WORST_CASE(Omega(n^1), O(n^5)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^5). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 511 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 7 ms] (8) CpxTypedWeightedCompleteTrs (9) NarrowingProof [BOTH BOUNDS(ID, ID), 68 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 62 ms] (12) CpxRNTS (13) InliningProof [UPPER BOUND(ID), 6375 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 24 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 6 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 323 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 95 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 7 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 138 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 6 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 130 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 3 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 210 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 74 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 13 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 502 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 124 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 644 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 186 ms] (60) CpxRNTS (61) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) IntTrsBoundProof [UPPER BOUND(ID), 118 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 42 ms] (66) CpxRNTS (67) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) IntTrsBoundProof [UPPER BOUND(ID), 77 ms] (70) CpxRNTS (71) IntTrsBoundProof [UPPER BOUND(ID), 23 ms] (72) CpxRNTS (73) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (74) CpxRNTS (75) IntTrsBoundProof [UPPER BOUND(ID), 147 ms] (76) CpxRNTS (77) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (78) CpxRNTS (79) ResultPropagationProof [UPPER BOUND(ID), 6 ms] (80) CpxRNTS (81) IntTrsBoundProof [UPPER BOUND(ID), 33.2 s] (82) CpxRNTS (83) IntTrsBoundProof [UPPER BOUND(ID), 23.2 s] (84) CpxRNTS (85) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (86) CpxRNTS (87) IntTrsBoundProof [UPPER BOUND(ID), 1144 ms] (88) CpxRNTS (89) IntTrsBoundProof [UPPER BOUND(ID), 454 ms] (90) CpxRNTS (91) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (92) CpxRNTS (93) IntTrsBoundProof [UPPER BOUND(ID), 947 ms] (94) CpxRNTS (95) IntTrsBoundProof [UPPER BOUND(ID), 522 ms] (96) CpxRNTS (97) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (98) CpxRNTS (99) IntTrsBoundProof [UPPER BOUND(ID), 1981 ms] (100) CpxRNTS (101) IntTrsBoundProof [UPPER BOUND(ID), 355 ms] (102) CpxRNTS (103) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (104) CpxRNTS (105) IntTrsBoundProof [UPPER BOUND(ID), 8521 ms] (106) CpxRNTS (107) IntTrsBoundProof [UPPER BOUND(ID), 767 ms] (108) CpxRNTS (109) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (110) CpxRNTS (111) IntTrsBoundProof [UPPER BOUND(ID), 1105 ms] (112) CpxRNTS (113) IntTrsBoundProof [UPPER BOUND(ID), 149 ms] (114) CpxRNTS (115) FinalProof [FINISHED, 0 ms] (116) BOUNDS(1, n^5) (117) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (118) TRS for Loop Detection (119) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (120) BEST (121) proven lower bound (122) LowerBoundPropagationProof [FINISHED, 0 ms] (123) BOUNDS(n^1, INF) (124) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(name, node), node, Cons(CN(cl, N(name, adjs)), xs)) eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, eqColorList(cs1, cs2)) revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) revapp(Nil, rest) -> rest possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, colorof(x, colorednodes)), color, Cons(x, xs), colorednodes) possible(color, Nil, colorednodes) -> True colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) colorrest(cs, ncs, colorednodes, Nil) -> colorednodes colorof(node, Nil) -> NoColor colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](possible(x, ns, colorednodes), Cons(x, xs), N(n, ns), colorednodes) colornode(Nil, node, colorednodes) -> NotPossible colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible(x, ns, colorednodes), cs, Cons(x, xs), N(n, ns), colorednodes, rest) colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(colornode(cs, x, Nil), Nil), xs)) eqColorList(Cons(c1, cs1), Nil) -> False eqColorList(Nil, Cons(c2, cs2)) -> False eqColorList(Nil, Nil) -> True eqColor(Yellow, NoColor) -> False eqColor(Yellow, Yellow) -> True eqColor(Yellow, Blue) -> False eqColor(Yellow, Red) -> False eqColor(Blue, NoColor) -> False eqColor(Blue, Yellow) -> False eqColor(Blue, Blue) -> True eqColor(Blue, Red) -> False eqColor(Red, NoColor) -> False eqColor(Red, Yellow) -> False eqColor(Red, Blue) -> False eqColor(Red, Red) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False getNodeName(N(name, adjs)) -> name getNodeFromCN(CN(cl, n)) -> n getColorListFromCN(CN(cl, n)) -> cl getAdjs(N(n, ns)) -> ns eqColor(NoColor, b) -> False reverse(xs) -> revapp(xs, Nil) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^5). The TRS R consists of the following rules: colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(name, node), node, Cons(CN(cl, N(name, adjs)), xs)) eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, eqColorList(cs1, cs2)) eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, eqColorList(cs1, cs2)) revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) revapp(Nil, rest) -> rest possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, colorof(x, colorednodes)), color, Cons(x, xs), colorednodes) possible(color, Nil, colorednodes) -> True colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) colorrest(cs, ncs, colorednodes, Nil) -> colorednodes colorof(node, Nil) -> NoColor colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](possible(x, ns, colorednodes), Cons(x, xs), N(n, ns), colorednodes) colornode(Nil, node, colorednodes) -> NotPossible colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible(x, ns, colorednodes), cs, Cons(x, xs), N(n, ns), colorednodes, rest) colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(colornode(cs, x, Nil), Nil), xs)) eqColorList(Cons(c1, cs1), Nil) -> False eqColorList(Nil, Cons(c2, cs2)) -> False eqColorList(Nil, Nil) -> True eqColor(Yellow, NoColor) -> False eqColor(Yellow, Yellow) -> True eqColor(Yellow, Blue) -> False eqColor(Yellow, Red) -> False eqColor(Blue, NoColor) -> False eqColor(Blue, Yellow) -> False eqColor(Blue, Blue) -> True eqColor(Blue, Red) -> False eqColor(Red, NoColor) -> False eqColor(Red, Yellow) -> False eqColor(Red, Blue) -> False eqColor(Red, Red) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False getNodeName(N(name, adjs)) -> name getNodeFromCN(CN(cl, n)) -> n getColorListFromCN(CN(cl, n)) -> cl getAdjs(N(n, ns)) -> ns eqColor(NoColor, b) -> False reverse(xs) -> revapp(xs, Nil) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^5). The TRS R consists of the following rules: colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(name, node), node, Cons(CN(cl, N(name, adjs)), xs)) [1] eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] revapp(Nil, rest) -> rest [1] possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, colorof(x, colorednodes)), color, Cons(x, xs), colorednodes) [1] possible(color, Nil, colorednodes) -> True [1] colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) [1] colorrest(cs, ncs, colorednodes, Nil) -> colorednodes [1] colorof(node, Nil) -> NoColor [1] colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](possible(x, ns, colorednodes), Cons(x, xs), N(n, ns), colorednodes) [1] colornode(Nil, node, colorednodes) -> NotPossible [1] colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible(x, ns, colorednodes), cs, Cons(x, xs), N(n, ns), colorednodes, rest) [1] colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil [1] graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(colornode(cs, x, Nil), Nil), xs)) [1] eqColorList(Cons(c1, cs1), Nil) -> False [1] eqColorList(Nil, Cons(c2, cs2)) -> False [1] eqColorList(Nil, Nil) -> True [1] eqColor(Yellow, NoColor) -> False [1] eqColor(Yellow, Yellow) -> True [1] eqColor(Yellow, Blue) -> False [1] eqColor(Yellow, Red) -> False [1] eqColor(Blue, NoColor) -> False [1] eqColor(Blue, Yellow) -> False [1] eqColor(Blue, Blue) -> True [1] eqColor(Blue, Red) -> False [1] eqColor(Red, NoColor) -> False [1] eqColor(Red, Yellow) -> False [1] eqColor(Red, Blue) -> False [1] eqColor(Red, Red) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] getNodeName(N(name, adjs)) -> name [1] getNodeFromCN(CN(cl, n)) -> n [1] getColorListFromCN(CN(cl, n)) -> cl [1] getAdjs(N(n, ns)) -> ns [1] eqColor(NoColor, b) -> False [1] reverse(xs) -> revapp(xs, Nil) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x [0] possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) [0] colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) [0] colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) [0] colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) [0] colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) [0] possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False [0] colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (6) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(name, node), node, Cons(CN(cl, N(name, adjs)), xs)) [1] eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] revapp(Nil, rest) -> rest [1] possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, colorof(x, colorednodes)), color, Cons(x, xs), colorednodes) [1] possible(color, Nil, colorednodes) -> True [1] colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) [1] colorrest(cs, ncs, colorednodes, Nil) -> colorednodes [1] colorof(node, Nil) -> NoColor [1] colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](possible(x, ns, colorednodes), Cons(x, xs), N(n, ns), colorednodes) [1] colornode(Nil, node, colorednodes) -> NotPossible [1] colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible(x, ns, colorednodes), cs, Cons(x, xs), N(n, ns), colorednodes, rest) [1] colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil [1] graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(colornode(cs, x, Nil), Nil), xs)) [1] eqColorList(Cons(c1, cs1), Nil) -> False [1] eqColorList(Nil, Cons(c2, cs2)) -> False [1] eqColorList(Nil, Nil) -> True [1] eqColor(Yellow, NoColor) -> False [1] eqColor(Yellow, Yellow) -> True [1] eqColor(Yellow, Blue) -> False [1] eqColor(Yellow, Red) -> False [1] eqColor(Blue, NoColor) -> False [1] eqColor(Blue, Yellow) -> False [1] eqColor(Blue, Blue) -> True [1] eqColor(Blue, Red) -> False [1] eqColor(Red, NoColor) -> False [1] eqColor(Red, Yellow) -> False [1] eqColor(Red, Blue) -> False [1] eqColor(Red, Red) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] getNodeName(N(name, adjs)) -> name [1] getNodeFromCN(CN(cl, n)) -> n [1] getColorListFromCN(CN(cl, n)) -> cl [1] getAdjs(N(n, ns)) -> ns [1] eqColor(NoColor, b) -> False [1] reverse(xs) -> revapp(xs, Nil) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x [0] possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) [0] colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) [0] colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) [0] colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) [0] colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) [0] possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False [0] colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) [0] The TRS has the following type information: colorof :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 Cons :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] CN :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 N :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 colorof[Ite][True][Ite] :: False:True -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 !EQ :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> False:True eqColorList :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True Yellow :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 NoColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 and :: False:True -> False:True -> False:True False :: False:True True :: False:True Blue :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 Red :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 revapp :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] Nil :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] possible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True possible[Ite][True][Ite] :: False:True -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True eqColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> False:True colorrest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colorednoderest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colornode :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 colornode[Ite][True][Ite] :: False:True -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 NotPossible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 colorednoderest[Ite][True][Ite] :: False:True -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] graphcolour :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] reverse :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] notEmpty :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True getNodeName :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 getNodeFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 getColorListFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] getAdjs :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] S :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 0 :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 colorednoderest[Ite][True][Ite][True][Let] :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0 -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] Rewrite Strategy: INNERMOST ---------------------------------------- (7) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: revapp_2 graphcolour_2 notEmpty_1 getNodeName_1 getNodeFromCN_1 getColorListFromCN_1 getAdjs_1 reverse_1 (c) The following functions are completely defined: possible_3 eqColorList_2 colorrest_4 colornode_3 eqColor_2 colorof_2 colorednoderest_5 and_2 !EQ_2 colorof[Ite][True][Ite]_3 possible[Ite][True][Ite]_4 colornode[Ite][True][Ite]_4 colorednoderest[Ite][True][Ite]_6 Due to the following rules being added: and(v0, v1) -> null_and [0] !EQ(v0, v1) -> null_!EQ [0] colorof[Ite][True][Ite](v0, v1, v2) -> null_colorof[Ite][True][Ite] [0] possible[Ite][True][Ite](v0, v1, v2, v3) -> null_possible[Ite][True][Ite] [0] colornode[Ite][True][Ite](v0, v1, v2, v3) -> null_colornode[Ite][True][Ite] [0] colorednoderest[Ite][True][Ite](v0, v1, v2, v3, v4, v5) -> Nil [0] possible(v0, v1, v2) -> null_possible [0] eqColorList(v0, v1) -> null_eqColorList [0] colorrest(v0, v1, v2, v3) -> Nil [0] colornode(v0, v1, v2) -> null_colornode [0] eqColor(v0, v1) -> null_eqColor [0] colorof(v0, v1) -> null_colorof [0] colorednoderest(v0, v1, v2, v3, v4) -> Nil [0] And the following fresh constants: null_and, null_!EQ, null_colorof[Ite][True][Ite], null_possible[Ite][True][Ite], null_colornode[Ite][True][Ite], null_possible, null_eqColorList, null_colornode, null_eqColor, null_colorof ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(name, node), node, Cons(CN(cl, N(name, adjs)), xs)) [1] eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, eqColorList(cs1, cs2)) [1] eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, eqColorList(cs1, cs2)) [1] revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] revapp(Nil, rest) -> rest [1] possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, colorof(x, colorednodes)), color, Cons(x, xs), colorednodes) [1] possible(color, Nil, colorednodes) -> True [1] colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) [1] colorrest(cs, ncs, colorednodes, Nil) -> colorednodes [1] colorof(node, Nil) -> NoColor [1] colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](possible(x, ns, colorednodes), Cons(x, xs), N(n, ns), colorednodes) [1] colornode(Nil, node, colorednodes) -> NotPossible [1] colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible(x, ns, colorednodes), cs, Cons(x, xs), N(n, ns), colorednodes, rest) [1] colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil [1] graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(colornode(cs, x, Nil), Nil), xs)) [1] eqColorList(Cons(c1, cs1), Nil) -> False [1] eqColorList(Nil, Cons(c2, cs2)) -> False [1] eqColorList(Nil, Nil) -> True [1] eqColor(Yellow, NoColor) -> False [1] eqColor(Yellow, Yellow) -> True [1] eqColor(Yellow, Blue) -> False [1] eqColor(Yellow, Red) -> False [1] eqColor(Blue, NoColor) -> False [1] eqColor(Blue, Yellow) -> False [1] eqColor(Blue, Blue) -> True [1] eqColor(Blue, Red) -> False [1] eqColor(Red, NoColor) -> False [1] eqColor(Red, Yellow) -> False [1] eqColor(Red, Blue) -> False [1] eqColor(Red, Red) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] getNodeName(N(name, adjs)) -> name [1] getNodeFromCN(CN(cl, n)) -> n [1] getColorListFromCN(CN(cl, n)) -> cl [1] getAdjs(N(n, ns)) -> ns [1] eqColor(NoColor, b) -> False [1] reverse(xs) -> revapp(xs, Nil) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x [0] possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) [0] colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) [0] colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) [0] colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) [0] colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) [0] possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False [0] colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) [0] and(v0, v1) -> null_and [0] !EQ(v0, v1) -> null_!EQ [0] colorof[Ite][True][Ite](v0, v1, v2) -> null_colorof[Ite][True][Ite] [0] possible[Ite][True][Ite](v0, v1, v2, v3) -> null_possible[Ite][True][Ite] [0] colornode[Ite][True][Ite](v0, v1, v2, v3) -> null_colornode[Ite][True][Ite] [0] colorednoderest[Ite][True][Ite](v0, v1, v2, v3, v4, v5) -> Nil [0] possible(v0, v1, v2) -> null_possible [0] eqColorList(v0, v1) -> null_eqColorList [0] colorrest(v0, v1, v2, v3) -> Nil [0] colornode(v0, v1, v2) -> null_colornode [0] eqColor(v0, v1) -> null_eqColor [0] colorof(v0, v1) -> null_colorof [0] colorednoderest(v0, v1, v2, v3, v4) -> Nil [0] The TRS has the following type information: colorof :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Cons :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] CN :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof N :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorof[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof !EQ :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor eqColorList :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor Yellow :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof NoColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof and :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor False :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor True :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor Blue :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Red :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof revapp :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] Nil :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] possible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor possible[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor eqColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor colorrest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colorednoderest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colornode :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colornode[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof NotPossible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorednoderest[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] graphcolour :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] reverse :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] notEmpty :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor getNodeName :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof getNodeFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof getColorListFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] getAdjs :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] S :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof 0 :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorednoderest[Ite][True][Ite][True][Let] :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] null_and :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_!EQ :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colorof[Ite][True][Ite] :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_possible[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colornode[Ite][True][Ite] :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_possible :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_eqColorList :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colornode :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_eqColor :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colorof :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Rewrite Strategy: INNERMOST ---------------------------------------- (9) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: colorof(S(y'), Cons(CN(cl, N(S(x'), adjs)), xs)) -> colorof[Ite][True][Ite](!EQ(x', y'), S(y'), Cons(CN(cl, N(S(x'), adjs)), xs)) [1] colorof(S(y''), Cons(CN(cl, N(0, adjs)), xs)) -> colorof[Ite][True][Ite](False, S(y''), Cons(CN(cl, N(0, adjs)), xs)) [1] colorof(0, Cons(CN(cl, N(S(x''), adjs)), xs)) -> colorof[Ite][True][Ite](False, 0, Cons(CN(cl, N(S(x''), adjs)), xs)) [1] colorof(0, Cons(CN(cl, N(0, adjs)), xs)) -> colorof[Ite][True][Ite](True, 0, Cons(CN(cl, N(0, adjs)), xs)) [1] colorof(node, Cons(CN(cl, N(name, adjs)), xs)) -> colorof[Ite][True][Ite](null_!EQ, node, Cons(CN(cl, N(name, adjs)), xs)) [1] eqColorList(Cons(Yellow, Cons(Yellow, cs1')), Cons(NoColor, Cons(NoColor, cs2'))) -> and(False, and(False, eqColorList(cs1', cs2'))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs1'')), Cons(NoColor, Cons(Yellow, cs2''))) -> and(False, and(True, eqColorList(cs1'', cs2''))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs11)), Cons(NoColor, Cons(Blue, cs21))) -> and(False, and(False, eqColorList(cs11, cs21))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs12)), Cons(NoColor, Cons(Red, cs22))) -> and(False, and(False, eqColorList(cs12, cs22))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs13)), Cons(NoColor, Cons(NoColor, cs23))) -> and(False, and(False, eqColorList(cs13, cs23))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs14)), Cons(NoColor, Cons(Yellow, cs24))) -> and(False, and(False, eqColorList(cs14, cs24))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs15)), Cons(NoColor, Cons(Blue, cs25))) -> and(False, and(True, eqColorList(cs15, cs25))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs16)), Cons(NoColor, Cons(Red, cs26))) -> and(False, and(False, eqColorList(cs16, cs26))) [2] eqColorList(Cons(Yellow, Cons(Red, cs17)), Cons(NoColor, Cons(NoColor, cs27))) -> and(False, and(False, eqColorList(cs17, cs27))) [2] eqColorList(Cons(Yellow, Cons(Red, cs18)), Cons(NoColor, Cons(Yellow, cs28))) -> and(False, and(False, eqColorList(cs18, cs28))) [2] eqColorList(Cons(Yellow, Cons(Red, cs19)), Cons(NoColor, Cons(Blue, cs29))) -> and(False, and(False, eqColorList(cs19, cs29))) [2] eqColorList(Cons(Yellow, Cons(Red, cs110)), Cons(NoColor, Cons(Red, cs210))) -> and(False, and(True, eqColorList(cs110, cs210))) [2] eqColorList(Cons(Yellow, Cons(NoColor, cs111)), Cons(NoColor, Cons(b', cs211))) -> and(False, and(False, eqColorList(cs111, cs211))) [2] eqColorList(Cons(Yellow, Cons(c1', cs112)), Cons(NoColor, Nil)) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(NoColor, Cons(c2', cs212))) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(NoColor, Nil)) -> and(False, True) [2] eqColorList(Cons(Yellow, cs1), Cons(NoColor, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Yellow, Cons(Yellow, cs113)), Cons(Yellow, Cons(NoColor, cs213))) -> and(True, and(False, eqColorList(cs113, cs213))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs114)), Cons(Yellow, Cons(Yellow, cs214))) -> and(True, and(True, eqColorList(cs114, cs214))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs115)), Cons(Yellow, Cons(Blue, cs215))) -> and(True, and(False, eqColorList(cs115, cs215))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs116)), Cons(Yellow, Cons(Red, cs216))) -> and(True, and(False, eqColorList(cs116, cs216))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs117)), Cons(Yellow, Cons(NoColor, cs217))) -> and(True, and(False, eqColorList(cs117, cs217))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs118)), Cons(Yellow, Cons(Yellow, cs218))) -> and(True, and(False, eqColorList(cs118, cs218))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs119)), Cons(Yellow, Cons(Blue, cs219))) -> and(True, and(True, eqColorList(cs119, cs219))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs120)), Cons(Yellow, Cons(Red, cs220))) -> and(True, and(False, eqColorList(cs120, cs220))) [2] eqColorList(Cons(Yellow, Cons(Red, cs121)), Cons(Yellow, Cons(NoColor, cs221))) -> and(True, and(False, eqColorList(cs121, cs221))) [2] eqColorList(Cons(Yellow, Cons(Red, cs122)), Cons(Yellow, Cons(Yellow, cs222))) -> and(True, and(False, eqColorList(cs122, cs222))) [2] eqColorList(Cons(Yellow, Cons(Red, cs123)), Cons(Yellow, Cons(Blue, cs223))) -> and(True, and(False, eqColorList(cs123, cs223))) [2] eqColorList(Cons(Yellow, Cons(Red, cs124)), Cons(Yellow, Cons(Red, cs224))) -> and(True, and(True, eqColorList(cs124, cs224))) [2] eqColorList(Cons(Yellow, Cons(NoColor, cs125)), Cons(Yellow, Cons(b'', cs225))) -> and(True, and(False, eqColorList(cs125, cs225))) [2] eqColorList(Cons(Yellow, Cons(c1'', cs126)), Cons(Yellow, Nil)) -> and(True, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Yellow, Cons(c2'', cs226))) -> and(True, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Yellow, Nil)) -> and(True, True) [2] eqColorList(Cons(Yellow, cs1), Cons(Yellow, cs2)) -> and(True, null_eqColorList) [1] eqColorList(Cons(Yellow, Cons(Yellow, cs127)), Cons(Blue, Cons(NoColor, cs227))) -> and(False, and(False, eqColorList(cs127, cs227))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs128)), Cons(Blue, Cons(Yellow, cs228))) -> and(False, and(True, eqColorList(cs128, cs228))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs129)), Cons(Blue, Cons(Blue, cs229))) -> and(False, and(False, eqColorList(cs129, cs229))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs130)), Cons(Blue, Cons(Red, cs230))) -> and(False, and(False, eqColorList(cs130, cs230))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs131)), Cons(Blue, Cons(NoColor, cs231))) -> and(False, and(False, eqColorList(cs131, cs231))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs132)), Cons(Blue, Cons(Yellow, cs232))) -> and(False, and(False, eqColorList(cs132, cs232))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs133)), Cons(Blue, Cons(Blue, cs233))) -> and(False, and(True, eqColorList(cs133, cs233))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs134)), Cons(Blue, Cons(Red, cs234))) -> and(False, and(False, eqColorList(cs134, cs234))) [2] eqColorList(Cons(Yellow, Cons(Red, cs135)), Cons(Blue, Cons(NoColor, cs235))) -> and(False, and(False, eqColorList(cs135, cs235))) [2] eqColorList(Cons(Yellow, Cons(Red, cs136)), Cons(Blue, Cons(Yellow, cs236))) -> and(False, and(False, eqColorList(cs136, cs236))) [2] eqColorList(Cons(Yellow, Cons(Red, cs137)), Cons(Blue, Cons(Blue, cs237))) -> and(False, and(False, eqColorList(cs137, cs237))) [2] eqColorList(Cons(Yellow, Cons(Red, cs138)), Cons(Blue, Cons(Red, cs238))) -> and(False, and(True, eqColorList(cs138, cs238))) [2] eqColorList(Cons(Yellow, Cons(NoColor, cs139)), Cons(Blue, Cons(b1, cs239))) -> and(False, and(False, eqColorList(cs139, cs239))) [2] eqColorList(Cons(Yellow, Cons(c11, cs140)), Cons(Blue, Nil)) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Blue, Cons(c21, cs240))) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Blue, Nil)) -> and(False, True) [2] eqColorList(Cons(Yellow, cs1), Cons(Blue, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Yellow, Cons(Yellow, cs141)), Cons(Red, Cons(NoColor, cs241))) -> and(False, and(False, eqColorList(cs141, cs241))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs142)), Cons(Red, Cons(Yellow, cs242))) -> and(False, and(True, eqColorList(cs142, cs242))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs143)), Cons(Red, Cons(Blue, cs243))) -> and(False, and(False, eqColorList(cs143, cs243))) [2] eqColorList(Cons(Yellow, Cons(Yellow, cs144)), Cons(Red, Cons(Red, cs244))) -> and(False, and(False, eqColorList(cs144, cs244))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs145)), Cons(Red, Cons(NoColor, cs245))) -> and(False, and(False, eqColorList(cs145, cs245))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs146)), Cons(Red, Cons(Yellow, cs246))) -> and(False, and(False, eqColorList(cs146, cs246))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs147)), Cons(Red, Cons(Blue, cs247))) -> and(False, and(True, eqColorList(cs147, cs247))) [2] eqColorList(Cons(Yellow, Cons(Blue, cs148)), Cons(Red, Cons(Red, cs248))) -> and(False, and(False, eqColorList(cs148, cs248))) [2] eqColorList(Cons(Yellow, Cons(Red, cs149)), Cons(Red, Cons(NoColor, cs249))) -> and(False, and(False, eqColorList(cs149, cs249))) [2] eqColorList(Cons(Yellow, Cons(Red, cs150)), Cons(Red, Cons(Yellow, cs250))) -> and(False, and(False, eqColorList(cs150, cs250))) [2] eqColorList(Cons(Yellow, Cons(Red, cs151)), Cons(Red, Cons(Blue, cs251))) -> and(False, and(False, eqColorList(cs151, cs251))) [2] eqColorList(Cons(Yellow, Cons(Red, cs152)), Cons(Red, Cons(Red, cs252))) -> and(False, and(True, eqColorList(cs152, cs252))) [2] eqColorList(Cons(Yellow, Cons(NoColor, cs153)), Cons(Red, Cons(b2, cs253))) -> and(False, and(False, eqColorList(cs153, cs253))) [2] eqColorList(Cons(Yellow, Cons(c12, cs154)), Cons(Red, Nil)) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Red, Cons(c22, cs254))) -> and(False, False) [2] eqColorList(Cons(Yellow, Nil), Cons(Red, Nil)) -> and(False, True) [2] eqColorList(Cons(Yellow, cs1), Cons(Red, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Blue, Cons(Yellow, cs155)), Cons(NoColor, Cons(NoColor, cs255))) -> and(False, and(False, eqColorList(cs155, cs255))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs156)), Cons(NoColor, Cons(Yellow, cs256))) -> and(False, and(True, eqColorList(cs156, cs256))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs157)), Cons(NoColor, Cons(Blue, cs257))) -> and(False, and(False, eqColorList(cs157, cs257))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs158)), Cons(NoColor, Cons(Red, cs258))) -> and(False, and(False, eqColorList(cs158, cs258))) [2] eqColorList(Cons(Blue, Cons(Blue, cs159)), Cons(NoColor, Cons(NoColor, cs259))) -> and(False, and(False, eqColorList(cs159, cs259))) [2] eqColorList(Cons(Blue, Cons(Blue, cs160)), Cons(NoColor, Cons(Yellow, cs260))) -> and(False, and(False, eqColorList(cs160, cs260))) [2] eqColorList(Cons(Blue, Cons(Blue, cs161)), Cons(NoColor, Cons(Blue, cs261))) -> and(False, and(True, eqColorList(cs161, cs261))) [2] eqColorList(Cons(Blue, Cons(Blue, cs162)), Cons(NoColor, Cons(Red, cs262))) -> and(False, and(False, eqColorList(cs162, cs262))) [2] eqColorList(Cons(Blue, Cons(Red, cs163)), Cons(NoColor, Cons(NoColor, cs263))) -> and(False, and(False, eqColorList(cs163, cs263))) [2] eqColorList(Cons(Blue, Cons(Red, cs164)), Cons(NoColor, Cons(Yellow, cs264))) -> and(False, and(False, eqColorList(cs164, cs264))) [2] eqColorList(Cons(Blue, Cons(Red, cs165)), Cons(NoColor, Cons(Blue, cs265))) -> and(False, and(False, eqColorList(cs165, cs265))) [2] eqColorList(Cons(Blue, Cons(Red, cs166)), Cons(NoColor, Cons(Red, cs266))) -> and(False, and(True, eqColorList(cs166, cs266))) [2] eqColorList(Cons(Blue, Cons(NoColor, cs167)), Cons(NoColor, Cons(b3, cs267))) -> and(False, and(False, eqColorList(cs167, cs267))) [2] eqColorList(Cons(Blue, Cons(c13, cs168)), Cons(NoColor, Nil)) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(NoColor, Cons(c23, cs268))) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(NoColor, Nil)) -> and(False, True) [2] eqColorList(Cons(Blue, cs1), Cons(NoColor, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Blue, Cons(Yellow, cs169)), Cons(Yellow, Cons(NoColor, cs269))) -> and(False, and(False, eqColorList(cs169, cs269))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs170)), Cons(Yellow, Cons(Yellow, cs270))) -> and(False, and(True, eqColorList(cs170, cs270))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs171)), Cons(Yellow, Cons(Blue, cs271))) -> and(False, and(False, eqColorList(cs171, cs271))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs172)), Cons(Yellow, Cons(Red, cs272))) -> and(False, and(False, eqColorList(cs172, cs272))) [2] eqColorList(Cons(Blue, Cons(Blue, cs173)), Cons(Yellow, Cons(NoColor, cs273))) -> and(False, and(False, eqColorList(cs173, cs273))) [2] eqColorList(Cons(Blue, Cons(Blue, cs174)), Cons(Yellow, Cons(Yellow, cs274))) -> and(False, and(False, eqColorList(cs174, cs274))) [2] eqColorList(Cons(Blue, Cons(Blue, cs175)), Cons(Yellow, Cons(Blue, cs275))) -> and(False, and(True, eqColorList(cs175, cs275))) [2] eqColorList(Cons(Blue, Cons(Blue, cs176)), Cons(Yellow, Cons(Red, cs276))) -> and(False, and(False, eqColorList(cs176, cs276))) [2] eqColorList(Cons(Blue, Cons(Red, cs177)), Cons(Yellow, Cons(NoColor, cs277))) -> and(False, and(False, eqColorList(cs177, cs277))) [2] eqColorList(Cons(Blue, Cons(Red, cs178)), Cons(Yellow, Cons(Yellow, cs278))) -> and(False, and(False, eqColorList(cs178, cs278))) [2] eqColorList(Cons(Blue, Cons(Red, cs179)), Cons(Yellow, Cons(Blue, cs279))) -> and(False, and(False, eqColorList(cs179, cs279))) [2] eqColorList(Cons(Blue, Cons(Red, cs180)), Cons(Yellow, Cons(Red, cs280))) -> and(False, and(True, eqColorList(cs180, cs280))) [2] eqColorList(Cons(Blue, Cons(NoColor, cs181)), Cons(Yellow, Cons(b4, cs281))) -> and(False, and(False, eqColorList(cs181, cs281))) [2] eqColorList(Cons(Blue, Cons(c14, cs182)), Cons(Yellow, Nil)) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(Yellow, Cons(c24, cs282))) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(Yellow, Nil)) -> and(False, True) [2] eqColorList(Cons(Blue, cs1), Cons(Yellow, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Blue, Cons(Yellow, cs183)), Cons(Blue, Cons(NoColor, cs283))) -> and(True, and(False, eqColorList(cs183, cs283))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs184)), Cons(Blue, Cons(Yellow, cs284))) -> and(True, and(True, eqColorList(cs184, cs284))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs185)), Cons(Blue, Cons(Blue, cs285))) -> and(True, and(False, eqColorList(cs185, cs285))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs186)), Cons(Blue, Cons(Red, cs286))) -> and(True, and(False, eqColorList(cs186, cs286))) [2] eqColorList(Cons(Blue, Cons(Blue, cs187)), Cons(Blue, Cons(NoColor, cs287))) -> and(True, and(False, eqColorList(cs187, cs287))) [2] eqColorList(Cons(Blue, Cons(Blue, cs188)), Cons(Blue, Cons(Yellow, cs288))) -> and(True, and(False, eqColorList(cs188, cs288))) [2] eqColorList(Cons(Blue, Cons(Blue, cs189)), Cons(Blue, Cons(Blue, cs289))) -> and(True, and(True, eqColorList(cs189, cs289))) [2] eqColorList(Cons(Blue, Cons(Blue, cs190)), Cons(Blue, Cons(Red, cs290))) -> and(True, and(False, eqColorList(cs190, cs290))) [2] eqColorList(Cons(Blue, Cons(Red, cs191)), Cons(Blue, Cons(NoColor, cs291))) -> and(True, and(False, eqColorList(cs191, cs291))) [2] eqColorList(Cons(Blue, Cons(Red, cs192)), Cons(Blue, Cons(Yellow, cs292))) -> and(True, and(False, eqColorList(cs192, cs292))) [2] eqColorList(Cons(Blue, Cons(Red, cs193)), Cons(Blue, Cons(Blue, cs293))) -> and(True, and(False, eqColorList(cs193, cs293))) [2] eqColorList(Cons(Blue, Cons(Red, cs194)), Cons(Blue, Cons(Red, cs294))) -> and(True, and(True, eqColorList(cs194, cs294))) [2] eqColorList(Cons(Blue, Cons(NoColor, cs195)), Cons(Blue, Cons(b5, cs295))) -> and(True, and(False, eqColorList(cs195, cs295))) [2] eqColorList(Cons(Blue, Cons(c15, cs196)), Cons(Blue, Nil)) -> and(True, False) [2] eqColorList(Cons(Blue, Nil), Cons(Blue, Cons(c25, cs296))) -> and(True, False) [2] eqColorList(Cons(Blue, Nil), Cons(Blue, Nil)) -> and(True, True) [2] eqColorList(Cons(Blue, cs1), Cons(Blue, cs2)) -> and(True, null_eqColorList) [1] eqColorList(Cons(Blue, Cons(Yellow, cs197)), Cons(Red, Cons(NoColor, cs297))) -> and(False, and(False, eqColorList(cs197, cs297))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs198)), Cons(Red, Cons(Yellow, cs298))) -> and(False, and(True, eqColorList(cs198, cs298))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs199)), Cons(Red, Cons(Blue, cs299))) -> and(False, and(False, eqColorList(cs199, cs299))) [2] eqColorList(Cons(Blue, Cons(Yellow, cs1100)), Cons(Red, Cons(Red, cs2100))) -> and(False, and(False, eqColorList(cs1100, cs2100))) [2] eqColorList(Cons(Blue, Cons(Blue, cs1101)), Cons(Red, Cons(NoColor, cs2101))) -> and(False, and(False, eqColorList(cs1101, cs2101))) [2] eqColorList(Cons(Blue, Cons(Blue, cs1102)), Cons(Red, Cons(Yellow, cs2102))) -> and(False, and(False, eqColorList(cs1102, cs2102))) [2] eqColorList(Cons(Blue, Cons(Blue, cs1103)), Cons(Red, Cons(Blue, cs2103))) -> and(False, and(True, eqColorList(cs1103, cs2103))) [2] eqColorList(Cons(Blue, Cons(Blue, cs1104)), Cons(Red, Cons(Red, cs2104))) -> and(False, and(False, eqColorList(cs1104, cs2104))) [2] eqColorList(Cons(Blue, Cons(Red, cs1105)), Cons(Red, Cons(NoColor, cs2105))) -> and(False, and(False, eqColorList(cs1105, cs2105))) [2] eqColorList(Cons(Blue, Cons(Red, cs1106)), Cons(Red, Cons(Yellow, cs2106))) -> and(False, and(False, eqColorList(cs1106, cs2106))) [2] eqColorList(Cons(Blue, Cons(Red, cs1107)), Cons(Red, Cons(Blue, cs2107))) -> and(False, and(False, eqColorList(cs1107, cs2107))) [2] eqColorList(Cons(Blue, Cons(Red, cs1108)), Cons(Red, Cons(Red, cs2108))) -> and(False, and(True, eqColorList(cs1108, cs2108))) [2] eqColorList(Cons(Blue, Cons(NoColor, cs1109)), Cons(Red, Cons(b6, cs2109))) -> and(False, and(False, eqColorList(cs1109, cs2109))) [2] eqColorList(Cons(Blue, Cons(c16, cs1110)), Cons(Red, Nil)) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(Red, Cons(c26, cs2110))) -> and(False, False) [2] eqColorList(Cons(Blue, Nil), Cons(Red, Nil)) -> and(False, True) [2] eqColorList(Cons(Blue, cs1), Cons(Red, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Red, Cons(Yellow, cs1111)), Cons(NoColor, Cons(NoColor, cs2111))) -> and(False, and(False, eqColorList(cs1111, cs2111))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1112)), Cons(NoColor, Cons(Yellow, cs2112))) -> and(False, and(True, eqColorList(cs1112, cs2112))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1113)), Cons(NoColor, Cons(Blue, cs2113))) -> and(False, and(False, eqColorList(cs1113, cs2113))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1114)), Cons(NoColor, Cons(Red, cs2114))) -> and(False, and(False, eqColorList(cs1114, cs2114))) [2] eqColorList(Cons(Red, Cons(Blue, cs1115)), Cons(NoColor, Cons(NoColor, cs2115))) -> and(False, and(False, eqColorList(cs1115, cs2115))) [2] eqColorList(Cons(Red, Cons(Blue, cs1116)), Cons(NoColor, Cons(Yellow, cs2116))) -> and(False, and(False, eqColorList(cs1116, cs2116))) [2] eqColorList(Cons(Red, Cons(Blue, cs1117)), Cons(NoColor, Cons(Blue, cs2117))) -> and(False, and(True, eqColorList(cs1117, cs2117))) [2] eqColorList(Cons(Red, Cons(Blue, cs1118)), Cons(NoColor, Cons(Red, cs2118))) -> and(False, and(False, eqColorList(cs1118, cs2118))) [2] eqColorList(Cons(Red, Cons(Red, cs1119)), Cons(NoColor, Cons(NoColor, cs2119))) -> and(False, and(False, eqColorList(cs1119, cs2119))) [2] eqColorList(Cons(Red, Cons(Red, cs1120)), Cons(NoColor, Cons(Yellow, cs2120))) -> and(False, and(False, eqColorList(cs1120, cs2120))) [2] eqColorList(Cons(Red, Cons(Red, cs1121)), Cons(NoColor, Cons(Blue, cs2121))) -> and(False, and(False, eqColorList(cs1121, cs2121))) [2] eqColorList(Cons(Red, Cons(Red, cs1122)), Cons(NoColor, Cons(Red, cs2122))) -> and(False, and(True, eqColorList(cs1122, cs2122))) [2] eqColorList(Cons(Red, Cons(NoColor, cs1123)), Cons(NoColor, Cons(b7, cs2123))) -> and(False, and(False, eqColorList(cs1123, cs2123))) [2] eqColorList(Cons(Red, Cons(c17, cs1124)), Cons(NoColor, Nil)) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(NoColor, Cons(c27, cs2124))) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(NoColor, Nil)) -> and(False, True) [2] eqColorList(Cons(Red, cs1), Cons(NoColor, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Red, Cons(Yellow, cs1125)), Cons(Yellow, Cons(NoColor, cs2125))) -> and(False, and(False, eqColorList(cs1125, cs2125))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1126)), Cons(Yellow, Cons(Yellow, cs2126))) -> and(False, and(True, eqColorList(cs1126, cs2126))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1127)), Cons(Yellow, Cons(Blue, cs2127))) -> and(False, and(False, eqColorList(cs1127, cs2127))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1128)), Cons(Yellow, Cons(Red, cs2128))) -> and(False, and(False, eqColorList(cs1128, cs2128))) [2] eqColorList(Cons(Red, Cons(Blue, cs1129)), Cons(Yellow, Cons(NoColor, cs2129))) -> and(False, and(False, eqColorList(cs1129, cs2129))) [2] eqColorList(Cons(Red, Cons(Blue, cs1130)), Cons(Yellow, Cons(Yellow, cs2130))) -> and(False, and(False, eqColorList(cs1130, cs2130))) [2] eqColorList(Cons(Red, Cons(Blue, cs1131)), Cons(Yellow, Cons(Blue, cs2131))) -> and(False, and(True, eqColorList(cs1131, cs2131))) [2] eqColorList(Cons(Red, Cons(Blue, cs1132)), Cons(Yellow, Cons(Red, cs2132))) -> and(False, and(False, eqColorList(cs1132, cs2132))) [2] eqColorList(Cons(Red, Cons(Red, cs1133)), Cons(Yellow, Cons(NoColor, cs2133))) -> and(False, and(False, eqColorList(cs1133, cs2133))) [2] eqColorList(Cons(Red, Cons(Red, cs1134)), Cons(Yellow, Cons(Yellow, cs2134))) -> and(False, and(False, eqColorList(cs1134, cs2134))) [2] eqColorList(Cons(Red, Cons(Red, cs1135)), Cons(Yellow, Cons(Blue, cs2135))) -> and(False, and(False, eqColorList(cs1135, cs2135))) [2] eqColorList(Cons(Red, Cons(Red, cs1136)), Cons(Yellow, Cons(Red, cs2136))) -> and(False, and(True, eqColorList(cs1136, cs2136))) [2] eqColorList(Cons(Red, Cons(NoColor, cs1137)), Cons(Yellow, Cons(b8, cs2137))) -> and(False, and(False, eqColorList(cs1137, cs2137))) [2] eqColorList(Cons(Red, Cons(c18, cs1138)), Cons(Yellow, Nil)) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(Yellow, Cons(c28, cs2138))) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(Yellow, Nil)) -> and(False, True) [2] eqColorList(Cons(Red, cs1), Cons(Yellow, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Red, Cons(Yellow, cs1139)), Cons(Blue, Cons(NoColor, cs2139))) -> and(False, and(False, eqColorList(cs1139, cs2139))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1140)), Cons(Blue, Cons(Yellow, cs2140))) -> and(False, and(True, eqColorList(cs1140, cs2140))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1141)), Cons(Blue, Cons(Blue, cs2141))) -> and(False, and(False, eqColorList(cs1141, cs2141))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1142)), Cons(Blue, Cons(Red, cs2142))) -> and(False, and(False, eqColorList(cs1142, cs2142))) [2] eqColorList(Cons(Red, Cons(Blue, cs1143)), Cons(Blue, Cons(NoColor, cs2143))) -> and(False, and(False, eqColorList(cs1143, cs2143))) [2] eqColorList(Cons(Red, Cons(Blue, cs1144)), Cons(Blue, Cons(Yellow, cs2144))) -> and(False, and(False, eqColorList(cs1144, cs2144))) [2] eqColorList(Cons(Red, Cons(Blue, cs1145)), Cons(Blue, Cons(Blue, cs2145))) -> and(False, and(True, eqColorList(cs1145, cs2145))) [2] eqColorList(Cons(Red, Cons(Blue, cs1146)), Cons(Blue, Cons(Red, cs2146))) -> and(False, and(False, eqColorList(cs1146, cs2146))) [2] eqColorList(Cons(Red, Cons(Red, cs1147)), Cons(Blue, Cons(NoColor, cs2147))) -> and(False, and(False, eqColorList(cs1147, cs2147))) [2] eqColorList(Cons(Red, Cons(Red, cs1148)), Cons(Blue, Cons(Yellow, cs2148))) -> and(False, and(False, eqColorList(cs1148, cs2148))) [2] eqColorList(Cons(Red, Cons(Red, cs1149)), Cons(Blue, Cons(Blue, cs2149))) -> and(False, and(False, eqColorList(cs1149, cs2149))) [2] eqColorList(Cons(Red, Cons(Red, cs1150)), Cons(Blue, Cons(Red, cs2150))) -> and(False, and(True, eqColorList(cs1150, cs2150))) [2] eqColorList(Cons(Red, Cons(NoColor, cs1151)), Cons(Blue, Cons(b9, cs2151))) -> and(False, and(False, eqColorList(cs1151, cs2151))) [2] eqColorList(Cons(Red, Cons(c19, cs1152)), Cons(Blue, Nil)) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(Blue, Cons(c29, cs2152))) -> and(False, False) [2] eqColorList(Cons(Red, Nil), Cons(Blue, Nil)) -> and(False, True) [2] eqColorList(Cons(Red, cs1), Cons(Blue, cs2)) -> and(False, null_eqColorList) [1] eqColorList(Cons(Red, Cons(Yellow, cs1153)), Cons(Red, Cons(NoColor, cs2153))) -> and(True, and(False, eqColorList(cs1153, cs2153))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1154)), Cons(Red, Cons(Yellow, cs2154))) -> and(True, and(True, eqColorList(cs1154, cs2154))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1155)), Cons(Red, Cons(Blue, cs2155))) -> and(True, and(False, eqColorList(cs1155, cs2155))) [2] eqColorList(Cons(Red, Cons(Yellow, cs1156)), Cons(Red, Cons(Red, cs2156))) -> and(True, and(False, eqColorList(cs1156, cs2156))) [2] eqColorList(Cons(Red, Cons(Blue, cs1157)), Cons(Red, Cons(NoColor, cs2157))) -> and(True, and(False, eqColorList(cs1157, cs2157))) [2] eqColorList(Cons(Red, Cons(Blue, cs1158)), Cons(Red, Cons(Yellow, cs2158))) -> and(True, and(False, eqColorList(cs1158, cs2158))) [2] eqColorList(Cons(Red, Cons(Blue, cs1159)), Cons(Red, Cons(Blue, cs2159))) -> and(True, and(True, eqColorList(cs1159, cs2159))) [2] eqColorList(Cons(Red, Cons(Blue, cs1160)), Cons(Red, Cons(Red, cs2160))) -> and(True, and(False, eqColorList(cs1160, cs2160))) [2] eqColorList(Cons(Red, Cons(Red, cs1161)), Cons(Red, Cons(NoColor, cs2161))) -> and(True, and(False, eqColorList(cs1161, cs2161))) [2] eqColorList(Cons(Red, Cons(Red, cs1162)), Cons(Red, Cons(Yellow, cs2162))) -> and(True, and(False, eqColorList(cs1162, cs2162))) [2] eqColorList(Cons(Red, Cons(Red, cs1163)), Cons(Red, Cons(Blue, cs2163))) -> and(True, and(False, eqColorList(cs1163, cs2163))) [2] eqColorList(Cons(Red, Cons(Red, cs1164)), Cons(Red, Cons(Red, cs2164))) -> and(True, and(True, eqColorList(cs1164, cs2164))) [2] eqColorList(Cons(Red, Cons(NoColor, cs1165)), Cons(Red, Cons(b10, cs2165))) -> and(True, and(False, eqColorList(cs1165, cs2165))) [2] eqColorList(Cons(Red, Cons(c110, cs1166)), Cons(Red, Nil)) -> and(True, False) [2] eqColorList(Cons(Red, Nil), Cons(Red, Cons(c210, cs2166))) -> and(True, False) [2] eqColorList(Cons(Red, Nil), Cons(Red, Nil)) -> and(True, True) [2] eqColorList(Cons(Red, cs1), Cons(Red, cs2)) -> and(True, null_eqColorList) [1] eqColorList(Cons(NoColor, Cons(Yellow, cs1167)), Cons(b, Cons(NoColor, cs2167))) -> and(False, and(False, eqColorList(cs1167, cs2167))) [2] eqColorList(Cons(NoColor, Cons(Yellow, cs1168)), Cons(b, Cons(Yellow, cs2168))) -> and(False, and(True, eqColorList(cs1168, cs2168))) [2] eqColorList(Cons(NoColor, Cons(Yellow, cs1169)), Cons(b, Cons(Blue, cs2169))) -> and(False, and(False, eqColorList(cs1169, cs2169))) [2] eqColorList(Cons(NoColor, Cons(Yellow, cs1170)), Cons(b, Cons(Red, cs2170))) -> and(False, and(False, eqColorList(cs1170, cs2170))) [2] eqColorList(Cons(NoColor, Cons(Blue, cs1171)), Cons(b, Cons(NoColor, cs2171))) -> and(False, and(False, eqColorList(cs1171, cs2171))) [2] eqColorList(Cons(NoColor, Cons(Blue, cs1172)), Cons(b, Cons(Yellow, cs2172))) -> and(False, and(False, eqColorList(cs1172, cs2172))) [2] eqColorList(Cons(NoColor, Cons(Blue, cs1173)), Cons(b, Cons(Blue, cs2173))) -> and(False, and(True, eqColorList(cs1173, cs2173))) [2] eqColorList(Cons(NoColor, Cons(Blue, cs1174)), Cons(b, Cons(Red, cs2174))) -> and(False, and(False, eqColorList(cs1174, cs2174))) [2] eqColorList(Cons(NoColor, Cons(Red, cs1175)), Cons(b, Cons(NoColor, cs2175))) -> and(False, and(False, eqColorList(cs1175, cs2175))) [2] eqColorList(Cons(NoColor, Cons(Red, cs1176)), Cons(b, Cons(Yellow, cs2176))) -> and(False, and(False, eqColorList(cs1176, cs2176))) [2] eqColorList(Cons(NoColor, Cons(Red, cs1177)), Cons(b, Cons(Blue, cs2177))) -> and(False, and(False, eqColorList(cs1177, cs2177))) [2] eqColorList(Cons(NoColor, Cons(Red, cs1178)), Cons(b, Cons(Red, cs2178))) -> and(False, and(True, eqColorList(cs1178, cs2178))) [2] eqColorList(Cons(NoColor, Cons(NoColor, cs1179)), Cons(b, Cons(b11, cs2179))) -> and(False, and(False, eqColorList(cs1179, cs2179))) [2] eqColorList(Cons(NoColor, Cons(c111, cs1180)), Cons(b, Nil)) -> and(False, False) [2] eqColorList(Cons(NoColor, Nil), Cons(b, Cons(c211, cs2180))) -> and(False, False) [2] eqColorList(Cons(NoColor, Nil), Cons(b, Nil)) -> and(False, True) [2] eqColorList(Cons(NoColor, cs1), Cons(b, cs2)) -> and(False, null_eqColorList) [1] revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] revapp(Nil, rest) -> rest [1] possible(color, Cons(x, xs), Cons(CN(cl', N(name', adjs')), xs'')) -> possible[Ite][True][Ite](eqColor(color, colorof[Ite][True][Ite](!EQ(name', x), x, Cons(CN(cl', N(name', adjs')), xs''))), color, Cons(x, xs), Cons(CN(cl', N(name', adjs')), xs'')) [2] possible(color, Cons(x, xs), Nil) -> possible[Ite][True][Ite](eqColor(color, NoColor), color, Cons(x, xs), Nil) [2] possible(color, Cons(x, xs), colorednodes) -> possible[Ite][True][Ite](eqColor(color, null_colorof), color, Cons(x, xs), colorednodes) [1] possible(color, Nil, colorednodes) -> True [1] colorrest(cs, ncs, colorednodes, Cons(x, xs)) -> colorednoderest(cs, ncs, x, colorednodes, Cons(x, xs)) [1] colorrest(cs, ncs, colorednodes, Nil) -> colorednodes [1] colorof(node, Nil) -> NoColor [1] colornode(Cons(x, xs), N(n, Cons(x1, xs1)), colorednodes) -> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, colorednodes)), x, Cons(x1, xs1), colorednodes), Cons(x, xs), N(n, Cons(x1, xs1)), colorednodes) [2] colornode(Cons(x, xs), N(n, Nil), colorednodes) -> colornode[Ite][True][Ite](True, Cons(x, xs), N(n, Nil), colorednodes) [2] colornode(Cons(x, xs), N(n, ns), colorednodes) -> colornode[Ite][True][Ite](null_possible, Cons(x, xs), N(n, ns), colorednodes) [1] colornode(Nil, node, colorednodes) -> NotPossible [1] colorednoderest(cs, Cons(x, xs), N(n, Cons(x2, xs2)), colorednodes, rest) -> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, colorednodes)), x, Cons(x2, xs2), colorednodes), cs, Cons(x, xs), N(n, Cons(x2, xs2)), colorednodes, rest) [2] colorednoderest(cs, Cons(x, xs), N(n, Nil), colorednodes, rest) -> colorednoderest[Ite][True][Ite](True, cs, Cons(x, xs), N(n, Nil), colorednodes, rest) [2] colorednoderest(cs, Cons(x, xs), N(n, ns), colorednodes, rest) -> colorednoderest[Ite][True][Ite](null_possible, cs, Cons(x, xs), N(n, ns), colorednodes, rest) [1] colorednoderest(cs, Nil, node, colorednodes, rest) -> Nil [1] graphcolour(Cons(N(n', ns'), xs), Cons(x3, xs3)) -> reverse(colorrest(Cons(x3, xs3), Cons(x3, xs3), Cons(colornode[Ite][True][Ite](possible(x3, ns', Nil), Cons(x3, xs3), N(n', ns'), Nil), Nil), xs)) [2] graphcolour(Cons(x, xs), Nil) -> reverse(colorrest(Nil, Nil, Cons(NotPossible, Nil), xs)) [2] graphcolour(Cons(x, xs), cs) -> reverse(colorrest(cs, cs, Cons(null_colornode, Nil), xs)) [1] eqColorList(Cons(c1, cs1), Nil) -> False [1] eqColorList(Nil, Cons(c2, cs2)) -> False [1] eqColorList(Nil, Nil) -> True [1] eqColor(Yellow, NoColor) -> False [1] eqColor(Yellow, Yellow) -> True [1] eqColor(Yellow, Blue) -> False [1] eqColor(Yellow, Red) -> False [1] eqColor(Blue, NoColor) -> False [1] eqColor(Blue, Yellow) -> False [1] eqColor(Blue, Blue) -> True [1] eqColor(Blue, Red) -> False [1] eqColor(Red, NoColor) -> False [1] eqColor(Red, Yellow) -> False [1] eqColor(Red, Blue) -> False [1] eqColor(Red, Red) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] getNodeName(N(name, adjs)) -> name [1] getNodeFromCN(CN(cl, n)) -> n [1] getColorListFromCN(CN(cl, n)) -> cl [1] getAdjs(N(n, ns)) -> ns [1] eqColor(NoColor, b) -> False [1] reverse(xs) -> revapp(xs, Nil) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] colorof[Ite][True][Ite](True, node, Cons(CN(Cons(x, xs), n), xs')) -> x [0] possible[Ite][True][Ite](False, color, Cons(x, xs), colorednodes) -> possible(color, xs, colorednodes) [0] colorof[Ite][True][Ite](False, node, Cons(x, xs)) -> colorof(node, xs) [0] colornode[Ite][True][Ite](False, Cons(x, xs), node, colorednodes) -> colornode(xs, node, colorednodes) [0] colorednoderest[Ite][True][Ite](False, cs, Cons(x, xs), node, colorednodes, rest) -> colorednoderest(cs, xs, node, colorednodes, rest) [0] colorednoderest[Ite][True][Ite](True, cs, ncs, node, colorednodes, Cons(x, xs)) -> colorednoderest[Ite][True][Ite][True][Let](cs, ncs, node, colorednodes, Cons(x, xs), colorrest(cs, cs, Cons(CN(ncs, node), colorednodes), xs)) [0] possible[Ite][True][Ite](True, color, adjs, colorednodes) -> False [0] colornode[Ite][True][Ite](True, cs, node, colorednodes) -> CN(cs, node) [0] and(v0, v1) -> null_and [0] !EQ(v0, v1) -> null_!EQ [0] colorof[Ite][True][Ite](v0, v1, v2) -> null_colorof[Ite][True][Ite] [0] possible[Ite][True][Ite](v0, v1, v2, v3) -> null_possible[Ite][True][Ite] [0] colornode[Ite][True][Ite](v0, v1, v2, v3) -> null_colornode[Ite][True][Ite] [0] colorednoderest[Ite][True][Ite](v0, v1, v2, v3, v4, v5) -> Nil [0] possible(v0, v1, v2) -> null_possible [0] eqColorList(v0, v1) -> null_eqColorList [0] colorrest(v0, v1, v2, v3) -> Nil [0] colornode(v0, v1, v2) -> null_colornode [0] eqColor(v0, v1) -> null_eqColor [0] colorof(v0, v1) -> null_colorof [0] colorednoderest(v0, v1, v2, v3, v4) -> Nil [0] The TRS has the following type information: colorof :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Cons :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] CN :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof N :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorof[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof !EQ :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor eqColorList :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor Yellow :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof NoColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof and :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor False :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor True :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor Blue :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Red :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof revapp :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] Nil :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] possible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor possible[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor eqColor :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor colorrest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colorednoderest :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] colornode :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colornode[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof NotPossible :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorednoderest[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] graphcolour :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] reverse :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] notEmpty :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor getNodeName :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof getNodeFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof getColorListFromCN :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] getAdjs :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] S :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof 0 :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof colorednoderest[Ite][True][Ite][True][Let] :: Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] -> Cons:Nil:colorednoderest[Ite][True][Ite][True][Let] null_and :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_!EQ :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colorof[Ite][True][Ite] :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_possible[Ite][True][Ite] :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colornode[Ite][True][Ite] :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_possible :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_eqColorList :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colornode :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof null_eqColor :: False:True:null_and:null_!EQ:null_possible[Ite][True][Ite]:null_possible:null_eqColorList:null_eqColor null_colorof :: N:CN:Yellow:NoColor:Blue:Red:NotPossible:S:0:null_colorof[Ite][True][Ite]:null_colornode[Ite][True][Ite]:null_colornode:null_colorof Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: Yellow => 5 NoColor => 2 False => 1 True => 2 Blue => 1 Red => 4 Nil => 0 NotPossible => 3 0 => 0 null_and => 0 null_!EQ => 0 null_colorof[Ite][True][Ite] => 0 null_possible[Ite][True][Ite] => 0 null_colornode[Ite][True][Ite] => 0 null_possible => 0 null_eqColorList => 0 null_colornode => 0 null_eqColor => 0 null_colorof => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, colorednodes)), x, 1 + x2 + xs2, colorednodes), cs, 1 + x + xs, 1 + n + (1 + x2 + xs2), colorednodes, rest) :|: z'' = 1 + n + (1 + x2 + xs2), z2 = rest, xs >= 0, n >= 0, z' = 1 + x + xs, cs >= 0, x2 >= 0, xs2 >= 0, colorednodes >= 0, z1 = colorednodes, x >= 0, z = cs, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, cs, 1 + x + xs, 1 + n + 0, colorednodes, rest) :|: z2 = rest, xs >= 0, n >= 0, colorednodes >= 0, z' = 1 + x + xs, z'' = 1 + n + 0, z1 = colorednodes, x >= 0, z = cs, cs >= 0, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, cs, 1 + x + xs, 1 + n + ns, colorednodes, rest) :|: z2 = rest, xs >= 0, n >= 0, ns >= 0, colorednodes >= 0, z' = 1 + x + xs, z1 = colorednodes, z'' = 1 + n + ns, x >= 0, z = cs, cs >= 0, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z2 = rest, colorednodes >= 0, z1 = colorednodes, z = cs, z'' = node, cs >= 0, rest >= 0, z' = 0, node >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(cs, xs, node, colorednodes, rest) :|: xs >= 0, colorednodes >= 0, z = 1, z' = cs, x >= 0, z2 = colorednodes, z1 = node, z'' = 1 + x + xs, cs >= 0, z3 = rest, rest >= 0, node >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z1 = v3, z3 = v5, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + cs + ncs + node + colorednodes + (1 + x + xs) + colorrest(cs, cs, 1 + (1 + ncs + node) + colorednodes, xs) :|: z = 2, xs >= 0, colorednodes >= 0, z' = cs, x >= 0, z2 = colorednodes, z'' = ncs, z1 = node, ncs >= 0, cs >= 0, z3 = 1 + x + xs, node >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, colorednodes)), x, 1 + x1 + xs1, colorednodes), 1 + x + xs, 1 + n + (1 + x1 + xs1), colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, colorednodes >= 0, x >= 0, xs1 >= 0, z'' = colorednodes, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + n + 0, colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, colorednodes >= 0, x >= 0, z' = 1 + n + 0, z'' = colorednodes colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, colorednodes >= 0, x >= 0, z' = 1 + n + ns, z'' = colorednodes colornode(z, z', z'') -{ 1 }-> 3 :|: z' = node, colorednodes >= 0, z'' = colorednodes, z = 0, node >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, node, colorednodes) :|: xs >= 0, colorednodes >= 0, z' = 1 + x + xs, z = 1, z1 = colorednodes, x >= 0, z'' = node, node >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + cs + node :|: z = 2, colorednodes >= 0, z1 = colorednodes, z' = cs, z'' = node, cs >= 0, node >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + y'', 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, z = 1 + y'', cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, y'' >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, node, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z = node, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, node >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', y'), 1 + y', 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z = 1 + y', y' >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z = node, z' = 0, node >= 0 colorof(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = node, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', node >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(node, xs) :|: z' = node, xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, node >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednodes :|: z1 = 0, colorednodes >= 0, z = cs, ncs >= 0, cs >= 0, z'' = colorednodes, z' = ncs colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(cs, ncs, x, colorednodes, 1 + x + xs) :|: xs >= 0, colorednodes >= 0, z1 = 1 + x + xs, x >= 0, z = cs, ncs >= 0, cs >= 0, z'' = colorednodes, z' = ncs colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, b >= 0, z' = b eqColor(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs114, cs214))) :|: cs114 >= 0, cs214 >= 0, z = 1 + 5 + (1 + 5 + cs114), z' = 1 + 5 + (1 + 5 + cs214) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1154, cs2154))) :|: z' = 1 + 4 + (1 + 5 + cs2154), cs1154 >= 0, cs2154 >= 0, z = 1 + 4 + (1 + 5 + cs1154) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1159, cs2159))) :|: z = 1 + 4 + (1 + 1 + cs1159), cs2159 >= 0, cs1159 >= 0, z' = 1 + 4 + (1 + 1 + cs2159) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1164, cs2164))) :|: z' = 1 + 4 + (1 + 4 + cs2164), cs1164 >= 0, z = 1 + 4 + (1 + 4 + cs1164), cs2164 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs119, cs219))) :|: cs219 >= 0, z = 1 + 5 + (1 + 1 + cs119), cs119 >= 0, z' = 1 + 5 + (1 + 1 + cs219) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs124, cs224))) :|: z = 1 + 5 + (1 + 4 + cs124), cs124 >= 0, cs224 >= 0, z' = 1 + 5 + (1 + 4 + cs224) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs184, cs284))) :|: cs184 >= 0, z = 1 + 1 + (1 + 5 + cs184), cs284 >= 0, z' = 1 + 1 + (1 + 5 + cs284) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs189, cs289))) :|: z = 1 + 1 + (1 + 1 + cs189), cs289 >= 0, z' = 1 + 1 + (1 + 1 + cs289), cs189 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs194, cs294))) :|: z' = 1 + 1 + (1 + 4 + cs294), cs194 >= 0, z = 1 + 1 + (1 + 4 + cs194), cs294 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs113, cs213))) :|: cs113 >= 0, cs213 >= 0, z' = 1 + 5 + (1 + 2 + cs213), z = 1 + 5 + (1 + 5 + cs113) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs115, cs215))) :|: z = 1 + 5 + (1 + 5 + cs115), cs115 >= 0, cs215 >= 0, z' = 1 + 5 + (1 + 1 + cs215) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1153, cs2153))) :|: cs1153 >= 0, cs2153 >= 0, z = 1 + 4 + (1 + 5 + cs1153), z' = 1 + 4 + (1 + 2 + cs2153) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1155, cs2155))) :|: cs2155 >= 0, z = 1 + 4 + (1 + 5 + cs1155), z' = 1 + 4 + (1 + 1 + cs2155), cs1155 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1156, cs2156))) :|: z = 1 + 4 + (1 + 5 + cs1156), cs1156 >= 0, cs2156 >= 0, z' = 1 + 4 + (1 + 4 + cs2156) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1157, cs2157))) :|: z = 1 + 4 + (1 + 1 + cs1157), cs1157 >= 0, cs2157 >= 0, z' = 1 + 4 + (1 + 2 + cs2157) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1158, cs2158))) :|: z = 1 + 4 + (1 + 1 + cs1158), cs2158 >= 0, z' = 1 + 4 + (1 + 5 + cs2158), cs1158 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs116, cs216))) :|: cs216 >= 0, z' = 1 + 5 + (1 + 4 + cs216), z = 1 + 5 + (1 + 5 + cs116), cs116 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1160, cs2160))) :|: cs1160 >= 0, z = 1 + 4 + (1 + 1 + cs1160), z' = 1 + 4 + (1 + 4 + cs2160), cs2160 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1161, cs2161))) :|: z = 1 + 4 + (1 + 4 + cs1161), cs2161 >= 0, cs1161 >= 0, z' = 1 + 4 + (1 + 2 + cs2161) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1162, cs2162))) :|: z = 1 + 4 + (1 + 4 + cs1162), z' = 1 + 4 + (1 + 5 + cs2162), cs2162 >= 0, cs1162 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1163, cs2163))) :|: z = 1 + 4 + (1 + 4 + cs1163), cs2163 >= 0, z' = 1 + 4 + (1 + 1 + cs2163), cs1163 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1165, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z = 1 + 4 + (1 + 2 + cs1165), cs1165 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs117, cs217))) :|: z' = 1 + 5 + (1 + 2 + cs217), cs117 >= 0, cs217 >= 0, z = 1 + 5 + (1 + 1 + cs117) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs118, cs218))) :|: cs218 >= 0, z = 1 + 5 + (1 + 1 + cs118), cs118 >= 0, z' = 1 + 5 + (1 + 5 + cs218) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs120, cs220))) :|: z = 1 + 5 + (1 + 1 + cs120), z' = 1 + 5 + (1 + 4 + cs220), cs220 >= 0, cs120 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs121, cs221))) :|: z = 1 + 5 + (1 + 4 + cs121), cs121 >= 0, cs221 >= 0, z' = 1 + 5 + (1 + 2 + cs221) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs122, cs222))) :|: z = 1 + 5 + (1 + 4 + cs122), cs222 >= 0, cs122 >= 0, z' = 1 + 5 + (1 + 5 + cs222) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs123, cs223))) :|: z = 1 + 5 + (1 + 4 + cs123), cs123 >= 0, cs223 >= 0, z' = 1 + 5 + (1 + 1 + cs223) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs125, cs225))) :|: z = 1 + 5 + (1 + 2 + cs125), b'' >= 0, cs125 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs183, cs283))) :|: z' = 1 + 1 + (1 + 2 + cs283), cs183 >= 0, z = 1 + 1 + (1 + 5 + cs183), cs283 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs185, cs285))) :|: cs285 >= 0, z' = 1 + 1 + (1 + 1 + cs285), cs185 >= 0, z = 1 + 1 + (1 + 5 + cs185) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs186, cs286))) :|: cs186 >= 0, z' = 1 + 1 + (1 + 4 + cs286), z = 1 + 1 + (1 + 5 + cs186), cs286 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs187, cs287))) :|: z' = 1 + 1 + (1 + 2 + cs287), z = 1 + 1 + (1 + 1 + cs187), cs287 >= 0, cs187 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs188, cs288))) :|: cs188 >= 0, z' = 1 + 1 + (1 + 5 + cs288), cs288 >= 0, z = 1 + 1 + (1 + 1 + cs188) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs190, cs290))) :|: cs290 >= 0, z = 1 + 1 + (1 + 1 + cs190), z' = 1 + 1 + (1 + 4 + cs290), cs190 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs191, cs291))) :|: z = 1 + 1 + (1 + 4 + cs191), cs291 >= 0, cs191 >= 0, z' = 1 + 1 + (1 + 2 + cs291) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs192, cs292))) :|: z = 1 + 1 + (1 + 4 + cs192), cs192 >= 0, z' = 1 + 1 + (1 + 5 + cs292), cs292 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs193, cs293))) :|: cs193 >= 0, z = 1 + 1 + (1 + 4 + cs193), cs293 >= 0, z' = 1 + 1 + (1 + 1 + cs293) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs195, cs295))) :|: b5 >= 0, z = 1 + 1 + (1 + 2 + cs195), cs195 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 2) :|: z' = 1 + 5 + 0, z = 1 + 5 + 0 eqColorList(z, z') -{ 2 }-> and(2, 2) :|: z = 1 + 1 + 0, z' = 1 + 1 + 0 eqColorList(z, z') -{ 2 }-> and(2, 2) :|: z = 1 + 4 + 0, z' = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0 eqColorList(z, z') -{ 2 }-> and(2, 1) :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0 eqColorList(z, z') -{ 1 }-> and(2, 0) :|: z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0, z' = 1 + 5 + cs2 eqColorList(z, z') -{ 1 }-> and(2, 0) :|: cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1, z' = 1 + 1 + cs2 eqColorList(z, z') -{ 1 }-> and(2, 0) :|: z' = 1 + 4 + cs2, cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1'', cs2''))) :|: cs1'' >= 0, z' = 1 + 2 + (1 + 5 + cs2''), z = 1 + 5 + (1 + 5 + cs1''), cs2'' >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs110, cs210))) :|: z' = 1 + 2 + (1 + 4 + cs210), cs210 >= 0, z = 1 + 5 + (1 + 4 + cs110), cs110 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1103, cs2103))) :|: cs2103 >= 0, z' = 1 + 4 + (1 + 1 + cs2103), z = 1 + 1 + (1 + 1 + cs1103), cs1103 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1108, cs2108))) :|: cs1108 >= 0, z' = 1 + 4 + (1 + 4 + cs2108), cs2108 >= 0, z = 1 + 1 + (1 + 4 + cs1108) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1112, cs2112))) :|: cs2112 >= 0, z' = 1 + 2 + (1 + 5 + cs2112), z = 1 + 4 + (1 + 5 + cs1112), cs1112 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1117, cs2117))) :|: cs2117 >= 0, cs1117 >= 0, z = 1 + 4 + (1 + 1 + cs1117), z' = 1 + 2 + (1 + 1 + cs2117) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1122, cs2122))) :|: z = 1 + 4 + (1 + 4 + cs1122), cs2122 >= 0, z' = 1 + 2 + (1 + 4 + cs2122), cs1122 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1126, cs2126))) :|: z' = 1 + 5 + (1 + 5 + cs2126), z = 1 + 4 + (1 + 5 + cs1126), cs1126 >= 0, cs2126 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1131, cs2131))) :|: z' = 1 + 5 + (1 + 1 + cs2131), cs2131 >= 0, cs1131 >= 0, z = 1 + 4 + (1 + 1 + cs1131) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1136, cs2136))) :|: cs1136 >= 0, z = 1 + 4 + (1 + 4 + cs1136), z' = 1 + 5 + (1 + 4 + cs2136), cs2136 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1140, cs2140))) :|: cs2140 >= 0, z' = 1 + 1 + (1 + 5 + cs2140), cs1140 >= 0, z = 1 + 4 + (1 + 5 + cs1140) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1145, cs2145))) :|: z = 1 + 4 + (1 + 1 + cs1145), cs1145 >= 0, cs2145 >= 0, z' = 1 + 1 + (1 + 1 + cs2145) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1150, cs2150))) :|: z = 1 + 4 + (1 + 4 + cs1150), z' = 1 + 1 + (1 + 4 + cs2150), cs1150 >= 0, cs2150 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1168, cs2168))) :|: b >= 0, cs1168 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0, z = 1 + 2 + (1 + 5 + cs1168) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1173, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), z = 1 + 2 + (1 + 1 + cs1173), cs2173 >= 0, cs1173 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1178, cs2178))) :|: z = 1 + 2 + (1 + 4 + cs1178), b >= 0, cs1178 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs128, cs228))) :|: z = 1 + 5 + (1 + 5 + cs128), cs228 >= 0, z' = 1 + 1 + (1 + 5 + cs228), cs128 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs133, cs233))) :|: cs233 >= 0, cs133 >= 0, z' = 1 + 1 + (1 + 1 + cs233), z = 1 + 5 + (1 + 1 + cs133) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs138, cs238))) :|: cs138 >= 0, z = 1 + 5 + (1 + 4 + cs138), z' = 1 + 1 + (1 + 4 + cs238), cs238 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs142, cs242))) :|: z = 1 + 5 + (1 + 5 + cs142), cs242 >= 0, cs142 >= 0, z' = 1 + 4 + (1 + 5 + cs242) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs147, cs247))) :|: z = 1 + 5 + (1 + 1 + cs147), cs247 >= 0, z' = 1 + 4 + (1 + 1 + cs247), cs147 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs15, cs25))) :|: z = 1 + 5 + (1 + 1 + cs15), cs15 >= 0, cs25 >= 0, z' = 1 + 2 + (1 + 1 + cs25) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs152, cs252))) :|: z = 1 + 5 + (1 + 4 + cs152), cs152 >= 0, cs252 >= 0, z' = 1 + 4 + (1 + 4 + cs252) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs156, cs256))) :|: z = 1 + 1 + (1 + 5 + cs156), cs156 >= 0, z' = 1 + 2 + (1 + 5 + cs256), cs256 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs161, cs261))) :|: cs161 >= 0, cs261 >= 0, z = 1 + 1 + (1 + 1 + cs161), z' = 1 + 2 + (1 + 1 + cs261) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs166, cs266))) :|: cs166 >= 0, z' = 1 + 2 + (1 + 4 + cs266), z = 1 + 1 + (1 + 4 + cs166), cs266 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs170, cs270))) :|: cs170 >= 0, z' = 1 + 5 + (1 + 5 + cs270), z = 1 + 1 + (1 + 5 + cs170), cs270 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs175, cs275))) :|: cs275 >= 0, z' = 1 + 5 + (1 + 1 + cs275), cs175 >= 0, z = 1 + 1 + (1 + 1 + cs175) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs180, cs280))) :|: z = 1 + 1 + (1 + 4 + cs180), cs280 >= 0, z' = 1 + 5 + (1 + 4 + cs280), cs180 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs198, cs298))) :|: z = 1 + 1 + (1 + 5 + cs198), z' = 1 + 4 + (1 + 5 + cs298), cs298 >= 0, cs198 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1', cs2'))) :|: z = 1 + 5 + (1 + 5 + cs1'), cs2' >= 0, cs1' >= 0, z' = 1 + 2 + (1 + 2 + cs2') eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs11, cs21))) :|: z' = 1 + 2 + (1 + 1 + cs21), cs11 >= 0, cs21 >= 0, z = 1 + 5 + (1 + 5 + cs11) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1100, cs2100))) :|: cs1100 >= 0, z = 1 + 1 + (1 + 5 + cs1100), cs2100 >= 0, z' = 1 + 4 + (1 + 4 + cs2100) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1101, cs2101))) :|: cs1101 >= 0, cs2101 >= 0, z = 1 + 1 + (1 + 1 + cs1101), z' = 1 + 4 + (1 + 2 + cs2101) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1102, cs2102))) :|: cs2102 >= 0, z' = 1 + 4 + (1 + 5 + cs2102), z = 1 + 1 + (1 + 1 + cs1102), cs1102 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1104, cs2104))) :|: cs1104 >= 0, cs2104 >= 0, z' = 1 + 4 + (1 + 4 + cs2104), z = 1 + 1 + (1 + 1 + cs1104) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1105, cs2105))) :|: cs1105 >= 0, z = 1 + 1 + (1 + 4 + cs1105), z' = 1 + 4 + (1 + 2 + cs2105), cs2105 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1106, cs2106))) :|: z' = 1 + 4 + (1 + 5 + cs2106), cs1106 >= 0, z = 1 + 1 + (1 + 4 + cs1106), cs2106 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1107, cs2107))) :|: cs2107 >= 0, cs1107 >= 0, z = 1 + 1 + (1 + 4 + cs1107), z' = 1 + 4 + (1 + 1 + cs2107) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1109, cs2109))) :|: b6 >= 0, cs1109 >= 0, cs2109 >= 0, z = 1 + 1 + (1 + 2 + cs1109), z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs111, cs211))) :|: b' >= 0, cs211 >= 0, cs111 >= 0, z = 1 + 5 + (1 + 2 + cs111), z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1111, cs2111))) :|: cs1111 >= 0, z = 1 + 4 + (1 + 5 + cs1111), z' = 1 + 2 + (1 + 2 + cs2111), cs2111 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1113, cs2113))) :|: cs2113 >= 0, z' = 1 + 2 + (1 + 1 + cs2113), cs1113 >= 0, z = 1 + 4 + (1 + 5 + cs1113) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1114, cs2114))) :|: z = 1 + 4 + (1 + 5 + cs1114), z' = 1 + 2 + (1 + 4 + cs2114), cs1114 >= 0, cs2114 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1115, cs2115))) :|: cs1115 >= 0, z' = 1 + 2 + (1 + 2 + cs2115), z = 1 + 4 + (1 + 1 + cs1115), cs2115 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1116, cs2116))) :|: cs1116 >= 0, z' = 1 + 2 + (1 + 5 + cs2116), cs2116 >= 0, z = 1 + 4 + (1 + 1 + cs1116) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1118, cs2118))) :|: cs1118 >= 0, cs2118 >= 0, z = 1 + 4 + (1 + 1 + cs1118), z' = 1 + 2 + (1 + 4 + cs2118) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1119, cs2119))) :|: z' = 1 + 2 + (1 + 2 + cs2119), cs1119 >= 0, cs2119 >= 0, z = 1 + 4 + (1 + 4 + cs1119) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1120, cs2120))) :|: z' = 1 + 2 + (1 + 5 + cs2120), cs2120 >= 0, cs1120 >= 0, z = 1 + 4 + (1 + 4 + cs1120) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1121, cs2121))) :|: cs1121 >= 0, z' = 1 + 2 + (1 + 1 + cs2121), z = 1 + 4 + (1 + 4 + cs1121), cs2121 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1123, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, z = 1 + 4 + (1 + 2 + cs1123), b7 >= 0, cs1123 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1125, cs2125))) :|: cs1125 >= 0, z' = 1 + 5 + (1 + 2 + cs2125), z = 1 + 4 + (1 + 5 + cs1125), cs2125 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1127, cs2127))) :|: cs2127 >= 0, z = 1 + 4 + (1 + 5 + cs1127), z' = 1 + 5 + (1 + 1 + cs2127), cs1127 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1128, cs2128))) :|: cs2128 >= 0, cs1128 >= 0, z = 1 + 4 + (1 + 5 + cs1128), z' = 1 + 5 + (1 + 4 + cs2128) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1129, cs2129))) :|: cs1129 >= 0, z = 1 + 4 + (1 + 1 + cs1129), cs2129 >= 0, z' = 1 + 5 + (1 + 2 + cs2129) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1130, cs2130))) :|: cs2130 >= 0, z' = 1 + 5 + (1 + 5 + cs2130), cs1130 >= 0, z = 1 + 4 + (1 + 1 + cs1130) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1132, cs2132))) :|: cs1132 >= 0, z = 1 + 4 + (1 + 1 + cs1132), cs2132 >= 0, z' = 1 + 5 + (1 + 4 + cs2132) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1133, cs2133))) :|: z = 1 + 4 + (1 + 4 + cs1133), cs2133 >= 0, z' = 1 + 5 + (1 + 2 + cs2133), cs1133 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1134, cs2134))) :|: z' = 1 + 5 + (1 + 5 + cs2134), cs2134 >= 0, cs1134 >= 0, z = 1 + 4 + (1 + 4 + cs1134) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1135, cs2135))) :|: cs1135 >= 0, cs2135 >= 0, z = 1 + 4 + (1 + 4 + cs1135), z' = 1 + 5 + (1 + 1 + cs2135) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1137, cs2137))) :|: cs1137 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, z = 1 + 4 + (1 + 2 + cs1137), cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1139, cs2139))) :|: cs2139 >= 0, z' = 1 + 1 + (1 + 2 + cs2139), cs1139 >= 0, z = 1 + 4 + (1 + 5 + cs1139) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1141, cs2141))) :|: cs2141 >= 0, z = 1 + 4 + (1 + 5 + cs1141), z' = 1 + 1 + (1 + 1 + cs2141), cs1141 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1142, cs2142))) :|: z' = 1 + 1 + (1 + 4 + cs2142), cs2142 >= 0, z = 1 + 4 + (1 + 5 + cs1142), cs1142 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1143, cs2143))) :|: z' = 1 + 1 + (1 + 2 + cs2143), z = 1 + 4 + (1 + 1 + cs1143), cs2143 >= 0, cs1143 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1144, cs2144))) :|: cs2144 >= 0, z = 1 + 4 + (1 + 1 + cs1144), cs1144 >= 0, z' = 1 + 1 + (1 + 5 + cs2144) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1146, cs2146))) :|: z' = 1 + 1 + (1 + 4 + cs2146), cs1146 >= 0, z = 1 + 4 + (1 + 1 + cs1146), cs2146 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1147, cs2147))) :|: cs1147 >= 0, z = 1 + 4 + (1 + 4 + cs1147), z' = 1 + 1 + (1 + 2 + cs2147), cs2147 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1148, cs2148))) :|: cs2148 >= 0, z = 1 + 4 + (1 + 4 + cs1148), cs1148 >= 0, z' = 1 + 1 + (1 + 5 + cs2148) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1149, cs2149))) :|: z' = 1 + 1 + (1 + 1 + cs2149), cs2149 >= 0, z = 1 + 4 + (1 + 4 + cs1149), cs1149 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1151, cs2151))) :|: cs2151 >= 0, b9 >= 0, cs1151 >= 0, z = 1 + 4 + (1 + 2 + cs1151), z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1167, cs2167))) :|: b >= 0, cs1167 >= 0, z = 1 + 2 + (1 + 5 + cs1167), cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1169, cs2169))) :|: b >= 0, cs2169 >= 0, z = 1 + 2 + (1 + 5 + cs1169), cs1169 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1170, cs2170))) :|: z = 1 + 2 + (1 + 5 + cs1170), cs1170 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1171, cs2171))) :|: b >= 0, z = 1 + 2 + (1 + 1 + cs1171), cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), cs1171 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1172, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, cs1172 >= 0, z = 1 + 2 + (1 + 1 + cs1172) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1174, cs2174))) :|: b >= 0, cs1174 >= 0, z = 1 + 2 + (1 + 1 + cs1174), cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1175, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), cs1175 >= 0, z = 1 + 2 + (1 + 4 + cs1175), cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1176, cs2176))) :|: b >= 0, cs2176 >= 0, z = 1 + 2 + (1 + 4 + cs1176), cs1176 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1177, cs2177))) :|: b >= 0, z = 1 + 2 + (1 + 4 + cs1177), cs1177 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1179, cs2179))) :|: b >= 0, z = 1 + 2 + (1 + 2 + cs1179), cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, cs1179 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs12, cs22))) :|: cs22 >= 0, z' = 1 + 2 + (1 + 4 + cs22), z = 1 + 5 + (1 + 5 + cs12), cs12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs127, cs227))) :|: z = 1 + 5 + (1 + 5 + cs127), z' = 1 + 1 + (1 + 2 + cs227), cs127 >= 0, cs227 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs129, cs229))) :|: z = 1 + 5 + (1 + 5 + cs129), z' = 1 + 1 + (1 + 1 + cs229), cs229 >= 0, cs129 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs13, cs23))) :|: z = 1 + 5 + (1 + 1 + cs13), z' = 1 + 2 + (1 + 2 + cs23), cs13 >= 0, cs23 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs130, cs230))) :|: cs130 >= 0, z' = 1 + 1 + (1 + 4 + cs230), cs230 >= 0, z = 1 + 5 + (1 + 5 + cs130) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs131, cs231))) :|: cs231 >= 0, z = 1 + 5 + (1 + 1 + cs131), z' = 1 + 1 + (1 + 2 + cs231), cs131 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs132, cs232))) :|: z' = 1 + 1 + (1 + 5 + cs232), cs232 >= 0, z = 1 + 5 + (1 + 1 + cs132), cs132 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs134, cs234))) :|: cs134 >= 0, cs234 >= 0, z = 1 + 5 + (1 + 1 + cs134), z' = 1 + 1 + (1 + 4 + cs234) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs135, cs235))) :|: cs135 >= 0, z' = 1 + 1 + (1 + 2 + cs235), cs235 >= 0, z = 1 + 5 + (1 + 4 + cs135) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs136, cs236))) :|: z' = 1 + 1 + (1 + 5 + cs236), cs136 >= 0, cs236 >= 0, z = 1 + 5 + (1 + 4 + cs136) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs137, cs237))) :|: cs237 >= 0, z' = 1 + 1 + (1 + 1 + cs237), z = 1 + 5 + (1 + 4 + cs137), cs137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs139, cs239))) :|: b1 >= 0, z = 1 + 5 + (1 + 2 + cs139), cs239 >= 0, cs139 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs14, cs24))) :|: z = 1 + 5 + (1 + 1 + cs14), z' = 1 + 2 + (1 + 5 + cs24), cs24 >= 0, cs14 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs141, cs241))) :|: z' = 1 + 4 + (1 + 2 + cs241), cs141 >= 0, cs241 >= 0, z = 1 + 5 + (1 + 5 + cs141) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs143, cs243))) :|: z = 1 + 5 + (1 + 5 + cs143), cs143 >= 0, cs243 >= 0, z' = 1 + 4 + (1 + 1 + cs243) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs144, cs244))) :|: cs244 >= 0, cs144 >= 0, z' = 1 + 4 + (1 + 4 + cs244), z = 1 + 5 + (1 + 5 + cs144) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs145, cs245))) :|: cs145 >= 0, z' = 1 + 4 + (1 + 2 + cs245), z = 1 + 5 + (1 + 1 + cs145), cs245 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs146, cs246))) :|: z = 1 + 5 + (1 + 1 + cs146), cs146 >= 0, z' = 1 + 4 + (1 + 5 + cs246), cs246 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs148, cs248))) :|: z = 1 + 5 + (1 + 1 + cs148), cs248 >= 0, z' = 1 + 4 + (1 + 4 + cs248), cs148 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs149, cs249))) :|: cs149 >= 0, z' = 1 + 4 + (1 + 2 + cs249), z = 1 + 5 + (1 + 4 + cs149), cs249 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs150, cs250))) :|: cs250 >= 0, z = 1 + 5 + (1 + 4 + cs150), z' = 1 + 4 + (1 + 5 + cs250), cs150 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs151, cs251))) :|: cs151 >= 0, cs251 >= 0, z' = 1 + 4 + (1 + 1 + cs251), z = 1 + 5 + (1 + 4 + cs151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs153, cs253))) :|: b2 >= 0, cs253 >= 0, cs153 >= 0, z = 1 + 5 + (1 + 2 + cs153), z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs155, cs255))) :|: cs155 >= 0, z' = 1 + 2 + (1 + 2 + cs255), cs255 >= 0, z = 1 + 1 + (1 + 5 + cs155) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs157, cs257))) :|: z' = 1 + 2 + (1 + 1 + cs257), z = 1 + 1 + (1 + 5 + cs157), cs157 >= 0, cs257 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs158, cs258))) :|: z' = 1 + 2 + (1 + 4 + cs258), cs258 >= 0, z = 1 + 1 + (1 + 5 + cs158), cs158 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs159, cs259))) :|: cs159 >= 0, z' = 1 + 2 + (1 + 2 + cs259), cs259 >= 0, z = 1 + 1 + (1 + 1 + cs159) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs16, cs26))) :|: z = 1 + 5 + (1 + 1 + cs16), cs26 >= 0, cs16 >= 0, z' = 1 + 2 + (1 + 4 + cs26) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs160, cs260))) :|: z' = 1 + 2 + (1 + 5 + cs260), cs260 >= 0, z = 1 + 1 + (1 + 1 + cs160), cs160 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs162, cs262))) :|: cs162 >= 0, cs262 >= 0, z' = 1 + 2 + (1 + 4 + cs262), z = 1 + 1 + (1 + 1 + cs162) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs163, cs263))) :|: z = 1 + 1 + (1 + 4 + cs163), cs163 >= 0, cs263 >= 0, z' = 1 + 2 + (1 + 2 + cs263) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs164, cs264))) :|: z = 1 + 1 + (1 + 4 + cs164), cs264 >= 0, z' = 1 + 2 + (1 + 5 + cs264), cs164 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs165, cs265))) :|: z = 1 + 1 + (1 + 4 + cs165), cs165 >= 0, z' = 1 + 2 + (1 + 1 + cs265), cs265 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs167, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z = 1 + 1 + (1 + 2 + cs167), cs167 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs169, cs269))) :|: cs169 >= 0, z = 1 + 1 + (1 + 5 + cs169), cs269 >= 0, z' = 1 + 5 + (1 + 2 + cs269) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs17, cs27))) :|: cs27 >= 0, cs17 >= 0, z = 1 + 5 + (1 + 4 + cs17), z' = 1 + 2 + (1 + 2 + cs27) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs171, cs271))) :|: cs271 >= 0, cs171 >= 0, z = 1 + 1 + (1 + 5 + cs171), z' = 1 + 5 + (1 + 1 + cs271) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs172, cs272))) :|: cs172 >= 0, z' = 1 + 5 + (1 + 4 + cs272), cs272 >= 0, z = 1 + 1 + (1 + 5 + cs172) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs173, cs273))) :|: cs173 >= 0, z' = 1 + 5 + (1 + 2 + cs273), cs273 >= 0, z = 1 + 1 + (1 + 1 + cs173) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs174, cs274))) :|: cs274 >= 0, z = 1 + 1 + (1 + 1 + cs174), cs174 >= 0, z' = 1 + 5 + (1 + 5 + cs274) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs176, cs276))) :|: cs176 >= 0, z = 1 + 1 + (1 + 1 + cs176), z' = 1 + 5 + (1 + 4 + cs276), cs276 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs177, cs277))) :|: cs277 >= 0, z' = 1 + 5 + (1 + 2 + cs277), z = 1 + 1 + (1 + 4 + cs177), cs177 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs178, cs278))) :|: z' = 1 + 5 + (1 + 5 + cs278), cs278 >= 0, z = 1 + 1 + (1 + 4 + cs178), cs178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs179, cs279))) :|: cs279 >= 0, cs179 >= 0, z = 1 + 1 + (1 + 4 + cs179), z' = 1 + 5 + (1 + 1 + cs279) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs18, cs28))) :|: cs18 >= 0, z' = 1 + 2 + (1 + 5 + cs28), z = 1 + 5 + (1 + 4 + cs18), cs28 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs181, cs281))) :|: cs281 >= 0, z = 1 + 1 + (1 + 2 + cs181), z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, cs181 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs19, cs29))) :|: cs19 >= 0, cs29 >= 0, z' = 1 + 2 + (1 + 1 + cs29), z = 1 + 5 + (1 + 4 + cs19) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs197, cs297))) :|: z' = 1 + 4 + (1 + 2 + cs297), z = 1 + 1 + (1 + 5 + cs197), cs297 >= 0, cs197 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs199, cs299))) :|: z = 1 + 1 + (1 + 5 + cs199), cs299 >= 0, z' = 1 + 4 + (1 + 1 + cs299), cs199 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 5 + 0, z' = 1 + 2 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 5 + 0, z' = 1 + 1 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 5 + 0, z' = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 1 + 0, z' = 1 + 2 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 1 + 0, z' = 1 + 5 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 1 + 0, z' = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 4 + 0, z' = 1 + 2 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z' = 1 + 5 + 0, z = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: z = 1 + 4 + 0, z' = 1 + 1 + 0 eqColorList(z, z') -{ 2 }-> and(1, 2) :|: b >= 0, z' = 1 + b + 0, z = 1 + 2 + 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268) eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282) eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138) eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152) eqColorList(z, z') -{ 2 }-> and(1, 1) :|: b >= 0, z' = 1 + b + 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0 eqColorList(z, z') -{ 2 }-> and(1, 1) :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180) eqColorList(z, z') -{ 1 }-> and(1, 0) :|: z = 1 + 5 + cs1, cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0, z' = 1 + 1 + cs2 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: z' = 1 + 4 + cs2, z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0, z = 1 + 1 + cs1 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1, z' = 1 + 5 + cs2 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: z' = 1 + 4 + cs2, cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0, z = 1 + 4 + cs1 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1, z' = 1 + 5 + cs2 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1, z' = 1 + 1 + cs2 eqColorList(z, z') -{ 1 }-> and(1, 0) :|: b >= 0, cs2 >= 0, cs1 >= 0, z' = 1 + b + cs2, z = 1 + 2 + cs1 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(cs, cs, 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, z' = cs, x >= 0, cs >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(color, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), color, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: z = color, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, color >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(color, 2), color, 1 + x + xs, 0) :|: z'' = 0, z = color, xs >= 0, z' = 1 + x + xs, x >= 0, color >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(color, 0), color, 1 + x + xs, colorednodes) :|: z = color, xs >= 0, colorednodes >= 0, z' = 1 + x + xs, x >= 0, z'' = colorednodes, color >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z = color, colorednodes >= 0, z'' = colorednodes, color >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(color, xs, colorednodes) :|: xs >= 0, colorednodes >= 0, z = 1, z1 = colorednodes, x >= 0, z' = color, z'' = 1 + x + xs, color >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, colorednodes >= 0, z1 = colorednodes, z' = color, z'' = adjs, adjs >= 0, color >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 revapp(z, z') -{ 1 }-> rest :|: z' = rest, rest >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + rest) :|: z = 1 + x + xs, xs >= 0, z' = rest, x >= 0, rest >= 0 reverse(z) -{ 1 }-> revapp(xs, 0) :|: xs >= 0, z = xs ---------------------------------------- (13) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, colorednodes)), x, 1 + x2 + xs2, colorednodes), cs, 1 + x + xs, 1 + n + (1 + x2 + xs2), colorednodes, rest) :|: z'' = 1 + n + (1 + x2 + xs2), z2 = rest, xs >= 0, n >= 0, z' = 1 + x + xs, cs >= 0, x2 >= 0, xs2 >= 0, colorednodes >= 0, z1 = colorednodes, x >= 0, z = cs, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, cs, 1 + x + xs, 1 + n + 0, colorednodes, rest) :|: z2 = rest, xs >= 0, n >= 0, colorednodes >= 0, z' = 1 + x + xs, z'' = 1 + n + 0, z1 = colorednodes, x >= 0, z = cs, cs >= 0, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, cs, 1 + x + xs, 1 + n + ns, colorednodes, rest) :|: z2 = rest, xs >= 0, n >= 0, ns >= 0, colorednodes >= 0, z' = 1 + x + xs, z1 = colorednodes, z'' = 1 + n + ns, x >= 0, z = cs, cs >= 0, rest >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z2 = rest, colorednodes >= 0, z1 = colorednodes, z = cs, z'' = node, cs >= 0, rest >= 0, z' = 0, node >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(cs, xs, node, colorednodes, rest) :|: xs >= 0, colorednodes >= 0, z = 1, z' = cs, x >= 0, z2 = colorednodes, z1 = node, z'' = 1 + x + xs, cs >= 0, z3 = rest, rest >= 0, node >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z1 = v3, z3 = v5, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, v5 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + cs + ncs + node + colorednodes + (1 + x + xs) + colorrest(cs, cs, 1 + (1 + ncs + node) + colorednodes, xs) :|: z = 2, xs >= 0, colorednodes >= 0, z' = cs, x >= 0, z2 = colorednodes, z'' = ncs, z1 = node, ncs >= 0, cs >= 0, z3 = 1 + x + xs, node >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, colorednodes)), x, 1 + x1 + xs1, colorednodes), 1 + x + xs, 1 + n + (1 + x1 + xs1), colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, colorednodes >= 0, x >= 0, xs1 >= 0, z'' = colorednodes, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + n + 0, colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, colorednodes >= 0, x >= 0, z' = 1 + n + 0, z'' = colorednodes colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, colorednodes) :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, colorednodes >= 0, x >= 0, z' = 1 + n + ns, z'' = colorednodes colornode(z, z', z'') -{ 1 }-> 3 :|: z' = node, colorednodes >= 0, z'' = colorednodes, z = 0, node >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, node, colorednodes) :|: xs >= 0, colorednodes >= 0, z' = 1 + x + xs, z = 1, z1 = colorednodes, x >= 0, z'' = node, node >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + cs + node :|: z = 2, colorednodes >= 0, z1 = colorednodes, z' = cs, z'' = node, cs >= 0, node >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + y'', 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, z = 1 + y'', cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, y'' >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, node, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z = node, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, node >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', y'), 1 + y', 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z = 1 + y', y' >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z = node, z' = 0, node >= 0 colorof(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = node, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', node >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(node, xs) :|: z' = node, xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, node >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednodes :|: z1 = 0, colorednodes >= 0, z = cs, ncs >= 0, cs >= 0, z'' = colorednodes, z' = ncs colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(cs, ncs, x, colorednodes, 1 + x + xs) :|: xs >= 0, colorednodes >= 0, z1 = 1 + x + xs, x >= 0, z = cs, ncs >= 0, cs >= 0, z'' = colorednodes, z' = ncs colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, b >= 0, z' = b eqColor(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs114, cs214))) :|: cs114 >= 0, cs214 >= 0, z = 1 + 5 + (1 + 5 + cs114), z' = 1 + 5 + (1 + 5 + cs214) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1154, cs2154))) :|: z' = 1 + 4 + (1 + 5 + cs2154), cs1154 >= 0, cs2154 >= 0, z = 1 + 4 + (1 + 5 + cs1154) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1159, cs2159))) :|: z = 1 + 4 + (1 + 1 + cs1159), cs2159 >= 0, cs1159 >= 0, z' = 1 + 4 + (1 + 1 + cs2159) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs1164, cs2164))) :|: z' = 1 + 4 + (1 + 4 + cs2164), cs1164 >= 0, z = 1 + 4 + (1 + 4 + cs1164), cs2164 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs119, cs219))) :|: cs219 >= 0, z = 1 + 5 + (1 + 1 + cs119), cs119 >= 0, z' = 1 + 5 + (1 + 1 + cs219) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs124, cs224))) :|: z = 1 + 5 + (1 + 4 + cs124), cs124 >= 0, cs224 >= 0, z' = 1 + 5 + (1 + 4 + cs224) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs184, cs284))) :|: cs184 >= 0, z = 1 + 1 + (1 + 5 + cs184), cs284 >= 0, z' = 1 + 1 + (1 + 5 + cs284) eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs189, cs289))) :|: z = 1 + 1 + (1 + 1 + cs189), cs289 >= 0, z' = 1 + 1 + (1 + 1 + cs289), cs189 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(cs194, cs294))) :|: z' = 1 + 1 + (1 + 4 + cs294), cs194 >= 0, z = 1 + 1 + (1 + 4 + cs194), cs294 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs113, cs213))) :|: cs113 >= 0, cs213 >= 0, z' = 1 + 5 + (1 + 2 + cs213), z = 1 + 5 + (1 + 5 + cs113) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs115, cs215))) :|: z = 1 + 5 + (1 + 5 + cs115), cs115 >= 0, cs215 >= 0, z' = 1 + 5 + (1 + 1 + cs215) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1153, cs2153))) :|: cs1153 >= 0, cs2153 >= 0, z = 1 + 4 + (1 + 5 + cs1153), z' = 1 + 4 + (1 + 2 + cs2153) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1155, cs2155))) :|: cs2155 >= 0, z = 1 + 4 + (1 + 5 + cs1155), z' = 1 + 4 + (1 + 1 + cs2155), cs1155 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1156, cs2156))) :|: z = 1 + 4 + (1 + 5 + cs1156), cs1156 >= 0, cs2156 >= 0, z' = 1 + 4 + (1 + 4 + cs2156) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1157, cs2157))) :|: z = 1 + 4 + (1 + 1 + cs1157), cs1157 >= 0, cs2157 >= 0, z' = 1 + 4 + (1 + 2 + cs2157) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1158, cs2158))) :|: z = 1 + 4 + (1 + 1 + cs1158), cs2158 >= 0, z' = 1 + 4 + (1 + 5 + cs2158), cs1158 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs116, cs216))) :|: cs216 >= 0, z' = 1 + 5 + (1 + 4 + cs216), z = 1 + 5 + (1 + 5 + cs116), cs116 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1160, cs2160))) :|: cs1160 >= 0, z = 1 + 4 + (1 + 1 + cs1160), z' = 1 + 4 + (1 + 4 + cs2160), cs2160 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1161, cs2161))) :|: z = 1 + 4 + (1 + 4 + cs1161), cs2161 >= 0, cs1161 >= 0, z' = 1 + 4 + (1 + 2 + cs2161) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1162, cs2162))) :|: z = 1 + 4 + (1 + 4 + cs1162), z' = 1 + 4 + (1 + 5 + cs2162), cs2162 >= 0, cs1162 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1163, cs2163))) :|: z = 1 + 4 + (1 + 4 + cs1163), cs2163 >= 0, z' = 1 + 4 + (1 + 1 + cs2163), cs1163 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs1165, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z = 1 + 4 + (1 + 2 + cs1165), cs1165 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs117, cs217))) :|: z' = 1 + 5 + (1 + 2 + cs217), cs117 >= 0, cs217 >= 0, z = 1 + 5 + (1 + 1 + cs117) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs118, cs218))) :|: cs218 >= 0, z = 1 + 5 + (1 + 1 + cs118), cs118 >= 0, z' = 1 + 5 + (1 + 5 + cs218) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs120, cs220))) :|: z = 1 + 5 + (1 + 1 + cs120), z' = 1 + 5 + (1 + 4 + cs220), cs220 >= 0, cs120 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs121, cs221))) :|: z = 1 + 5 + (1 + 4 + cs121), cs121 >= 0, cs221 >= 0, z' = 1 + 5 + (1 + 2 + cs221) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs122, cs222))) :|: z = 1 + 5 + (1 + 4 + cs122), cs222 >= 0, cs122 >= 0, z' = 1 + 5 + (1 + 5 + cs222) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs123, cs223))) :|: z = 1 + 5 + (1 + 4 + cs123), cs123 >= 0, cs223 >= 0, z' = 1 + 5 + (1 + 1 + cs223) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs125, cs225))) :|: z = 1 + 5 + (1 + 2 + cs125), b'' >= 0, cs125 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs183, cs283))) :|: z' = 1 + 1 + (1 + 2 + cs283), cs183 >= 0, z = 1 + 1 + (1 + 5 + cs183), cs283 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs185, cs285))) :|: cs285 >= 0, z' = 1 + 1 + (1 + 1 + cs285), cs185 >= 0, z = 1 + 1 + (1 + 5 + cs185) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs186, cs286))) :|: cs186 >= 0, z' = 1 + 1 + (1 + 4 + cs286), z = 1 + 1 + (1 + 5 + cs186), cs286 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs187, cs287))) :|: z' = 1 + 1 + (1 + 2 + cs287), z = 1 + 1 + (1 + 1 + cs187), cs287 >= 0, cs187 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs188, cs288))) :|: cs188 >= 0, z' = 1 + 1 + (1 + 5 + cs288), cs288 >= 0, z = 1 + 1 + (1 + 1 + cs188) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs190, cs290))) :|: cs290 >= 0, z = 1 + 1 + (1 + 1 + cs190), z' = 1 + 1 + (1 + 4 + cs290), cs190 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs191, cs291))) :|: z = 1 + 1 + (1 + 4 + cs191), cs291 >= 0, cs191 >= 0, z' = 1 + 1 + (1 + 2 + cs291) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs192, cs292))) :|: z = 1 + 1 + (1 + 4 + cs192), cs192 >= 0, z' = 1 + 1 + (1 + 5 + cs292), cs292 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs193, cs293))) :|: cs193 >= 0, z = 1 + 1 + (1 + 4 + cs193), cs293 >= 0, z' = 1 + 1 + (1 + 1 + cs293) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(cs195, cs295))) :|: b5 >= 0, z = 1 + 1 + (1 + 2 + cs195), cs195 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1'', cs2''))) :|: cs1'' >= 0, z' = 1 + 2 + (1 + 5 + cs2''), z = 1 + 5 + (1 + 5 + cs1''), cs2'' >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs110, cs210))) :|: z' = 1 + 2 + (1 + 4 + cs210), cs210 >= 0, z = 1 + 5 + (1 + 4 + cs110), cs110 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1103, cs2103))) :|: cs2103 >= 0, z' = 1 + 4 + (1 + 1 + cs2103), z = 1 + 1 + (1 + 1 + cs1103), cs1103 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1108, cs2108))) :|: cs1108 >= 0, z' = 1 + 4 + (1 + 4 + cs2108), cs2108 >= 0, z = 1 + 1 + (1 + 4 + cs1108) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1112, cs2112))) :|: cs2112 >= 0, z' = 1 + 2 + (1 + 5 + cs2112), z = 1 + 4 + (1 + 5 + cs1112), cs1112 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1117, cs2117))) :|: cs2117 >= 0, cs1117 >= 0, z = 1 + 4 + (1 + 1 + cs1117), z' = 1 + 2 + (1 + 1 + cs2117) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1122, cs2122))) :|: z = 1 + 4 + (1 + 4 + cs1122), cs2122 >= 0, z' = 1 + 2 + (1 + 4 + cs2122), cs1122 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1126, cs2126))) :|: z' = 1 + 5 + (1 + 5 + cs2126), z = 1 + 4 + (1 + 5 + cs1126), cs1126 >= 0, cs2126 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1131, cs2131))) :|: z' = 1 + 5 + (1 + 1 + cs2131), cs2131 >= 0, cs1131 >= 0, z = 1 + 4 + (1 + 1 + cs1131) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1136, cs2136))) :|: cs1136 >= 0, z = 1 + 4 + (1 + 4 + cs1136), z' = 1 + 5 + (1 + 4 + cs2136), cs2136 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1140, cs2140))) :|: cs2140 >= 0, z' = 1 + 1 + (1 + 5 + cs2140), cs1140 >= 0, z = 1 + 4 + (1 + 5 + cs1140) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1145, cs2145))) :|: z = 1 + 4 + (1 + 1 + cs1145), cs1145 >= 0, cs2145 >= 0, z' = 1 + 1 + (1 + 1 + cs2145) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1150, cs2150))) :|: z = 1 + 4 + (1 + 4 + cs1150), z' = 1 + 1 + (1 + 4 + cs2150), cs1150 >= 0, cs2150 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1168, cs2168))) :|: b >= 0, cs1168 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0, z = 1 + 2 + (1 + 5 + cs1168) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1173, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), z = 1 + 2 + (1 + 1 + cs1173), cs2173 >= 0, cs1173 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs1178, cs2178))) :|: z = 1 + 2 + (1 + 4 + cs1178), b >= 0, cs1178 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs128, cs228))) :|: z = 1 + 5 + (1 + 5 + cs128), cs228 >= 0, z' = 1 + 1 + (1 + 5 + cs228), cs128 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs133, cs233))) :|: cs233 >= 0, cs133 >= 0, z' = 1 + 1 + (1 + 1 + cs233), z = 1 + 5 + (1 + 1 + cs133) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs138, cs238))) :|: cs138 >= 0, z = 1 + 5 + (1 + 4 + cs138), z' = 1 + 1 + (1 + 4 + cs238), cs238 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs142, cs242))) :|: z = 1 + 5 + (1 + 5 + cs142), cs242 >= 0, cs142 >= 0, z' = 1 + 4 + (1 + 5 + cs242) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs147, cs247))) :|: z = 1 + 5 + (1 + 1 + cs147), cs247 >= 0, z' = 1 + 4 + (1 + 1 + cs247), cs147 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs15, cs25))) :|: z = 1 + 5 + (1 + 1 + cs15), cs15 >= 0, cs25 >= 0, z' = 1 + 2 + (1 + 1 + cs25) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs152, cs252))) :|: z = 1 + 5 + (1 + 4 + cs152), cs152 >= 0, cs252 >= 0, z' = 1 + 4 + (1 + 4 + cs252) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs156, cs256))) :|: z = 1 + 1 + (1 + 5 + cs156), cs156 >= 0, z' = 1 + 2 + (1 + 5 + cs256), cs256 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs161, cs261))) :|: cs161 >= 0, cs261 >= 0, z = 1 + 1 + (1 + 1 + cs161), z' = 1 + 2 + (1 + 1 + cs261) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs166, cs266))) :|: cs166 >= 0, z' = 1 + 2 + (1 + 4 + cs266), z = 1 + 1 + (1 + 4 + cs166), cs266 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs170, cs270))) :|: cs170 >= 0, z' = 1 + 5 + (1 + 5 + cs270), z = 1 + 1 + (1 + 5 + cs170), cs270 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs175, cs275))) :|: cs275 >= 0, z' = 1 + 5 + (1 + 1 + cs275), cs175 >= 0, z = 1 + 1 + (1 + 1 + cs175) eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs180, cs280))) :|: z = 1 + 1 + (1 + 4 + cs180), cs280 >= 0, z' = 1 + 5 + (1 + 4 + cs280), cs180 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(cs198, cs298))) :|: z = 1 + 1 + (1 + 5 + cs198), z' = 1 + 4 + (1 + 5 + cs298), cs298 >= 0, cs198 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1', cs2'))) :|: z = 1 + 5 + (1 + 5 + cs1'), cs2' >= 0, cs1' >= 0, z' = 1 + 2 + (1 + 2 + cs2') eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs11, cs21))) :|: z' = 1 + 2 + (1 + 1 + cs21), cs11 >= 0, cs21 >= 0, z = 1 + 5 + (1 + 5 + cs11) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1100, cs2100))) :|: cs1100 >= 0, z = 1 + 1 + (1 + 5 + cs1100), cs2100 >= 0, z' = 1 + 4 + (1 + 4 + cs2100) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1101, cs2101))) :|: cs1101 >= 0, cs2101 >= 0, z = 1 + 1 + (1 + 1 + cs1101), z' = 1 + 4 + (1 + 2 + cs2101) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1102, cs2102))) :|: cs2102 >= 0, z' = 1 + 4 + (1 + 5 + cs2102), z = 1 + 1 + (1 + 1 + cs1102), cs1102 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1104, cs2104))) :|: cs1104 >= 0, cs2104 >= 0, z' = 1 + 4 + (1 + 4 + cs2104), z = 1 + 1 + (1 + 1 + cs1104) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1105, cs2105))) :|: cs1105 >= 0, z = 1 + 1 + (1 + 4 + cs1105), z' = 1 + 4 + (1 + 2 + cs2105), cs2105 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1106, cs2106))) :|: z' = 1 + 4 + (1 + 5 + cs2106), cs1106 >= 0, z = 1 + 1 + (1 + 4 + cs1106), cs2106 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1107, cs2107))) :|: cs2107 >= 0, cs1107 >= 0, z = 1 + 1 + (1 + 4 + cs1107), z' = 1 + 4 + (1 + 1 + cs2107) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1109, cs2109))) :|: b6 >= 0, cs1109 >= 0, cs2109 >= 0, z = 1 + 1 + (1 + 2 + cs1109), z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs111, cs211))) :|: b' >= 0, cs211 >= 0, cs111 >= 0, z = 1 + 5 + (1 + 2 + cs111), z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1111, cs2111))) :|: cs1111 >= 0, z = 1 + 4 + (1 + 5 + cs1111), z' = 1 + 2 + (1 + 2 + cs2111), cs2111 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1113, cs2113))) :|: cs2113 >= 0, z' = 1 + 2 + (1 + 1 + cs2113), cs1113 >= 0, z = 1 + 4 + (1 + 5 + cs1113) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1114, cs2114))) :|: z = 1 + 4 + (1 + 5 + cs1114), z' = 1 + 2 + (1 + 4 + cs2114), cs1114 >= 0, cs2114 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1115, cs2115))) :|: cs1115 >= 0, z' = 1 + 2 + (1 + 2 + cs2115), z = 1 + 4 + (1 + 1 + cs1115), cs2115 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1116, cs2116))) :|: cs1116 >= 0, z' = 1 + 2 + (1 + 5 + cs2116), cs2116 >= 0, z = 1 + 4 + (1 + 1 + cs1116) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1118, cs2118))) :|: cs1118 >= 0, cs2118 >= 0, z = 1 + 4 + (1 + 1 + cs1118), z' = 1 + 2 + (1 + 4 + cs2118) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1119, cs2119))) :|: z' = 1 + 2 + (1 + 2 + cs2119), cs1119 >= 0, cs2119 >= 0, z = 1 + 4 + (1 + 4 + cs1119) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1120, cs2120))) :|: z' = 1 + 2 + (1 + 5 + cs2120), cs2120 >= 0, cs1120 >= 0, z = 1 + 4 + (1 + 4 + cs1120) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1121, cs2121))) :|: cs1121 >= 0, z' = 1 + 2 + (1 + 1 + cs2121), z = 1 + 4 + (1 + 4 + cs1121), cs2121 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1123, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, z = 1 + 4 + (1 + 2 + cs1123), b7 >= 0, cs1123 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1125, cs2125))) :|: cs1125 >= 0, z' = 1 + 5 + (1 + 2 + cs2125), z = 1 + 4 + (1 + 5 + cs1125), cs2125 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1127, cs2127))) :|: cs2127 >= 0, z = 1 + 4 + (1 + 5 + cs1127), z' = 1 + 5 + (1 + 1 + cs2127), cs1127 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1128, cs2128))) :|: cs2128 >= 0, cs1128 >= 0, z = 1 + 4 + (1 + 5 + cs1128), z' = 1 + 5 + (1 + 4 + cs2128) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1129, cs2129))) :|: cs1129 >= 0, z = 1 + 4 + (1 + 1 + cs1129), cs2129 >= 0, z' = 1 + 5 + (1 + 2 + cs2129) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1130, cs2130))) :|: cs2130 >= 0, z' = 1 + 5 + (1 + 5 + cs2130), cs1130 >= 0, z = 1 + 4 + (1 + 1 + cs1130) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1132, cs2132))) :|: cs1132 >= 0, z = 1 + 4 + (1 + 1 + cs1132), cs2132 >= 0, z' = 1 + 5 + (1 + 4 + cs2132) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1133, cs2133))) :|: z = 1 + 4 + (1 + 4 + cs1133), cs2133 >= 0, z' = 1 + 5 + (1 + 2 + cs2133), cs1133 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1134, cs2134))) :|: z' = 1 + 5 + (1 + 5 + cs2134), cs2134 >= 0, cs1134 >= 0, z = 1 + 4 + (1 + 4 + cs1134) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1135, cs2135))) :|: cs1135 >= 0, cs2135 >= 0, z = 1 + 4 + (1 + 4 + cs1135), z' = 1 + 5 + (1 + 1 + cs2135) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1137, cs2137))) :|: cs1137 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, z = 1 + 4 + (1 + 2 + cs1137), cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1139, cs2139))) :|: cs2139 >= 0, z' = 1 + 1 + (1 + 2 + cs2139), cs1139 >= 0, z = 1 + 4 + (1 + 5 + cs1139) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1141, cs2141))) :|: cs2141 >= 0, z = 1 + 4 + (1 + 5 + cs1141), z' = 1 + 1 + (1 + 1 + cs2141), cs1141 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1142, cs2142))) :|: z' = 1 + 1 + (1 + 4 + cs2142), cs2142 >= 0, z = 1 + 4 + (1 + 5 + cs1142), cs1142 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1143, cs2143))) :|: z' = 1 + 1 + (1 + 2 + cs2143), z = 1 + 4 + (1 + 1 + cs1143), cs2143 >= 0, cs1143 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1144, cs2144))) :|: cs2144 >= 0, z = 1 + 4 + (1 + 1 + cs1144), cs1144 >= 0, z' = 1 + 1 + (1 + 5 + cs2144) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1146, cs2146))) :|: z' = 1 + 1 + (1 + 4 + cs2146), cs1146 >= 0, z = 1 + 4 + (1 + 1 + cs1146), cs2146 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1147, cs2147))) :|: cs1147 >= 0, z = 1 + 4 + (1 + 4 + cs1147), z' = 1 + 1 + (1 + 2 + cs2147), cs2147 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1148, cs2148))) :|: cs2148 >= 0, z = 1 + 4 + (1 + 4 + cs1148), cs1148 >= 0, z' = 1 + 1 + (1 + 5 + cs2148) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1149, cs2149))) :|: z' = 1 + 1 + (1 + 1 + cs2149), cs2149 >= 0, z = 1 + 4 + (1 + 4 + cs1149), cs1149 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1151, cs2151))) :|: cs2151 >= 0, b9 >= 0, cs1151 >= 0, z = 1 + 4 + (1 + 2 + cs1151), z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1167, cs2167))) :|: b >= 0, cs1167 >= 0, z = 1 + 2 + (1 + 5 + cs1167), cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1169, cs2169))) :|: b >= 0, cs2169 >= 0, z = 1 + 2 + (1 + 5 + cs1169), cs1169 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1170, cs2170))) :|: z = 1 + 2 + (1 + 5 + cs1170), cs1170 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1171, cs2171))) :|: b >= 0, z = 1 + 2 + (1 + 1 + cs1171), cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), cs1171 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1172, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, cs1172 >= 0, z = 1 + 2 + (1 + 1 + cs1172) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1174, cs2174))) :|: b >= 0, cs1174 >= 0, z = 1 + 2 + (1 + 1 + cs1174), cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1175, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), cs1175 >= 0, z = 1 + 2 + (1 + 4 + cs1175), cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1176, cs2176))) :|: b >= 0, cs2176 >= 0, z = 1 + 2 + (1 + 4 + cs1176), cs1176 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1177, cs2177))) :|: b >= 0, z = 1 + 2 + (1 + 4 + cs1177), cs1177 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs1179, cs2179))) :|: b >= 0, z = 1 + 2 + (1 + 2 + cs1179), cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, cs1179 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs12, cs22))) :|: cs22 >= 0, z' = 1 + 2 + (1 + 4 + cs22), z = 1 + 5 + (1 + 5 + cs12), cs12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs127, cs227))) :|: z = 1 + 5 + (1 + 5 + cs127), z' = 1 + 1 + (1 + 2 + cs227), cs127 >= 0, cs227 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs129, cs229))) :|: z = 1 + 5 + (1 + 5 + cs129), z' = 1 + 1 + (1 + 1 + cs229), cs229 >= 0, cs129 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs13, cs23))) :|: z = 1 + 5 + (1 + 1 + cs13), z' = 1 + 2 + (1 + 2 + cs23), cs13 >= 0, cs23 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs130, cs230))) :|: cs130 >= 0, z' = 1 + 1 + (1 + 4 + cs230), cs230 >= 0, z = 1 + 5 + (1 + 5 + cs130) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs131, cs231))) :|: cs231 >= 0, z = 1 + 5 + (1 + 1 + cs131), z' = 1 + 1 + (1 + 2 + cs231), cs131 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs132, cs232))) :|: z' = 1 + 1 + (1 + 5 + cs232), cs232 >= 0, z = 1 + 5 + (1 + 1 + cs132), cs132 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs134, cs234))) :|: cs134 >= 0, cs234 >= 0, z = 1 + 5 + (1 + 1 + cs134), z' = 1 + 1 + (1 + 4 + cs234) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs135, cs235))) :|: cs135 >= 0, z' = 1 + 1 + (1 + 2 + cs235), cs235 >= 0, z = 1 + 5 + (1 + 4 + cs135) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs136, cs236))) :|: z' = 1 + 1 + (1 + 5 + cs236), cs136 >= 0, cs236 >= 0, z = 1 + 5 + (1 + 4 + cs136) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs137, cs237))) :|: cs237 >= 0, z' = 1 + 1 + (1 + 1 + cs237), z = 1 + 5 + (1 + 4 + cs137), cs137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs139, cs239))) :|: b1 >= 0, z = 1 + 5 + (1 + 2 + cs139), cs239 >= 0, cs139 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs14, cs24))) :|: z = 1 + 5 + (1 + 1 + cs14), z' = 1 + 2 + (1 + 5 + cs24), cs24 >= 0, cs14 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs141, cs241))) :|: z' = 1 + 4 + (1 + 2 + cs241), cs141 >= 0, cs241 >= 0, z = 1 + 5 + (1 + 5 + cs141) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs143, cs243))) :|: z = 1 + 5 + (1 + 5 + cs143), cs143 >= 0, cs243 >= 0, z' = 1 + 4 + (1 + 1 + cs243) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs144, cs244))) :|: cs244 >= 0, cs144 >= 0, z' = 1 + 4 + (1 + 4 + cs244), z = 1 + 5 + (1 + 5 + cs144) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs145, cs245))) :|: cs145 >= 0, z' = 1 + 4 + (1 + 2 + cs245), z = 1 + 5 + (1 + 1 + cs145), cs245 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs146, cs246))) :|: z = 1 + 5 + (1 + 1 + cs146), cs146 >= 0, z' = 1 + 4 + (1 + 5 + cs246), cs246 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs148, cs248))) :|: z = 1 + 5 + (1 + 1 + cs148), cs248 >= 0, z' = 1 + 4 + (1 + 4 + cs248), cs148 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs149, cs249))) :|: cs149 >= 0, z' = 1 + 4 + (1 + 2 + cs249), z = 1 + 5 + (1 + 4 + cs149), cs249 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs150, cs250))) :|: cs250 >= 0, z = 1 + 5 + (1 + 4 + cs150), z' = 1 + 4 + (1 + 5 + cs250), cs150 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs151, cs251))) :|: cs151 >= 0, cs251 >= 0, z' = 1 + 4 + (1 + 1 + cs251), z = 1 + 5 + (1 + 4 + cs151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs153, cs253))) :|: b2 >= 0, cs253 >= 0, cs153 >= 0, z = 1 + 5 + (1 + 2 + cs153), z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs155, cs255))) :|: cs155 >= 0, z' = 1 + 2 + (1 + 2 + cs255), cs255 >= 0, z = 1 + 1 + (1 + 5 + cs155) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs157, cs257))) :|: z' = 1 + 2 + (1 + 1 + cs257), z = 1 + 1 + (1 + 5 + cs157), cs157 >= 0, cs257 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs158, cs258))) :|: z' = 1 + 2 + (1 + 4 + cs258), cs258 >= 0, z = 1 + 1 + (1 + 5 + cs158), cs158 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs159, cs259))) :|: cs159 >= 0, z' = 1 + 2 + (1 + 2 + cs259), cs259 >= 0, z = 1 + 1 + (1 + 1 + cs159) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs16, cs26))) :|: z = 1 + 5 + (1 + 1 + cs16), cs26 >= 0, cs16 >= 0, z' = 1 + 2 + (1 + 4 + cs26) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs160, cs260))) :|: z' = 1 + 2 + (1 + 5 + cs260), cs260 >= 0, z = 1 + 1 + (1 + 1 + cs160), cs160 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs162, cs262))) :|: cs162 >= 0, cs262 >= 0, z' = 1 + 2 + (1 + 4 + cs262), z = 1 + 1 + (1 + 1 + cs162) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs163, cs263))) :|: z = 1 + 1 + (1 + 4 + cs163), cs163 >= 0, cs263 >= 0, z' = 1 + 2 + (1 + 2 + cs263) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs164, cs264))) :|: z = 1 + 1 + (1 + 4 + cs164), cs264 >= 0, z' = 1 + 2 + (1 + 5 + cs264), cs164 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs165, cs265))) :|: z = 1 + 1 + (1 + 4 + cs165), cs165 >= 0, z' = 1 + 2 + (1 + 1 + cs265), cs265 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs167, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z = 1 + 1 + (1 + 2 + cs167), cs167 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs169, cs269))) :|: cs169 >= 0, z = 1 + 1 + (1 + 5 + cs169), cs269 >= 0, z' = 1 + 5 + (1 + 2 + cs269) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs17, cs27))) :|: cs27 >= 0, cs17 >= 0, z = 1 + 5 + (1 + 4 + cs17), z' = 1 + 2 + (1 + 2 + cs27) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs171, cs271))) :|: cs271 >= 0, cs171 >= 0, z = 1 + 1 + (1 + 5 + cs171), z' = 1 + 5 + (1 + 1 + cs271) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs172, cs272))) :|: cs172 >= 0, z' = 1 + 5 + (1 + 4 + cs272), cs272 >= 0, z = 1 + 1 + (1 + 5 + cs172) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs173, cs273))) :|: cs173 >= 0, z' = 1 + 5 + (1 + 2 + cs273), cs273 >= 0, z = 1 + 1 + (1 + 1 + cs173) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs174, cs274))) :|: cs274 >= 0, z = 1 + 1 + (1 + 1 + cs174), cs174 >= 0, z' = 1 + 5 + (1 + 5 + cs274) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs176, cs276))) :|: cs176 >= 0, z = 1 + 1 + (1 + 1 + cs176), z' = 1 + 5 + (1 + 4 + cs276), cs276 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs177, cs277))) :|: cs277 >= 0, z' = 1 + 5 + (1 + 2 + cs277), z = 1 + 1 + (1 + 4 + cs177), cs177 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs178, cs278))) :|: z' = 1 + 5 + (1 + 5 + cs278), cs278 >= 0, z = 1 + 1 + (1 + 4 + cs178), cs178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs179, cs279))) :|: cs279 >= 0, cs179 >= 0, z = 1 + 1 + (1 + 4 + cs179), z' = 1 + 5 + (1 + 1 + cs279) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs18, cs28))) :|: cs18 >= 0, z' = 1 + 2 + (1 + 5 + cs28), z = 1 + 5 + (1 + 4 + cs18), cs28 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs181, cs281))) :|: cs281 >= 0, z = 1 + 1 + (1 + 2 + cs181), z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, cs181 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs19, cs29))) :|: cs19 >= 0, cs29 >= 0, z' = 1 + 2 + (1 + 1 + cs29), z = 1 + 5 + (1 + 4 + cs19) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs197, cs297))) :|: z' = 1 + 4 + (1 + 2 + cs297), z = 1 + 1 + (1 + 5 + cs197), cs297 >= 0, cs197 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(cs199, cs299))) :|: z = 1 + 1 + (1 + 5 + cs199), cs299 >= 0, z' = 1 + 4 + (1 + 1 + cs299), cs199 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z' = 1 + b + 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z' = 1 + b + 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z = 1 + 5 + cs1, cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0, z' = 1 + 5 + cs2, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0, z' = 1 + 1 + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' = 1 + 4 + cs2, z = 1 + 5 + cs1, cs2 >= 0, cs1 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0, z = 1 + 1 + cs1, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1, z' = 1 + 5 + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1, z' = 1 + 1 + cs2, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' = 1 + 4 + cs2, cs2 >= 0, cs1 >= 0, z = 1 + 1 + cs1, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, z' = 1 + 2 + cs2, cs1 >= 0, z = 1 + 4 + cs1, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1, z' = 1 + 5 + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1, z' = 1 + 1 + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' = 1 + 4 + cs2, cs2 >= 0, cs1 >= 0, z = 1 + 4 + cs1, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z' = 1 + b + 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z' = 1 + b + 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, cs1 >= 0, z' = 1 + b + cs2, z = 1 + 2 + cs1, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(cs, cs, 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, z' = cs, x >= 0, cs >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(color, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), color, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: z = color, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, color >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(color, 2), color, 1 + x + xs, 0) :|: z'' = 0, z = color, xs >= 0, z' = 1 + x + xs, x >= 0, color >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(color, 0), color, 1 + x + xs, colorednodes) :|: z = color, xs >= 0, colorednodes >= 0, z' = 1 + x + xs, x >= 0, z'' = colorednodes, color >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z = color, colorednodes >= 0, z'' = colorednodes, color >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(color, xs, colorednodes) :|: xs >= 0, colorednodes >= 0, z = 1, z1 = colorednodes, x >= 0, z' = color, z'' = 1 + x + xs, color >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, colorednodes >= 0, z1 = colorednodes, z' = color, z'' = adjs, adjs >= 0, color >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 revapp(z, z') -{ 1 }-> rest :|: z' = rest, rest >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + rest) :|: z = 1 + x + xs, xs >= 0, z' = rest, x >= 0, rest >= 0 reverse(z) -{ 1 }-> revapp(xs, 0) :|: xs >= 0, z = xs ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 reverse(z) -{ 1 }-> revapp(z, 0) :|: z >= 0 ---------------------------------------- (17) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { revapp } { notEmpty } { getColorListFromCN } { and } { getNodeFromCN } { !EQ } { eqColor } { getAdjs } { getNodeName } { reverse } { eqColorList } { colorof, colorof[Ite][True][Ite] } { possible, possible[Ite][True][Ite] } { colornode[Ite][True][Ite], colornode } { colorrest, colorednoderest, colorednoderest[Ite][True][Ite] } { graphcolour } ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 reverse(z) -{ 1 }-> revapp(z, 0) :|: z >= 0 Function symbols to be analyzed: {revapp}, {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} ---------------------------------------- (19) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 reverse(z) -{ 1 }-> revapp(z, 0) :|: z >= 0 Function symbols to be analyzed: {revapp}, {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} ---------------------------------------- (21) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: revapp after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z + z' ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 reverse(z) -{ 1 }-> revapp(z, 0) :|: z >= 0 Function symbols to be analyzed: {revapp}, {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: ?, size: O(n^1) [z + z'] ---------------------------------------- (23) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: revapp after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 reverse(z) -{ 1 }-> revapp(z, 0) :|: z >= 0 Function symbols to be analyzed: {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] ---------------------------------------- (25) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] ---------------------------------------- (27) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: notEmpty after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {notEmpty}, {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: ?, size: O(1) [2] ---------------------------------------- (29) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: notEmpty after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (31) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (33) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getColorListFromCN after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getColorListFromCN}, {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: ?, size: O(n^1) [z] ---------------------------------------- (35) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getColorListFromCN after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (37) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (39) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: and after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {and}, {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: ?, size: O(1) [2] ---------------------------------------- (41) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: and after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (43) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (45) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getNodeFromCN after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeFromCN}, {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: ?, size: O(n^1) [z] ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getNodeFromCN after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (49) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (51) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: !EQ after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {!EQ}, {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: ?, size: O(1) [2] ---------------------------------------- (53) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: !EQ after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](!EQ(x', z - 1), 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](!EQ(name', x), x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (55) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (57) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: eqColor after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {eqColor}, {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: ?, size: O(1) [2] ---------------------------------------- (59) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: eqColor after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, 2), z, 1 + x + xs, 0) :|: z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> possible[Ite][True][Ite](eqColor(z, 0), z, 1 + x + xs, z'') :|: xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (61) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 3 }-> possible[Ite][True][Ite](s3, z, 1 + x + xs, 0) :|: s3 >= 0, s3 <= 2, z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](s4, z, 1 + x + xs, z'') :|: s4 >= 0, s4 <= 2, xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (63) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getAdjs after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 3 }-> possible[Ite][True][Ite](s3, z, 1 + x + xs, 0) :|: s3 >= 0, s3 <= 2, z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](s4, z, 1 + x + xs, z'') :|: s4 >= 0, s4 <= 2, xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getAdjs}, {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] getAdjs: runtime: ?, size: O(n^1) [z] ---------------------------------------- (65) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getAdjs after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 3 }-> possible[Ite][True][Ite](s3, z, 1 + x + xs, 0) :|: s3 >= 0, s3 <= 2, z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](s4, z, 1 + x + xs, z'') :|: s4 >= 0, s4 <= 2, xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] getAdjs: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (67) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 3 }-> possible[Ite][True][Ite](s3, z, 1 + x + xs, 0) :|: s3 >= 0, s3 <= 2, z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](s4, z, 1 + x + xs, z'') :|: s4 >= 0, s4 <= 2, xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] getAdjs: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (69) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getNodeName after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 12))) :|: z' - 12 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 11))) :|: z - 4 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 10))) :|: z - 4 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 7))) :|: z - 12 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 6))) :|: z' - 6 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 5))) :|: z - 12 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 4))) :|: z' - 4 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 12, z' - 10))) :|: z' - 10 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 6))) :|: z' - 6 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 5))) :|: z - 11 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 4))) :|: z' - 4 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 11, z' - 11))) :|: z' - 11 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 9))) :|: z' - 9 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 8))) :|: z - 10 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 6))) :|: z - 10 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 5))) :|: z - 10 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 4))) :|: z' - 4 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 10, z' - 12))) :|: z' - 12 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqColorList(z, z') -{ 2 }-> 2 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, 2 = 2 eqColorList(z, z') -{ 2 }-> 2 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, 2 = 2 eqColorList(z, z') -{ 1 }-> 1 :|: cs1 >= 0, c1 >= 0, z = 1 + c1 + cs1, z' = 0 eqColorList(z, z') -{ 1 }-> 1 :|: z' = 1 + c2 + cs2, c2 >= 0, cs2 >= 0, z = 0 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), 1 = 1 eqColorList(z, z') -{ 2 }-> 1 :|: z' - 1 >= 0, z = 1 + 2 + 0, 2 = 2, 1 = 1 eqColorList(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1' + cs112), cs112 >= 0, z' = 1 + 2 + 0, c1' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs212 >= 0, z = 1 + 5 + 0, z' = 1 + 2 + (1 + c2' + cs212), c2' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + (1 + c1'' + cs126), z' = 1 + 5 + 0, c1'' >= 0, cs126 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c2'' >= 0, z' = 1 + 5 + (1 + c2'' + cs226), z = 1 + 5 + 0, cs226 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c11 >= 0, z = 1 + 5 + (1 + c11 + cs140), z' = 1 + 1 + 0, cs140 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs240 >= 0, z' = 1 + 1 + (1 + c21 + cs240), z = 1 + 5 + 0, c21 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c12 >= 0, cs154 >= 0, z = 1 + 5 + (1 + c12 + cs154), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs254 >= 0, c22 >= 0, z' = 1 + 4 + (1 + c22 + cs254), z = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 5 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 6 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + (1 + c13 + cs168), c13 >= 0, z' = 1 + 2 + 0, cs168 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs268 >= 0, c23 >= 0, z' = 1 + 2 + (1 + c23 + cs268), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs182 >= 0, z' = 1 + 5 + 0, z = 1 + 1 + (1 + c14 + cs182), c14 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, cs282 >= 0, c24 >= 0, z' = 1 + 5 + (1 + c24 + cs282), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 5 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c15 >= 0, z' = 1 + 1 + 0, z = 1 + 1 + (1 + c15 + cs196), cs196 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + (1 + c25 + cs296), c25 >= 0, cs296 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c16 >= 0, cs1110 >= 0, z = 1 + 1 + (1 + c16 + cs1110), z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c26 >= 0, z = 1 + 1 + 0, z' = 1 + 4 + (1 + c26 + cs2110), cs2110 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 1 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c17 + cs1124), cs1124 >= 0, z' = 1 + 2 + 0, c17 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2124 >= 0, z' = 1 + 2 + (1 + c27 + cs2124), z = 1 + 4 + 0, c27 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 3 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c18 + cs1138), z' = 1 + 5 + 0, cs1138 >= 0, c18 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: cs2138 >= 0, c28 >= 0, z = 1 + 4 + 0, z' = 1 + 5 + (1 + c28 + cs2138), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 5 + 0, z = 1 + 4 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 6 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c19 >= 0, z = 1 + 4 + (1 + c19 + cs1152), z' = 1 + 1 + 0, cs1152 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: c29 >= 0, cs2152 >= 0, z = 1 + 4 + 0, z' = 1 + 1 + (1 + c29 + cs2152), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 2 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + (1 + c110 + cs1166), cs1166 >= 0, z' = 1 + 4 + 0, c110 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' = 1 + 4 + (1 + c210 + cs2166), z = 1 + 4 + 0, cs2166 >= 0, c210 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z = 1 + 4 + 0, z' = 1 + 4 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: z' - 5 >= 0, z - 5 >= 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, cs1180 >= 0, z = 1 + 2 + (1 + c111 + cs1180), c111 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: b >= 0, z = 1 + 2 + 0, cs2180 >= 0, c211 >= 0, z' = 1 + b + (1 + c211 + cs2180), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1 eqColorList(z, z') -{ 2 }-> 0 :|: z' - 1 >= 0, z = 1 + 2 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1 eqColorList(z, z') -{ 1 }-> 0 :|: b >= 0, cs2 >= 0, z - 3 >= 0, z' = 1 + b + cs2, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1 getAdjs(z) -{ 1 }-> ns :|: n >= 0, ns >= 0, z = 1 + n + ns getColorListFromCN(z) -{ 1 }-> cl :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeFromCN(z) -{ 1 }-> n :|: n >= 0, cl >= 0, z = 1 + cl + n getNodeName(z) -{ 1 }-> name :|: z = 1 + name + adjs, adjs >= 0, name >= 0 graphcolour(z, z') -{ 1 }-> reverse(colorrest(z', z', 1 + 0 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(0, 0, 1 + 3 + 0, xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 graphcolour(z, z') -{ 2 }-> reverse(colorrest(1 + x3 + xs3, 1 + x3 + xs3, 1 + colornode[Ite][True][Ite](possible(x3, ns', 0), 1 + x3 + xs3, 1 + n' + ns', 0) + 0, xs)) :|: z = 1 + (1 + n' + ns') + xs, xs >= 0, z' = 1 + x3 + xs3, n' >= 0, ns' >= 0, x3 >= 0, xs3 >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 possible(z, z', z'') -{ 3 }-> possible[Ite][True][Ite](s3, z, 1 + x + xs, 0) :|: s3 >= 0, s3 <= 2, z'' = 0, xs >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](s4, z, 1 + x + xs, z'') :|: s4 >= 0, s4 <= 2, xs >= 0, z'' >= 0, z' = 1 + x + xs, x >= 0, z >= 0 possible(z, z', z'') -{ 2 }-> possible[Ite][True][Ite](eqColor(z, colorof[Ite][True][Ite](s1, x, 1 + (1 + cl' + (1 + name' + adjs')) + xs'')), z, 1 + x + xs, 1 + (1 + cl' + (1 + name' + adjs')) + xs'') :|: s1 >= 0, s1 <= 2, xs >= 0, adjs' >= 0, z'' = 1 + (1 + cl' + (1 + name' + adjs')) + xs'', cl' >= 0, z' = 1 + x + xs, x >= 0, xs'' >= 0, name' >= 0, z >= 0 possible(z, z', z'') -{ 1 }-> 2 :|: z'' >= 0, z >= 0, z' = 0 possible(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> possible(z', xs, z1) :|: xs >= 0, z1 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 :|: z = 2, z1 >= 0, z'' >= 0, z' >= 0 possible[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 revapp(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0 revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 reverse(z) -{ 2 + z }-> s' :|: s' >= 0, s' <= z + 0, z >= 0 Function symbols to be analyzed: {getNodeName}, {reverse}, {eqColorList}, {colorof,colorof[Ite][True][Ite]}, {possible,possible[Ite][True][Ite]}, {colornode[Ite][True][Ite],colornode}, {colorrest,colorednoderest,colorednoderest[Ite][True][Ite]}, {graphcolour} Previous analysis results are: revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z'] notEmpty: runtime: O(1) [1], size: O(1) [2] getColorListFromCN: runtime: O(1) [1], size: O(n^1) [z] and: runtime: O(1) [0], size: O(1) [2] getNodeFromCN: runtime: O(1) [1], size: O(n^1) [z] !EQ: runtime: O(1) [0], size: O(1) [2] eqColor: runtime: O(1) [1], size: O(1) [2] getAdjs: runtime: O(1) [1], size: O(n^1) [z] getNodeName: runtime: ?, size: O(n^1) [z] ---------------------------------------- (71) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getNodeName after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (72) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x2, z1)), x, 1 + x2 + xs2, z1), z, 1 + x + xs, 1 + n + (1 + x2 + xs2), z1, z2) :|: z'' = 1 + n + (1 + x2 + xs2), xs >= 0, n >= 0, z' = 1 + x + xs, z >= 0, x2 >= 0, xs2 >= 0, z1 >= 0, x >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 2 }-> colorednoderest[Ite][True][Ite](2, z, 1 + x + xs, 1 + (z'' - 1) + 0, z1, z2) :|: xs >= 0, z'' - 1 >= 0, z1 >= 0, z' = 1 + x + xs, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> colorednoderest[Ite][True][Ite](0, z, 1 + x + xs, 1 + n + ns, z1, z2) :|: xs >= 0, n >= 0, ns >= 0, z1 >= 0, z' = 1 + x + xs, z'' = 1 + n + ns, x >= 0, z >= 0, z2 >= 0 colorednoderest(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z1 >= 0, z >= 0, z2 >= 0, z' = 0, z'' >= 0 colorednoderest(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> colorednoderest(z', xs, z1, z2, z3) :|: xs >= 0, z2 >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0, z3 >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z3 >= 0, z'' >= 0, z1 >= 0 colorednoderest[Ite][True][Ite](z, z', z'', z1, z2, z3) -{ 0 }-> 1 + z' + z'' + z1 + z2 + (1 + x + xs) + colorrest(z', z', 1 + (1 + z'' + z1) + z2, xs) :|: z = 2, xs >= 0, z2 >= 0, x >= 0, z'' >= 0, z' >= 0, z3 = 1 + x + xs, z1 >= 0 colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](possible[Ite][True][Ite](eqColor(x, colorof(x1, z'')), x, 1 + x1 + xs1, z''), 1 + x + xs, 1 + n + (1 + x1 + xs1), z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, x1 >= 0, z'' >= 0, x >= 0, xs1 >= 0, z' = 1 + n + (1 + x1 + xs1) colornode(z, z', z'') -{ 2 }-> colornode[Ite][True][Ite](2, 1 + x + xs, 1 + (z' - 1) + 0, z'') :|: z = 1 + x + xs, xs >= 0, z' - 1 >= 0, z'' >= 0, x >= 0 colornode(z, z', z'') -{ 1 }-> colornode[Ite][True][Ite](0, 1 + x + xs, 1 + n + ns, z'') :|: z = 1 + x + xs, xs >= 0, n >= 0, ns >= 0, z'' >= 0, x >= 0, z' = 1 + n + ns colornode(z, z', z'') -{ 1 }-> 3 :|: z'' >= 0, z = 0, z' >= 0 colornode(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> colornode(xs, z'', z1) :|: xs >= 0, z1 >= 0, z' = 1 + x + xs, z = 1, x >= 0, z'' >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 colornode[Ite][True][Ite](z, z', z'', z1) -{ 0 }-> 1 + z' + z'' :|: z = 2, z1 >= 0, z' >= 0, z'' >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](s'', 1 + (z - 1), 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs) :|: s'' >= 0, s'' <= 2, xs >= 0, cl >= 0, x' >= 0, z - 1 >= 0, adjs >= 0, z' = 1 + (1 + cl + (1 + (1 + x') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](2, 0, 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, adjs >= 0, z = 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 0, 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs) :|: xs >= 0, cl >= 0, x'' >= 0, adjs >= 0, z = 0, z' = 1 + (1 + cl + (1 + (1 + x'') + adjs)) + xs colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](1, 1 + (z - 1), 1 + (1 + cl + (1 + 0 + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + 0 + adjs)) + xs, z - 1 >= 0, adjs >= 0 colorof(z, z') -{ 1 }-> colorof[Ite][True][Ite](0, z, 1 + (1 + cl + (1 + name + adjs)) + xs) :|: xs >= 0, cl >= 0, z' = 1 + (1 + cl + (1 + name + adjs)) + xs, adjs >= 0, z >= 0, name >= 0 colorof(z, z') -{ 1 }-> 2 :|: z' = 0, z >= 0 colorof(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> x :|: z = 2, xs >= 0, n >= 0, x >= 0, xs' >= 0, z'' = 1 + (1 + (1 + x + xs) + n) + xs', z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> colorof(z', xs) :|: xs >= 0, z = 1, x >= 0, z'' = 1 + x + xs, z' >= 0 colorof[Ite][True][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 colorrest(z, z', z'', z1) -{ 1 }-> z'' :|: z1 = 0, z'' >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 1 }-> colorednoderest(z, z', x, z'', 1 + x + xs) :|: xs >= 0, z'' >= 0, z1 = 1 + x + xs, x >= 0, z' >= 0, z >= 0 colorrest(z, z', z'', z1) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z1 >= 0 eqColor(z, z') -{ 1 }-> 2 :|: z = 5, z' = 5 eqColor(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 eqColor(z, z') -{ 1 }-> 2 :|: z' = 4, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z = 5, z' = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z = 1, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 4, z = 1 eqColor(z, z') -{ 1 }-> 1 :|: z' = 2, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 4, z' = 5 eqColor(z, z') -{ 1 }-> 1 :|: z' = 1, z = 4 eqColor(z, z') -{ 1 }-> 1 :|: z = 2, z' >= 0 eqColor(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 7, z' - 7))) :|: z - 7 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 4, z' - 4))) :|: z' - 4 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 12, z' - 12))) :|: z - 12 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 11, z' - 11))) :|: z - 11 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(2, eqColorList(z - 10, z' - 10))) :|: z - 10 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 9, cs225))) :|: b'' >= 0, z - 9 >= 0, cs225 >= 0, z' = 1 + 5 + (1 + b'' + cs225) eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, cs2165))) :|: z' = 1 + 4 + (1 + b10 + cs2165), z - 8 >= 0, b10 >= 0, cs2165 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 12))) :|: z' - 12 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 5, cs295))) :|: b5 >= 0, z - 5 >= 0, z' = 1 + 1 + (1 + b5 + cs295), cs295 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 4, z' - 5))) :|: z' - 5 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 8))) :|: z - 12 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 9))) :|: z - 11 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 8))) :|: z - 11 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 7))) :|: z' - 7 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 12))) :|: z' - 12 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 7))) :|: z' - 7 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(2, and(1, eqColorList(z - 10, z' - 11))) :|: z' - 11 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 9, cs2168))) :|: b >= 0, z - 9 >= 0, z' = 1 + b + (1 + 5 + cs2168), cs2168 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, cs2178))) :|: b >= 0, z - 8 >= 0, z' = 1 + b + (1 + 4 + cs2178), cs2178 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 9))) :|: z - 8 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 7))) :|: z' - 7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 5))) :|: z - 8 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 4))) :|: z' - 4 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 12))) :|: z - 8 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 8, z' - 11))) :|: z' - 11 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 8))) :|: z - 7 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 5))) :|: z' - 5 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 4))) :|: z - 7 >= 0, z' - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 11))) :|: z' - 11 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 7, z' - 10))) :|: z - 7 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 5, cs2173))) :|: b >= 0, z' = 1 + b + (1 + 1 + cs2173), cs2173 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 8))) :|: z' - 8 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 7))) :|: z' - 7 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 4, z' - 5))) :|: z - 4 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 9))) :|: z - 12 >= 0, z' - 9 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 8))) :|: z' - 8 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 12, z' - 11))) :|: z' - 11 >= 0, z - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 9))) :|: z' - 9 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 8))) :|: z' - 8 >= 0, z - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 7))) :|: z - 11 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 12))) :|: z - 11 >= 0, z' - 12 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 11, z' - 10))) :|: z - 11 >= 0, z' - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 8))) :|: z' - 8 >= 0, z - 10 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 7))) :|: z - 10 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(2, eqColorList(z - 10, z' - 11))) :|: z - 10 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs211))) :|: b' >= 0, cs211 >= 0, z - 9 >= 0, z' = 1 + 2 + (1 + b' + cs211) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2167))) :|: b >= 0, z - 9 >= 0, cs2167 >= 0, z' = 1 + b + (1 + 2 + cs2167) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2169))) :|: b >= 0, cs2169 >= 0, z - 9 >= 0, z' = 1 + b + (1 + 1 + cs2169) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs2170))) :|: z - 9 >= 0, b >= 0, cs2170 >= 0, z' = 1 + b + (1 + 4 + cs2170) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs239))) :|: b1 >= 0, cs239 >= 0, z - 9 >= 0, z' = 1 + 1 + (1 + b1 + cs239) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 9, cs253))) :|: b2 >= 0, cs253 >= 0, z - 9 >= 0, z' = 1 + 4 + (1 + b2 + cs253) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2123))) :|: z' = 1 + 2 + (1 + b7 + cs2123), cs2123 >= 0, b7 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2137))) :|: z - 8 >= 0, z' = 1 + 5 + (1 + b8 + cs2137), b8 >= 0, cs2137 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2151))) :|: cs2151 >= 0, b9 >= 0, z - 8 >= 0, z' = 1 + 1 + (1 + b9 + cs2151) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2175))) :|: b >= 0, z' = 1 + b + (1 + 2 + cs2175), z - 8 >= 0, cs2175 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2176))) :|: b >= 0, cs2176 >= 0, z - 8 >= 0, z' = 1 + b + (1 + 5 + cs2176) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, cs2177))) :|: b >= 0, z - 8 >= 0, cs2177 >= 0, z' = 1 + b + (1 + 1 + cs2177) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 9))) :|: z' - 9 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 8))) :|: z' - 8 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 7))) :|: z - 8 >= 0, z' - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 6))) :|: z - 8 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 5))) :|: z' - 5 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 11))) :|: z - 8 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 8, z' - 10))) :|: z' - 10 >= 0, z - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 9))) :|: z' - 9 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 8))) :|: z' - 8 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 7))) :|: z' - 7 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 6))) :|: z - 7 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 5))) :|: z - 7 >= 0, z' - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 12))) :|: z' - 12 >= 0, z - 7 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 7, z' - 11))) :|: z - 7 >= 0, z' - 11 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 6, cs2179))) :|: b >= 0, cs2179 >= 0, z' = 1 + b + (1 + b11 + cs2179), b11 >= 0, z - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2109))) :|: b6 >= 0, z - 5 >= 0, cs2109 >= 0, z' = 1 + 4 + (1 + b6 + cs2109) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2171))) :|: b >= 0, cs2171 >= 0, z' = 1 + b + (1 + 2 + cs2171), z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2172))) :|: z' = 1 + b + (1 + 5 + cs2172), b >= 0, cs2172 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs2174))) :|: b >= 0, z - 5 >= 0, cs2174 >= 0, z' = 1 + b + (1 + 4 + cs2174) eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs267))) :|: z' = 1 + 2 + (1 + b3 + cs267), cs267 >= 0, z - 5 >= 0, b3 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 5, cs281))) :|: cs281 >= 0, z' = 1 + 5 + (1 + b4 + cs281), b4 >= 0, z - 5 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 9))) :|: z' - 9 >= 0, z - 4 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 8))) :|: z - 4 >= 0, z' - 8 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z - 4, z' - 6))) :|: z - 4 >= 0, z' - 6 >= 0 eqColorList(z, z') -{ 2 }-> and(1, and(1, eqColorList(z -