22 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.22 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.22 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.22 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.22 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.22 fst(ok(X)) -> ok(fst(X)) 102.08/27.22 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.22 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.22 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.22 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.22 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.22 U46(ok(X)) -> ok(U46(X)) 102.08/27.22 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.22 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.22 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.22 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.22 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.22 U56(ok(X)) -> ok(U56(X)) 102.08/27.22 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.22 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.22 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.22 U63(ok(X)) -> ok(U63(X)) 102.08/27.22 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.22 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.22 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.22 U73(ok(X)) -> ok(U73(X)) 102.08/27.22 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.22 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.22 U83(ok(X)) -> ok(U83(X)) 102.08/27.22 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.22 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.22 U93(ok(X)) -> ok(U93(X)) 102.08/27.22 tail(ok(X)) -> ok(tail(X)) 102.08/27.22 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.22 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.22 top(mark(X)) -> top(proper(X)) 102.08/27.22 top(ok(X)) -> top(active(X)) 102.08/27.22 102.08/27.22 Types: 102.08/27.22 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 tt :: tt:mark:nil:0':ok 102.08/27.22 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 nil :: tt:mark:nil:0':ok 102.08/27.22 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 0' :: tt:mark:nil:0':ok 102.08/27.22 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.22 top :: tt:mark:nil:0':ok -> top 102.08/27.22 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.22 hole_top2_0 :: top 102.08/27.22 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.22 102.08/27.22 102.08/27.22 Lemmas: 102.08/27.22 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.22 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.22 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.22 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.22 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.22 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.22 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.22 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.22 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.22 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.22 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.22 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.22 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.22 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.22 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.22 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.22 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.22 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.22 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.22 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.22 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.22 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.22 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.22 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.22 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.22 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.22 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.22 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.22 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.22 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.22 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.22 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.22 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.22 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.22 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.22 U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0))) -> *4_0, rt in Omega(n610318_0) 102.08/27.22 U262(gen_tt:mark:nil:0':ok3_0(+(1, n618182_0))) -> *4_0, rt in Omega(n618182_0) 102.08/27.22 102.08/27.22 102.08/27.22 Generator Equations: 102.08/27.22 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.22 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.22 102.08/27.22 102.08/27.22 The following defined symbols remain to be analysed: 102.08/27.22 U272, active, U282, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.22 102.08/27.22 They will be analysed ascendingly in the following order: 102.08/27.22 U272 < active 102.08/27.22 U282 < active 102.08/27.22 cons < active 102.08/27.22 natsFrom < active 102.08/27.22 s < active 102.08/27.22 U292 < active 102.08/27.22 U293 < active 102.08/27.22 U294 < active 102.08/27.22 head < active 102.08/27.22 afterNth < active 102.08/27.22 U302 < active 102.08/27.22 U303 < active 102.08/27.22 U304 < active 102.08/27.22 U32 < active 102.08/27.22 U312 < active 102.08/27.22 pair < active 102.08/27.22 U33 < active 102.08/27.22 U322 < active 102.08/27.22 U323 < active 102.08/27.22 U324 < active 102.08/27.22 U325 < active 102.08/27.22 U326 < active 102.08/27.22 U327 < active 102.08/27.22 U34 < active 102.08/27.22 U332 < active 102.08/27.22 U333 < active 102.08/27.22 U334 < active 102.08/27.22 U342 < active 102.08/27.22 U343 < active 102.08/27.22 U344 < active 102.08/27.22 fst < active 102.08/27.22 U42 < active 102.08/27.22 U43 < active 102.08/27.22 U44 < active 102.08/27.22 U45 < active 102.08/27.22 U46 < active 102.08/27.22 U52 < active 102.08/27.22 U53 < active 102.08/27.22 U54 < active 102.08/27.22 U55 < active 102.08/27.22 U56 < active 102.08/27.22 U62 < active 102.08/27.22 isPLNatKind < active 102.08/27.22 U63 < active 102.08/27.22 isPLNat < active 102.08/27.22 U72 < active 102.08/27.22 U73 < active 102.08/27.22 U82 < active 102.08/27.22 U83 < active 102.08/27.22 U92 < active 102.08/27.22 U93 < active 102.08/27.22 U11 < active 102.08/27.22 U21 < active 102.08/27.22 U31 < active 102.08/27.22 U41 < active 102.08/27.22 U51 < active 102.08/27.22 U61 < active 102.08/27.22 U71 < active 102.08/27.22 U81 < active 102.08/27.22 U91 < active 102.08/27.22 U101 < active 102.08/27.22 U111 < active 102.08/27.22 U121 < active 102.08/27.22 U131 < active 102.08/27.22 U141 < active 102.08/27.22 U151 < active 102.08/27.22 U161 < active 102.08/27.22 U171 < active 102.08/27.22 U181 < active 102.08/27.22 U191 < active 102.08/27.22 U201 < active 102.08/27.22 U211 < active 102.08/27.22 U221 < active 102.08/27.22 U231 < active 102.08/27.22 U241 < active 102.08/27.22 U251 < active 102.08/27.22 U261 < active 102.08/27.22 U271 < active 102.08/27.22 U281 < active 102.08/27.22 U291 < active 102.08/27.22 U301 < active 102.08/27.22 U311 < active 102.08/27.22 U321 < active 102.08/27.22 U331 < active 102.08/27.22 U341 < active 102.08/27.22 tail < active 102.08/27.22 take < active 102.08/27.22 sel < active 102.08/27.22 active < top 102.08/27.22 U272 < proper 102.08/27.22 U282 < proper 102.08/27.22 cons < proper 102.08/27.22 natsFrom < proper 102.08/27.22 s < proper 102.08/27.22 U292 < proper 102.08/27.22 U293 < proper 102.08/27.22 U294 < proper 102.08/27.22 head < proper 102.08/27.22 afterNth < proper 102.08/27.22 U302 < proper 102.08/27.22 U303 < proper 102.08/27.22 U304 < proper 102.08/27.22 U32 < proper 102.08/27.22 U312 < proper 102.08/27.22 pair < proper 102.08/27.22 U33 < proper 102.08/27.22 U322 < proper 102.08/27.22 U323 < proper 102.08/27.22 U324 < proper 102.08/27.22 U325 < proper 102.08/27.22 U326 < proper 102.08/27.22 U327 < proper 102.08/27.22 U34 < proper 102.08/27.22 U332 < proper 102.08/27.22 U333 < proper 102.08/27.22 U334 < proper 102.08/27.22 U342 < proper 102.08/27.22 U343 < proper 102.08/27.22 U344 < proper 102.08/27.22 fst < proper 102.08/27.22 U42 < proper 102.08/27.22 U43 < proper 102.08/27.22 U44 < proper 102.08/27.22 U45 < proper 102.08/27.22 U46 < proper 102.08/27.22 U52 < proper 102.08/27.22 U53 < proper 102.08/27.22 U54 < proper 102.08/27.22 U55 < proper 102.08/27.22 U56 < proper 102.08/27.22 U62 < proper 102.08/27.22 isPLNatKind < proper 102.08/27.22 U63 < proper 102.08/27.22 isPLNat < proper 102.08/27.22 U72 < proper 102.08/27.22 U73 < proper 102.08/27.22 U82 < proper 102.08/27.22 U83 < proper 102.08/27.22 U92 < proper 102.08/27.22 U93 < proper 102.08/27.22 U11 < proper 102.08/27.22 U21 < proper 102.08/27.22 U31 < proper 102.08/27.22 U41 < proper 102.08/27.22 U51 < proper 102.08/27.22 U61 < proper 102.08/27.22 U71 < proper 102.08/27.22 U81 < proper 102.08/27.22 U91 < proper 102.08/27.22 U101 < proper 102.08/27.22 U111 < proper 102.08/27.22 U121 < proper 102.08/27.22 U131 < proper 102.08/27.22 U141 < proper 102.08/27.22 U151 < proper 102.08/27.22 U161 < proper 102.08/27.22 U171 < proper 102.08/27.22 U181 < proper 102.08/27.22 U191 < proper 102.08/27.22 U201 < proper 102.08/27.22 U211 < proper 102.08/27.22 U221 < proper 102.08/27.22 U231 < proper 102.08/27.22 U241 < proper 102.08/27.22 U251 < proper 102.08/27.22 U261 < proper 102.08/27.22 U271 < proper 102.08/27.22 U281 < proper 102.08/27.22 U291 < proper 102.08/27.22 U301 < proper 102.08/27.22 U311 < proper 102.08/27.22 U321 < proper 102.08/27.22 U331 < proper 102.08/27.22 U341 < proper 102.08/27.22 tail < proper 102.08/27.22 take < proper 102.08/27.22 sel < proper 102.08/27.22 proper < top 102.08/27.22 102.08/27.22 ---------------------------------------- 102.08/27.22 102.08/27.22 (103) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.22 Proved the following rewrite lemma: 102.08/27.22 U272(gen_tt:mark:nil:0':ok3_0(+(1, n626147_0))) -> *4_0, rt in Omega(n626147_0) 102.08/27.22 102.08/27.22 Induction Base: 102.08/27.22 U272(gen_tt:mark:nil:0':ok3_0(+(1, 0))) 102.08/27.22 102.08/27.22 Induction Step: 102.08/27.22 U272(gen_tt:mark:nil:0':ok3_0(+(1, +(n626147_0, 1)))) ->_R^Omega(1) 102.08/27.22 mark(U272(gen_tt:mark:nil:0':ok3_0(+(1, n626147_0)))) ->_IH 102.08/27.22 mark(*4_0) 102.08/27.22 102.08/27.22 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.22 ---------------------------------------- 102.08/27.22 102.08/27.22 (104) 102.08/27.22 Obligation: 102.08/27.22 TRS: 102.08/27.22 Rules: 102.08/27.22 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.22 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.22 active(U106(tt)) -> mark(tt) 102.08/27.22 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.22 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.22 active(U112(tt)) -> mark(tt) 102.08/27.22 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.22 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.22 active(U122(tt)) -> mark(tt) 102.08/27.22 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.22 active(U131(tt)) -> mark(tt) 102.08/27.22 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.22 active(U141(tt)) -> mark(tt) 102.08/27.22 active(U151(tt)) -> mark(tt) 102.08/27.22 active(U161(tt)) -> mark(tt) 102.08/27.22 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.22 active(U172(tt)) -> mark(tt) 102.08/27.22 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.22 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.22 active(U183(tt)) -> mark(tt) 102.08/27.22 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.22 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.22 active(U193(tt)) -> mark(tt) 102.08/27.22 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.22 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.22 active(U206(tt)) -> mark(tt) 102.08/27.22 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.22 active(U211(tt)) -> mark(tt) 102.08/27.22 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.22 active(U221(tt)) -> mark(tt) 102.08/27.22 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.22 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.22 active(U232(tt)) -> mark(tt) 102.08/27.22 active(U24(tt, X)) -> mark(X) 102.08/27.22 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.22 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.22 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.22 active(U246(tt)) -> mark(tt) 102.08/27.22 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.22 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.22 active(U256(tt)) -> mark(tt) 102.08/27.22 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.22 active(U262(tt)) -> mark(tt) 102.08/27.22 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.22 active(U272(tt)) -> mark(tt) 102.08/27.22 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.22 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.22 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.22 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.22 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.22 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.22 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.22 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.22 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.22 active(U304(tt, Y)) -> mark(Y) 102.08/27.22 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.22 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.22 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.22 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.22 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.22 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.22 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.22 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.22 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.22 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.22 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.22 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.22 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.22 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.22 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.22 active(U334(tt, XS)) -> mark(XS) 102.08/27.22 active(U34(tt, N)) -> mark(N) 102.08/27.22 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.22 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.22 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.22 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.22 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.22 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.22 active(U46(tt)) -> mark(tt) 102.08/27.22 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.22 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.22 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.22 active(U56(tt)) -> mark(tt) 102.08/27.22 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.22 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.22 active(U63(tt)) -> mark(tt) 102.08/27.22 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.22 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.22 active(U73(tt)) -> mark(tt) 102.08/27.22 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.22 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.22 active(U83(tt)) -> mark(tt) 102.08/27.22 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.22 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.22 active(U93(tt)) -> mark(tt) 102.08/27.22 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.22 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.22 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.22 active(isLNat(nil)) -> mark(tt) 102.08/27.22 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.22 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.22 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.22 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.22 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isLNatKind(nil)) -> mark(tt) 102.08/27.22 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.22 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.22 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.22 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.22 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.22 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.22 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.22 active(isNatural(0')) -> mark(tt) 102.08/27.22 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.22 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.22 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isNaturalKind(0')) -> mark(tt) 102.08/27.22 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.22 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.22 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.22 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.22 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.22 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.22 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.22 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.22 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.22 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.22 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.22 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.22 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.22 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.22 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.22 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.22 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.22 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.22 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.22 active(U106(X)) -> U106(active(X)) 102.08/27.22 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.22 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.22 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.22 active(U112(X)) -> U112(active(X)) 102.08/27.22 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.22 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.22 active(U122(X)) -> U122(active(X)) 102.08/27.22 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.22 active(U131(X)) -> U131(active(X)) 102.08/27.22 active(snd(X)) -> snd(active(X)) 102.08/27.22 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.22 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.22 active(U141(X)) -> U141(active(X)) 102.08/27.22 active(U151(X)) -> U151(active(X)) 102.08/27.22 active(U161(X)) -> U161(active(X)) 102.08/27.22 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.22 active(U172(X)) -> U172(active(X)) 102.08/27.22 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.22 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.22 active(U183(X)) -> U183(active(X)) 102.08/27.22 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.22 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.22 active(U193(X)) -> U193(active(X)) 102.08/27.22 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.22 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.22 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.22 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.22 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.22 active(U206(X)) -> U206(active(X)) 102.08/27.22 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.22 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.22 active(U211(X)) -> U211(active(X)) 102.08/27.22 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.22 active(U221(X)) -> U221(active(X)) 102.08/27.22 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.22 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.22 active(U232(X)) -> U232(active(X)) 102.08/27.22 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.22 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.22 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.22 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.22 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.22 active(U246(X)) -> U246(active(X)) 102.08/27.22 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.22 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.22 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.22 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.22 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.22 active(U256(X)) -> U256(active(X)) 102.08/27.22 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.22 active(U262(X)) -> U262(active(X)) 102.08/27.22 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.22 active(U272(X)) -> U272(active(X)) 102.08/27.22 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.22 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.22 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.22 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.22 active(s(X)) -> s(active(X)) 102.08/27.22 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.22 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.22 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.22 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.22 active(head(X)) -> head(active(X)) 102.08/27.22 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.22 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.22 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.22 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.22 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.22 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.22 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.22 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.22 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.22 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.22 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.22 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.22 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.22 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.22 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.22 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.22 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.22 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.22 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.22 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.22 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.22 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.22 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.22 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.22 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.22 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.22 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.22 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.22 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.22 active(fst(X)) -> fst(active(X)) 102.08/27.22 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.22 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.22 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.22 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.22 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.22 active(U46(X)) -> U46(active(X)) 102.08/27.22 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.22 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.22 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.22 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.22 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.22 active(U56(X)) -> U56(active(X)) 102.08/27.22 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.22 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.22 active(U63(X)) -> U63(active(X)) 102.08/27.22 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.22 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.22 active(U73(X)) -> U73(active(X)) 102.08/27.22 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.22 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.22 active(U83(X)) -> U83(active(X)) 102.08/27.22 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.22 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.22 active(U93(X)) -> U93(active(X)) 102.08/27.22 active(tail(X)) -> tail(active(X)) 102.08/27.22 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.22 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.22 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.22 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.22 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.22 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.22 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.22 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.22 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.22 U106(mark(X)) -> mark(U106(X)) 102.08/27.22 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.22 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.22 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.22 U112(mark(X)) -> mark(U112(X)) 102.08/27.22 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.22 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.22 U122(mark(X)) -> mark(U122(X)) 102.08/27.22 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.22 U131(mark(X)) -> mark(U131(X)) 102.08/27.22 snd(mark(X)) -> mark(snd(X)) 102.08/27.22 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.22 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.22 U141(mark(X)) -> mark(U141(X)) 102.08/27.22 U151(mark(X)) -> mark(U151(X)) 102.08/27.22 U161(mark(X)) -> mark(U161(X)) 102.08/27.22 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.22 U172(mark(X)) -> mark(U172(X)) 102.08/27.22 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.22 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.22 U183(mark(X)) -> mark(U183(X)) 102.08/27.22 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.22 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.22 U193(mark(X)) -> mark(U193(X)) 102.08/27.22 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.22 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.22 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.22 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.22 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.22 U206(mark(X)) -> mark(U206(X)) 102.08/27.22 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.22 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.22 U211(mark(X)) -> mark(U211(X)) 102.08/27.22 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.22 U221(mark(X)) -> mark(U221(X)) 102.08/27.22 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.22 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.22 U232(mark(X)) -> mark(U232(X)) 102.08/27.22 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.22 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.22 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.22 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.22 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.22 U246(mark(X)) -> mark(U246(X)) 102.08/27.22 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.22 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.22 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.22 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.22 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.22 U256(mark(X)) -> mark(U256(X)) 102.08/27.22 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.22 U262(mark(X)) -> mark(U262(X)) 102.08/27.22 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.22 U272(mark(X)) -> mark(U272(X)) 102.08/27.22 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.22 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.22 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.22 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.22 s(mark(X)) -> mark(s(X)) 102.08/27.22 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.22 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.22 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.22 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.22 head(mark(X)) -> mark(head(X)) 102.08/27.22 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.22 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.22 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.22 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.22 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.22 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.22 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.22 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.22 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.22 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.22 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.22 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.22 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.22 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.22 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.22 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.22 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.22 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.22 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.22 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.22 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.22 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.22 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.22 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.22 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.22 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.22 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.22 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.22 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.22 fst(mark(X)) -> mark(fst(X)) 102.08/27.22 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.22 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.22 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.22 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.22 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.22 U46(mark(X)) -> mark(U46(X)) 102.08/27.22 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.22 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.22 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.22 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.22 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.22 U56(mark(X)) -> mark(U56(X)) 102.08/27.22 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.22 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.22 U63(mark(X)) -> mark(U63(X)) 102.08/27.22 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.22 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.22 U73(mark(X)) -> mark(U73(X)) 102.08/27.22 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.22 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.22 U83(mark(X)) -> mark(U83(X)) 102.08/27.22 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.22 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.22 U93(mark(X)) -> mark(U93(X)) 102.08/27.22 tail(mark(X)) -> mark(tail(X)) 102.08/27.22 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.22 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.22 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.22 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.22 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(tt) -> ok(tt) 102.08/27.22 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.22 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.22 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.22 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.22 proper(U106(X)) -> U106(proper(X)) 102.08/27.22 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.22 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.22 proper(U112(X)) -> U112(proper(X)) 102.08/27.22 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.22 proper(U122(X)) -> U122(proper(X)) 102.08/27.22 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U131(X)) -> U131(proper(X)) 102.08/27.22 proper(snd(X)) -> snd(proper(X)) 102.08/27.22 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.22 proper(U141(X)) -> U141(proper(X)) 102.08/27.22 proper(U151(X)) -> U151(proper(X)) 102.08/27.22 proper(U161(X)) -> U161(proper(X)) 102.08/27.22 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.22 proper(U172(X)) -> U172(proper(X)) 102.08/27.22 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.22 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.22 proper(U183(X)) -> U183(proper(X)) 102.08/27.22 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.22 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.22 proper(U193(X)) -> U193(proper(X)) 102.08/27.22 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.22 proper(U206(X)) -> U206(proper(X)) 102.08/27.22 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U211(X)) -> U211(proper(X)) 102.08/27.22 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U221(X)) -> U221(proper(X)) 102.08/27.22 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.22 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.22 proper(U232(X)) -> U232(proper(X)) 102.08/27.22 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.22 proper(U246(X)) -> U246(proper(X)) 102.08/27.22 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.22 proper(U256(X)) -> U256(proper(X)) 102.08/27.22 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.22 proper(U262(X)) -> U262(proper(X)) 102.08/27.22 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.22 proper(U272(X)) -> U272(proper(X)) 102.08/27.22 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.22 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.22 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.22 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.22 proper(s(X)) -> s(proper(X)) 102.08/27.22 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(head(X)) -> head(proper(X)) 102.08/27.22 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.22 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.22 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.22 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.22 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.22 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.22 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.22 proper(nil) -> ok(nil) 102.08/27.22 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.22 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.22 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.22 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.22 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.22 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.22 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(fst(X)) -> fst(proper(X)) 102.08/27.22 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.22 proper(U46(X)) -> U46(proper(X)) 102.08/27.22 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.22 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.22 proper(U56(X)) -> U56(proper(X)) 102.08/27.22 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.22 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.22 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.22 proper(U63(X)) -> U63(proper(X)) 102.08/27.22 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.22 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.22 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.22 proper(U73(X)) -> U73(proper(X)) 102.08/27.22 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.22 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.22 proper(U83(X)) -> U83(proper(X)) 102.08/27.22 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.22 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.22 proper(U93(X)) -> U93(proper(X)) 102.08/27.22 proper(tail(X)) -> tail(proper(X)) 102.08/27.22 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.22 proper(0') -> ok(0') 102.08/27.22 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.22 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.22 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.22 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.22 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.22 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.22 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.22 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.22 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.22 U106(ok(X)) -> ok(U106(X)) 102.08/27.22 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.22 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.22 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.22 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.22 U112(ok(X)) -> ok(U112(X)) 102.08/27.22 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.22 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.22 U122(ok(X)) -> ok(U122(X)) 102.08/27.22 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.22 U131(ok(X)) -> ok(U131(X)) 102.08/27.22 snd(ok(X)) -> ok(snd(X)) 102.08/27.22 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.22 U141(ok(X)) -> ok(U141(X)) 102.08/27.22 U151(ok(X)) -> ok(U151(X)) 102.08/27.22 U161(ok(X)) -> ok(U161(X)) 102.08/27.22 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.22 U172(ok(X)) -> ok(U172(X)) 102.08/27.22 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.22 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.22 U183(ok(X)) -> ok(U183(X)) 102.08/27.22 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.22 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.22 U193(ok(X)) -> ok(U193(X)) 102.08/27.22 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.22 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.22 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.22 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.22 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.22 U206(ok(X)) -> ok(U206(X)) 102.08/27.22 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.22 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.22 U211(ok(X)) -> ok(U211(X)) 102.08/27.22 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.22 U221(ok(X)) -> ok(U221(X)) 102.08/27.22 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.22 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.22 U232(ok(X)) -> ok(U232(X)) 102.08/27.22 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.22 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.22 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.22 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.22 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.22 U246(ok(X)) -> ok(U246(X)) 102.08/27.22 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.22 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.22 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.23 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.23 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.23 U256(ok(X)) -> ok(U256(X)) 102.08/27.23 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.23 U262(ok(X)) -> ok(U262(X)) 102.08/27.23 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.23 U272(ok(X)) -> ok(U272(X)) 102.08/27.23 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.23 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.23 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.23 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.23 s(ok(X)) -> ok(s(X)) 102.08/27.23 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.23 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.23 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.23 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.23 head(ok(X)) -> ok(head(X)) 102.08/27.23 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.23 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.23 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.23 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.23 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.23 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.23 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.23 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.23 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.23 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.23 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.23 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.23 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.23 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.23 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.23 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.23 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.23 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.23 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.23 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.23 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.23 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.23 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.23 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.23 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.23 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.23 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.23 fst(ok(X)) -> ok(fst(X)) 102.08/27.23 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.23 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.23 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.23 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.23 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.23 U46(ok(X)) -> ok(U46(X)) 102.08/27.23 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.23 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.23 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.23 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.23 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.23 U56(ok(X)) -> ok(U56(X)) 102.08/27.23 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.23 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.23 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.23 U63(ok(X)) -> ok(U63(X)) 102.08/27.23 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.23 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.23 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.23 U73(ok(X)) -> ok(U73(X)) 102.08/27.23 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.23 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.23 U83(ok(X)) -> ok(U83(X)) 102.08/27.23 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.23 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.23 U93(ok(X)) -> ok(U93(X)) 102.08/27.23 tail(ok(X)) -> ok(tail(X)) 102.08/27.23 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.23 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.23 top(mark(X)) -> top(proper(X)) 102.08/27.23 top(ok(X)) -> top(active(X)) 102.08/27.23 102.08/27.23 Types: 102.08/27.23 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 tt :: tt:mark:nil:0':ok 102.08/27.23 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 nil :: tt:mark:nil:0':ok 102.08/27.23 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 0' :: tt:mark:nil:0':ok 102.08/27.23 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 top :: tt:mark:nil:0':ok -> top 102.08/27.23 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.23 hole_top2_0 :: top 102.08/27.23 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.23 102.08/27.23 102.08/27.23 Lemmas: 102.08/27.23 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.23 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.23 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.23 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.23 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.23 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.23 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.23 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.23 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.23 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.23 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.23 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.23 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.23 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.23 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.23 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.23 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.23 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.23 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.23 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.23 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.23 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.23 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.23 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.23 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.23 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.23 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.23 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.23 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.23 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.23 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.23 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.23 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.23 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.23 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.23 U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0))) -> *4_0, rt in Omega(n610318_0) 102.08/27.23 U262(gen_tt:mark:nil:0':ok3_0(+(1, n618182_0))) -> *4_0, rt in Omega(n618182_0) 102.08/27.23 U272(gen_tt:mark:nil:0':ok3_0(+(1, n626147_0))) -> *4_0, rt in Omega(n626147_0) 102.08/27.23 102.08/27.23 102.08/27.23 Generator Equations: 102.08/27.23 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.23 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.23 102.08/27.23 102.08/27.23 The following defined symbols remain to be analysed: 102.08/27.23 U282, active, cons, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.23 102.08/27.23 They will be analysed ascendingly in the following order: 102.08/27.23 U282 < active 102.08/27.23 cons < active 102.08/27.23 natsFrom < active 102.08/27.23 s < active 102.08/27.23 U292 < active 102.08/27.23 U293 < active 102.08/27.23 U294 < active 102.08/27.23 head < active 102.08/27.23 afterNth < active 102.08/27.23 U302 < active 102.08/27.23 U303 < active 102.08/27.23 U304 < active 102.08/27.23 U32 < active 102.08/27.23 U312 < active 102.08/27.23 pair < active 102.08/27.23 U33 < active 102.08/27.23 U322 < active 102.08/27.23 U323 < active 102.08/27.23 U324 < active 102.08/27.23 U325 < active 102.08/27.23 U326 < active 102.08/27.23 U327 < active 102.08/27.23 U34 < active 102.08/27.23 U332 < active 102.08/27.23 U333 < active 102.08/27.23 U334 < active 102.08/27.23 U342 < active 102.08/27.23 U343 < active 102.08/27.23 U344 < active 102.08/27.23 fst < active 102.08/27.23 U42 < active 102.08/27.23 U43 < active 102.08/27.23 U44 < active 102.08/27.23 U45 < active 102.08/27.23 U46 < active 102.08/27.23 U52 < active 102.08/27.23 U53 < active 102.08/27.23 U54 < active 102.08/27.23 U55 < active 102.08/27.23 U56 < active 102.08/27.23 U62 < active 102.08/27.23 isPLNatKind < active 102.08/27.23 U63 < active 102.08/27.23 isPLNat < active 102.08/27.23 U72 < active 102.08/27.23 U73 < active 102.08/27.23 U82 < active 102.08/27.23 U83 < active 102.08/27.23 U92 < active 102.08/27.23 U93 < active 102.08/27.23 U11 < active 102.08/27.23 U21 < active 102.08/27.23 U31 < active 102.08/27.23 U41 < active 102.08/27.23 U51 < active 102.08/27.23 U61 < active 102.08/27.23 U71 < active 102.08/27.23 U81 < active 102.08/27.23 U91 < active 102.08/27.23 U101 < active 102.08/27.23 U111 < active 102.08/27.23 U121 < active 102.08/27.23 U131 < active 102.08/27.23 U141 < active 102.08/27.23 U151 < active 102.08/27.23 U161 < active 102.08/27.23 U171 < active 102.08/27.23 U181 < active 102.08/27.23 U191 < active 102.08/27.23 U201 < active 102.08/27.23 U211 < active 102.08/27.23 U221 < active 102.08/27.23 U231 < active 102.08/27.23 U241 < active 102.08/27.23 U251 < active 102.08/27.23 U261 < active 102.08/27.23 U271 < active 102.08/27.23 U281 < active 102.08/27.23 U291 < active 102.08/27.23 U301 < active 102.08/27.23 U311 < active 102.08/27.23 U321 < active 102.08/27.23 U331 < active 102.08/27.23 U341 < active 102.08/27.23 tail < active 102.08/27.23 take < active 102.08/27.23 sel < active 102.08/27.23 active < top 102.08/27.23 U282 < proper 102.08/27.23 cons < proper 102.08/27.23 natsFrom < proper 102.08/27.23 s < proper 102.08/27.23 U292 < proper 102.08/27.23 U293 < proper 102.08/27.23 U294 < proper 102.08/27.23 head < proper 102.08/27.23 afterNth < proper 102.08/27.23 U302 < proper 102.08/27.23 U303 < proper 102.08/27.23 U304 < proper 102.08/27.23 U32 < proper 102.08/27.23 U312 < proper 102.08/27.23 pair < proper 102.08/27.23 U33 < proper 102.08/27.23 U322 < proper 102.08/27.23 U323 < proper 102.08/27.23 U324 < proper 102.08/27.23 U325 < proper 102.08/27.23 U326 < proper 102.08/27.23 U327 < proper 102.08/27.23 U34 < proper 102.08/27.23 U332 < proper 102.08/27.23 U333 < proper 102.08/27.23 U334 < proper 102.08/27.23 U342 < proper 102.08/27.23 U343 < proper 102.08/27.23 U344 < proper 102.08/27.23 fst < proper 102.08/27.23 U42 < proper 102.08/27.23 U43 < proper 102.08/27.23 U44 < proper 102.08/27.23 U45 < proper 102.08/27.23 U46 < proper 102.08/27.23 U52 < proper 102.08/27.23 U53 < proper 102.08/27.23 U54 < proper 102.08/27.23 U55 < proper 102.08/27.23 U56 < proper 102.08/27.23 U62 < proper 102.08/27.23 isPLNatKind < proper 102.08/27.23 U63 < proper 102.08/27.23 isPLNat < proper 102.08/27.23 U72 < proper 102.08/27.23 U73 < proper 102.08/27.23 U82 < proper 102.08/27.23 U83 < proper 102.08/27.23 U92 < proper 102.08/27.23 U93 < proper 102.08/27.23 U11 < proper 102.08/27.23 U21 < proper 102.08/27.23 U31 < proper 102.08/27.23 U41 < proper 102.08/27.23 U51 < proper 102.08/27.23 U61 < proper 102.08/27.23 U71 < proper 102.08/27.23 U81 < proper 102.08/27.23 U91 < proper 102.08/27.23 U101 < proper 102.08/27.23 U111 < proper 102.08/27.23 U121 < proper 102.08/27.23 U131 < proper 102.08/27.23 U141 < proper 102.08/27.23 U151 < proper 102.08/27.23 U161 < proper 102.08/27.23 U171 < proper 102.08/27.23 U181 < proper 102.08/27.23 U191 < proper 102.08/27.23 U201 < proper 102.08/27.23 U211 < proper 102.08/27.23 U221 < proper 102.08/27.23 U231 < proper 102.08/27.23 U241 < proper 102.08/27.23 U251 < proper 102.08/27.23 U261 < proper 102.08/27.23 U271 < proper 102.08/27.23 U281 < proper 102.08/27.23 U291 < proper 102.08/27.23 U301 < proper 102.08/27.23 U311 < proper 102.08/27.23 U321 < proper 102.08/27.23 U331 < proper 102.08/27.23 U341 < proper 102.08/27.23 tail < proper 102.08/27.23 take < proper 102.08/27.23 sel < proper 102.08/27.23 proper < top 102.08/27.23 102.08/27.23 ---------------------------------------- 102.08/27.23 102.08/27.23 (105) RewriteLemmaProof (LOWER BOUND(ID)) 102.08/27.23 Proved the following rewrite lemma: 102.08/27.23 U282(gen_tt:mark:nil:0':ok3_0(+(1, n634213_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n634213_0) 102.08/27.23 102.08/27.23 Induction Base: 102.08/27.23 U282(gen_tt:mark:nil:0':ok3_0(+(1, 0)), gen_tt:mark:nil:0':ok3_0(b)) 102.08/27.23 102.08/27.23 Induction Step: 102.08/27.23 U282(gen_tt:mark:nil:0':ok3_0(+(1, +(n634213_0, 1))), gen_tt:mark:nil:0':ok3_0(b)) ->_R^Omega(1) 102.08/27.23 mark(U282(gen_tt:mark:nil:0':ok3_0(+(1, n634213_0)), gen_tt:mark:nil:0':ok3_0(b))) ->_IH 102.08/27.23 mark(*4_0) 102.08/27.23 102.08/27.23 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). 102.08/27.23 ---------------------------------------- 102.08/27.23 102.08/27.23 (106) 102.08/27.23 Obligation: 102.08/27.23 TRS: 102.08/27.23 Rules: 102.08/27.23 active(U101(tt, V1, V2)) -> mark(U102(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(U102(tt, V1, V2)) -> mark(U103(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U103(tt, V1, V2)) -> mark(U104(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U104(tt, V1, V2)) -> mark(U105(isNatural(V1), V2)) 102.08/27.23 active(U105(tt, V2)) -> mark(U106(isLNat(V2))) 102.08/27.23 active(U106(tt)) -> mark(tt) 102.08/27.23 active(U11(tt, N, XS)) -> mark(U12(isNaturalKind(N), N, XS)) 102.08/27.23 active(U111(tt, V2)) -> mark(U112(isLNatKind(V2))) 102.08/27.23 active(U112(tt)) -> mark(tt) 102.08/27.23 active(U12(tt, N, XS)) -> mark(U13(isLNat(XS), N, XS)) 102.08/27.23 active(U121(tt, V2)) -> mark(U122(isLNatKind(V2))) 102.08/27.23 active(U122(tt)) -> mark(tt) 102.08/27.23 active(U13(tt, N, XS)) -> mark(U14(isLNatKind(XS), N, XS)) 102.08/27.23 active(U131(tt)) -> mark(tt) 102.08/27.23 active(U14(tt, N, XS)) -> mark(snd(splitAt(N, XS))) 102.08/27.23 active(U141(tt)) -> mark(tt) 102.08/27.23 active(U151(tt)) -> mark(tt) 102.08/27.23 active(U161(tt)) -> mark(tt) 102.08/27.23 active(U171(tt, V2)) -> mark(U172(isLNatKind(V2))) 102.08/27.23 active(U172(tt)) -> mark(tt) 102.08/27.23 active(U181(tt, V1)) -> mark(U182(isLNatKind(V1), V1)) 102.08/27.23 active(U182(tt, V1)) -> mark(U183(isLNat(V1))) 102.08/27.23 active(U183(tt)) -> mark(tt) 102.08/27.23 active(U191(tt, V1)) -> mark(U192(isNaturalKind(V1), V1)) 102.08/27.23 active(U192(tt, V1)) -> mark(U193(isNatural(V1))) 102.08/27.23 active(U193(tt)) -> mark(tt) 102.08/27.23 active(U201(tt, V1, V2)) -> mark(U202(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(U202(tt, V1, V2)) -> mark(U203(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U203(tt, V1, V2)) -> mark(U204(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U204(tt, V1, V2)) -> mark(U205(isNatural(V1), V2)) 102.08/27.23 active(U205(tt, V2)) -> mark(U206(isLNat(V2))) 102.08/27.23 active(U206(tt)) -> mark(tt) 102.08/27.23 active(U21(tt, X, Y)) -> mark(U22(isLNatKind(X), X, Y)) 102.08/27.23 active(U211(tt)) -> mark(tt) 102.08/27.23 active(U22(tt, X, Y)) -> mark(U23(isLNat(Y), X, Y)) 102.08/27.23 active(U221(tt)) -> mark(tt) 102.08/27.23 active(U23(tt, X, Y)) -> mark(U24(isLNatKind(Y), X)) 102.08/27.23 active(U231(tt, V2)) -> mark(U232(isLNatKind(V2))) 102.08/27.23 active(U232(tt)) -> mark(tt) 102.08/27.23 active(U24(tt, X)) -> mark(X) 102.08/27.23 active(U241(tt, V1, V2)) -> mark(U242(isLNatKind(V1), V1, V2)) 102.08/27.23 active(U242(tt, V1, V2)) -> mark(U243(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U243(tt, V1, V2)) -> mark(U244(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U244(tt, V1, V2)) -> mark(U245(isLNat(V1), V2)) 102.08/27.23 active(U245(tt, V2)) -> mark(U246(isLNat(V2))) 102.08/27.23 active(U246(tt)) -> mark(tt) 102.08/27.23 active(U251(tt, V1, V2)) -> mark(U252(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(U252(tt, V1, V2)) -> mark(U253(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U253(tt, V1, V2)) -> mark(U254(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U254(tt, V1, V2)) -> mark(U255(isNatural(V1), V2)) 102.08/27.23 active(U255(tt, V2)) -> mark(U256(isLNat(V2))) 102.08/27.23 active(U256(tt)) -> mark(tt) 102.08/27.23 active(U261(tt, V2)) -> mark(U262(isLNatKind(V2))) 102.08/27.23 active(U262(tt)) -> mark(tt) 102.08/27.23 active(U271(tt, V2)) -> mark(U272(isLNatKind(V2))) 102.08/27.23 active(U272(tt)) -> mark(tt) 102.08/27.23 active(U281(tt, N)) -> mark(U282(isNaturalKind(N), N)) 102.08/27.23 active(U282(tt, N)) -> mark(cons(N, natsFrom(s(N)))) 102.08/27.23 active(U291(tt, N, XS)) -> mark(U292(isNaturalKind(N), N, XS)) 102.08/27.23 active(U292(tt, N, XS)) -> mark(U293(isLNat(XS), N, XS)) 102.08/27.23 active(U293(tt, N, XS)) -> mark(U294(isLNatKind(XS), N, XS)) 102.08/27.23 active(U294(tt, N, XS)) -> mark(head(afterNth(N, XS))) 102.08/27.23 active(U301(tt, X, Y)) -> mark(U302(isLNatKind(X), Y)) 102.08/27.23 active(U302(tt, Y)) -> mark(U303(isLNat(Y), Y)) 102.08/27.23 active(U303(tt, Y)) -> mark(U304(isLNatKind(Y), Y)) 102.08/27.23 active(U304(tt, Y)) -> mark(Y) 102.08/27.23 active(U31(tt, N, XS)) -> mark(U32(isNaturalKind(N), N, XS)) 102.08/27.23 active(U311(tt, XS)) -> mark(U312(isLNatKind(XS), XS)) 102.08/27.23 active(U312(tt, XS)) -> mark(pair(nil, XS)) 102.08/27.23 active(U32(tt, N, XS)) -> mark(U33(isLNat(XS), N, XS)) 102.08/27.23 active(U321(tt, N, X, XS)) -> mark(U322(isNaturalKind(N), N, X, XS)) 102.08/27.23 active(U322(tt, N, X, XS)) -> mark(U323(isNatural(X), N, X, XS)) 102.08/27.23 active(U323(tt, N, X, XS)) -> mark(U324(isNaturalKind(X), N, X, XS)) 102.08/27.23 active(U324(tt, N, X, XS)) -> mark(U325(isLNat(XS), N, X, XS)) 102.08/27.23 active(U325(tt, N, X, XS)) -> mark(U326(isLNatKind(XS), N, X, XS)) 102.08/27.23 active(U326(tt, N, X, XS)) -> mark(U327(splitAt(N, XS), X)) 102.08/27.23 active(U327(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS)) 102.08/27.23 active(U33(tt, N, XS)) -> mark(U34(isLNatKind(XS), N)) 102.08/27.23 active(U331(tt, N, XS)) -> mark(U332(isNaturalKind(N), XS)) 102.08/27.23 active(U332(tt, XS)) -> mark(U333(isLNat(XS), XS)) 102.08/27.23 active(U333(tt, XS)) -> mark(U334(isLNatKind(XS), XS)) 102.08/27.23 active(U334(tt, XS)) -> mark(XS) 102.08/27.23 active(U34(tt, N)) -> mark(N) 102.08/27.23 active(U341(tt, N, XS)) -> mark(U342(isNaturalKind(N), N, XS)) 102.08/27.23 active(U342(tt, N, XS)) -> mark(U343(isLNat(XS), N, XS)) 102.08/27.23 active(U343(tt, N, XS)) -> mark(U344(isLNatKind(XS), N, XS)) 102.08/27.23 active(U344(tt, N, XS)) -> mark(fst(splitAt(N, XS))) 102.08/27.23 active(U41(tt, V1, V2)) -> mark(U42(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(U42(tt, V1, V2)) -> mark(U43(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U43(tt, V1, V2)) -> mark(U44(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U44(tt, V1, V2)) -> mark(U45(isNatural(V1), V2)) 102.08/27.23 active(U45(tt, V2)) -> mark(U46(isLNat(V2))) 102.08/27.23 active(U46(tt)) -> mark(tt) 102.08/27.23 active(U51(tt, V1, V2)) -> mark(U52(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(U52(tt, V1, V2)) -> mark(U53(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U53(tt, V1, V2)) -> mark(U54(isLNatKind(V2), V1, V2)) 102.08/27.23 active(U54(tt, V1, V2)) -> mark(U55(isNatural(V1), V2)) 102.08/27.23 active(U55(tt, V2)) -> mark(U56(isLNat(V2))) 102.08/27.23 active(U56(tt)) -> mark(tt) 102.08/27.23 active(U61(tt, V1)) -> mark(U62(isPLNatKind(V1), V1)) 102.08/27.23 active(U62(tt, V1)) -> mark(U63(isPLNat(V1))) 102.08/27.23 active(U63(tt)) -> mark(tt) 102.08/27.23 active(U71(tt, V1)) -> mark(U72(isNaturalKind(V1), V1)) 102.08/27.23 active(U72(tt, V1)) -> mark(U73(isNatural(V1))) 102.08/27.23 active(U73(tt)) -> mark(tt) 102.08/27.23 active(U81(tt, V1)) -> mark(U82(isPLNatKind(V1), V1)) 102.08/27.23 active(U82(tt, V1)) -> mark(U83(isPLNat(V1))) 102.08/27.23 active(U83(tt)) -> mark(tt) 102.08/27.23 active(U91(tt, V1)) -> mark(U92(isLNatKind(V1), V1)) 102.08/27.23 active(U92(tt, V1)) -> mark(U93(isLNat(V1))) 102.08/27.23 active(U93(tt)) -> mark(tt) 102.08/27.23 active(afterNth(N, XS)) -> mark(U11(isNatural(N), N, XS)) 102.08/27.23 active(fst(pair(X, Y))) -> mark(U21(isLNat(X), X, Y)) 102.08/27.23 active(head(cons(N, XS))) -> mark(U31(isNatural(N), N, XS)) 102.08/27.23 active(isLNat(nil)) -> mark(tt) 102.08/27.23 active(isLNat(afterNth(V1, V2))) -> mark(U41(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(isLNat(cons(V1, V2))) -> mark(U51(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1), V1)) 102.08/27.23 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1), V1)) 102.08/27.23 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1), V1)) 102.08/27.23 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1), V1)) 102.08/27.23 active(isLNat(take(V1, V2))) -> mark(U101(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(isLNatKind(nil)) -> mark(tt) 102.08/27.23 active(isLNatKind(afterNth(V1, V2))) -> mark(U111(isNaturalKind(V1), V2)) 102.08/27.23 active(isLNatKind(cons(V1, V2))) -> mark(U121(isNaturalKind(V1), V2)) 102.08/27.23 active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1))) 102.08/27.23 active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1))) 102.08/27.23 active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1))) 102.08/27.23 active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1))) 102.08/27.23 active(isLNatKind(take(V1, V2))) -> mark(U171(isNaturalKind(V1), V2)) 102.08/27.23 active(isNatural(0')) -> mark(tt) 102.08/27.23 active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1), V1)) 102.08/27.23 active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1), V1)) 102.08/27.23 active(isNatural(sel(V1, V2))) -> mark(U201(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(isNaturalKind(0')) -> mark(tt) 102.08/27.23 active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1))) 102.08/27.23 active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1))) 102.08/27.23 active(isNaturalKind(sel(V1, V2))) -> mark(U231(isNaturalKind(V1), V2)) 102.08/27.23 active(isPLNat(pair(V1, V2))) -> mark(U241(isLNatKind(V1), V1, V2)) 102.08/27.23 active(isPLNat(splitAt(V1, V2))) -> mark(U251(isNaturalKind(V1), V1, V2)) 102.08/27.23 active(isPLNatKind(pair(V1, V2))) -> mark(U261(isLNatKind(V1), V2)) 102.08/27.23 active(isPLNatKind(splitAt(V1, V2))) -> mark(U271(isNaturalKind(V1), V2)) 102.08/27.23 active(natsFrom(N)) -> mark(U281(isNatural(N), N)) 102.08/27.23 active(sel(N, XS)) -> mark(U291(isNatural(N), N, XS)) 102.08/27.23 active(snd(pair(X, Y))) -> mark(U301(isLNat(X), X, Y)) 102.08/27.23 active(splitAt(0', XS)) -> mark(U311(isLNat(XS), XS)) 102.08/27.23 active(splitAt(s(N), cons(X, XS))) -> mark(U321(isNatural(N), N, X, XS)) 102.08/27.23 active(tail(cons(N, XS))) -> mark(U331(isNatural(N), N, XS)) 102.08/27.23 active(take(N, XS)) -> mark(U341(isNatural(N), N, XS)) 102.08/27.23 active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3) 102.08/27.23 active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3) 102.08/27.23 active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3) 102.08/27.23 active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3) 102.08/27.23 active(U105(X1, X2)) -> U105(active(X1), X2) 102.08/27.23 active(U106(X)) -> U106(active(X)) 102.08/27.23 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 102.08/27.23 active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) 102.08/27.23 active(U111(X1, X2)) -> U111(active(X1), X2) 102.08/27.23 active(U112(X)) -> U112(active(X)) 102.08/27.23 active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3) 102.08/27.23 active(U121(X1, X2)) -> U121(active(X1), X2) 102.08/27.23 active(U122(X)) -> U122(active(X)) 102.08/27.23 active(U14(X1, X2, X3)) -> U14(active(X1), X2, X3) 102.08/27.23 active(U131(X)) -> U131(active(X)) 102.08/27.23 active(snd(X)) -> snd(active(X)) 102.08/27.23 active(splitAt(X1, X2)) -> splitAt(active(X1), X2) 102.08/27.23 active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) 102.08/27.23 active(U141(X)) -> U141(active(X)) 102.08/27.23 active(U151(X)) -> U151(active(X)) 102.08/27.23 active(U161(X)) -> U161(active(X)) 102.08/27.23 active(U171(X1, X2)) -> U171(active(X1), X2) 102.08/27.23 active(U172(X)) -> U172(active(X)) 102.08/27.23 active(U181(X1, X2)) -> U181(active(X1), X2) 102.08/27.23 active(U182(X1, X2)) -> U182(active(X1), X2) 102.08/27.23 active(U183(X)) -> U183(active(X)) 102.08/27.23 active(U191(X1, X2)) -> U191(active(X1), X2) 102.08/27.23 active(U192(X1, X2)) -> U192(active(X1), X2) 102.08/27.23 active(U193(X)) -> U193(active(X)) 102.08/27.23 active(U201(X1, X2, X3)) -> U201(active(X1), X2, X3) 102.08/27.23 active(U202(X1, X2, X3)) -> U202(active(X1), X2, X3) 102.08/27.23 active(U203(X1, X2, X3)) -> U203(active(X1), X2, X3) 102.08/27.23 active(U204(X1, X2, X3)) -> U204(active(X1), X2, X3) 102.08/27.23 active(U205(X1, X2)) -> U205(active(X1), X2) 102.08/27.23 active(U206(X)) -> U206(active(X)) 102.08/27.23 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 102.08/27.23 active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) 102.08/27.23 active(U211(X)) -> U211(active(X)) 102.08/27.23 active(U23(X1, X2, X3)) -> U23(active(X1), X2, X3) 102.08/27.23 active(U221(X)) -> U221(active(X)) 102.08/27.23 active(U24(X1, X2)) -> U24(active(X1), X2) 102.08/27.23 active(U231(X1, X2)) -> U231(active(X1), X2) 102.08/27.23 active(U232(X)) -> U232(active(X)) 102.08/27.23 active(U241(X1, X2, X3)) -> U241(active(X1), X2, X3) 102.08/27.23 active(U242(X1, X2, X3)) -> U242(active(X1), X2, X3) 102.08/27.23 active(U243(X1, X2, X3)) -> U243(active(X1), X2, X3) 102.08/27.23 active(U244(X1, X2, X3)) -> U244(active(X1), X2, X3) 102.08/27.23 active(U245(X1, X2)) -> U245(active(X1), X2) 102.08/27.23 active(U246(X)) -> U246(active(X)) 102.08/27.23 active(U251(X1, X2, X3)) -> U251(active(X1), X2, X3) 102.08/27.23 active(U252(X1, X2, X3)) -> U252(active(X1), X2, X3) 102.08/27.23 active(U253(X1, X2, X3)) -> U253(active(X1), X2, X3) 102.08/27.23 active(U254(X1, X2, X3)) -> U254(active(X1), X2, X3) 102.08/27.23 active(U255(X1, X2)) -> U255(active(X1), X2) 102.08/27.23 active(U256(X)) -> U256(active(X)) 102.08/27.23 active(U261(X1, X2)) -> U261(active(X1), X2) 102.08/27.23 active(U262(X)) -> U262(active(X)) 102.08/27.23 active(U271(X1, X2)) -> U271(active(X1), X2) 102.08/27.23 active(U272(X)) -> U272(active(X)) 102.08/27.23 active(U281(X1, X2)) -> U281(active(X1), X2) 102.08/27.23 active(U282(X1, X2)) -> U282(active(X1), X2) 102.08/27.23 active(cons(X1, X2)) -> cons(active(X1), X2) 102.08/27.23 active(natsFrom(X)) -> natsFrom(active(X)) 102.08/27.23 active(s(X)) -> s(active(X)) 102.08/27.23 active(U291(X1, X2, X3)) -> U291(active(X1), X2, X3) 102.08/27.23 active(U292(X1, X2, X3)) -> U292(active(X1), X2, X3) 102.08/27.23 active(U293(X1, X2, X3)) -> U293(active(X1), X2, X3) 102.08/27.23 active(U294(X1, X2, X3)) -> U294(active(X1), X2, X3) 102.08/27.23 active(head(X)) -> head(active(X)) 102.08/27.23 active(afterNth(X1, X2)) -> afterNth(active(X1), X2) 102.08/27.23 active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) 102.08/27.23 active(U301(X1, X2, X3)) -> U301(active(X1), X2, X3) 102.08/27.23 active(U302(X1, X2)) -> U302(active(X1), X2) 102.08/27.23 active(U303(X1, X2)) -> U303(active(X1), X2) 102.08/27.23 active(U304(X1, X2)) -> U304(active(X1), X2) 102.08/27.23 active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3) 102.08/27.23 active(U32(X1, X2, X3)) -> U32(active(X1), X2, X3) 102.08/27.23 active(U311(X1, X2)) -> U311(active(X1), X2) 102.08/27.23 active(U312(X1, X2)) -> U312(active(X1), X2) 102.08/27.23 active(pair(X1, X2)) -> pair(active(X1), X2) 102.08/27.23 active(pair(X1, X2)) -> pair(X1, active(X2)) 102.08/27.23 active(U33(X1, X2, X3)) -> U33(active(X1), X2, X3) 102.08/27.23 active(U321(X1, X2, X3, X4)) -> U321(active(X1), X2, X3, X4) 102.08/27.23 active(U322(X1, X2, X3, X4)) -> U322(active(X1), X2, X3, X4) 102.08/27.23 active(U323(X1, X2, X3, X4)) -> U323(active(X1), X2, X3, X4) 102.08/27.23 active(U324(X1, X2, X3, X4)) -> U324(active(X1), X2, X3, X4) 102.08/27.23 active(U325(X1, X2, X3, X4)) -> U325(active(X1), X2, X3, X4) 102.08/27.23 active(U326(X1, X2, X3, X4)) -> U326(active(X1), X2, X3, X4) 102.08/27.23 active(U327(X1, X2)) -> U327(active(X1), X2) 102.08/27.23 active(U34(X1, X2)) -> U34(active(X1), X2) 102.08/27.23 active(U331(X1, X2, X3)) -> U331(active(X1), X2, X3) 102.08/27.23 active(U332(X1, X2)) -> U332(active(X1), X2) 102.08/27.23 active(U333(X1, X2)) -> U333(active(X1), X2) 102.08/27.23 active(U334(X1, X2)) -> U334(active(X1), X2) 102.08/27.23 active(U341(X1, X2, X3)) -> U341(active(X1), X2, X3) 102.08/27.23 active(U342(X1, X2, X3)) -> U342(active(X1), X2, X3) 102.08/27.23 active(U343(X1, X2, X3)) -> U343(active(X1), X2, X3) 102.08/27.23 active(U344(X1, X2, X3)) -> U344(active(X1), X2, X3) 102.08/27.23 active(fst(X)) -> fst(active(X)) 102.08/27.23 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 102.08/27.23 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 102.08/27.23 active(U43(X1, X2, X3)) -> U43(active(X1), X2, X3) 102.08/27.23 active(U44(X1, X2, X3)) -> U44(active(X1), X2, X3) 102.08/27.23 active(U45(X1, X2)) -> U45(active(X1), X2) 102.08/27.23 active(U46(X)) -> U46(active(X)) 102.08/27.23 active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3) 102.08/27.23 active(U52(X1, X2, X3)) -> U52(active(X1), X2, X3) 102.08/27.23 active(U53(X1, X2, X3)) -> U53(active(X1), X2, X3) 102.08/27.23 active(U54(X1, X2, X3)) -> U54(active(X1), X2, X3) 102.08/27.23 active(U55(X1, X2)) -> U55(active(X1), X2) 102.08/27.23 active(U56(X)) -> U56(active(X)) 102.08/27.23 active(U61(X1, X2)) -> U61(active(X1), X2) 102.08/27.23 active(U62(X1, X2)) -> U62(active(X1), X2) 102.08/27.23 active(U63(X)) -> U63(active(X)) 102.08/27.23 active(U71(X1, X2)) -> U71(active(X1), X2) 102.08/27.23 active(U72(X1, X2)) -> U72(active(X1), X2) 102.08/27.23 active(U73(X)) -> U73(active(X)) 102.08/27.23 active(U81(X1, X2)) -> U81(active(X1), X2) 102.08/27.23 active(U82(X1, X2)) -> U82(active(X1), X2) 102.08/27.23 active(U83(X)) -> U83(active(X)) 102.08/27.23 active(U91(X1, X2)) -> U91(active(X1), X2) 102.08/27.23 active(U92(X1, X2)) -> U92(active(X1), X2) 102.08/27.23 active(U93(X)) -> U93(active(X)) 102.08/27.23 active(tail(X)) -> tail(active(X)) 102.08/27.23 active(take(X1, X2)) -> take(active(X1), X2) 102.08/27.23 active(take(X1, X2)) -> take(X1, active(X2)) 102.08/27.23 active(sel(X1, X2)) -> sel(active(X1), X2) 102.08/27.23 active(sel(X1, X2)) -> sel(X1, active(X2)) 102.08/27.23 U101(mark(X1), X2, X3) -> mark(U101(X1, X2, X3)) 102.08/27.23 U102(mark(X1), X2, X3) -> mark(U102(X1, X2, X3)) 102.08/27.23 U103(mark(X1), X2, X3) -> mark(U103(X1, X2, X3)) 102.08/27.23 U104(mark(X1), X2, X3) -> mark(U104(X1, X2, X3)) 102.08/27.23 U105(mark(X1), X2) -> mark(U105(X1, X2)) 102.08/27.23 U106(mark(X)) -> mark(U106(X)) 102.08/27.23 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 102.08/27.23 U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) 102.08/27.23 U111(mark(X1), X2) -> mark(U111(X1, X2)) 102.08/27.23 U112(mark(X)) -> mark(U112(X)) 102.08/27.23 U13(mark(X1), X2, X3) -> mark(U13(X1, X2, X3)) 102.08/27.23 U121(mark(X1), X2) -> mark(U121(X1, X2)) 102.08/27.23 U122(mark(X)) -> mark(U122(X)) 102.08/27.23 U14(mark(X1), X2, X3) -> mark(U14(X1, X2, X3)) 102.08/27.23 U131(mark(X)) -> mark(U131(X)) 102.08/27.23 snd(mark(X)) -> mark(snd(X)) 102.08/27.23 splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) 102.08/27.23 splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) 102.08/27.23 U141(mark(X)) -> mark(U141(X)) 102.08/27.23 U151(mark(X)) -> mark(U151(X)) 102.08/27.23 U161(mark(X)) -> mark(U161(X)) 102.08/27.23 U171(mark(X1), X2) -> mark(U171(X1, X2)) 102.08/27.23 U172(mark(X)) -> mark(U172(X)) 102.08/27.23 U181(mark(X1), X2) -> mark(U181(X1, X2)) 102.08/27.23 U182(mark(X1), X2) -> mark(U182(X1, X2)) 102.08/27.23 U183(mark(X)) -> mark(U183(X)) 102.08/27.23 U191(mark(X1), X2) -> mark(U191(X1, X2)) 102.08/27.23 U192(mark(X1), X2) -> mark(U192(X1, X2)) 102.08/27.23 U193(mark(X)) -> mark(U193(X)) 102.08/27.23 U201(mark(X1), X2, X3) -> mark(U201(X1, X2, X3)) 102.08/27.23 U202(mark(X1), X2, X3) -> mark(U202(X1, X2, X3)) 102.08/27.23 U203(mark(X1), X2, X3) -> mark(U203(X1, X2, X3)) 102.08/27.23 U204(mark(X1), X2, X3) -> mark(U204(X1, X2, X3)) 102.08/27.23 U205(mark(X1), X2) -> mark(U205(X1, X2)) 102.08/27.23 U206(mark(X)) -> mark(U206(X)) 102.08/27.23 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 102.08/27.23 U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) 102.08/27.23 U211(mark(X)) -> mark(U211(X)) 102.08/27.23 U23(mark(X1), X2, X3) -> mark(U23(X1, X2, X3)) 102.08/27.23 U221(mark(X)) -> mark(U221(X)) 102.08/27.23 U24(mark(X1), X2) -> mark(U24(X1, X2)) 102.08/27.23 U231(mark(X1), X2) -> mark(U231(X1, X2)) 102.08/27.23 U232(mark(X)) -> mark(U232(X)) 102.08/27.23 U241(mark(X1), X2, X3) -> mark(U241(X1, X2, X3)) 102.08/27.23 U242(mark(X1), X2, X3) -> mark(U242(X1, X2, X3)) 102.08/27.23 U243(mark(X1), X2, X3) -> mark(U243(X1, X2, X3)) 102.08/27.23 U244(mark(X1), X2, X3) -> mark(U244(X1, X2, X3)) 102.08/27.23 U245(mark(X1), X2) -> mark(U245(X1, X2)) 102.08/27.23 U246(mark(X)) -> mark(U246(X)) 102.08/27.23 U251(mark(X1), X2, X3) -> mark(U251(X1, X2, X3)) 102.08/27.23 U252(mark(X1), X2, X3) -> mark(U252(X1, X2, X3)) 102.08/27.23 U253(mark(X1), X2, X3) -> mark(U253(X1, X2, X3)) 102.08/27.23 U254(mark(X1), X2, X3) -> mark(U254(X1, X2, X3)) 102.08/27.23 U255(mark(X1), X2) -> mark(U255(X1, X2)) 102.08/27.23 U256(mark(X)) -> mark(U256(X)) 102.08/27.23 U261(mark(X1), X2) -> mark(U261(X1, X2)) 102.08/27.23 U262(mark(X)) -> mark(U262(X)) 102.08/27.23 U271(mark(X1), X2) -> mark(U271(X1, X2)) 102.08/27.23 U272(mark(X)) -> mark(U272(X)) 102.08/27.23 U281(mark(X1), X2) -> mark(U281(X1, X2)) 102.08/27.23 U282(mark(X1), X2) -> mark(U282(X1, X2)) 102.08/27.23 cons(mark(X1), X2) -> mark(cons(X1, X2)) 102.08/27.23 natsFrom(mark(X)) -> mark(natsFrom(X)) 102.08/27.23 s(mark(X)) -> mark(s(X)) 102.08/27.23 U291(mark(X1), X2, X3) -> mark(U291(X1, X2, X3)) 102.08/27.23 U292(mark(X1), X2, X3) -> mark(U292(X1, X2, X3)) 102.08/27.23 U293(mark(X1), X2, X3) -> mark(U293(X1, X2, X3)) 102.08/27.23 U294(mark(X1), X2, X3) -> mark(U294(X1, X2, X3)) 102.08/27.23 head(mark(X)) -> mark(head(X)) 102.08/27.23 afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) 102.08/27.23 afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) 102.08/27.23 U301(mark(X1), X2, X3) -> mark(U301(X1, X2, X3)) 102.08/27.23 U302(mark(X1), X2) -> mark(U302(X1, X2)) 102.08/27.23 U303(mark(X1), X2) -> mark(U303(X1, X2)) 102.08/27.23 U304(mark(X1), X2) -> mark(U304(X1, X2)) 102.08/27.23 U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3)) 102.08/27.23 U32(mark(X1), X2, X3) -> mark(U32(X1, X2, X3)) 102.08/27.23 U311(mark(X1), X2) -> mark(U311(X1, X2)) 102.08/27.23 U312(mark(X1), X2) -> mark(U312(X1, X2)) 102.08/27.23 pair(mark(X1), X2) -> mark(pair(X1, X2)) 102.08/27.23 pair(X1, mark(X2)) -> mark(pair(X1, X2)) 102.08/27.23 U33(mark(X1), X2, X3) -> mark(U33(X1, X2, X3)) 102.08/27.23 U321(mark(X1), X2, X3, X4) -> mark(U321(X1, X2, X3, X4)) 102.08/27.23 U322(mark(X1), X2, X3, X4) -> mark(U322(X1, X2, X3, X4)) 102.08/27.23 U323(mark(X1), X2, X3, X4) -> mark(U323(X1, X2, X3, X4)) 102.08/27.23 U324(mark(X1), X2, X3, X4) -> mark(U324(X1, X2, X3, X4)) 102.08/27.23 U325(mark(X1), X2, X3, X4) -> mark(U325(X1, X2, X3, X4)) 102.08/27.23 U326(mark(X1), X2, X3, X4) -> mark(U326(X1, X2, X3, X4)) 102.08/27.23 U327(mark(X1), X2) -> mark(U327(X1, X2)) 102.08/27.23 U34(mark(X1), X2) -> mark(U34(X1, X2)) 102.08/27.23 U331(mark(X1), X2, X3) -> mark(U331(X1, X2, X3)) 102.08/27.23 U332(mark(X1), X2) -> mark(U332(X1, X2)) 102.08/27.23 U333(mark(X1), X2) -> mark(U333(X1, X2)) 102.08/27.23 U334(mark(X1), X2) -> mark(U334(X1, X2)) 102.08/27.23 U341(mark(X1), X2, X3) -> mark(U341(X1, X2, X3)) 102.08/27.23 U342(mark(X1), X2, X3) -> mark(U342(X1, X2, X3)) 102.08/27.23 U343(mark(X1), X2, X3) -> mark(U343(X1, X2, X3)) 102.08/27.23 U344(mark(X1), X2, X3) -> mark(U344(X1, X2, X3)) 102.08/27.23 fst(mark(X)) -> mark(fst(X)) 102.08/27.23 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 102.08/27.23 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 102.08/27.23 U43(mark(X1), X2, X3) -> mark(U43(X1, X2, X3)) 102.08/27.23 U44(mark(X1), X2, X3) -> mark(U44(X1, X2, X3)) 102.08/27.23 U45(mark(X1), X2) -> mark(U45(X1, X2)) 102.08/27.23 U46(mark(X)) -> mark(U46(X)) 102.08/27.23 U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3)) 102.08/27.23 U52(mark(X1), X2, X3) -> mark(U52(X1, X2, X3)) 102.08/27.23 U53(mark(X1), X2, X3) -> mark(U53(X1, X2, X3)) 102.08/27.23 U54(mark(X1), X2, X3) -> mark(U54(X1, X2, X3)) 102.08/27.23 U55(mark(X1), X2) -> mark(U55(X1, X2)) 102.08/27.23 U56(mark(X)) -> mark(U56(X)) 102.08/27.23 U61(mark(X1), X2) -> mark(U61(X1, X2)) 102.08/27.23 U62(mark(X1), X2) -> mark(U62(X1, X2)) 102.08/27.23 U63(mark(X)) -> mark(U63(X)) 102.08/27.23 U71(mark(X1), X2) -> mark(U71(X1, X2)) 102.08/27.23 U72(mark(X1), X2) -> mark(U72(X1, X2)) 102.08/27.23 U73(mark(X)) -> mark(U73(X)) 102.08/27.23 U81(mark(X1), X2) -> mark(U81(X1, X2)) 102.08/27.23 U82(mark(X1), X2) -> mark(U82(X1, X2)) 102.08/27.23 U83(mark(X)) -> mark(U83(X)) 102.08/27.23 U91(mark(X1), X2) -> mark(U91(X1, X2)) 102.08/27.23 U92(mark(X1), X2) -> mark(U92(X1, X2)) 102.08/27.23 U93(mark(X)) -> mark(U93(X)) 102.08/27.23 tail(mark(X)) -> mark(tail(X)) 102.08/27.23 take(mark(X1), X2) -> mark(take(X1, X2)) 102.08/27.23 take(X1, mark(X2)) -> mark(take(X1, X2)) 102.08/27.23 sel(mark(X1), X2) -> mark(sel(X1, X2)) 102.08/27.23 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 102.08/27.23 proper(U101(X1, X2, X3)) -> U101(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(tt) -> ok(tt) 102.08/27.23 proper(U102(X1, X2, X3)) -> U102(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(isNaturalKind(X)) -> isNaturalKind(proper(X)) 102.08/27.23 proper(U103(X1, X2, X3)) -> U103(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(isLNatKind(X)) -> isLNatKind(proper(X)) 102.08/27.23 proper(U104(X1, X2, X3)) -> U104(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U105(X1, X2)) -> U105(proper(X1), proper(X2)) 102.08/27.23 proper(isNatural(X)) -> isNatural(proper(X)) 102.08/27.23 proper(U106(X)) -> U106(proper(X)) 102.08/27.23 proper(isLNat(X)) -> isLNat(proper(X)) 102.08/27.23 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U111(X1, X2)) -> U111(proper(X1), proper(X2)) 102.08/27.23 proper(U112(X)) -> U112(proper(X)) 102.08/27.23 proper(U13(X1, X2, X3)) -> U13(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U121(X1, X2)) -> U121(proper(X1), proper(X2)) 102.08/27.23 proper(U122(X)) -> U122(proper(X)) 102.08/27.23 proper(U14(X1, X2, X3)) -> U14(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U131(X)) -> U131(proper(X)) 102.08/27.23 proper(snd(X)) -> snd(proper(X)) 102.08/27.23 proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) 102.08/27.23 proper(U141(X)) -> U141(proper(X)) 102.08/27.23 proper(U151(X)) -> U151(proper(X)) 102.08/27.23 proper(U161(X)) -> U161(proper(X)) 102.08/27.23 proper(U171(X1, X2)) -> U171(proper(X1), proper(X2)) 102.08/27.23 proper(U172(X)) -> U172(proper(X)) 102.08/27.23 proper(U181(X1, X2)) -> U181(proper(X1), proper(X2)) 102.08/27.23 proper(U182(X1, X2)) -> U182(proper(X1), proper(X2)) 102.08/27.23 proper(U183(X)) -> U183(proper(X)) 102.08/27.23 proper(U191(X1, X2)) -> U191(proper(X1), proper(X2)) 102.08/27.23 proper(U192(X1, X2)) -> U192(proper(X1), proper(X2)) 102.08/27.23 proper(U193(X)) -> U193(proper(X)) 102.08/27.23 proper(U201(X1, X2, X3)) -> U201(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U202(X1, X2, X3)) -> U202(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U203(X1, X2, X3)) -> U203(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U204(X1, X2, X3)) -> U204(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U205(X1, X2)) -> U205(proper(X1), proper(X2)) 102.08/27.23 proper(U206(X)) -> U206(proper(X)) 102.08/27.23 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U211(X)) -> U211(proper(X)) 102.08/27.23 proper(U23(X1, X2, X3)) -> U23(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U221(X)) -> U221(proper(X)) 102.08/27.23 proper(U24(X1, X2)) -> U24(proper(X1), proper(X2)) 102.08/27.23 proper(U231(X1, X2)) -> U231(proper(X1), proper(X2)) 102.08/27.23 proper(U232(X)) -> U232(proper(X)) 102.08/27.23 proper(U241(X1, X2, X3)) -> U241(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U242(X1, X2, X3)) -> U242(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U243(X1, X2, X3)) -> U243(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U244(X1, X2, X3)) -> U244(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U245(X1, X2)) -> U245(proper(X1), proper(X2)) 102.08/27.23 proper(U246(X)) -> U246(proper(X)) 102.08/27.23 proper(U251(X1, X2, X3)) -> U251(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U252(X1, X2, X3)) -> U252(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U253(X1, X2, X3)) -> U253(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U254(X1, X2, X3)) -> U254(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U255(X1, X2)) -> U255(proper(X1), proper(X2)) 102.08/27.23 proper(U256(X)) -> U256(proper(X)) 102.08/27.23 proper(U261(X1, X2)) -> U261(proper(X1), proper(X2)) 102.08/27.23 proper(U262(X)) -> U262(proper(X)) 102.08/27.23 proper(U271(X1, X2)) -> U271(proper(X1), proper(X2)) 102.08/27.23 proper(U272(X)) -> U272(proper(X)) 102.08/27.23 proper(U281(X1, X2)) -> U281(proper(X1), proper(X2)) 102.08/27.23 proper(U282(X1, X2)) -> U282(proper(X1), proper(X2)) 102.08/27.23 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 102.08/27.23 proper(natsFrom(X)) -> natsFrom(proper(X)) 102.08/27.23 proper(s(X)) -> s(proper(X)) 102.08/27.23 proper(U291(X1, X2, X3)) -> U291(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U292(X1, X2, X3)) -> U292(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U293(X1, X2, X3)) -> U293(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U294(X1, X2, X3)) -> U294(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(head(X)) -> head(proper(X)) 102.08/27.23 proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) 102.08/27.23 proper(U301(X1, X2, X3)) -> U301(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U302(X1, X2)) -> U302(proper(X1), proper(X2)) 102.08/27.23 proper(U303(X1, X2)) -> U303(proper(X1), proper(X2)) 102.08/27.23 proper(U304(X1, X2)) -> U304(proper(X1), proper(X2)) 102.08/27.23 proper(U31(X1, X2, X3)) -> U31(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U32(X1, X2, X3)) -> U32(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U311(X1, X2)) -> U311(proper(X1), proper(X2)) 102.08/27.23 proper(U312(X1, X2)) -> U312(proper(X1), proper(X2)) 102.08/27.23 proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) 102.08/27.23 proper(nil) -> ok(nil) 102.08/27.23 proper(U33(X1, X2, X3)) -> U33(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U321(X1, X2, X3, X4)) -> U321(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U322(X1, X2, X3, X4)) -> U322(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U323(X1, X2, X3, X4)) -> U323(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U324(X1, X2, X3, X4)) -> U324(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U325(X1, X2, X3, X4)) -> U325(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U326(X1, X2, X3, X4)) -> U326(proper(X1), proper(X2), proper(X3), proper(X4)) 102.08/27.23 proper(U327(X1, X2)) -> U327(proper(X1), proper(X2)) 102.08/27.23 proper(U34(X1, X2)) -> U34(proper(X1), proper(X2)) 102.08/27.23 proper(U331(X1, X2, X3)) -> U331(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U332(X1, X2)) -> U332(proper(X1), proper(X2)) 102.08/27.23 proper(U333(X1, X2)) -> U333(proper(X1), proper(X2)) 102.08/27.23 proper(U334(X1, X2)) -> U334(proper(X1), proper(X2)) 102.08/27.23 proper(U341(X1, X2, X3)) -> U341(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U342(X1, X2, X3)) -> U342(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U343(X1, X2, X3)) -> U343(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U344(X1, X2, X3)) -> U344(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(fst(X)) -> fst(proper(X)) 102.08/27.23 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U43(X1, X2, X3)) -> U43(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U44(X1, X2, X3)) -> U44(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U45(X1, X2)) -> U45(proper(X1), proper(X2)) 102.08/27.23 proper(U46(X)) -> U46(proper(X)) 102.08/27.23 proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U52(X1, X2, X3)) -> U52(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U53(X1, X2, X3)) -> U53(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U54(X1, X2, X3)) -> U54(proper(X1), proper(X2), proper(X3)) 102.08/27.23 proper(U55(X1, X2)) -> U55(proper(X1), proper(X2)) 102.08/27.23 proper(U56(X)) -> U56(proper(X)) 102.08/27.23 proper(U61(X1, X2)) -> U61(proper(X1), proper(X2)) 102.08/27.23 proper(U62(X1, X2)) -> U62(proper(X1), proper(X2)) 102.08/27.23 proper(isPLNatKind(X)) -> isPLNatKind(proper(X)) 102.08/27.23 proper(U63(X)) -> U63(proper(X)) 102.08/27.23 proper(isPLNat(X)) -> isPLNat(proper(X)) 102.08/27.23 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)) 102.08/27.23 proper(U72(X1, X2)) -> U72(proper(X1), proper(X2)) 102.08/27.23 proper(U73(X)) -> U73(proper(X)) 102.08/27.23 proper(U81(X1, X2)) -> U81(proper(X1), proper(X2)) 102.08/27.23 proper(U82(X1, X2)) -> U82(proper(X1), proper(X2)) 102.08/27.23 proper(U83(X)) -> U83(proper(X)) 102.08/27.23 proper(U91(X1, X2)) -> U91(proper(X1), proper(X2)) 102.08/27.23 proper(U92(X1, X2)) -> U92(proper(X1), proper(X2)) 102.08/27.23 proper(U93(X)) -> U93(proper(X)) 102.08/27.23 proper(tail(X)) -> tail(proper(X)) 102.08/27.23 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 102.08/27.23 proper(0') -> ok(0') 102.08/27.23 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 102.08/27.23 U101(ok(X1), ok(X2), ok(X3)) -> ok(U101(X1, X2, X3)) 102.08/27.23 U102(ok(X1), ok(X2), ok(X3)) -> ok(U102(X1, X2, X3)) 102.08/27.23 isNaturalKind(ok(X)) -> ok(isNaturalKind(X)) 102.08/27.23 U103(ok(X1), ok(X2), ok(X3)) -> ok(U103(X1, X2, X3)) 102.08/27.23 isLNatKind(ok(X)) -> ok(isLNatKind(X)) 102.08/27.23 U104(ok(X1), ok(X2), ok(X3)) -> ok(U104(X1, X2, X3)) 102.08/27.23 U105(ok(X1), ok(X2)) -> ok(U105(X1, X2)) 102.08/27.23 isNatural(ok(X)) -> ok(isNatural(X)) 102.08/27.23 U106(ok(X)) -> ok(U106(X)) 102.08/27.23 isLNat(ok(X)) -> ok(isLNat(X)) 102.08/27.23 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 102.08/27.23 U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) 102.08/27.23 U111(ok(X1), ok(X2)) -> ok(U111(X1, X2)) 102.08/27.23 U112(ok(X)) -> ok(U112(X)) 102.08/27.23 U13(ok(X1), ok(X2), ok(X3)) -> ok(U13(X1, X2, X3)) 102.08/27.23 U121(ok(X1), ok(X2)) -> ok(U121(X1, X2)) 102.08/27.23 U122(ok(X)) -> ok(U122(X)) 102.08/27.23 U14(ok(X1), ok(X2), ok(X3)) -> ok(U14(X1, X2, X3)) 102.08/27.23 U131(ok(X)) -> ok(U131(X)) 102.08/27.23 snd(ok(X)) -> ok(snd(X)) 102.08/27.23 splitAt(ok(X1), ok(X2)) -> ok(splitAt(X1, X2)) 102.08/27.23 U141(ok(X)) -> ok(U141(X)) 102.08/27.23 U151(ok(X)) -> ok(U151(X)) 102.08/27.23 U161(ok(X)) -> ok(U161(X)) 102.08/27.23 U171(ok(X1), ok(X2)) -> ok(U171(X1, X2)) 102.08/27.23 U172(ok(X)) -> ok(U172(X)) 102.08/27.23 U181(ok(X1), ok(X2)) -> ok(U181(X1, X2)) 102.08/27.23 U182(ok(X1), ok(X2)) -> ok(U182(X1, X2)) 102.08/27.23 U183(ok(X)) -> ok(U183(X)) 102.08/27.23 U191(ok(X1), ok(X2)) -> ok(U191(X1, X2)) 102.08/27.23 U192(ok(X1), ok(X2)) -> ok(U192(X1, X2)) 102.08/27.23 U193(ok(X)) -> ok(U193(X)) 102.08/27.23 U201(ok(X1), ok(X2), ok(X3)) -> ok(U201(X1, X2, X3)) 102.08/27.23 U202(ok(X1), ok(X2), ok(X3)) -> ok(U202(X1, X2, X3)) 102.08/27.23 U203(ok(X1), ok(X2), ok(X3)) -> ok(U203(X1, X2, X3)) 102.08/27.23 U204(ok(X1), ok(X2), ok(X3)) -> ok(U204(X1, X2, X3)) 102.08/27.23 U205(ok(X1), ok(X2)) -> ok(U205(X1, X2)) 102.08/27.23 U206(ok(X)) -> ok(U206(X)) 102.08/27.23 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 102.08/27.23 U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) 102.08/27.23 U211(ok(X)) -> ok(U211(X)) 102.08/27.23 U23(ok(X1), ok(X2), ok(X3)) -> ok(U23(X1, X2, X3)) 102.08/27.23 U221(ok(X)) -> ok(U221(X)) 102.08/27.23 U24(ok(X1), ok(X2)) -> ok(U24(X1, X2)) 102.08/27.23 U231(ok(X1), ok(X2)) -> ok(U231(X1, X2)) 102.08/27.23 U232(ok(X)) -> ok(U232(X)) 102.08/27.23 U241(ok(X1), ok(X2), ok(X3)) -> ok(U241(X1, X2, X3)) 102.08/27.23 U242(ok(X1), ok(X2), ok(X3)) -> ok(U242(X1, X2, X3)) 102.08/27.23 U243(ok(X1), ok(X2), ok(X3)) -> ok(U243(X1, X2, X3)) 102.08/27.23 U244(ok(X1), ok(X2), ok(X3)) -> ok(U244(X1, X2, X3)) 102.08/27.23 U245(ok(X1), ok(X2)) -> ok(U245(X1, X2)) 102.08/27.23 U246(ok(X)) -> ok(U246(X)) 102.08/27.23 U251(ok(X1), ok(X2), ok(X3)) -> ok(U251(X1, X2, X3)) 102.08/27.23 U252(ok(X1), ok(X2), ok(X3)) -> ok(U252(X1, X2, X3)) 102.08/27.23 U253(ok(X1), ok(X2), ok(X3)) -> ok(U253(X1, X2, X3)) 102.08/27.23 U254(ok(X1), ok(X2), ok(X3)) -> ok(U254(X1, X2, X3)) 102.08/27.23 U255(ok(X1), ok(X2)) -> ok(U255(X1, X2)) 102.08/27.23 U256(ok(X)) -> ok(U256(X)) 102.08/27.23 U261(ok(X1), ok(X2)) -> ok(U261(X1, X2)) 102.08/27.23 U262(ok(X)) -> ok(U262(X)) 102.08/27.23 U271(ok(X1), ok(X2)) -> ok(U271(X1, X2)) 102.08/27.23 U272(ok(X)) -> ok(U272(X)) 102.08/27.23 U281(ok(X1), ok(X2)) -> ok(U281(X1, X2)) 102.08/27.23 U282(ok(X1), ok(X2)) -> ok(U282(X1, X2)) 102.08/27.23 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 102.08/27.23 natsFrom(ok(X)) -> ok(natsFrom(X)) 102.08/27.23 s(ok(X)) -> ok(s(X)) 102.08/27.23 U291(ok(X1), ok(X2), ok(X3)) -> ok(U291(X1, X2, X3)) 102.08/27.23 U292(ok(X1), ok(X2), ok(X3)) -> ok(U292(X1, X2, X3)) 102.08/27.23 U293(ok(X1), ok(X2), ok(X3)) -> ok(U293(X1, X2, X3)) 102.08/27.23 U294(ok(X1), ok(X2), ok(X3)) -> ok(U294(X1, X2, X3)) 102.08/27.23 head(ok(X)) -> ok(head(X)) 102.08/27.23 afterNth(ok(X1), ok(X2)) -> ok(afterNth(X1, X2)) 102.08/27.23 U301(ok(X1), ok(X2), ok(X3)) -> ok(U301(X1, X2, X3)) 102.08/27.23 U302(ok(X1), ok(X2)) -> ok(U302(X1, X2)) 102.08/27.23 U303(ok(X1), ok(X2)) -> ok(U303(X1, X2)) 102.08/27.23 U304(ok(X1), ok(X2)) -> ok(U304(X1, X2)) 102.08/27.23 U31(ok(X1), ok(X2), ok(X3)) -> ok(U31(X1, X2, X3)) 102.08/27.23 U32(ok(X1), ok(X2), ok(X3)) -> ok(U32(X1, X2, X3)) 102.08/27.23 U311(ok(X1), ok(X2)) -> ok(U311(X1, X2)) 102.08/27.23 U312(ok(X1), ok(X2)) -> ok(U312(X1, X2)) 102.08/27.23 pair(ok(X1), ok(X2)) -> ok(pair(X1, X2)) 102.08/27.23 U33(ok(X1), ok(X2), ok(X3)) -> ok(U33(X1, X2, X3)) 102.08/27.23 U321(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U321(X1, X2, X3, X4)) 102.08/27.23 U322(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U322(X1, X2, X3, X4)) 102.08/27.23 U323(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U323(X1, X2, X3, X4)) 102.08/27.23 U324(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U324(X1, X2, X3, X4)) 102.08/27.23 U325(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U325(X1, X2, X3, X4)) 102.08/27.23 U326(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U326(X1, X2, X3, X4)) 102.08/27.23 U327(ok(X1), ok(X2)) -> ok(U327(X1, X2)) 102.08/27.23 U34(ok(X1), ok(X2)) -> ok(U34(X1, X2)) 102.08/27.23 U331(ok(X1), ok(X2), ok(X3)) -> ok(U331(X1, X2, X3)) 102.08/27.23 U332(ok(X1), ok(X2)) -> ok(U332(X1, X2)) 102.08/27.23 U333(ok(X1), ok(X2)) -> ok(U333(X1, X2)) 102.08/27.23 U334(ok(X1), ok(X2)) -> ok(U334(X1, X2)) 102.08/27.23 U341(ok(X1), ok(X2), ok(X3)) -> ok(U341(X1, X2, X3)) 102.08/27.23 U342(ok(X1), ok(X2), ok(X3)) -> ok(U342(X1, X2, X3)) 102.08/27.23 U343(ok(X1), ok(X2), ok(X3)) -> ok(U343(X1, X2, X3)) 102.08/27.23 U344(ok(X1), ok(X2), ok(X3)) -> ok(U344(X1, X2, X3)) 102.08/27.23 fst(ok(X)) -> ok(fst(X)) 102.08/27.23 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 102.08/27.23 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 102.08/27.23 U43(ok(X1), ok(X2), ok(X3)) -> ok(U43(X1, X2, X3)) 102.08/27.23 U44(ok(X1), ok(X2), ok(X3)) -> ok(U44(X1, X2, X3)) 102.08/27.23 U45(ok(X1), ok(X2)) -> ok(U45(X1, X2)) 102.08/27.23 U46(ok(X)) -> ok(U46(X)) 102.08/27.23 U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3)) 102.08/27.23 U52(ok(X1), ok(X2), ok(X3)) -> ok(U52(X1, X2, X3)) 102.08/27.23 U53(ok(X1), ok(X2), ok(X3)) -> ok(U53(X1, X2, X3)) 102.08/27.23 U54(ok(X1), ok(X2), ok(X3)) -> ok(U54(X1, X2, X3)) 102.08/27.23 U55(ok(X1), ok(X2)) -> ok(U55(X1, X2)) 102.08/27.23 U56(ok(X)) -> ok(U56(X)) 102.08/27.23 U61(ok(X1), ok(X2)) -> ok(U61(X1, X2)) 102.08/27.23 U62(ok(X1), ok(X2)) -> ok(U62(X1, X2)) 102.08/27.23 isPLNatKind(ok(X)) -> ok(isPLNatKind(X)) 102.08/27.23 U63(ok(X)) -> ok(U63(X)) 102.08/27.23 isPLNat(ok(X)) -> ok(isPLNat(X)) 102.08/27.23 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)) 102.08/27.23 U72(ok(X1), ok(X2)) -> ok(U72(X1, X2)) 102.08/27.23 U73(ok(X)) -> ok(U73(X)) 102.08/27.23 U81(ok(X1), ok(X2)) -> ok(U81(X1, X2)) 102.08/27.23 U82(ok(X1), ok(X2)) -> ok(U82(X1, X2)) 102.08/27.23 U83(ok(X)) -> ok(U83(X)) 102.08/27.23 U91(ok(X1), ok(X2)) -> ok(U91(X1, X2)) 102.08/27.23 U92(ok(X1), ok(X2)) -> ok(U92(X1, X2)) 102.08/27.23 U93(ok(X)) -> ok(U93(X)) 102.08/27.23 tail(ok(X)) -> ok(tail(X)) 102.08/27.23 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 102.08/27.23 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 102.08/27.23 top(mark(X)) -> top(proper(X)) 102.08/27.23 top(ok(X)) -> top(active(X)) 102.08/27.23 102.08/27.23 Types: 102.08/27.23 active :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U101 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 tt :: tt:mark:nil:0':ok 102.08/27.23 mark :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U102 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isNaturalKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U103 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U104 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U105 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isNatural :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U106 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U11 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U12 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U111 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U112 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U13 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U121 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U122 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U14 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U131 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 snd :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 splitAt :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U141 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U151 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U161 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U171 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U172 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U181 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U182 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U183 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U191 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U192 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U193 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U201 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U202 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U203 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U204 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U205 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U206 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U21 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U22 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U211 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U23 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U221 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U24 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U231 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U232 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U241 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U242 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U243 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U244 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U245 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U246 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U251 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U252 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U253 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U254 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U255 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U256 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U261 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U262 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U271 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U272 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U281 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U282 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 cons :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 natsFrom :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 s :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U291 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U292 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U293 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U294 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 head :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 afterNth :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U301 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U302 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U303 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U304 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U31 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U32 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U311 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U312 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 pair :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 nil :: tt:mark:nil:0':ok 102.08/27.23 U33 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U321 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U322 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U323 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U324 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U325 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U326 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U327 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U34 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U331 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U332 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U333 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U334 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U341 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U342 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U343 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U344 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 fst :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U41 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U42 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U43 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U44 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U45 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U46 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U51 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U52 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U53 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U54 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U55 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U56 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U61 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U62 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isPLNatKind :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U63 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 isPLNat :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U71 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U72 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U73 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U81 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U82 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U83 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U91 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U92 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 U93 :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 tail :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 take :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 0' :: tt:mark:nil:0':ok 102.08/27.23 sel :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 proper :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 ok :: tt:mark:nil:0':ok -> tt:mark:nil:0':ok 102.08/27.23 top :: tt:mark:nil:0':ok -> top 102.08/27.23 hole_tt:mark:nil:0':ok1_0 :: tt:mark:nil:0':ok 102.08/27.23 hole_top2_0 :: top 102.08/27.23 gen_tt:mark:nil:0':ok3_0 :: Nat -> tt:mark:nil:0':ok 102.08/27.23 102.08/27.23 102.08/27.23 Lemmas: 102.08/27.23 U102(gen_tt:mark:nil:0':ok3_0(+(1, n5_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n5_0) 102.08/27.23 U103(gen_tt:mark:nil:0':ok3_0(+(1, n17319_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n17319_0) 102.08/27.23 U104(gen_tt:mark:nil:0':ok3_0(+(1, n35249_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n35249_0) 102.08/27.23 U105(gen_tt:mark:nil:0':ok3_0(+(1, n53770_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n53770_0) 102.08/27.23 U106(gen_tt:mark:nil:0':ok3_0(+(1, n64799_0))) -> *4_0, rt in Omega(n64799_0) 102.08/27.23 U12(gen_tt:mark:nil:0':ok3_0(+(1, n67850_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n67850_0) 102.08/27.23 U112(gen_tt:mark:nil:0':ok3_0(+(1, n87757_0))) -> *4_0, rt in Omega(n87757_0) 102.08/27.23 U13(gen_tt:mark:nil:0':ok3_0(+(1, n91075_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n91075_0) 102.08/27.23 U122(gen_tt:mark:nil:0':ok3_0(+(1, n111906_0))) -> *4_0, rt in Omega(n111906_0) 102.08/27.23 U14(gen_tt:mark:nil:0':ok3_0(+(1, n115524_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n115524_0) 102.08/27.23 snd(gen_tt:mark:nil:0':ok3_0(+(1, n137279_0))) -> *4_0, rt in Omega(n137279_0) 102.08/27.23 splitAt(gen_tt:mark:nil:0':ok3_0(+(1, n141197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n141197_0) 102.08/27.23 U172(gen_tt:mark:nil:0':ok3_0(+(1, n154745_0))) -> *4_0, rt in Omega(n154745_0) 102.08/27.23 U182(gen_tt:mark:nil:0':ok3_0(+(1, n158914_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n158914_0) 102.08/27.23 U183(gen_tt:mark:nil:0':ok3_0(+(1, n172777_0))) -> *4_0, rt in Omega(n172777_0) 102.08/27.23 U192(gen_tt:mark:nil:0':ok3_0(+(1, n177197_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n177197_0) 102.08/27.23 U193(gen_tt:mark:nil:0':ok3_0(+(1, n191574_0))) -> *4_0, rt in Omega(n191574_0) 102.08/27.23 U202(gen_tt:mark:nil:0':ok3_0(+(1, n196245_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n196245_0) 102.08/27.23 U203(gen_tt:mark:nil:0':ok3_0(+(1, n221255_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n221255_0) 102.08/27.23 U204(gen_tt:mark:nil:0':ok3_0(+(1, n246874_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n246874_0) 102.08/27.23 U205(gen_tt:mark:nil:0':ok3_0(+(1, n273102_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n273102_0) 102.08/27.23 U206(gen_tt:mark:nil:0':ok3_0(+(1, n289205_0))) -> *4_0, rt in Omega(n289205_0) 102.08/27.23 U22(gen_tt:mark:nil:0':ok3_0(+(1, n294724_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n294724_0) 102.08/27.23 U23(gen_tt:mark:nil:0':ok3_0(+(1, n322338_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n322338_0) 102.08/27.23 U24(gen_tt:mark:nil:0':ok3_0(+(1, n350561_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n350561_0) 102.08/27.23 U232(gen_tt:mark:nil:0':ok3_0(+(1, n367986_0))) -> *4_0, rt in Omega(n367986_0) 102.08/27.23 U242(gen_tt:mark:nil:0':ok3_0(+(1, n374154_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n374154_0) 102.08/27.23 U243(gen_tt:mark:nil:0':ok3_0(+(1, n403763_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n403763_0) 102.08/27.23 U244(gen_tt:mark:nil:0':ok3_0(+(1, n433981_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n433981_0) 102.08/27.23 U245(gen_tt:mark:nil:0':ok3_0(+(1, n464808_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n464808_0) 102.08/27.23 U246(gen_tt:mark:nil:0':ok3_0(+(1, n483959_0))) -> *4_0, rt in Omega(n483959_0) 102.08/27.23 U252(gen_tt:mark:nil:0':ok3_0(+(1, n490975_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n490975_0) 102.08/27.23 U253(gen_tt:mark:nil:0':ok3_0(+(1, n523188_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n523188_0) 102.08/27.23 U254(gen_tt:mark:nil:0':ok3_0(+(1, n556010_0)), gen_tt:mark:nil:0':ok3_0(b), gen_tt:mark:nil:0':ok3_0(c)) -> *4_0, rt in Omega(n556010_0) 102.08/27.23 U255(gen_tt:mark:nil:0':ok3_0(+(1, n589441_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n589441_0) 102.08/27.23 U256(gen_tt:mark:nil:0':ok3_0(+(1, n610318_0))) -> *4_0, rt in Omega(n610318_0) 102.08/27.23 U262(gen_tt:mark:nil:0':ok3_0(+(1, n618182_0))) -> *4_0, rt in Omega(n618182_0) 102.08/27.23 U272(gen_tt:mark:nil:0':ok3_0(+(1, n626147_0))) -> *4_0, rt in Omega(n626147_0) 102.08/27.23 U282(gen_tt:mark:nil:0':ok3_0(+(1, n634213_0)), gen_tt:mark:nil:0':ok3_0(b)) -> *4_0, rt in Omega(n634213_0) 102.08/27.23 102.08/27.23 102.08/27.23 Generator Equations: 102.08/27.23 gen_tt:mark:nil:0':ok3_0(0) <=> tt 102.08/27.23 gen_tt:mark:nil:0':ok3_0(+(x, 1)) <=> mark(gen_tt:mark:nil:0':ok3_0(x)) 102.08/27.23 102.08/27.23 102.08/27.23 The following defined symbols remain to be analysed: 102.08/27.23 cons, active, natsFrom, s, U292, U293, U294, head, afterNth, U302, U303, U304, U32, U312, pair, U33, U322, U323, U324, U325, U326, U327, U34, U332, U333, U334, U342, U343, U344, fst, U42, U43, U44, U45, U46, U52, U53, U54, U55, U56, U62, isPLNatKind, U63, isPLNat, U72, U73, U82, U83, U92, U93, U11, U21, U31, U41, U51, U61, U71, U81, U91, U101, U111, U121, U131, U141, U151, U161, U171, U181, U191, U201, U211, U221, U231, U241, U251, U261, U271, U281, U291, U301, U311, U321, U331, U341, tail, take, sel, proper, top 102.08/27.23 102.08/27.23 They will be analysed ascendingly in the following order: 102.08/27.23 cons < active 102.08/27.23 natsFrom < active 102.08/27.23 s < active 102.08/27.23 U292 < active 102.08/27.23 U293 < active 102.08/27.23 U294 < active 102.08/27.23 head < active 102.08/27.23 afterNth < active 102.08/27.23 U302 < active 102.08/27.23 U303 < active 102.08/27.23 U304 < active 102.08/27.23 U32 < active 102.08/27.23 U312 < active 102.08/27.23 pair < active 102.08/27.23 U33 < active 102.08/27.23 U322 < active 102.08/27.23 U323 < active 102.08/27.23 U324 < active 102.08/27.23 U325 < active 102.08/27.23 U326 < active 102.08/27.23 U327 < active 102.08/27.23 U34 < active 102.08/27.23 U332 < active 102.08/27.23 U333 < active 102.08/27.23 U334 < active 102.08/27.23 U342 < active 102.08/27.23 U343 < active 102.08/27.23 U344 < active 102.08/27.23 fst < active 102.08/27.23 U42 < active 102.08/27.23 U43 < active 102.08/27.23 U44 < active 102.08/27.23 U45 < active 102.08/27.23 U46 < active 102.08/27.23 U52 < active 102.08/27.23 U53 < active 102.08/27.23 U54 < active 102.08/27.23 U55 < active 102.08/27.23 U56 < active 102.08/27.23 U62 < active 102.08/27.23 isPLNatKind < active 102.08/27.23 U63 < active 102.08/27.23 isPLNat < active 102.08/27.23 U72 < active 102.08/27.23 U73 < active 102.08/27.23 U82 < active 102.08/27.23 U83 < active 102.08/27.23 U92 < active 102.08/27.23 U93 < active 102.08/27.23 U11 < active 102.08/27.23 U21 < active 102.08/27.23 U31 < active 102.08/27.23 U41 < active 102.08/27.23 U51 < active 102.08/27.23 U61 < active 102.08/27.23 U71 < active 102.08/27.23 U81 < active 102.08/27.23 U91 < active 102.08/27.23 U101 < active 102.08/27.23 U111 < active 102.08/27.23 U121 < active 102.08/27.23 U131 < active 102.08/27.23 U141 < active 102.08/27.23 U151 < active 102.08/27.23 U161 < active 102.08/27.23 U171 < active 102.08/27.23 U181 < active 102.08/27.23 U191 < active 102.08/27.23 U201 < active 102.08/27.23 U211 < active 102.08/27.23 U221 < active 102.08/27.23 U231 < active 102.08/27.23 U241 < active 102.08/27.23 U251 < active 102.08/27.23 U261 < active 102.08/27.23 U271 < active 102.08/27.23 U281 < active 102.08/27.23 U291 < active 102.08/27.23 U301 < active 102.08/27.23 U311 < active 102.08/27.23 U321 < active 102.08/27.23 U331 < active 102.08/27.23 U341 < active 102.08/27.23 tail < active 102.08/27.23 take < active 102.08/27.23 sel < active 102.08/27.23 active < top 102.08/27.23 cons < proper 102.08/27.23 natsFrom < proper 102.08/27.23 s < proper 102.08/27.23 U292 < proper 102.08/27.23 U293 < proper 102.08/27.23 U294 < proper 102.08/27.23 head < proper 102.08/27.23 afterNth < proper 102.08/27.23 U302 < proper 102.08/27.23 U303 < proper 102.08/27.23 U304 < proper 102.08/27.23 U32 < proper 102.08/27.23 U312 < proper 102.08/27.23 pair < proper 102.08/27.23 U33 < proper 102.08/27.23 U322 < proper 102.08/27.23 U323 < proper 102.08/27.23 U324 < proper 102.08/27.23 U325 < proper 102.08/27.23 U326 < proper 102.08/27.23 U327 < proper 102.08/27.23 U34 < proper 102.08/27.23 U332 < proper 102.08/27.23 U333 < proper 102.08/27.23 U334 < proper 102.08/27.23 U342 < proper 102.08/27.23 U343 < proper 102.08/27.23 U344 < proper 102.08/27.23 fst < proper 102.08/27.23 U42 < proper 102.08/27.23 U43 < proper 102.08/27.23 U44 < proper 102.08/27.23 U45 < proper 102.08/27.23 U46 < proper 102.08/27.23 U52 < proper 102.08/27.23 U53 < proper 102.08/27.23 U54 < proper 102.08/27.23 U55 < proper 102.08/27.23 U56 < proper 102.08/27.23 U62 < proper 102.08/27.23 isPLNatKind < proper 102.08/27.23 U63 < proper 102.08/27.23 isPLNat < proper 102.08/27.23 U72 < proper 102.08/27.23 U73 < proper 102.08/27.23 U82 < proper 102.08/27.23 U83 < proper 102.08/27.23 U92 < proper 102.08/27.23 U93 < proper 102.08/27.23 U11 < proper 102.08/27.23 U21 < proper 102.08/27.23 U31 < proper 102.08/27.23 U41 < proper 102.08/27.23 U51 < proper 102.08/27.23 U61 < proper 102.08/27.23 U71 < proper 102.08/27.23 U81 < proper 102.08/27.23 U91 < proper 102.08/27.23 U101 < proper 102.08/27.23 U111 < proper 102.08/27.23 U121 < proper 102.08/27.23 U131 < proper 102.08/27.23 U141 < proper 102.08/27.23 U151 < proper 102.08/27.23 U161 < proper 102.08/27.23 U171 < proper 102.08/27.23 U181 < proper 102.08/27.23 U191 < proper 102.08/27.23 U201 < proper 102.08/27.23 U211 < proper 102.08/27.23 U221 < proper 102.08/27.23 U231 < proper 102.08/27.23 U241 < proper 102.08/27.23 U251 < proper 102.08/27.23 U261 < proper 102.08/27.23 U271 < proper 102.08/27.23 U281 < proper 102.08/27.23 U291 < proper 102.08/27.23 U301 < proper 102.08/27.23 U311 < proper 102.08/27.23 U321 < proper 102.08/27.23 U331 < proper 102.08/27.23 U341 < proper 102.08/27.23 tail < proper 102.08/27.23 take < proper 102.08/27.23 sel < proper 102.08/27.23 proper < top 102.26/27.35 EOF