YES(O(1), O(n^2)) 377.57/113.48 YES(O(1), O(n^2)) 377.78/113.58 377.78/113.58 377.78/113.58
377.78/113.58 377.78/113.580 CpxTRS377.78/113.58
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳2 CdtProblem377.78/113.58
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳4 CdtProblem377.78/113.58
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳6 CdtProblem377.78/113.58
↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳8 CdtProblem377.78/113.58
↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳10 CdtProblem377.78/113.58
↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳12 CdtProblem377.78/113.58
↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳14 CdtProblem377.78/113.58
↳15 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳16 CdtProblem377.78/113.58
↳17 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳18 CdtProblem377.78/113.58
↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳20 CdtProblem377.78/113.58
↳21 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳22 CdtProblem377.78/113.58
↳23 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳24 CdtProblem377.78/113.58
↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳26 CdtProblem377.78/113.58
↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳28 CdtProblem377.78/113.58
↳29 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳30 CdtProblem377.78/113.58
↳31 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳32 CdtProblem377.78/113.58
↳33 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳34 CdtProblem377.78/113.58
↳35 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳36 CdtProblem377.78/113.58
↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳38 CdtProblem377.78/113.58
↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳40 CdtProblem377.78/113.58
↳41 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳42 CdtProblem377.78/113.58
↳43 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳44 CdtProblem377.78/113.58
↳45 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳46 CdtProblem377.78/113.58
↳47 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳48 CdtProblem377.78/113.58
↳49 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳50 CdtProblem377.78/113.58
↳51 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳52 CdtProblem377.78/113.58
↳53 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳54 CdtProblem377.78/113.58
↳55 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳56 CdtProblem377.78/113.58
↳57 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳58 CdtProblem377.78/113.58
↳59 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳60 CdtProblem377.78/113.58
↳61 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳62 CdtProblem377.78/113.58
↳63 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳64 CdtProblem377.78/113.58
↳65 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳66 CdtProblem377.78/113.58
↳67 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳68 CdtProblem377.78/113.58
↳69 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳70 CdtProblem377.78/113.58
↳71 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳72 CdtProblem377.78/113.58
↳73 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳74 CdtProblem377.78/113.58
↳75 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳76 CdtProblem377.78/113.58
↳77 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳78 CdtProblem377.78/113.58
↳79 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳80 CdtProblem377.78/113.58
↳81 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳82 CdtProblem377.78/113.58
↳83 CdtNarrowingProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳84 CdtProblem377.78/113.58
↳85 CdtUnreachableProof (⇔)377.78/113.58
↳86 CdtProblem377.78/113.58
↳87 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳88 CdtProblem377.78/113.58
↳89 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳90 CdtProblem377.78/113.58
↳91 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))377.78/113.58
↳92 CdtProblem377.78/113.58
↳93 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳94 CdtProblem377.78/113.58
↳95 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳96 CdtProblem377.78/113.58
↳97 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳98 CdtProblem377.78/113.58
↳99 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳100 CdtProblem377.78/113.58
↳101 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳102 CdtProblem377.78/113.58
↳103 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳104 CdtProblem377.78/113.58
↳105 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳106 CdtProblem377.78/113.58
↳107 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳108 CdtProblem377.78/113.58
↳109 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳110 CdtProblem377.78/113.58
↳111 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳112 CdtProblem377.78/113.58
↳113 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳114 CdtProblem377.78/113.58
↳115 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳116 CdtProblem377.78/113.58
↳117 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))377.78/113.58
↳118 CdtProblem377.78/113.58
↳119 SIsEmptyProof (BOTH BOUNDS(ID, ID))377.78/113.58
↳120 BOUNDS(O(1), O(1))377.78/113.58
active(U11(tt, N)) → mark(N) 377.78/113.58
active(U21(tt, M, N)) → mark(s(plus(N, M))) 377.78/113.58
active(U31(tt)) → mark(0) 377.78/113.58
active(U41(tt, M, N)) → mark(plus(x(N, M), N)) 377.78/113.58
active(and(tt, X)) → mark(X) 377.78/113.58
active(isNat(0)) → mark(tt) 377.78/113.58
active(isNat(plus(V1, V2))) → mark(and(isNat(V1), isNat(V2))) 377.78/113.58
active(isNat(s(V1))) → mark(isNat(V1)) 377.78/113.58
active(isNat(x(V1, V2))) → mark(and(isNat(V1), isNat(V2))) 377.78/113.58
active(plus(N, 0)) → mark(U11(isNat(N), N)) 377.78/113.58
active(plus(N, s(M))) → mark(U21(and(isNat(M), isNat(N)), M, N)) 377.78/113.59
active(x(N, 0)) → mark(U31(isNat(N))) 377.78/113.59
active(x(N, s(M))) → mark(U41(and(isNat(M), isNat(N)), M, N)) 377.78/113.59
active(U11(X1, X2)) → U11(active(X1), X2) 377.78/113.59
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3) 377.78/113.59
active(s(X)) → s(active(X)) 377.78/113.59
active(plus(X1, X2)) → plus(active(X1), X2) 377.78/113.59
active(plus(X1, X2)) → plus(X1, active(X2)) 377.78/113.59
active(U31(X)) → U31(active(X)) 377.78/113.59
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3) 377.78/113.59
active(x(X1, X2)) → x(active(X1), X2) 377.78/113.59
active(x(X1, X2)) → x(X1, active(X2)) 377.78/113.59
active(and(X1, X2)) → and(active(X1), X2) 377.78/113.59
U11(mark(X1), X2) → mark(U11(X1, X2)) 377.78/113.59
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3)) 377.78/113.59
s(mark(X)) → mark(s(X)) 377.78/113.59
plus(mark(X1), X2) → mark(plus(X1, X2)) 377.78/113.59
plus(X1, mark(X2)) → mark(plus(X1, X2)) 377.78/113.59
U31(mark(X)) → mark(U31(X)) 377.78/113.59
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3)) 377.78/113.59
x(mark(X1), X2) → mark(x(X1, X2)) 377.78/113.59
x(X1, mark(X2)) → mark(x(X1, X2)) 377.78/113.59
and(mark(X1), X2) → mark(and(X1, X2)) 377.78/113.59
proper(U11(X1, X2)) → U11(proper(X1), proper(X2)) 377.78/113.59
proper(tt) → ok(tt) 377.78/113.59
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3)) 377.78/113.59
proper(s(X)) → s(proper(X)) 377.78/113.59
proper(plus(X1, X2)) → plus(proper(X1), proper(X2)) 377.78/113.59
proper(U31(X)) → U31(proper(X)) 377.78/113.59
proper(0) → ok(0) 377.78/113.59
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3)) 377.78/113.59
proper(x(X1, X2)) → x(proper(X1), proper(X2)) 377.78/113.59
proper(and(X1, X2)) → and(proper(X1), proper(X2)) 377.78/113.59
proper(isNat(X)) → isNat(proper(X)) 377.78/113.59
U11(ok(X1), ok(X2)) → ok(U11(X1, X2)) 377.78/113.59
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3)) 377.78/113.59
s(ok(X)) → ok(s(X)) 377.78/113.59
plus(ok(X1), ok(X2)) → ok(plus(X1, X2)) 377.78/113.59
U31(ok(X)) → ok(U31(X)) 377.78/113.59
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3)) 377.78/113.59
x(ok(X1), ok(X2)) → ok(x(X1, X2)) 377.78/113.59
and(ok(X1), ok(X2)) → ok(and(X1, X2)) 377.78/113.59
isNat(ok(X)) → ok(isNat(X)) 377.78/113.59
top(mark(X)) → top(proper(X)) 377.78/113.59
top(ok(X)) → top(active(X))
Tuples:
active(U11(tt, z0)) → mark(z0) 377.78/113.59
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 377.78/113.59
active(U31(tt)) → mark(0) 377.78/113.59
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 377.78/113.59
active(and(tt, z0)) → mark(z0) 377.78/113.59
active(isNat(0)) → mark(tt) 377.78/113.59
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 377.78/113.59
active(isNat(s(z0))) → mark(isNat(z0)) 377.78/113.59
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 377.78/113.59
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 377.78/113.59
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 377.78/113.59
active(x(z0, 0)) → mark(U31(isNat(z0))) 377.78/113.59
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 377.78/113.59
active(U11(z0, z1)) → U11(active(z0), z1) 377.78/113.59
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 377.78/113.59
active(s(z0)) → s(active(z0)) 377.78/113.59
active(plus(z0, z1)) → plus(active(z0), z1) 377.78/113.59
active(plus(z0, z1)) → plus(z0, active(z1)) 377.78/113.59
active(U31(z0)) → U31(active(z0)) 377.78/113.59
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 377.78/113.59
active(x(z0, z1)) → x(active(z0), z1) 377.78/113.59
active(x(z0, z1)) → x(z0, active(z1)) 377.78/113.59
active(and(z0, z1)) → and(active(z0), z1) 377.78/113.59
U11(mark(z0), z1) → mark(U11(z0, z1)) 377.78/113.59
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 377.78/113.59
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 377.78/113.59
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 377.78/113.59
s(mark(z0)) → mark(s(z0)) 377.78/113.59
s(ok(z0)) → ok(s(z0)) 377.78/113.59
plus(mark(z0), z1) → mark(plus(z0, z1)) 377.78/113.59
plus(z0, mark(z1)) → mark(plus(z0, z1)) 377.78/113.59
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 377.78/113.59
U31(mark(z0)) → mark(U31(z0)) 377.78/113.59
U31(ok(z0)) → ok(U31(z0)) 377.78/113.59
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 377.78/113.59
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 377.78/113.59
x(mark(z0), z1) → mark(x(z0, z1)) 377.78/113.59
x(z0, mark(z1)) → mark(x(z0, z1)) 377.78/113.59
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 377.78/113.59
and(mark(z0), z1) → mark(and(z0, z1)) 377.78/113.59
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 377.78/113.59
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 377.78/113.59
proper(tt) → ok(tt) 377.78/113.59
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 377.78/113.59
proper(s(z0)) → s(proper(z0)) 377.78/113.59
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 377.78/113.59
proper(U31(z0)) → U31(proper(z0)) 377.78/113.59
proper(0) → ok(0) 377.78/113.59
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 377.78/113.59
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 377.78/113.59
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 377.78/113.59
proper(isNat(z0)) → isNat(proper(z0)) 377.78/113.59
isNat(ok(z0)) → ok(isNat(z0)) 377.78/113.59
top(mark(z0)) → top(proper(z0)) 377.78/113.59
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(U21(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 377.78/113.59
ACTIVE(U41(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 377.78/113.59
ACTIVE(isNat(plus(z0, z1))) → c6(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 377.78/113.59
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 377.78/113.59
ACTIVE(isNat(x(z0, z1))) → c8(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 377.78/113.59
ACTIVE(plus(z0, 0)) → c9(U11'(isNat(z0), z0), ISNAT(z0)) 377.78/113.59
ACTIVE(plus(z0, s(z1))) → c10(U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) 377.78/113.59
ACTIVE(x(z0, 0)) → c11(U31'(isNat(z0)), ISNAT(z0)) 377.78/113.59
ACTIVE(x(z0, s(z1))) → c12(U41'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) 377.78/113.59
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 377.78/113.59
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 377.78/113.59
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 377.78/113.59
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 377.78/113.59
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 377.78/113.59
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 377.78/113.59
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 377.78/113.59
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 377.78/113.59
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 377.78/113.59
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 377.78/113.59
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 377.78/113.59
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 377.78/113.59
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 377.78/113.59
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 377.78/113.59
S(mark(z0)) → c27(S(z0)) 377.78/113.59
S(ok(z0)) → c28(S(z0)) 377.78/113.59
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 377.78/113.59
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 377.78/113.59
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 377.78/113.59
U31'(mark(z0)) → c32(U31'(z0)) 377.78/113.59
U31'(ok(z0)) → c33(U31'(z0)) 377.78/113.59
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 377.78/113.59
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 377.78/113.60
X(mark(z0), z1) → c36(X(z0, z1)) 377.78/113.60
X(z0, mark(z1)) → c37(X(z0, z1)) 377.78/113.60
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 377.78/113.60
AND(mark(z0), z1) → c39(AND(z0, z1)) 377.78/113.60
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 377.78/113.60
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 377.78/113.60
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 377.78/113.60
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 377.78/113.60
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 377.78/113.60
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 377.78/113.60
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 377.78/113.60
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 377.78/113.60
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 377.78/113.60
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 377.78/113.60
ISNAT(ok(z0)) → c52(ISNAT(z0)) 377.78/113.60
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 377.78/113.60
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0))
K tuples:none
ACTIVE(U21(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 377.78/113.60
ACTIVE(U41(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 377.78/113.60
ACTIVE(isNat(plus(z0, z1))) → c6(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 377.78/113.60
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 377.78/113.60
ACTIVE(isNat(x(z0, z1))) → c8(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 377.78/113.60
ACTIVE(plus(z0, 0)) → c9(U11'(isNat(z0), z0), ISNAT(z0)) 377.78/113.60
ACTIVE(plus(z0, s(z1))) → c10(U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) 377.78/113.60
ACTIVE(x(z0, 0)) → c11(U31'(isNat(z0)), ISNAT(z0)) 377.78/113.60
ACTIVE(x(z0, s(z1))) → c12(U41'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) 377.78/113.60
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 377.78/113.60
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 377.78/113.60
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 377.78/113.60
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 377.78/113.60
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 377.78/113.60
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 377.78/113.60
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 377.78/113.60
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 377.78/113.60
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 377.78/113.60
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 377.78/113.60
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 377.78/113.60
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 377.78/113.60
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 377.78/113.60
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.65
S(mark(z0)) → c27(S(z0)) 378.14/113.65
S(ok(z0)) → c28(S(z0)) 378.14/113.65
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.65
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.65
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.65
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.65
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.65
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.65
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.65
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.65
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.65
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.65
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.65
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.65
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.65
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.65
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.65
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c1, c3, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54
Tuples:
active(U11(tt, z0)) → mark(z0) 378.14/113.65
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.14/113.65
active(U31(tt)) → mark(0) 378.14/113.65
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.14/113.65
active(and(tt, z0)) → mark(z0) 378.14/113.65
active(isNat(0)) → mark(tt) 378.14/113.65
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.65
active(isNat(s(z0))) → mark(isNat(z0)) 378.14/113.65
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.65
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.14/113.65
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.65
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.14/113.65
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.65
active(U11(z0, z1)) → U11(active(z0), z1) 378.14/113.65
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.14/113.65
active(s(z0)) → s(active(z0)) 378.14/113.65
active(plus(z0, z1)) → plus(active(z0), z1) 378.14/113.65
active(plus(z0, z1)) → plus(z0, active(z1)) 378.14/113.65
active(U31(z0)) → U31(active(z0)) 378.14/113.65
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.14/113.65
active(x(z0, z1)) → x(active(z0), z1) 378.14/113.65
active(x(z0, z1)) → x(z0, active(z1)) 378.14/113.65
active(and(z0, z1)) → and(active(z0), z1) 378.14/113.65
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.14/113.65
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.14/113.65
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.14/113.65
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.14/113.65
s(mark(z0)) → mark(s(z0)) 378.14/113.65
s(ok(z0)) → ok(s(z0)) 378.14/113.65
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.14/113.65
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.14/113.65
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.14/113.65
U31(mark(z0)) → mark(U31(z0)) 378.14/113.65
U31(ok(z0)) → ok(U31(z0)) 378.14/113.65
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.14/113.65
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.14/113.65
x(mark(z0), z1) → mark(x(z0, z1)) 378.14/113.65
x(z0, mark(z1)) → mark(x(z0, z1)) 378.14/113.65
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.14/113.65
and(mark(z0), z1) → mark(and(z0, z1)) 378.14/113.65
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.14/113.65
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.14/113.65
proper(tt) → ok(tt) 378.14/113.65
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.14/113.65
proper(s(z0)) → s(proper(z0)) 378.14/113.65
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.14/113.65
proper(U31(z0)) → U31(proper(z0)) 378.14/113.65
proper(0) → ok(0) 378.14/113.65
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.14/113.65
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.14/113.65
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.14/113.65
proper(isNat(z0)) → isNat(proper(z0)) 378.14/113.65
isNat(ok(z0)) → ok(isNat(z0)) 378.14/113.65
top(mark(z0)) → top(proper(z0)) 378.14/113.65
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(U21(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 378.14/113.65
ACTIVE(U41(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 378.14/113.65
ACTIVE(isNat(plus(z0, z1))) → c6(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 378.14/113.65
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.65
ACTIVE(isNat(x(z0, z1))) → c8(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 378.14/113.65
ACTIVE(plus(z0, 0)) → c9(U11'(isNat(z0), z0), ISNAT(z0)) 378.14/113.65
ACTIVE(x(z0, 0)) → c11(U31'(isNat(z0)), ISNAT(z0)) 378.14/113.65
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.65
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.65
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.65
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.65
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.65
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.65
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.65
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.65
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.65
S(mark(z0)) → c27(S(z0)) 378.14/113.65
S(ok(z0)) → c28(S(z0)) 378.14/113.65
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.65
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.65
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.65
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.65
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.65
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.65
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.65
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.65
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.65
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.65
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.65
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.65
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.65
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.65
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.65
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1), ISNAT(z0)) 378.14/113.65
ACTIVE(x(z0, s(z1))) → c12(ISNAT(z1), ISNAT(z0))
K tuples:none
ACTIVE(U21(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 378.14/113.65
ACTIVE(U41(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 378.14/113.65
ACTIVE(isNat(plus(z0, z1))) → c6(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 378.14/113.65
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.65
ACTIVE(isNat(x(z0, z1))) → c8(AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) 378.14/113.65
ACTIVE(plus(z0, 0)) → c9(U11'(isNat(z0), z0), ISNAT(z0)) 378.14/113.65
ACTIVE(x(z0, 0)) → c11(U31'(isNat(z0)), ISNAT(z0)) 378.14/113.65
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.65
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.65
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.65
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.65
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.65
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.65
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.65
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.65
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.65
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.65
S(mark(z0)) → c27(S(z0)) 378.14/113.65
S(ok(z0)) → c28(S(z0)) 378.14/113.65
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.65
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.65
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.65
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.65
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.65
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.65
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.65
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.65
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.65
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.65
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.65
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.65
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.65
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.65
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.65
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.65
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.65
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.65
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1), ISNAT(z0)) 378.14/113.65
ACTIVE(x(z0, s(z1))) → c12(ISNAT(z1), ISNAT(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c1, c3, c6, c7, c8, c9, c11, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c10, c12
Tuples:
active(U11(tt, z0)) → mark(z0) 378.14/113.66
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.14/113.66
active(U31(tt)) → mark(0) 378.14/113.66
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.14/113.66
active(and(tt, z0)) → mark(z0) 378.14/113.66
active(isNat(0)) → mark(tt) 378.14/113.66
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.66
active(isNat(s(z0))) → mark(isNat(z0)) 378.14/113.66
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.66
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.14/113.66
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.66
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.14/113.66
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.66
active(U11(z0, z1)) → U11(active(z0), z1) 378.14/113.66
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.14/113.66
active(s(z0)) → s(active(z0)) 378.14/113.66
active(plus(z0, z1)) → plus(active(z0), z1) 378.14/113.66
active(plus(z0, z1)) → plus(z0, active(z1)) 378.14/113.66
active(U31(z0)) → U31(active(z0)) 378.14/113.66
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.14/113.66
active(x(z0, z1)) → x(active(z0), z1) 378.14/113.66
active(x(z0, z1)) → x(z0, active(z1)) 378.14/113.66
active(and(z0, z1)) → and(active(z0), z1) 378.14/113.66
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.14/113.66
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.14/113.66
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.14/113.66
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.14/113.66
s(mark(z0)) → mark(s(z0)) 378.14/113.66
s(ok(z0)) → ok(s(z0)) 378.14/113.66
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.14/113.66
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.14/113.66
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.14/113.66
U31(mark(z0)) → mark(U31(z0)) 378.14/113.66
U31(ok(z0)) → ok(U31(z0)) 378.14/113.66
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.14/113.66
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.14/113.66
x(mark(z0), z1) → mark(x(z0, z1)) 378.14/113.66
x(z0, mark(z1)) → mark(x(z0, z1)) 378.14/113.66
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.14/113.66
and(mark(z0), z1) → mark(and(z0, z1)) 378.14/113.66
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.14/113.66
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.14/113.66
proper(tt) → ok(tt) 378.14/113.66
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.14/113.66
proper(s(z0)) → s(proper(z0)) 378.14/113.66
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.14/113.66
proper(U31(z0)) → U31(proper(z0)) 378.14/113.66
proper(0) → ok(0) 378.14/113.66
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.14/113.66
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.14/113.66
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.14/113.66
proper(isNat(z0)) → isNat(proper(z0)) 378.14/113.66
isNat(ok(z0)) → ok(isNat(z0)) 378.14/113.66
top(mark(z0)) → top(proper(z0)) 378.14/113.66
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.66
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.66
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.66
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.66
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.66
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.66
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.66
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.66
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.66
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.66
S(mark(z0)) → c27(S(z0)) 378.14/113.66
S(ok(z0)) → c28(S(z0)) 378.14/113.66
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.66
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.66
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.66
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.66
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.66
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.66
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.66
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.66
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.66
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.66
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.66
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.66
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.66
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.66
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.66
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.66
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.66
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.66
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.66
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.14/113.66
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.14/113.66
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.14/113.66
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.14/113.66
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.14/113.66
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.66
ACTIVE(U11(z0, z1)) → c13(U11'(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.66
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.66
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.66
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.66
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.66
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.66
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.66
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.66
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.66
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.66
S(mark(z0)) → c27(S(z0)) 378.14/113.66
S(ok(z0)) → c28(S(z0)) 378.14/113.66
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.66
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.66
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.66
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.66
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.66
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.66
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.66
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.66
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.66
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.66
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.66
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.66
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.66
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.66
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.66
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.66
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.66
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.66
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.66
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.66
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.66
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.14/113.66
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.14/113.66
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.14/113.66
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.14/113.66
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.14/113.66
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.66
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.66
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(U11(tt, z0))) 378.14/113.66
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.14/113.66
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.14/113.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.14/113.66
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.14/113.66
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1), ACTIVE(isNat(0))) 378.14/113.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 378.14/113.66
ACTIVE(U11(isNat(s(z0)), x1)) → c13(U11'(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 378.14/113.66
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 378.14/113.67
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.14/113.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.14/113.67
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.14/113.67
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.14/113.67
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.14/113.67
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.14/113.67
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.14/113.67
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.14/113.67
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.14/113.67
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.14/113.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.14/113.67
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.14/113.67
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.14/113.67
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 378.14/113.67
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.14/113.67
active(U31(tt)) → mark(0) 378.14/113.67
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.14/113.67
active(and(tt, z0)) → mark(z0) 378.14/113.67
active(isNat(0)) → mark(tt) 378.14/113.67
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.67
active(isNat(s(z0))) → mark(isNat(z0)) 378.14/113.67
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.14/113.67
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.14/113.67
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.67
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.14/113.67
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.14/113.67
active(U11(z0, z1)) → U11(active(z0), z1) 378.14/113.67
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.14/113.67
active(s(z0)) → s(active(z0)) 378.14/113.67
active(plus(z0, z1)) → plus(active(z0), z1) 378.14/113.67
active(plus(z0, z1)) → plus(z0, active(z1)) 378.14/113.67
active(U31(z0)) → U31(active(z0)) 378.14/113.67
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.14/113.67
active(x(z0, z1)) → x(active(z0), z1) 378.14/113.67
active(x(z0, z1)) → x(z0, active(z1)) 378.14/113.67
active(and(z0, z1)) → and(active(z0), z1) 378.14/113.67
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.14/113.67
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.14/113.67
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.14/113.67
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.14/113.67
s(mark(z0)) → mark(s(z0)) 378.14/113.67
s(ok(z0)) → ok(s(z0)) 378.14/113.67
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.14/113.67
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.14/113.67
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.14/113.67
U31(mark(z0)) → mark(U31(z0)) 378.14/113.67
U31(ok(z0)) → ok(U31(z0)) 378.14/113.67
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.14/113.67
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.14/113.67
x(mark(z0), z1) → mark(x(z0, z1)) 378.14/113.67
x(z0, mark(z1)) → mark(x(z0, z1)) 378.14/113.67
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.14/113.67
and(mark(z0), z1) → mark(and(z0, z1)) 378.14/113.67
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.14/113.67
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.14/113.67
proper(tt) → ok(tt) 378.14/113.67
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.14/113.67
proper(s(z0)) → s(proper(z0)) 378.14/113.67
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.14/113.67
proper(U31(z0)) → U31(proper(z0)) 378.14/113.67
proper(0) → ok(0) 378.14/113.67
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.14/113.67
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.14/113.67
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.14/113.67
proper(isNat(z0)) → isNat(proper(z0)) 378.14/113.67
isNat(ok(z0)) → ok(isNat(z0)) 378.14/113.67
top(mark(z0)) → top(proper(z0)) 378.14/113.67
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.67
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.67
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.67
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.67
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.67
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.67
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.67
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.67
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.67
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.67
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.67
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.67
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.67
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.67
S(mark(z0)) → c27(S(z0)) 378.14/113.67
S(ok(z0)) → c28(S(z0)) 378.14/113.67
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.67
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.67
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.67
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.67
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.67
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.67
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.67
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.67
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.67
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.67
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.67
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.67
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.67
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.67
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.67
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.67
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.67
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.67
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.67
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.67
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.67
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.67
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.67
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.67
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.14/113.67
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.14/113.67
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.14/113.67
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.14/113.67
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.67
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.14/113.67
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.67
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.14/113.67
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.14/113.67
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.14/113.67
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.67
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.67
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.67
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(U11(tt, z0))) 378.14/113.67
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.14/113.67
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.14/113.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.14/113.67
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.14/113.67
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1), ACTIVE(isNat(0))) 378.14/113.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 378.14/113.67
ACTIVE(U11(isNat(s(z0)), x1)) → c13(U11'(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 378.14/113.67
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 378.14/113.67
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.14/113.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.14/113.67
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.14/113.67
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.14/113.67
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.14/113.67
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.14/113.67
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.14/113.67
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.14/113.67
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.14/113.67
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.14/113.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.14/113.67
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.14/113.67
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.14/113.67
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.14/113.67
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.67
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.14/113.67
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.14/113.67
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.14/113.67
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.14/113.67
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.14/113.67
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.14/113.67
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.14/113.67
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.14/113.67
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.14/113.67
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.14/113.67
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.14/113.67
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.14/113.67
S(mark(z0)) → c27(S(z0)) 378.14/113.67
S(ok(z0)) → c28(S(z0)) 378.14/113.67
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.14/113.67
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.14/113.67
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.14/113.67
U31'(mark(z0)) → c32(U31'(z0)) 378.14/113.67
U31'(ok(z0)) → c33(U31'(z0)) 378.14/113.67
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.14/113.67
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.14/113.67
X(mark(z0), z1) → c36(X(z0, z1)) 378.14/113.67
X(z0, mark(z1)) → c37(X(z0, z1)) 378.14/113.67
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.14/113.67
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.14/113.67
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.14/113.67
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.67
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.67
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.14/113.67
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.68
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.14/113.68
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.14/113.68
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.68
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.14/113.68
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.14/113.68
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.14/113.68
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.14/113.68
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.14/113.68
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.14/113.68
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.14/113.68
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.14/113.68
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.14/113.68
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.68
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.14/113.68
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.14/113.68
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.14/113.68
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.14/113.68
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.14/113.68
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.68
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.14/113.68
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.14/113.68
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(U11(tt, z0))) 378.14/113.68
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.14/113.68
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.14/113.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.14/113.68
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.14/113.68
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1), ACTIVE(isNat(0))) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c13(U11'(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 378.58/113.72
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.72
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.72
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.72
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.72
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.72
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.72
active(U31(tt)) → mark(0) 378.58/113.72
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.72
active(and(tt, z0)) → mark(z0) 378.58/113.72
active(isNat(0)) → mark(tt) 378.58/113.72
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.72
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.72
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.72
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.72
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.72
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.72
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.72
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.72
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.72
active(s(z0)) → s(active(z0)) 378.58/113.72
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.72
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.72
active(U31(z0)) → U31(active(z0)) 378.58/113.72
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.72
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.72
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.72
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.72
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.72
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.72
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.72
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.72
s(mark(z0)) → mark(s(z0)) 378.58/113.72
s(ok(z0)) → ok(s(z0)) 378.58/113.72
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.72
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.72
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.72
U31(mark(z0)) → mark(U31(z0)) 378.58/113.72
U31(ok(z0)) → ok(U31(z0)) 378.58/113.72
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.72
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.72
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.72
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.72
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.72
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.72
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.72
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.72
proper(tt) → ok(tt) 378.58/113.72
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.72
proper(s(z0)) → s(proper(z0)) 378.58/113.72
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.72
proper(U31(z0)) → U31(proper(z0)) 378.58/113.72
proper(0) → ok(0) 378.58/113.72
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.72
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.72
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.72
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.72
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.72
top(mark(z0)) → top(proper(z0)) 378.58/113.72
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.72
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.72
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.72
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.72
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.72
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.72
S(mark(z0)) → c27(S(z0)) 378.58/113.72
S(ok(z0)) → c28(S(z0)) 378.58/113.72
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.72
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.72
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.72
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.72
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.72
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.72
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.72
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.72
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.72
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.72
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.72
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.72
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.72
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.72
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.72
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.72
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.72
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c13(U11'(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 378.58/113.72
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.72
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.72
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.72
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.72
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.72
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.72
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.72
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.72
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.72
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.72
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.72
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.72
S(mark(z0)) → c27(S(z0)) 378.58/113.72
S(ok(z0)) → c28(S(z0)) 378.58/113.72
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.72
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.72
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.72
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.72
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.72
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.72
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.72
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.72
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.72
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.72
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.72
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.72
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.72
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.72
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.72
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.72
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.72
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c13(U11'(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c13(U11'(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 378.58/113.72
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.72
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.72
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.72
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.72
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.72
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.72
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.72
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.72
active(U31(tt)) → mark(0) 378.58/113.72
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.72
active(and(tt, z0)) → mark(z0) 378.58/113.72
active(isNat(0)) → mark(tt) 378.58/113.72
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.72
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.72
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.72
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.72
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.72
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.72
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.72
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.72
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.72
active(s(z0)) → s(active(z0)) 378.58/113.72
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.72
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.72
active(U31(z0)) → U31(active(z0)) 378.58/113.72
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.72
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.72
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.72
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.72
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.72
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.72
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.72
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.72
s(mark(z0)) → mark(s(z0)) 378.58/113.72
s(ok(z0)) → ok(s(z0)) 378.58/113.72
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.72
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.72
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.72
U31(mark(z0)) → mark(U31(z0)) 378.58/113.72
U31(ok(z0)) → ok(U31(z0)) 378.58/113.72
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.72
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.72
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.72
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.72
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.72
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.72
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.72
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.72
proper(tt) → ok(tt) 378.58/113.72
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.72
proper(s(z0)) → s(proper(z0)) 378.58/113.72
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.72
proper(U31(z0)) → U31(proper(z0)) 378.58/113.72
proper(0) → ok(0) 378.58/113.72
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.72
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.72
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.72
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.72
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.72
top(mark(z0)) → top(proper(z0)) 378.58/113.72
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.72
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.72
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.72
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.72
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.72
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.72
S(mark(z0)) → c27(S(z0)) 378.58/113.72
S(ok(z0)) → c28(S(z0)) 378.58/113.72
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.72
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.72
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.72
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.72
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.72
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.72
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.72
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.72
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.72
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.72
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.72
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.72
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.72
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.72
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.72
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.72
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.72
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.72
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.72
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.72
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.72
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.72
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.72
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.72
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.72
ACTIVE(U21(z0, z1, z2)) → c14(U21'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.72
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.72
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.72
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.72
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.72
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.72
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.72
S(mark(z0)) → c27(S(z0)) 378.58/113.72
S(ok(z0)) → c28(S(z0)) 378.58/113.72
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.72
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.72
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.72
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.72
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.72
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.72
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.72
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.72
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.72
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.72
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.72
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.72
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.72
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.72
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.72
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.72
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.72
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.72
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.72
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.72
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.72
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.72
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.72
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.72
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.72
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.72
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.72
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.72
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.72
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.72
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.72
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.72
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.72
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.72
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.72
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.72
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.72
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.72
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.72
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 378.58/113.72
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c14(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.58/113.72
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.74
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.74
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.74
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2), ACTIVE(isNat(0))) 378.58/113.74
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.74
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c14(U21'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.58/113.74
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.58/113.74
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.74
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.74
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.74
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.74
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.74
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.74
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.74
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.74
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.74
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.74
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.74
active(U31(tt)) → mark(0) 378.58/113.74
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.74
active(and(tt, z0)) → mark(z0) 378.58/113.74
active(isNat(0)) → mark(tt) 378.58/113.74
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.74
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.74
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.74
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.74
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.74
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.74
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.74
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.74
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.74
active(s(z0)) → s(active(z0)) 378.58/113.74
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.74
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.74
active(U31(z0)) → U31(active(z0)) 378.58/113.74
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.74
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.74
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.74
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.74
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.74
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.74
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.74
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.74
s(mark(z0)) → mark(s(z0)) 378.58/113.74
s(ok(z0)) → ok(s(z0)) 378.58/113.74
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.74
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.74
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.74
U31(mark(z0)) → mark(U31(z0)) 378.58/113.74
U31(ok(z0)) → ok(U31(z0)) 378.58/113.74
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.74
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.74
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.74
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.74
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.74
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.74
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.74
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.74
proper(tt) → ok(tt) 378.58/113.74
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.74
proper(s(z0)) → s(proper(z0)) 378.58/113.74
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.74
proper(U31(z0)) → U31(proper(z0)) 378.58/113.74
proper(0) → ok(0) 378.58/113.74
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.74
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.74
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.74
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.74
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.74
top(mark(z0)) → top(proper(z0)) 378.58/113.74
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.74
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.74
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.74
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.74
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.74
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.74
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.74
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.74
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.74
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.74
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.74
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.74
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.74
S(mark(z0)) → c27(S(z0)) 378.58/113.74
S(ok(z0)) → c28(S(z0)) 378.58/113.74
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.74
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.74
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.74
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.74
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.74
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.74
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.74
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.74
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.74
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.74
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.74
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.74
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.74
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.74
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.74
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.74
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.74
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.74
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.74
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.74
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.74
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.74
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.74
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.74
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.74
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.74
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.74
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.74
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.74
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.74
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.74
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.74
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.74
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.74
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.74
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.74
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.74
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.74
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.74
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.74
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.74
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.74
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.74
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.74
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.74
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.74
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.74
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.74
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.74
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.74
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.74
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.74
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.74
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.74
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.74
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.74
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.74
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.74
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.74
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 378.58/113.74
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c14(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.58/113.74
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.74
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.74
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.74
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2), ACTIVE(isNat(0))) 378.58/113.74
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.74
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c14(U21'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.58/113.74
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.58/113.74
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.74
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.74
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.74
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.74
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.74
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.74
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.74
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.74
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.74
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.74
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.74
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.74
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.74
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.74
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.74
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.74
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.74
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.74
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.74
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.74
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.74
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.74
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.74
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.74
S(mark(z0)) → c27(S(z0)) 378.58/113.74
S(ok(z0)) → c28(S(z0)) 378.58/113.74
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.75
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.75
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.75
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.75
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.75
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.75
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.75
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.75
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.75
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.75
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.75
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.75
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.75
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.75
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.75
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.75
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.75
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.75
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.75
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.75
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.75
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.75
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.75
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.75
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.75
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.75
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.75
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.75
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.75
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.75
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.75
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.75
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.75
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.75
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.75
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.75
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.75
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.75
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.75
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.75
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.75
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.75
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.75
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.75
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.75
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.75
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.75
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.75
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.75
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.75
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.75
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.75
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.75
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.75
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.75
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.75
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.75
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.75
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.75
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.75
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 378.58/113.75
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c14(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.58/113.75
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.75
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.75
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.75
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2), ACTIVE(isNat(0))) 378.58/113.75
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.75
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c14(U21'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.58/113.75
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.58/113.75
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.75
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.75
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.75
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.75
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.78
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.78
active(U31(tt)) → mark(0) 378.58/113.78
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.78
active(and(tt, z0)) → mark(z0) 378.58/113.78
active(isNat(0)) → mark(tt) 378.58/113.78
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.78
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.78
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.78
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.78
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.78
active(s(z0)) → s(active(z0)) 378.58/113.78
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.78
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.78
active(U31(z0)) → U31(active(z0)) 378.58/113.78
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.78
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.78
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.78
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.78
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.78
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.78
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.78
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.78
s(mark(z0)) → mark(s(z0)) 378.58/113.78
s(ok(z0)) → ok(s(z0)) 378.58/113.78
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.78
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.78
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.78
U31(mark(z0)) → mark(U31(z0)) 378.58/113.78
U31(ok(z0)) → ok(U31(z0)) 378.58/113.78
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.78
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.78
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.78
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.78
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.78
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.78
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.78
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.78
proper(tt) → ok(tt) 378.58/113.78
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(s(z0)) → s(proper(z0)) 378.58/113.78
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.78
proper(U31(z0)) → U31(proper(z0)) 378.58/113.78
proper(0) → ok(0) 378.58/113.78
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.78
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.78
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.78
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.78
top(mark(z0)) → top(proper(z0)) 378.58/113.78
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.78
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.78
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.78
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.78
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.78
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.78
S(mark(z0)) → c27(S(z0)) 378.58/113.78
S(ok(z0)) → c28(S(z0)) 378.58/113.78
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.78
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.78
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.78
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.78
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.78
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.78
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.78
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.78
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.78
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.78
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.78
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.78
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.78
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.78
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.78
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.78
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.78
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c14(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c14(U21'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.78
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.78
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.78
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.78
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.78
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.78
S(mark(z0)) → c27(S(z0)) 378.58/113.78
S(ok(z0)) → c28(S(z0)) 378.58/113.78
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.78
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.78
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.78
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.78
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.78
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.78
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.78
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.78
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.78
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.78
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.78
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.78
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.78
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.78
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.78
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.78
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c13(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.78
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c14(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c14(U21'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c14(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.78
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.78
active(U31(tt)) → mark(0) 378.58/113.78
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.78
active(and(tt, z0)) → mark(z0) 378.58/113.78
active(isNat(0)) → mark(tt) 378.58/113.78
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.78
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.78
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.78
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.78
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.78
active(s(z0)) → s(active(z0)) 378.58/113.78
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.78
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.78
active(U31(z0)) → U31(active(z0)) 378.58/113.78
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.78
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.78
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.78
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.78
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.78
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.78
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.78
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.78
s(mark(z0)) → mark(s(z0)) 378.58/113.78
s(ok(z0)) → ok(s(z0)) 378.58/113.78
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.78
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.78
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.78
U31(mark(z0)) → mark(U31(z0)) 378.58/113.78
U31(ok(z0)) → ok(U31(z0)) 378.58/113.78
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.78
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.78
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.78
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.78
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.78
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.78
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.78
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.78
proper(tt) → ok(tt) 378.58/113.78
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(s(z0)) → s(proper(z0)) 378.58/113.78
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.78
proper(U31(z0)) → U31(proper(z0)) 378.58/113.78
proper(0) → ok(0) 378.58/113.78
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.78
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.78
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.78
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.78
top(mark(z0)) → top(proper(z0)) 378.58/113.78
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.78
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.78
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.78
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.78
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.78
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.78
S(mark(z0)) → c27(S(z0)) 378.58/113.78
S(ok(z0)) → c28(S(z0)) 378.58/113.78
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.78
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.78
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.78
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.78
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.78
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.78
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.78
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.78
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.78
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.78
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.78
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.78
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.78
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.78
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.78
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.78
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.78
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.78
ACTIVE(s(z0)) → c15(S(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.78
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.78
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.78
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.78
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.78
S(mark(z0)) → c27(S(z0)) 378.58/113.78
S(ok(z0)) → c28(S(z0)) 378.58/113.78
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.78
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.78
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.78
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.78
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.78
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.78
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.78
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.78
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.78
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.78
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.78
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.78
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.78
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.78
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.78
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.78
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.78
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0)), ACTIVE(U11(tt, z0))) 378.58/113.78
ACTIVE(s(U21(tt, z0, z1))) → c15(S(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(s(isNat(0))) → c15(S(mark(tt)), ACTIVE(isNat(0))) 378.58/113.78
ACTIVE(s(isNat(plus(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(s(isNat(s(z0)))) → c15(S(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(s(isNat(x(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.78
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.78
active(U31(tt)) → mark(0) 378.58/113.78
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.78
active(and(tt, z0)) → mark(z0) 378.58/113.78
active(isNat(0)) → mark(tt) 378.58/113.78
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.78
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.78
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.78
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.78
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.78
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.78
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.78
active(s(z0)) → s(active(z0)) 378.58/113.78
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.78
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.78
active(U31(z0)) → U31(active(z0)) 378.58/113.78
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.78
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.78
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.78
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.78
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.78
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.78
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.78
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.78
s(mark(z0)) → mark(s(z0)) 378.58/113.78
s(ok(z0)) → ok(s(z0)) 378.58/113.78
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.78
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.78
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.78
U31(mark(z0)) → mark(U31(z0)) 378.58/113.78
U31(ok(z0)) → ok(U31(z0)) 378.58/113.78
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.78
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.78
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.78
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.78
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.78
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.78
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.78
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.78
proper(tt) → ok(tt) 378.58/113.78
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(s(z0)) → s(proper(z0)) 378.58/113.78
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.78
proper(U31(z0)) → U31(proper(z0)) 378.58/113.78
proper(0) → ok(0) 378.58/113.78
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.78
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.78
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.78
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.78
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.78
top(mark(z0)) → top(proper(z0)) 378.58/113.78
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.78
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.78
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.78
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.78
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.78
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.78
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.78
S(mark(z0)) → c27(S(z0)) 378.58/113.78
S(ok(z0)) → c28(S(z0)) 378.58/113.78
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.78
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.78
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.78
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.78
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.78
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.78
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.78
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.78
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.78
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.78
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.78
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.78
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.78
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.78
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.78
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.78
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.78
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.78
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.78
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.78
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.78
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.78
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.78
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.78
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.78
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.78
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.78
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.78
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.78
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.78
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.78
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.78
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.78
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.78
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.78
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.78
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.78
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.78
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.78
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.78
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0)), ACTIVE(U11(tt, z0))) 378.58/113.78
ACTIVE(s(U21(tt, z0, z1))) → c15(S(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.78
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.78
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.78
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt)), ACTIVE(isNat(0))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c15(S(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.79
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.79
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.79
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.79
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.79
S(mark(z0)) → c27(S(z0)) 378.58/113.79
S(ok(z0)) → c28(S(z0)) 378.58/113.79
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.79
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.79
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.79
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.79
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.79
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.79
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.79
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.79
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.79
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.79
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.79
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.79
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.79
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.79
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.79
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.79
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.79
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0)), ACTIVE(U11(tt, z0))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c15(S(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt)), ACTIVE(isNat(0))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c15(S(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.79
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.79
active(U31(tt)) → mark(0) 378.58/113.79
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.79
active(and(tt, z0)) → mark(z0) 378.58/113.79
active(isNat(0)) → mark(tt) 378.58/113.79
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.79
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.79
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.79
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.79
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.79
active(s(z0)) → s(active(z0)) 378.58/113.79
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.79
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.79
active(U31(z0)) → U31(active(z0)) 378.58/113.79
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.79
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.79
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.79
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.79
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.79
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.79
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.79
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.79
s(mark(z0)) → mark(s(z0)) 378.58/113.79
s(ok(z0)) → ok(s(z0)) 378.58/113.79
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.79
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.79
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.79
U31(mark(z0)) → mark(U31(z0)) 378.58/113.79
U31(ok(z0)) → ok(U31(z0)) 378.58/113.79
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.79
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.79
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.79
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.79
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.79
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.79
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.79
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.79
proper(tt) → ok(tt) 378.58/113.79
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.79
proper(s(z0)) → s(proper(z0)) 378.58/113.79
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.79
proper(U31(z0)) → U31(proper(z0)) 378.58/113.79
proper(0) → ok(0) 378.58/113.79
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.79
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.79
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.79
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.79
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.79
top(mark(z0)) → top(proper(z0)) 378.58/113.79
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.79
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.79
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.79
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.79
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.79
S(mark(z0)) → c27(S(z0)) 378.58/113.79
S(ok(z0)) → c28(S(z0)) 378.58/113.79
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.79
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.79
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.79
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.79
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.79
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.79
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.79
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.79
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.79
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.79
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.79
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.79
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.79
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.79
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.79
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.79
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.79
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c15(S(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c15(S(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.79
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.79
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.79
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.79
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.79
S(mark(z0)) → c27(S(z0)) 378.58/113.79
S(ok(z0)) → c28(S(z0)) 378.58/113.79
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.79
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.79
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.79
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.79
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.79
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.79
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.79
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.79
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.79
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.79
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.79
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.79
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.79
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.79
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.79
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.79
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.79
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c15(S(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c15(S(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c15(S(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.79
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.79
active(U31(tt)) → mark(0) 378.58/113.79
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.79
active(and(tt, z0)) → mark(z0) 378.58/113.79
active(isNat(0)) → mark(tt) 378.58/113.79
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.79
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.79
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.79
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.79
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.79
active(s(z0)) → s(active(z0)) 378.58/113.79
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.79
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.79
active(U31(z0)) → U31(active(z0)) 378.58/113.79
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.79
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.79
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.79
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.79
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.79
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.79
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.79
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.79
s(mark(z0)) → mark(s(z0)) 378.58/113.79
s(ok(z0)) → ok(s(z0)) 378.58/113.79
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.79
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.79
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.79
U31(mark(z0)) → mark(U31(z0)) 378.58/113.79
U31(ok(z0)) → ok(U31(z0)) 378.58/113.79
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.79
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.79
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.79
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.79
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.79
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.79
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.79
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.79
proper(tt) → ok(tt) 378.58/113.79
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.58/113.79
proper(s(z0)) → s(proper(z0)) 378.58/113.79
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.58/113.79
proper(U31(z0)) → U31(proper(z0)) 378.58/113.79
proper(0) → ok(0) 378.58/113.79
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.58/113.79
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.58/113.79
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.58/113.79
proper(isNat(z0)) → isNat(proper(z0)) 378.58/113.79
isNat(ok(z0)) → ok(isNat(z0)) 378.58/113.79
top(mark(z0)) → top(proper(z0)) 378.58/113.79
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.79
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.79
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.79
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.79
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.79
S(mark(z0)) → c27(S(z0)) 378.58/113.79
S(ok(z0)) → c28(S(z0)) 378.58/113.79
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.79
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.79
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.79
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.79
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.79
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.79
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.79
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.79
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.79
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.79
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.79
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.79
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.79
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.79
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.79
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.79
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.79
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(U31(z0)) → c18(U31'(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.58/113.79
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.58/113.79
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.58/113.79
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.58/113.79
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.58/113.79
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.58/113.79
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.58/113.79
S(mark(z0)) → c27(S(z0)) 378.58/113.79
S(ok(z0)) → c28(S(z0)) 378.58/113.79
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.58/113.79
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.58/113.79
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.58/113.79
U31'(mark(z0)) → c32(U31'(z0)) 378.58/113.79
U31'(ok(z0)) → c33(U31'(z0)) 378.58/113.79
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.58/113.79
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.58/113.79
X(mark(z0), z1) → c36(X(z0, z1)) 378.58/113.79
X(z0, mark(z1)) → c37(X(z0, z1)) 378.58/113.79
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.58/113.79
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.58/113.79
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.58/113.79
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.58/113.79
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.58/113.79
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.58/113.79
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.58/113.79
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.58/113.79
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.58/113.79
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.58/113.79
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.58/113.79
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.58/113.79
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.58/113.79
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.58/113.79
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.58/113.79
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.58/113.79
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.58/113.79
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.58/113.79
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.58/113.79
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.58/113.79
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.58/113.79
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.58/113.79
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.58/113.79
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.58/113.79
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.58/113.79
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.58/113.79
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.58/113.79
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(U11(tt, z0))) 378.58/113.79
ACTIVE(U31(U21(tt, z0, z1))) → c18(U31'(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.58/113.79
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0)), ACTIVE(U31(tt))) 378.58/113.79
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.58/113.79
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.58/113.79
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt)), ACTIVE(isNat(0))) 378.58/113.79
ACTIVE(U31(isNat(plus(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.58/113.79
ACTIVE(U31(isNat(s(z0)))) → c18(U31'(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.58/113.79
ACTIVE(U31(isNat(x(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.58/113.79
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.58/113.79
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.58/113.79
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.58/113.79
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.58/113.79
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.58/113.79
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.58/113.79
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.58/113.79
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.58/113.79
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.58/113.79
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.58/113.79
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.58/113.79
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 378.58/113.79
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.58/113.79
active(U31(tt)) → mark(0) 378.58/113.79
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.58/113.79
active(and(tt, z0)) → mark(z0) 378.58/113.79
active(isNat(0)) → mark(tt) 378.58/113.79
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(isNat(s(z0))) → mark(isNat(z0)) 378.58/113.79
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.58/113.79
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.58/113.79
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.58/113.79
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.58/113.79
active(U11(z0, z1)) → U11(active(z0), z1) 378.58/113.79
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.58/113.79
active(s(z0)) → s(active(z0)) 378.58/113.79
active(plus(z0, z1)) → plus(active(z0), z1) 378.58/113.79
active(plus(z0, z1)) → plus(z0, active(z1)) 378.58/113.79
active(U31(z0)) → U31(active(z0)) 378.58/113.79
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.58/113.79
active(x(z0, z1)) → x(active(z0), z1) 378.58/113.79
active(x(z0, z1)) → x(z0, active(z1)) 378.58/113.79
active(and(z0, z1)) → and(active(z0), z1) 378.58/113.79
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.58/113.79
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.58/113.79
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.58/113.79
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.58/113.79
s(mark(z0)) → mark(s(z0)) 378.58/113.79
s(ok(z0)) → ok(s(z0)) 378.58/113.79
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.58/113.79
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.58/113.79
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.58/113.79
U31(mark(z0)) → mark(U31(z0)) 378.58/113.79
U31(ok(z0)) → ok(U31(z0)) 378.58/113.79
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.58/113.79
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.58/113.79
x(mark(z0), z1) → mark(x(z0, z1)) 378.58/113.79
x(z0, mark(z1)) → mark(x(z0, z1)) 378.58/113.79
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.58/113.79
and(mark(z0), z1) → mark(and(z0, z1)) 378.58/113.79
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.58/113.79
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.58/113.79
proper(tt) → ok(tt) 378.58/113.79
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.89/113.82
proper(s(z0)) → s(proper(z0)) 378.89/113.82
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.89/113.82
proper(U31(z0)) → U31(proper(z0)) 378.89/113.82
proper(0) → ok(0) 378.89/113.82
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.89/113.82
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.89/113.82
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.89/113.82
proper(isNat(z0)) → isNat(proper(z0)) 378.89/113.82
isNat(ok(z0)) → ok(isNat(z0)) 378.89/113.82
top(mark(z0)) → top(proper(z0)) 378.89/113.82
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.82
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.82
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.82
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.82
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.82
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.82
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.82
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.82
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.82
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.82
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.82
S(mark(z0)) → c27(S(z0)) 378.89/113.82
S(ok(z0)) → c28(S(z0)) 378.89/113.82
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.82
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.82
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.82
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.82
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.82
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.82
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.82
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.82
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.82
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.82
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.82
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.82
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.82
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.82
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.82
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.82
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.82
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.82
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.82
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.82
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.82
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.82
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.82
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.82
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.82
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.82
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.82
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.82
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.82
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.82
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.82
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.82
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.82
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.82
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.82
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.82
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.82
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.89/113.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.82
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.82
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.82
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.82
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.82
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.82
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.82
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.82
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.82
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.82
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.82
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.82
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.82
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.82
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.82
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.82
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.82
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.82
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.89/113.82
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.82
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.82
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.82
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.82
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.82
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.82
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.82
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.82
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.82
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.82
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.82
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.82
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.82
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.82
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.82
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.82
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.82
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.82
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.82
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.82
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.82
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.82
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.82
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.82
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.89/113.82
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.82
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.82
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.82
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.82
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.82
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.82
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.82
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.82
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.82
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.82
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.82
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.82
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.82
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.82
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.82
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.82
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.82
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.82
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.82
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.82
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.82
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.82
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(U11(tt, z0))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c18(U31'(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0)), ACTIVE(U31(tt))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt)), ACTIVE(isNat(0))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c18(U31'(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.84
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.84
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.84
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.84
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.84
S(mark(z0)) → c27(S(z0)) 378.89/113.84
S(ok(z0)) → c28(S(z0)) 378.89/113.84
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.84
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.84
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.84
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.84
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.84
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.84
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.84
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.84
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.84
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.84
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.84
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.84
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.84
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.84
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.84
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.84
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1), ACTIVE(U31(tt))) 378.89/113.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.84
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.89/113.84
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(s(U31(tt))) → c15(S(mark(0)), ACTIVE(U31(tt))) 378.89/113.84
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.84
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(U11(tt, z0))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c18(U31'(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0)), ACTIVE(U31(tt))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt)), ACTIVE(isNat(0))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c18(U31'(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18
Tuples:
active(U11(tt, z0)) → mark(z0) 378.89/113.84
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.89/113.84
active(U31(tt)) → mark(0) 378.89/113.84
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.89/113.84
active(and(tt, z0)) → mark(z0) 378.89/113.84
active(isNat(0)) → mark(tt) 378.89/113.84
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.84
active(isNat(s(z0))) → mark(isNat(z0)) 378.89/113.84
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.84
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.89/113.84
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.84
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.89/113.84
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.84
active(U11(z0, z1)) → U11(active(z0), z1) 378.89/113.84
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.89/113.84
active(s(z0)) → s(active(z0)) 378.89/113.84
active(plus(z0, z1)) → plus(active(z0), z1) 378.89/113.84
active(plus(z0, z1)) → plus(z0, active(z1)) 378.89/113.84
active(U31(z0)) → U31(active(z0)) 378.89/113.84
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.89/113.84
active(x(z0, z1)) → x(active(z0), z1) 378.89/113.84
active(x(z0, z1)) → x(z0, active(z1)) 378.89/113.84
active(and(z0, z1)) → and(active(z0), z1) 378.89/113.84
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.89/113.84
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.89/113.84
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.89/113.84
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.89/113.84
s(mark(z0)) → mark(s(z0)) 378.89/113.84
s(ok(z0)) → ok(s(z0)) 378.89/113.84
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.89/113.84
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.89/113.84
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.89/113.84
U31(mark(z0)) → mark(U31(z0)) 378.89/113.84
U31(ok(z0)) → ok(U31(z0)) 378.89/113.84
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.89/113.84
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.89/113.84
x(mark(z0), z1) → mark(x(z0, z1)) 378.89/113.84
x(z0, mark(z1)) → mark(x(z0, z1)) 378.89/113.84
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.89/113.84
and(mark(z0), z1) → mark(and(z0, z1)) 378.89/113.84
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.89/113.84
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.89/113.84
proper(tt) → ok(tt) 378.89/113.84
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.89/113.84
proper(s(z0)) → s(proper(z0)) 378.89/113.84
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.89/113.84
proper(U31(z0)) → U31(proper(z0)) 378.89/113.84
proper(0) → ok(0) 378.89/113.84
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.89/113.84
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.89/113.84
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.89/113.84
proper(isNat(z0)) → isNat(proper(z0)) 378.89/113.84
isNat(ok(z0)) → ok(isNat(z0)) 378.89/113.84
top(mark(z0)) → top(proper(z0)) 378.89/113.84
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.84
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.84
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.84
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.84
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.84
S(mark(z0)) → c27(S(z0)) 378.89/113.84
S(ok(z0)) → c28(S(z0)) 378.89/113.84
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.84
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.84
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.84
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.84
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.84
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.84
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.84
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.84
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.84
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.84
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.84
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.84
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.84
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.84
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.84
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.84
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.84
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.84
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c18(U31'(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c18(U31'(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 378.89/113.84
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 378.89/113.84
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.84
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.84
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.84
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.84
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.84
S(mark(z0)) → c27(S(z0)) 378.89/113.84
S(ok(z0)) → c28(S(z0)) 378.89/113.84
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.84
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.84
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.84
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.84
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.84
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.84
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.84
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.84
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.84
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.84
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.84
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.84
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.84
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.84
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.84
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.84
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.84
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.84
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c18(U31'(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c18(U31'(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c18(U31'(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 378.89/113.84
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 378.89/113.84
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18
Tuples:
active(U11(tt, z0)) → mark(z0) 378.89/113.84
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.89/113.84
active(U31(tt)) → mark(0) 378.89/113.84
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.89/113.84
active(and(tt, z0)) → mark(z0) 378.89/113.84
active(isNat(0)) → mark(tt) 378.89/113.84
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.84
active(isNat(s(z0))) → mark(isNat(z0)) 378.89/113.84
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.84
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.89/113.84
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.84
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.89/113.84
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.84
active(U11(z0, z1)) → U11(active(z0), z1) 378.89/113.84
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.89/113.84
active(s(z0)) → s(active(z0)) 378.89/113.84
active(plus(z0, z1)) → plus(active(z0), z1) 378.89/113.84
active(plus(z0, z1)) → plus(z0, active(z1)) 378.89/113.84
active(U31(z0)) → U31(active(z0)) 378.89/113.84
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.89/113.84
active(x(z0, z1)) → x(active(z0), z1) 378.89/113.84
active(x(z0, z1)) → x(z0, active(z1)) 378.89/113.84
active(and(z0, z1)) → and(active(z0), z1) 378.89/113.84
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.89/113.84
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.89/113.84
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.89/113.84
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.89/113.84
s(mark(z0)) → mark(s(z0)) 378.89/113.84
s(ok(z0)) → ok(s(z0)) 378.89/113.84
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.89/113.84
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.89/113.84
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.89/113.84
U31(mark(z0)) → mark(U31(z0)) 378.89/113.84
U31(ok(z0)) → ok(U31(z0)) 378.89/113.84
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.89/113.84
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.89/113.84
x(mark(z0), z1) → mark(x(z0, z1)) 378.89/113.84
x(z0, mark(z1)) → mark(x(z0, z1)) 378.89/113.84
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.89/113.84
and(mark(z0), z1) → mark(and(z0, z1)) 378.89/113.84
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.89/113.84
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.89/113.84
proper(tt) → ok(tt) 378.89/113.84
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.89/113.84
proper(s(z0)) → s(proper(z0)) 378.89/113.84
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.89/113.84
proper(U31(z0)) → U31(proper(z0)) 378.89/113.84
proper(0) → ok(0) 378.89/113.84
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.89/113.84
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.89/113.84
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.89/113.84
proper(isNat(z0)) → isNat(proper(z0)) 378.89/113.84
isNat(ok(z0)) → ok(isNat(z0)) 378.89/113.84
top(mark(z0)) → top(proper(z0)) 378.89/113.84
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.84
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.84
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.84
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.84
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.84
S(mark(z0)) → c27(S(z0)) 378.89/113.84
S(ok(z0)) → c28(S(z0)) 378.89/113.84
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.84
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.84
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.84
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.84
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.84
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.84
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.84
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.84
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.84
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.84
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.84
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.84
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.84
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.84
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.84
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.84
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.84
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.84
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 378.89/113.84
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 378.89/113.84
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(U41(z0, z1, z2)) → c19(U41'(active(z0), z1, z2), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.84
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.84
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.84
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.84
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.84
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.84
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.84
S(mark(z0)) → c27(S(z0)) 378.89/113.84
S(ok(z0)) → c28(S(z0)) 378.89/113.84
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.84
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.84
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.84
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.84
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.84
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.84
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.84
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.84
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.84
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.84
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.84
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.84
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.84
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.84
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.84
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.84
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.84
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.84
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.84
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.84
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.84
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.84
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.84
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.84
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.84
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.84
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.84
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.84
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.84
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.84
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.84
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.84
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.84
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.84
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.84
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.84
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.84
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.84
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.84
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.84
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.84
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 378.89/113.84
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 378.89/113.84
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 378.89/113.84
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 378.89/113.84
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 378.89/113.84
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 378.89/113.84
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 378.89/113.84
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 378.89/113.84
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 378.89/113.84
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c19(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 378.89/113.90
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2), ACTIVE(U31(tt))) 378.89/113.90
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c19(U41'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.90
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.90
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 378.89/113.90
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 378.89/113.90
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c19(U41'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 378.89/113.90
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 378.89/113.90
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.90
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.90
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.90
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.90
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.90
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.90
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.90
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.90
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.90
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 378.89/113.90
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 378.89/113.90
active(U31(tt)) → mark(0) 378.89/113.90
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 378.89/113.90
active(and(tt, z0)) → mark(z0) 378.89/113.90
active(isNat(0)) → mark(tt) 378.89/113.90
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.90
active(isNat(s(z0))) → mark(isNat(z0)) 378.89/113.90
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 378.89/113.90
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 378.89/113.90
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.90
active(x(z0, 0)) → mark(U31(isNat(z0))) 378.89/113.90
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 378.89/113.90
active(U11(z0, z1)) → U11(active(z0), z1) 378.89/113.90
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 378.89/113.90
active(s(z0)) → s(active(z0)) 378.89/113.90
active(plus(z0, z1)) → plus(active(z0), z1) 378.89/113.90
active(plus(z0, z1)) → plus(z0, active(z1)) 378.89/113.90
active(U31(z0)) → U31(active(z0)) 378.89/113.90
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 378.89/113.90
active(x(z0, z1)) → x(active(z0), z1) 378.89/113.90
active(x(z0, z1)) → x(z0, active(z1)) 378.89/113.90
active(and(z0, z1)) → and(active(z0), z1) 378.89/113.90
U11(mark(z0), z1) → mark(U11(z0, z1)) 378.89/113.90
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 378.89/113.90
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 378.89/113.90
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 378.89/113.90
s(mark(z0)) → mark(s(z0)) 378.89/113.90
s(ok(z0)) → ok(s(z0)) 378.89/113.90
plus(mark(z0), z1) → mark(plus(z0, z1)) 378.89/113.90
plus(z0, mark(z1)) → mark(plus(z0, z1)) 378.89/113.90
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 378.89/113.90
U31(mark(z0)) → mark(U31(z0)) 378.89/113.90
U31(ok(z0)) → ok(U31(z0)) 378.89/113.90
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 378.89/113.90
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 378.89/113.90
x(mark(z0), z1) → mark(x(z0, z1)) 378.89/113.90
x(z0, mark(z1)) → mark(x(z0, z1)) 378.89/113.90
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 378.89/113.90
and(mark(z0), z1) → mark(and(z0, z1)) 378.89/113.90
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 378.89/113.90
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 378.89/113.90
proper(tt) → ok(tt) 378.89/113.90
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 378.89/113.90
proper(s(z0)) → s(proper(z0)) 378.89/113.90
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 378.89/113.90
proper(U31(z0)) → U31(proper(z0)) 378.89/113.90
proper(0) → ok(0) 378.89/113.90
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 378.89/113.90
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 378.89/113.90
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 378.89/113.90
proper(isNat(z0)) → isNat(proper(z0)) 378.89/113.90
isNat(ok(z0)) → ok(isNat(z0)) 378.89/113.90
top(mark(z0)) → top(proper(z0)) 378.89/113.90
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 378.89/113.90
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 378.89/113.90
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 378.89/113.90
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 378.89/113.90
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 378.89/113.90
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 378.89/113.90
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 378.89/113.90
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 378.89/113.90
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 378.89/113.90
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 378.89/113.90
S(mark(z0)) → c27(S(z0)) 378.89/113.90
S(ok(z0)) → c28(S(z0)) 378.89/113.90
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 378.89/113.90
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 378.89/113.90
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 378.89/113.90
U31'(mark(z0)) → c32(U31'(z0)) 378.89/113.90
U31'(ok(z0)) → c33(U31'(z0)) 378.89/113.90
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 378.89/113.90
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 378.89/113.90
X(mark(z0), z1) → c36(X(z0, z1)) 378.89/113.90
X(z0, mark(z1)) → c37(X(z0, z1)) 378.89/113.90
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 378.89/113.90
AND(mark(z0), z1) → c39(AND(z0, z1)) 378.89/113.90
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 378.89/113.90
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.90
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.90
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 378.89/113.90
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.90
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 378.89/113.90
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 378.89/113.90
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.90
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 378.89/113.90
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 378.89/113.90
ISNAT(ok(z0)) → c52(ISNAT(z0)) 378.89/113.90
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 378.89/113.90
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 378.89/113.90
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 378.89/113.90
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 378.89/113.90
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 378.89/113.90
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 378.89/113.90
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.90
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 378.89/113.90
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 378.89/113.90
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 378.89/113.90
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 378.89/113.90
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 378.89/113.90
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.90
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 378.89/113.90
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 378.89/113.90
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 378.89/113.90
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 378.89/113.90
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 378.89/113.90
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 378.89/113.90
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 378.89/113.90
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 378.89/113.90
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 378.89/113.90
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 378.89/113.90
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 378.89/113.90
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 378.89/113.90
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 378.89/113.90
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 378.89/113.90
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 378.89/113.90
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 378.89/113.90
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.90
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.90
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 378.89/113.90
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 378.89/113.90
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 378.89/113.90
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 378.89/113.90
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 378.89/113.90
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 378.89/113.90
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 378.89/113.90
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 378.89/113.90
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 378.89/113.90
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 378.89/113.90
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 378.89/113.90
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 378.89/113.90
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 378.89/113.90
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 378.89/113.90
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 378.89/113.90
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 378.89/113.90
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 378.89/113.90
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 378.89/113.90
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 378.89/113.90
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.90
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 378.89/113.90
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 378.89/113.90
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.90
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.90
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 378.89/113.90
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 378.89/113.90
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 378.89/113.90
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 378.89/113.90
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.90
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.90
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.90
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.90
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.90
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.90
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.90
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.90
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 378.89/113.90
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.90
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.90
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 378.89/113.90
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 378.89/113.90
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 378.89/113.90
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 378.89/113.90
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 378.89/113.90
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.90
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 378.89/113.90
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 378.89/113.90
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 378.89/113.90
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 378.89/113.90
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 378.89/113.90
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 378.89/113.90
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 378.89/113.90
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 378.89/113.90
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 378.89/113.90
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 378.89/113.90
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 378.89/113.90
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 378.89/113.90
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 378.89/113.90
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 378.89/113.90
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 378.89/113.90
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 378.89/113.90
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 378.89/113.90
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 378.89/113.90
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.90
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.90
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.90
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.90
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.90
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.90
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.90
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.90
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.90
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.90
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.90
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.90
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.90
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 379.27/113.90
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c19(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2), ACTIVE(U31(tt))) 379.27/113.90
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c19(U41'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.90
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.90
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 379.27/113.90
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c19(U41'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 379.27/113.90
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 379.27/113.90
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.90
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.90
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.90
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.90
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.90
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.90
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.90
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.90
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.90
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.90
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.90
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.90
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.90
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.90
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 379.27/113.90
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.90
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.90
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.90
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.90
S(mark(z0)) → c27(S(z0)) 379.27/113.90
S(ok(z0)) → c28(S(z0)) 379.27/113.90
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.90
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.90
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.90
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.90
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.90
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.90
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.90
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.90
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.90
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.90
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.90
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.90
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.90
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.90
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.90
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.90
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.90
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.90
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.90
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.90
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.90
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.90
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.90
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.90
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.90
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.90
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.90
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.90
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.90
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.90
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.90
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.90
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.90
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.90
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.90
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.90
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.90
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.27/113.90
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.90
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.90
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.90
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.90
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.90
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.90
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.90
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.90
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.90
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.90
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.90
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.90
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.90
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.90
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.90
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.90
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.90
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.90
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.90
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.90
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.90
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.90
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.90
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.90
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.90
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.90
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.90
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.90
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.90
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.90
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.90
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.90
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.90
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.90
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.90
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.90
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.90
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.90
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.90
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.90
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.90
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.90
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.90
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.90
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.90
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.90
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.90
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.90
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.90
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.90
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.90
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.90
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.90
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.90
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.90
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.90
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.90
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.90
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.90
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.90
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.90
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.90
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.90
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.90
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.90
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.90
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.90
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.90
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.90
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.90
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.90
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.90
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.90
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.90
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.90
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.90
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.90
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.90
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.90
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.90
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.90
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.90
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.90
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.91
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(U11(tt, z0))) 379.27/113.91
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c19(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2), ACTIVE(U31(tt))) 379.27/113.91
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c19(U41'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 379.27/113.91
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c19(U41'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19
Tuples:
active(U11(tt, z0)) → mark(z0) 379.27/113.91
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.27/113.91
active(U31(tt)) → mark(0) 379.27/113.91
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.27/113.91
active(and(tt, z0)) → mark(z0) 379.27/113.91
active(isNat(0)) → mark(tt) 379.27/113.91
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.91
active(isNat(s(z0))) → mark(isNat(z0)) 379.27/113.91
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.91
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.27/113.91
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.91
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.27/113.91
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.91
active(U11(z0, z1)) → U11(active(z0), z1) 379.27/113.91
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.27/113.91
active(s(z0)) → s(active(z0)) 379.27/113.91
active(plus(z0, z1)) → plus(active(z0), z1) 379.27/113.91
active(plus(z0, z1)) → plus(z0, active(z1)) 379.27/113.91
active(U31(z0)) → U31(active(z0)) 379.27/113.91
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.27/113.91
active(x(z0, z1)) → x(active(z0), z1) 379.27/113.91
active(x(z0, z1)) → x(z0, active(z1)) 379.27/113.91
active(and(z0, z1)) → and(active(z0), z1) 379.27/113.91
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.27/113.91
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.27/113.91
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.27/113.91
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.27/113.91
s(mark(z0)) → mark(s(z0)) 379.27/113.91
s(ok(z0)) → ok(s(z0)) 379.27/113.91
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.27/113.91
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.27/113.91
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.27/113.91
U31(mark(z0)) → mark(U31(z0)) 379.27/113.91
U31(ok(z0)) → ok(U31(z0)) 379.27/113.91
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.27/113.91
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.27/113.91
x(mark(z0), z1) → mark(x(z0, z1)) 379.27/113.91
x(z0, mark(z1)) → mark(x(z0, z1)) 379.27/113.91
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.27/113.91
and(mark(z0), z1) → mark(and(z0, z1)) 379.27/113.91
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.27/113.91
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.27/113.91
proper(tt) → ok(tt) 379.27/113.91
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.27/113.91
proper(s(z0)) → s(proper(z0)) 379.27/113.91
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.27/113.91
proper(U31(z0)) → U31(proper(z0)) 379.27/113.91
proper(0) → ok(0) 379.27/113.91
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.27/113.91
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.27/113.91
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.27/113.91
proper(isNat(z0)) → isNat(proper(z0)) 379.27/113.91
isNat(ok(z0)) → ok(isNat(z0)) 379.27/113.91
top(mark(z0)) → top(proper(z0)) 379.27/113.91
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 379.27/113.91
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.91
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.91
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.91
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.91
S(mark(z0)) → c27(S(z0)) 379.27/113.91
S(ok(z0)) → c28(S(z0)) 379.27/113.91
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.91
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.91
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.91
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.91
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.91
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.91
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.91
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.91
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.91
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.91
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.91
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.91
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.91
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.91
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.91
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.91
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.91
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.91
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.91
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.91
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.91
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.91
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.91
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.91
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.91
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.91
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.91
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.91
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.91
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c19(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c19(U41'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c19(U41'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.91
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.91
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 379.27/113.91
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.91
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.91
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.91
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.91
S(mark(z0)) → c27(S(z0)) 379.27/113.91
S(ok(z0)) → c28(S(z0)) 379.27/113.91
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.91
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.91
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.91
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.91
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.91
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.91
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.91
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.91
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.91
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.91
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.91
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.91
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.91
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.91
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.91
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.91
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(U11(U41(tt, z0, z1), x1)) → c13(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.91
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c14(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(s(U41(tt, z0, z1))) → c15(S(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.91
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.91
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.91
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.91
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U31(U41(tt, z0, z1))) → c18(U31'(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.91
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.91
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.91
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.91
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.91
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.91
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.91
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.91
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.91
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c19(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c19(U41'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 379.27/113.91
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c19(U41'(mark(isNat(z0)), x1, x2), ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c19(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2), ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.91
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.91
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19
Tuples:
active(U11(tt, z0)) → mark(z0) 379.27/113.91
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.27/113.91
active(U31(tt)) → mark(0) 379.27/113.91
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.27/113.91
active(and(tt, z0)) → mark(z0) 379.27/113.91
active(isNat(0)) → mark(tt) 379.27/113.91
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.91
active(isNat(s(z0))) → mark(isNat(z0)) 379.27/113.91
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.91
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.27/113.91
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.91
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.27/113.91
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.91
active(U11(z0, z1)) → U11(active(z0), z1) 379.27/113.91
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.27/113.91
active(s(z0)) → s(active(z0)) 379.27/113.91
active(plus(z0, z1)) → plus(active(z0), z1) 379.27/113.91
active(plus(z0, z1)) → plus(z0, active(z1)) 379.27/113.91
active(U31(z0)) → U31(active(z0)) 379.27/113.91
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.27/113.91
active(x(z0, z1)) → x(active(z0), z1) 379.27/113.91
active(x(z0, z1)) → x(z0, active(z1)) 379.27/113.91
active(and(z0, z1)) → and(active(z0), z1) 379.27/113.91
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.27/113.91
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.27/113.91
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.27/113.91
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.27/113.91
s(mark(z0)) → mark(s(z0)) 379.27/113.91
s(ok(z0)) → ok(s(z0)) 379.27/113.91
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.27/113.91
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.27/113.91
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.27/113.91
U31(mark(z0)) → mark(U31(z0)) 379.27/113.91
U31(ok(z0)) → ok(U31(z0)) 379.27/113.91
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.27/113.91
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.27/113.91
x(mark(z0), z1) → mark(x(z0, z1)) 379.27/113.91
x(z0, mark(z1)) → mark(x(z0, z1)) 379.27/113.91
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.27/113.91
and(mark(z0), z1) → mark(and(z0, z1)) 379.27/113.91
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.27/113.91
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.27/113.91
proper(tt) → ok(tt) 379.27/113.91
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.27/113.91
proper(s(z0)) → s(proper(z0)) 379.27/113.91
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.27/113.91
proper(U31(z0)) → U31(proper(z0)) 379.27/113.91
proper(0) → ok(0) 379.27/113.91
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.27/113.91
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.27/113.91
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.27/113.91
proper(isNat(z0)) → isNat(proper(z0)) 379.27/113.91
isNat(ok(z0)) → ok(isNat(z0)) 379.27/113.91
top(mark(z0)) → top(proper(z0)) 379.27/113.91
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.91
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.91
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 379.27/113.91
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.91
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.91
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.91
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.91
S(mark(z0)) → c27(S(z0)) 379.27/113.91
S(ok(z0)) → c28(S(z0)) 379.27/113.91
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.91
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.91
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.91
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.91
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.91
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.91
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.91
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.91
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.91
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.91
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.91
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.91
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.91
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.91
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.91
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.91
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.91
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.91
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.91
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.91
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.91
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.91
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.91
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.91
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.91
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.91
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.91
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.91
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.91
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.91
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.91
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.91
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.91
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.91
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.91
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.91
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.91
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.91
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.91
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.91
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.91
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.92
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.92
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.92
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.92
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.92
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.92
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.92
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.92
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.92
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.92
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.92
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.92
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.92
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.92
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.92
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.92
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.92
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.92
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.27/113.92
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.27/113.92
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.92
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.92
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.92
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.27/113.92
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.92
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.27/113.92
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.92
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.92
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.92
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.92
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.92
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.27/113.92
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.92
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.92
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.92
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.92
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.92
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.92
ACTIVE(and(z0, z1)) → c22(AND(active(z0), z1), ACTIVE(z0)) 379.27/113.92
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.92
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.92
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.92
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.92
S(mark(z0)) → c27(S(z0)) 379.27/113.92
S(ok(z0)) → c28(S(z0)) 379.27/113.92
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.92
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.92
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.92
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.92
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.92
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.92
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.92
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.92
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.92
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.92
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.92
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.92
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.92
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.92
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.92
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.92
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.92
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.92
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.92
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.92
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.92
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.92
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.92
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.92
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.92
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.92
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.92
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.92
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.92
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.92
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.92
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.92
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.92
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.92
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.92
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.92
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.92
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.92
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.92
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.92
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.92
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.92
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.92
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.92
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.92
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.92
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.92
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.92
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.92
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.92
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.92
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.92
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.92
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.92
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.92
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.92
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.92
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.92
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.92
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.92
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.92
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.92
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.92
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.92
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.92
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.92
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.92
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.92
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.92
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.92
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.92
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.92
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.92
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.92
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.92
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.95
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.95
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.95
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.95
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.95
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.95
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.95
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.95
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.95
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.95
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.95
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.95
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.95
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.95
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.95
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.95
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.95
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.95
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.95
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.95
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.95
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.95
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.95
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.95
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.95
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.95
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.95
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.95
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.95
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.95
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.95
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.95
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.95
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.95
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.27/113.95
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.27/113.95
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.95
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.27/113.95
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.27/113.95
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.95
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.27/113.95
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.95
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.95
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.95
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.27/113.95
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.27/113.95
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.95
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(U11(tt, z0))) 379.27/113.95
ACTIVE(and(U21(tt, z0, z1), x1)) → c22(AND(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 379.27/113.95
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1), ACTIVE(U31(tt))) 379.27/113.95
ACTIVE(and(U41(tt, z0, z1), x1)) → c22(AND(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.27/113.95
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.95
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1), ACTIVE(isNat(0))) 379.27/113.95
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.95
ACTIVE(and(isNat(s(z0)), x1)) → c22(AND(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 379.27/113.95
ACTIVE(and(isNat(x(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 379.27/113.95
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.95
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.95
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.95
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.95
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.95
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.95
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.95
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.95
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.95
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.95
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.95
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 379.27/113.95
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.27/113.95
active(U31(tt)) → mark(0) 379.27/113.95
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.27/113.95
active(and(tt, z0)) → mark(z0) 379.27/113.95
active(isNat(0)) → mark(tt) 379.27/113.95
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.95
active(isNat(s(z0))) → mark(isNat(z0)) 379.27/113.95
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.27/113.95
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.27/113.95
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.95
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.27/113.95
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.27/113.95
active(U11(z0, z1)) → U11(active(z0), z1) 379.27/113.95
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.27/113.95
active(s(z0)) → s(active(z0)) 379.27/113.95
active(plus(z0, z1)) → plus(active(z0), z1) 379.27/113.95
active(plus(z0, z1)) → plus(z0, active(z1)) 379.27/113.95
active(U31(z0)) → U31(active(z0)) 379.27/113.95
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.27/113.95
active(x(z0, z1)) → x(active(z0), z1) 379.27/113.95
active(x(z0, z1)) → x(z0, active(z1)) 379.27/113.95
active(and(z0, z1)) → and(active(z0), z1) 379.27/113.95
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.27/113.95
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.27/113.95
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.27/113.95
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.27/113.95
s(mark(z0)) → mark(s(z0)) 379.27/113.95
s(ok(z0)) → ok(s(z0)) 379.27/113.95
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.27/113.95
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.27/113.95
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.27/113.95
U31(mark(z0)) → mark(U31(z0)) 379.27/113.95
U31(ok(z0)) → ok(U31(z0)) 379.27/113.95
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.27/113.95
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.27/113.95
x(mark(z0), z1) → mark(x(z0, z1)) 379.27/113.95
x(z0, mark(z1)) → mark(x(z0, z1)) 379.27/113.95
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.27/113.95
and(mark(z0), z1) → mark(and(z0, z1)) 379.27/113.95
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.27/113.95
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.27/113.95
proper(tt) → ok(tt) 379.27/113.95
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.27/113.95
proper(s(z0)) → s(proper(z0)) 379.27/113.95
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.27/113.95
proper(U31(z0)) → U31(proper(z0)) 379.27/113.95
proper(0) → ok(0) 379.27/113.95
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.27/113.95
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.27/113.95
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.27/113.95
proper(isNat(z0)) → isNat(proper(z0)) 379.27/113.95
isNat(ok(z0)) → ok(isNat(z0)) 379.27/113.95
top(mark(z0)) → top(proper(z0)) 379.27/113.95
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.95
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.99
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.99
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.99
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.99
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.99
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.99
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.99
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.99
S(mark(z0)) → c27(S(z0)) 379.27/113.99
S(ok(z0)) → c28(S(z0)) 379.27/113.99
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.99
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.99
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.99
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.99
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.99
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.99
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.99
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.99
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.99
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.99
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.99
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.99
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.99
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.99
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.99
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.99
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.99
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.99
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.99
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.99
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.99
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.99
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.99
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.99
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.99
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.99
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.99
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.99
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.99
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.99
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.99
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.99
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.99
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.99
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.99
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.99
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.99
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.99
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.99
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.99
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.99
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.99
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.99
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.99
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.99
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.99
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.99
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.27/113.99
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.27/113.99
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.99
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.27/113.99
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.27/113.99
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.99
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.99
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.27/113.99
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(U11(tt, z0))) 379.27/113.99
ACTIVE(and(U21(tt, z0, z1), x1)) → c22(AND(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1), ACTIVE(U31(tt))) 379.27/113.99
ACTIVE(and(U41(tt, z0, z1), x1)) → c22(AND(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1), ACTIVE(isNat(0))) 379.27/113.99
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(and(isNat(s(z0)), x1)) → c22(AND(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(and(isNat(x(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.27/113.99
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.27/113.99
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.27/113.99
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.27/113.99
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.27/113.99
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.27/113.99
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.27/113.99
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.27/113.99
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.27/113.99
S(mark(z0)) → c27(S(z0)) 379.27/113.99
S(ok(z0)) → c28(S(z0)) 379.27/113.99
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.27/113.99
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.27/113.99
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.27/113.99
U31'(mark(z0)) → c32(U31'(z0)) 379.27/113.99
U31'(ok(z0)) → c33(U31'(z0)) 379.27/113.99
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.27/113.99
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.27/113.99
X(mark(z0), z1) → c36(X(z0, z1)) 379.27/113.99
X(z0, mark(z1)) → c37(X(z0, z1)) 379.27/113.99
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.27/113.99
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.27/113.99
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.27/113.99
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.99
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.27/113.99
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.27/113.99
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.27/113.99
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.27/113.99
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.27/113.99
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.27/113.99
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.27/113.99
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.27/113.99
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.27/113.99
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.27/113.99
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.27/113.99
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.27/113.99
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.27/113.99
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.27/113.99
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.27/113.99
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.27/113.99
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.27/113.99
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.99
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.27/113.99
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.27/113.99
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.27/113.99
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.27/113.99
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.99
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.27/113.99
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.27/113.99
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.27/113.99
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.27/113.99
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.27/113.99
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0)), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.27/113.99
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.27/113.99
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.27/113.99
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.27/113.99
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.27/113.99
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.27/113.99
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.27/113.99
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.27/113.99
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.27/113.99
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.27/113.99
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.27/113.99
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.27/113.99
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2), ACTIVE(and(tt, z0))) 379.27/113.99
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.27/113.99
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.27/113.99
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.27/113.99
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.27/113.99
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.27/113.99
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.27/113.99
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.27/113.99
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.27/113.99
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.27/113.99
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.27/113.99
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.27/113.99
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.27/113.99
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.27/113.99
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.27/113.99
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.27/113.99
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.27/113.99
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.99
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.27/113.99
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.27/113.99
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.27/113.99
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.27/113.99
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.27/113.99
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.27/113.99
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.00
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.00
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.00
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.00
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.00
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.00
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.00
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(U11(tt, z0))) 379.66/114.00
ACTIVE(and(U21(tt, z0, z1), x1)) → c22(AND(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 379.66/114.00
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1), ACTIVE(U31(tt))) 379.66/114.00
ACTIVE(and(U41(tt, z0, z1), x1)) → c22(AND(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.66/114.00
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1), ACTIVE(and(tt, z0))) 379.66/114.00
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1), ACTIVE(isNat(0))) 379.66/114.00
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 379.66/114.00
ACTIVE(and(isNat(s(z0)), x1)) → c22(AND(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 379.66/114.00
ACTIVE(and(isNat(x(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 379.66/114.00
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.00
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.00
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.00
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.00
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.00
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.00
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.00
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.00
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.00
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.00
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.00
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.00
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.00
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22
Tuples:
active(U11(tt, z0)) → mark(z0) 379.66/114.00
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.66/114.00
active(U31(tt)) → mark(0) 379.66/114.00
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.66/114.00
active(and(tt, z0)) → mark(z0) 379.66/114.00
active(isNat(0)) → mark(tt) 379.66/114.00
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.00
active(isNat(s(z0))) → mark(isNat(z0)) 379.66/114.00
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.00
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.66/114.00
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.00
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.66/114.00
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.00
active(U11(z0, z1)) → U11(active(z0), z1) 379.66/114.00
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.66/114.00
active(s(z0)) → s(active(z0)) 379.66/114.00
active(plus(z0, z1)) → plus(active(z0), z1) 379.66/114.00
active(plus(z0, z1)) → plus(z0, active(z1)) 379.66/114.00
active(U31(z0)) → U31(active(z0)) 379.66/114.00
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.66/114.00
active(x(z0, z1)) → x(active(z0), z1) 379.66/114.00
active(x(z0, z1)) → x(z0, active(z1)) 379.66/114.00
active(and(z0, z1)) → and(active(z0), z1) 379.66/114.00
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.66/114.00
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.66/114.00
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.66/114.00
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.66/114.00
s(mark(z0)) → mark(s(z0)) 379.66/114.00
s(ok(z0)) → ok(s(z0)) 379.66/114.00
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.66/114.00
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.66/114.00
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.66/114.00
U31(mark(z0)) → mark(U31(z0)) 379.66/114.00
U31(ok(z0)) → ok(U31(z0)) 379.66/114.00
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.66/114.00
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.66/114.00
x(mark(z0), z1) → mark(x(z0, z1)) 379.66/114.00
x(z0, mark(z1)) → mark(x(z0, z1)) 379.66/114.00
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.66/114.00
and(mark(z0), z1) → mark(and(z0, z1)) 379.66/114.00
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.66/114.00
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.66/114.00
proper(tt) → ok(tt) 379.66/114.00
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.66/114.00
proper(s(z0)) → s(proper(z0)) 379.66/114.00
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.66/114.00
proper(U31(z0)) → U31(proper(z0)) 379.66/114.00
proper(0) → ok(0) 379.66/114.00
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.66/114.00
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.66/114.00
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.66/114.00
proper(isNat(z0)) → isNat(proper(z0)) 379.66/114.00
isNat(ok(z0)) → ok(isNat(z0)) 379.66/114.00
top(mark(z0)) → top(proper(z0)) 379.66/114.00
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.00
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.00
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.00
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.00
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.00
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.00
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.00
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.00
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.00
S(mark(z0)) → c27(S(z0)) 379.66/114.00
S(ok(z0)) → c28(S(z0)) 379.66/114.00
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.00
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.00
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.00
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.00
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.00
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.00
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.00
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.00
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.00
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.00
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.00
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.00
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.00
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.00
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.00
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.00
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.00
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.00
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.00
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.00
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.00
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.00
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.00
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.00
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.00
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.00
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.00
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.00
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.00
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.00
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.00
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.00
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.00
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.00
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.00
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.00
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.00
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.00
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.00
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.00
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.00
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.00
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.00
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.00
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.00
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.00
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.00
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.00
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.00
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.00
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.00
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.00
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.00
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.00
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.00
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.00
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.01
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.01
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.01
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c22(AND(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c22(AND(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c22(AND(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.01
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.01
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.01
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.01
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.01
S(mark(z0)) → c27(S(z0)) 379.66/114.01
S(ok(z0)) → c28(S(z0)) 379.66/114.01
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.01
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.01
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.01
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.01
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.01
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.01
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.01
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.01
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.01
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.01
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.01
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.01
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.01
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.01
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.01
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.01
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.01
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.01
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.01
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c22(AND(mark(s(plus(z1, z0))), x1), ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c22(AND(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c22(AND(mark(isNat(z0)), x1), ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c22(AND(mark(and(isNat(z0), isNat(z1))), x1), ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.01
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22
Tuples:
active(U11(tt, z0)) → mark(z0) 379.66/114.01
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.66/114.01
active(U31(tt)) → mark(0) 379.66/114.01
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.66/114.01
active(and(tt, z0)) → mark(z0) 379.66/114.01
active(isNat(0)) → mark(tt) 379.66/114.01
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.01
active(isNat(s(z0))) → mark(isNat(z0)) 379.66/114.01
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.01
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.66/114.01
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.01
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.66/114.01
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.01
active(U11(z0, z1)) → U11(active(z0), z1) 379.66/114.01
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.66/114.01
active(s(z0)) → s(active(z0)) 379.66/114.01
active(plus(z0, z1)) → plus(active(z0), z1) 379.66/114.01
active(plus(z0, z1)) → plus(z0, active(z1)) 379.66/114.01
active(U31(z0)) → U31(active(z0)) 379.66/114.01
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.66/114.01
active(x(z0, z1)) → x(active(z0), z1) 379.66/114.01
active(x(z0, z1)) → x(z0, active(z1)) 379.66/114.01
active(and(z0, z1)) → and(active(z0), z1) 379.66/114.01
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.66/114.01
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.66/114.01
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.66/114.01
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.66/114.01
s(mark(z0)) → mark(s(z0)) 379.66/114.01
s(ok(z0)) → ok(s(z0)) 379.66/114.01
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.66/114.01
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.66/114.01
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.66/114.01
U31(mark(z0)) → mark(U31(z0)) 379.66/114.01
U31(ok(z0)) → ok(U31(z0)) 379.66/114.01
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.66/114.01
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.66/114.01
x(mark(z0), z1) → mark(x(z0, z1)) 379.66/114.01
x(z0, mark(z1)) → mark(x(z0, z1)) 379.66/114.01
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.66/114.01
and(mark(z0), z1) → mark(and(z0, z1)) 379.66/114.01
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.66/114.01
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.66/114.01
proper(tt) → ok(tt) 379.66/114.01
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.66/114.01
proper(s(z0)) → s(proper(z0)) 379.66/114.01
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.66/114.01
proper(U31(z0)) → U31(proper(z0)) 379.66/114.01
proper(0) → ok(0) 379.66/114.01
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.66/114.01
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.66/114.01
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.66/114.01
proper(isNat(z0)) → isNat(proper(z0)) 379.66/114.01
isNat(ok(z0)) → ok(isNat(z0)) 379.66/114.01
top(mark(z0)) → top(proper(z0)) 379.66/114.01
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.01
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.01
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.01
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.01
S(mark(z0)) → c27(S(z0)) 379.66/114.01
S(ok(z0)) → c28(S(z0)) 379.66/114.01
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.01
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.01
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.01
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.01
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.01
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.01
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.01
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.01
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.01
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.01
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.01
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.01
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.01
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.01
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.01
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.01
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.01
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.01
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.01
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.01
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.01
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.01
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.01
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.01
S(mark(z0)) → c27(S(z0)) 379.66/114.01
S(ok(z0)) → c28(S(z0)) 379.66/114.01
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.01
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.01
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.01
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.01
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.01
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.01
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.01
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.01
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.01
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.01
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.01
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.01
PROPER(U11(z0, z1)) → c41(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.01
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.01
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.01
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.01
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.01
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.01
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.01
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.01
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.01
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.01
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.01
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.01
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.01
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.01
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.01
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.01
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.01
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.01
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.01
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.01
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.01
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.01
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.01
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.01
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.01
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.01
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.01
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.01
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.01
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.01
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.01
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.01
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.01
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.01
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.01
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.01
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.01
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.01
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.01
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.01
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.01
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 379.66/114.01
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.01
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 379.66/114.01
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.01
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 379.66/114.01
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 379.66/114.01
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 379.66/114.01
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 379.66/114.01
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 379.66/114.01
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 379.66/114.01
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 379.66/114.01
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 379.66/114.01
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 379.66/114.01
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 379.66/114.01
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 379.66/114.01
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 379.66/114.01
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 379.66/114.01
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 379.66/114.01
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 379.66/114.01
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 379.66/114.01
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 379.66/114.01
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 379.66/114.01
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 379.66/114.01
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 379.66/114.01
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 379.66/114.01
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
Tuples:
active(U11(tt, z0)) → mark(z0) 379.66/114.01
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.66/114.01
active(U31(tt)) → mark(0) 379.66/114.01
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.66/114.01
active(and(tt, z0)) → mark(z0) 379.66/114.01
active(isNat(0)) → mark(tt) 379.66/114.01
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.01
active(isNat(s(z0))) → mark(isNat(z0)) 379.66/114.01
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.01
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.66/114.01
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.01
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.66/114.01
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.01
active(U11(z0, z1)) → U11(active(z0), z1) 379.66/114.01
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.66/114.01
active(s(z0)) → s(active(z0)) 379.66/114.01
active(plus(z0, z1)) → plus(active(z0), z1) 379.66/114.01
active(plus(z0, z1)) → plus(z0, active(z1)) 379.66/114.01
active(U31(z0)) → U31(active(z0)) 379.66/114.01
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.66/114.01
active(x(z0, z1)) → x(active(z0), z1) 379.66/114.01
active(x(z0, z1)) → x(z0, active(z1)) 379.66/114.01
active(and(z0, z1)) → and(active(z0), z1) 379.66/114.01
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.66/114.01
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.66/114.01
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.66/114.01
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.66/114.01
s(mark(z0)) → mark(s(z0)) 379.66/114.01
s(ok(z0)) → ok(s(z0)) 379.66/114.01
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.66/114.01
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.66/114.01
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.66/114.01
U31(mark(z0)) → mark(U31(z0)) 379.66/114.01
U31(ok(z0)) → ok(U31(z0)) 379.66/114.01
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.66/114.01
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.66/114.01
x(mark(z0), z1) → mark(x(z0, z1)) 379.66/114.01
x(z0, mark(z1)) → mark(x(z0, z1)) 379.66/114.01
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.66/114.01
and(mark(z0), z1) → mark(and(z0, z1)) 379.66/114.01
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.66/114.01
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.66/114.01
proper(tt) → ok(tt) 379.66/114.01
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.66/114.01
proper(s(z0)) → s(proper(z0)) 379.66/114.01
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.66/114.01
proper(U31(z0)) → U31(proper(z0)) 379.66/114.01
proper(0) → ok(0) 379.66/114.01
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.66/114.01
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.66/114.01
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.66/114.01
proper(isNat(z0)) → isNat(proper(z0)) 379.66/114.01
isNat(ok(z0)) → ok(isNat(z0)) 379.66/114.01
top(mark(z0)) → top(proper(z0)) 379.66/114.01
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.01
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.01
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.01
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.01
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.01
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.01
S(mark(z0)) → c27(S(z0)) 379.66/114.01
S(ok(z0)) → c28(S(z0)) 379.66/114.01
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.01
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.01
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.01
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.01
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.01
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.01
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.01
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.01
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.01
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.05
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.05
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.05
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.05
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.05
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.05
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.05
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.05
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.05
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.05
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.05
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.05
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.05
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.05
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.05
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.05
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.05
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.05
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.05
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.05
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.05
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.05
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.05
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.05
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.05
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.05
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.05
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.05
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.05
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.05
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.05
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.05
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.05
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.05
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.05
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.05
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.05
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.05
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.05
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.05
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.05
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.05
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.05
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.05
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.05
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.05
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.05
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.05
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 379.66/114.05
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 379.66/114.05
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.05
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 379.66/114.05
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 379.66/114.05
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 379.66/114.05
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 379.66/114.05
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 379.66/114.05
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 379.66/114.05
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 379.66/114.05
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 379.66/114.05
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 379.66/114.05
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 379.66/114.05
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 379.66/114.05
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 379.66/114.05
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 379.66/114.05
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 379.66/114.05
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 379.66/114.05
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 379.66/114.05
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 379.66/114.05
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 379.66/114.05
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 379.66/114.05
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 379.66/114.05
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 379.66/114.05
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 379.66/114.05
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 379.66/114.05
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.05
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.05
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.05
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.05
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.05
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.05
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.05
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.05
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.05
S(mark(z0)) → c27(S(z0)) 379.66/114.05
S(ok(z0)) → c28(S(z0)) 379.66/114.05
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.05
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.05
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.05
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.05
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.05
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.05
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.05
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.05
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.05
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.05
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.05
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.05
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.05
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.05
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.05
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.05
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.05
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.05
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.05
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.05
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.05
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.05
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.05
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.05
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.05
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.05
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.05
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.05
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.05
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.05
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.05
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.05
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.05
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.05
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.05
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.05
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.05
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.05
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.05
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.05
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.05
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.05
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.05
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.05
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.05
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.05
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.05
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.05
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.05
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.05
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.05
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.05
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.05
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.05
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.05
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.05
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.05
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.05
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.05
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.05
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.05
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.05
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.05
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.05
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.05
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.06
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.06
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.06
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.06
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.06
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.06
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.06
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.06
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.06
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.06
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.06
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.06
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.06
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.06
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.06
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.06
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.06
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.06
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.06
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.06
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.06
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.06
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.06
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.06
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.06
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.06
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.06
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.06
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.06
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.06
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.06
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.06
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.06
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.06
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.06
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.06
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 379.66/114.06
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 379.66/114.06
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 379.66/114.06
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.06
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 379.66/114.06
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.06
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.06
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 379.66/114.06
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 379.66/114.06
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.06
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 379.66/114.06
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 379.66/114.06
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 379.66/114.06
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 379.66/114.06
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 379.66/114.06
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 379.66/114.06
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 379.66/114.06
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 379.66/114.06
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 379.66/114.06
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 379.66/114.06
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 379.66/114.06
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 379.66/114.06
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 379.66/114.06
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 379.66/114.06
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 379.66/114.06
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 379.66/114.06
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 379.66/114.06
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 379.66/114.06
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 379.66/114.06
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 379.66/114.06
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 379.66/114.06
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 379.66/114.06
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41
Tuples:
active(U11(tt, z0)) → mark(z0) 379.66/114.06
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 379.66/114.06
active(U31(tt)) → mark(0) 379.66/114.06
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 379.66/114.06
active(and(tt, z0)) → mark(z0) 379.66/114.06
active(isNat(0)) → mark(tt) 379.66/114.06
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.06
active(isNat(s(z0))) → mark(isNat(z0)) 379.66/114.06
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 379.66/114.06
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 379.66/114.06
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.06
active(x(z0, 0)) → mark(U31(isNat(z0))) 379.66/114.06
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 379.66/114.06
active(U11(z0, z1)) → U11(active(z0), z1) 379.66/114.06
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 379.66/114.06
active(s(z0)) → s(active(z0)) 379.66/114.06
active(plus(z0, z1)) → plus(active(z0), z1) 379.66/114.06
active(plus(z0, z1)) → plus(z0, active(z1)) 379.66/114.06
active(U31(z0)) → U31(active(z0)) 379.66/114.06
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 379.66/114.06
active(x(z0, z1)) → x(active(z0), z1) 379.66/114.06
active(x(z0, z1)) → x(z0, active(z1)) 379.66/114.06
active(and(z0, z1)) → and(active(z0), z1) 379.66/114.06
U11(mark(z0), z1) → mark(U11(z0, z1)) 379.66/114.06
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 379.66/114.06
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 379.66/114.06
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 379.66/114.06
s(mark(z0)) → mark(s(z0)) 379.66/114.06
s(ok(z0)) → ok(s(z0)) 379.66/114.06
plus(mark(z0), z1) → mark(plus(z0, z1)) 379.66/114.06
plus(z0, mark(z1)) → mark(plus(z0, z1)) 379.66/114.06
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 379.66/114.06
U31(mark(z0)) → mark(U31(z0)) 379.66/114.06
U31(ok(z0)) → ok(U31(z0)) 379.66/114.06
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 379.66/114.06
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 379.66/114.06
x(mark(z0), z1) → mark(x(z0, z1)) 379.66/114.06
x(z0, mark(z1)) → mark(x(z0, z1)) 379.66/114.06
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 379.66/114.06
and(mark(z0), z1) → mark(and(z0, z1)) 379.66/114.06
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 379.66/114.06
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 379.66/114.06
proper(tt) → ok(tt) 379.66/114.06
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 379.66/114.06
proper(s(z0)) → s(proper(z0)) 379.66/114.06
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 379.66/114.06
proper(U31(z0)) → U31(proper(z0)) 379.66/114.06
proper(0) → ok(0) 379.66/114.06
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 379.66/114.06
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 379.66/114.06
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 379.66/114.06
proper(isNat(z0)) → isNat(proper(z0)) 379.66/114.06
isNat(ok(z0)) → ok(isNat(z0)) 379.66/114.06
top(mark(z0)) → top(proper(z0)) 379.66/114.06
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.06
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.06
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.06
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.06
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.06
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.06
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.06
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.06
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.06
S(mark(z0)) → c27(S(z0)) 379.66/114.06
S(ok(z0)) → c28(S(z0)) 379.66/114.06
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.06
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.06
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.06
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.06
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.06
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.06
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.07
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.07
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.07
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.07
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.07
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.07
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.07
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.07
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.07
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.07
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.07
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.07
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.07
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.07
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.07
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.07
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.07
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.07
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.07
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.07
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 379.66/114.07
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.07
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 379.66/114.07
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.07
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.07
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 379.66/114.07
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 379.66/114.07
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.07
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.07
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 379.66/114.07
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.07
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 379.66/114.07
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 379.66/114.07
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 379.66/114.07
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.07
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 379.66/114.07
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 379.66/114.07
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 379.66/114.07
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 379.66/114.07
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 379.66/114.07
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.07
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 379.66/114.07
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 379.66/114.07
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 379.66/114.07
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.07
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 379.66/114.07
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 379.66/114.07
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.07
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 379.66/114.07
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 379.66/114.07
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.07
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.07
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 379.66/114.07
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 379.66/114.07
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 379.66/114.07
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 379.66/114.07
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.07
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 379.66/114.07
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 379.66/114.07
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 379.66/114.07
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 379.66/114.07
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 379.66/114.07
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 379.66/114.07
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 379.66/114.07
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 379.66/114.07
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 379.66/114.07
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 379.66/114.07
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 379.66/114.07
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.07
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 379.66/114.07
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 379.66/114.07
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 379.66/114.07
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 379.66/114.07
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 379.66/114.07
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 379.66/114.07
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 379.66/114.07
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.07
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 379.66/114.07
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 379.66/114.07
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 379.66/114.07
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 379.66/114.07
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 379.66/114.07
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 379.66/114.07
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 379.66/114.07
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 379.66/114.07
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 379.66/114.07
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 379.66/114.07
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 379.66/114.07
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 379.66/114.07
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 379.66/114.07
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 379.66/114.07
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 379.66/114.07
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 379.66/114.07
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 379.66/114.07
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 379.66/114.07
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 379.66/114.07
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 379.66/114.07
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 379.66/114.07
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 379.66/114.07
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 379.66/114.07
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 379.66/114.07
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 379.66/114.07
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 379.66/114.07
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 379.66/114.07
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 379.66/114.07
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 379.66/114.07
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 379.66/114.07
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 379.66/114.07
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 379.66/114.07
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 379.66/114.07
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 379.66/114.07
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 379.66/114.07
S(mark(z0)) → c27(S(z0)) 379.66/114.07
S(ok(z0)) → c28(S(z0)) 379.66/114.07
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 379.66/114.07
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 379.66/114.07
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 379.66/114.07
U31'(mark(z0)) → c32(U31'(z0)) 379.66/114.07
U31'(ok(z0)) → c33(U31'(z0)) 379.66/114.07
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 379.66/114.07
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 379.66/114.07
X(mark(z0), z1) → c36(X(z0, z1)) 379.66/114.07
X(z0, mark(z1)) → c37(X(z0, z1)) 379.66/114.07
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 379.66/114.07
AND(mark(z0), z1) → c39(AND(z0, z1)) 379.66/114.07
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 379.66/114.07
PROPER(U21(z0, z1, z2)) → c43(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.07
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 379.66/114.07
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 379.66/114.07
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 379.66/114.07
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 379.66/114.07
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 379.66/114.07
ISNAT(ok(z0)) → c52(ISNAT(z0)) 379.66/114.07
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 379.66/114.07
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 379.66/114.07
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 379.66/114.07
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 379.66/114.07
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 379.66/114.07
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 379.66/114.07
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 379.66/114.07
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 379.66/114.07
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 379.66/114.07
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 379.66/114.07
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 379.66/114.07
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 379.66/114.07
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 379.66/114.07
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 379.66/114.07
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 379.66/114.07
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 379.66/114.07
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 379.66/114.07
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.16
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.16
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.16
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.16
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.16
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.16
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.16
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.16
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.16
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.16
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.16
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.16
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.16
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.16
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.16
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.16
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.16
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.16
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.16
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.16
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.16
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.16
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.16
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.16
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.16
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.16
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.16
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.16
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.16
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.16
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c43, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.03/114.16
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.16
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.16
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.16
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.03/114.16
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.16
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.16
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.03/114.16
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.03/114.16
active(U31(tt)) → mark(0) 380.03/114.16
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.03/114.16
active(and(tt, z0)) → mark(z0) 380.03/114.16
active(isNat(0)) → mark(tt) 380.03/114.16
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.16
active(isNat(s(z0))) → mark(isNat(z0)) 380.03/114.16
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.16
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.03/114.16
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.16
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.03/114.16
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.16
active(U11(z0, z1)) → U11(active(z0), z1) 380.03/114.16
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.03/114.16
active(s(z0)) → s(active(z0)) 380.03/114.16
active(plus(z0, z1)) → plus(active(z0), z1) 380.03/114.16
active(plus(z0, z1)) → plus(z0, active(z1)) 380.03/114.16
active(U31(z0)) → U31(active(z0)) 380.03/114.16
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.03/114.16
active(x(z0, z1)) → x(active(z0), z1) 380.03/114.16
active(x(z0, z1)) → x(z0, active(z1)) 380.03/114.16
active(and(z0, z1)) → and(active(z0), z1) 380.03/114.16
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.03/114.16
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.03/114.16
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.03/114.16
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.03/114.16
s(mark(z0)) → mark(s(z0)) 380.03/114.16
s(ok(z0)) → ok(s(z0)) 380.03/114.16
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.03/114.16
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.03/114.16
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.03/114.16
U31(mark(z0)) → mark(U31(z0)) 380.03/114.16
U31(ok(z0)) → ok(U31(z0)) 380.03/114.16
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.03/114.16
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.03/114.16
x(mark(z0), z1) → mark(x(z0, z1)) 380.03/114.16
x(z0, mark(z1)) → mark(x(z0, z1)) 380.03/114.16
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.03/114.16
and(mark(z0), z1) → mark(and(z0, z1)) 380.03/114.16
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.03/114.16
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.03/114.16
proper(tt) → ok(tt) 380.03/114.16
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.03/114.16
proper(s(z0)) → s(proper(z0)) 380.03/114.16
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.03/114.16
proper(U31(z0)) → U31(proper(z0)) 380.03/114.16
proper(0) → ok(0) 380.03/114.16
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.03/114.16
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.03/114.16
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.03/114.16
proper(isNat(z0)) → isNat(proper(z0)) 380.03/114.16
isNat(ok(z0)) → ok(isNat(z0)) 380.03/114.16
top(mark(z0)) → top(proper(z0)) 380.03/114.16
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.16
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.16
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.16
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.16
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.16
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.16
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.16
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.16
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.16
S(mark(z0)) → c27(S(z0)) 380.03/114.16
S(ok(z0)) → c28(S(z0)) 380.03/114.16
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.16
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.16
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.16
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.16
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.16
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.16
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.16
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.16
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.16
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.16
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.16
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.16
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 380.03/114.16
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.16
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.16
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.16
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.16
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.16
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.16
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.16
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.16
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.16
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.16
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.16
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.16
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.16
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.16
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.16
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.16
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.16
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.16
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.16
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.16
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.16
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.16
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.16
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.16
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.16
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.16
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.16
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.16
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.16
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.16
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.16
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.16
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.16
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.16
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.16
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.16
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.16
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.16
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.16
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.16
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.16
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.16
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.16
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.16
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.03/114.16
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.16
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.16
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.16
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.03/114.16
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.16
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.16
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.16
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.16
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.16
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.16
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.16
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.16
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.16
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.16
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.16
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.16
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.16
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.16
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.16
S(mark(z0)) → c27(S(z0)) 380.03/114.16
S(ok(z0)) → c28(S(z0)) 380.03/114.16
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.16
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.16
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.16
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.16
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.16
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.16
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.16
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.16
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.16
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.16
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.16
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.16
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 380.03/114.16
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.16
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.16
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.16
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.16
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.16
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.16
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.16
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.16
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.16
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.16
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.16
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.16
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.16
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.16
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.16
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.16
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.16
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.16
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.16
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.16
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.16
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.16
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.16
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.16
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.16
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.16
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.16
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.16
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.16
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.16
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.16
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.16
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.16
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.16
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.16
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.16
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.16
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.16
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.16
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.16
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.16
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.16
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.16
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.16
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.17
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.17
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.17
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.17
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.17
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.17
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.17
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.17
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.17
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.03/114.17
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.17
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.17
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.03/114.17
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.17
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43
Tuples:
active(U11(tt, z0)) → mark(z0) 380.03/114.17
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.03/114.17
active(U31(tt)) → mark(0) 380.03/114.17
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.03/114.17
active(and(tt, z0)) → mark(z0) 380.03/114.17
active(isNat(0)) → mark(tt) 380.03/114.17
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.17
active(isNat(s(z0))) → mark(isNat(z0)) 380.03/114.17
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.17
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.03/114.17
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.17
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.03/114.17
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.17
active(U11(z0, z1)) → U11(active(z0), z1) 380.03/114.17
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.03/114.17
active(s(z0)) → s(active(z0)) 380.03/114.17
active(plus(z0, z1)) → plus(active(z0), z1) 380.03/114.17
active(plus(z0, z1)) → plus(z0, active(z1)) 380.03/114.17
active(U31(z0)) → U31(active(z0)) 380.03/114.17
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.03/114.17
active(x(z0, z1)) → x(active(z0), z1) 380.03/114.17
active(x(z0, z1)) → x(z0, active(z1)) 380.03/114.17
active(and(z0, z1)) → and(active(z0), z1) 380.03/114.17
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.03/114.17
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.03/114.17
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.03/114.17
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.03/114.17
s(mark(z0)) → mark(s(z0)) 380.03/114.17
s(ok(z0)) → ok(s(z0)) 380.03/114.17
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.03/114.17
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.03/114.17
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.03/114.17
U31(mark(z0)) → mark(U31(z0)) 380.03/114.17
U31(ok(z0)) → ok(U31(z0)) 380.03/114.17
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.03/114.17
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.03/114.17
x(mark(z0), z1) → mark(x(z0, z1)) 380.03/114.17
x(z0, mark(z1)) → mark(x(z0, z1)) 380.03/114.17
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.03/114.17
and(mark(z0), z1) → mark(and(z0, z1)) 380.03/114.17
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.03/114.17
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.03/114.17
proper(tt) → ok(tt) 380.03/114.17
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.03/114.17
proper(s(z0)) → s(proper(z0)) 380.03/114.17
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.03/114.17
proper(U31(z0)) → U31(proper(z0)) 380.03/114.17
proper(0) → ok(0) 380.03/114.17
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.03/114.17
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.03/114.17
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.03/114.17
proper(isNat(z0)) → isNat(proper(z0)) 380.03/114.17
isNat(ok(z0)) → ok(isNat(z0)) 380.03/114.17
top(mark(z0)) → top(proper(z0)) 380.03/114.17
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.17
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.17
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.17
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.17
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.17
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.17
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.17
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.17
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.17
S(mark(z0)) → c27(S(z0)) 380.03/114.17
S(ok(z0)) → c28(S(z0)) 380.03/114.17
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.17
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.17
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.17
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.17
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.17
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.17
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.17
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.17
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.17
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.17
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.17
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.17
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 380.03/114.17
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.17
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.17
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.17
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.17
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.17
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.17
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.17
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.17
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.17
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.17
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.17
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.17
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.17
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.17
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.17
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.17
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.17
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.17
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.17
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.17
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.17
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.17
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.17
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.17
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.17
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.17
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.17
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.17
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.17
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.17
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.17
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.17
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.17
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.17
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.17
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.17
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.17
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.17
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.17
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.17
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.17
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.17
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.17
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.17
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.17
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.17
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.17
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.17
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.17
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.17
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.17
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.17
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.17
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.17
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.17
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.17
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.17
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.17
S(mark(z0)) → c27(S(z0)) 380.03/114.17
S(ok(z0)) → c28(S(z0)) 380.03/114.17
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.17
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.17
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.17
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.17
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.17
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.17
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.17
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.17
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.17
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.17
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.17
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.17
PROPER(s(z0)) → c44(S(proper(z0)), PROPER(z0)) 380.03/114.17
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.17
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.17
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.17
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.17
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.17
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.17
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.17
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.17
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.17
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.17
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.17
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.17
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.17
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.17
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.17
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.17
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.17
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.17
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.17
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.17
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.17
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.17
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.17
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.17
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.17
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.17
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.17
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.17
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.17
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.17
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.17
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.17
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.17
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.17
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.17
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.17
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.17
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.17
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.17
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.17
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.17
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.17
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.17
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.17
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.17
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.17
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.17
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.17
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.17
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.17
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.17
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.17
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.17
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.17
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.17
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.17
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.17
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.17
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.17
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.17
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.17
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.17
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.17
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.17
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.17
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.17
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.17
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.17
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.17
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.17
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.17
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.17
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.17
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.17
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.17
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.17
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.17
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.03/114.17
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.17
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.17
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.17
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c44, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.03/114.17
PROPER(s(tt)) → c44(S(ok(tt)), PROPER(tt)) 380.03/114.17
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.03/114.17
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.03/114.17
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.03/114.17
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.03/114.17
PROPER(s(0)) → c44(S(ok(0)), PROPER(0)) 380.03/114.17
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.03/114.17
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.03/114.17
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.03/114.17
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.03/114.17
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.03/114.17
active(U31(tt)) → mark(0) 380.03/114.17
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.03/114.17
active(and(tt, z0)) → mark(z0) 380.03/114.17
active(isNat(0)) → mark(tt) 380.03/114.17
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.17
active(isNat(s(z0))) → mark(isNat(z0)) 380.03/114.17
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.17
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.03/114.17
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.17
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.03/114.17
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.17
active(U11(z0, z1)) → U11(active(z0), z1) 380.03/114.17
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.03/114.17
active(s(z0)) → s(active(z0)) 380.03/114.17
active(plus(z0, z1)) → plus(active(z0), z1) 380.03/114.17
active(plus(z0, z1)) → plus(z0, active(z1)) 380.03/114.17
active(U31(z0)) → U31(active(z0)) 380.03/114.17
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.03/114.17
active(x(z0, z1)) → x(active(z0), z1) 380.03/114.17
active(x(z0, z1)) → x(z0, active(z1)) 380.03/114.17
active(and(z0, z1)) → and(active(z0), z1) 380.03/114.17
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.03/114.17
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.03/114.17
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.03/114.17
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.03/114.17
s(mark(z0)) → mark(s(z0)) 380.03/114.17
s(ok(z0)) → ok(s(z0)) 380.03/114.17
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.03/114.17
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.03/114.17
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.03/114.17
U31(mark(z0)) → mark(U31(z0)) 380.03/114.17
U31(ok(z0)) → ok(U31(z0)) 380.03/114.17
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.03/114.17
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.03/114.17
x(mark(z0), z1) → mark(x(z0, z1)) 380.03/114.17
x(z0, mark(z1)) → mark(x(z0, z1)) 380.03/114.17
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.03/114.17
and(mark(z0), z1) → mark(and(z0, z1)) 380.03/114.17
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.03/114.17
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.03/114.17
proper(tt) → ok(tt) 380.03/114.17
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.03/114.17
proper(s(z0)) → s(proper(z0)) 380.03/114.17
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.03/114.17
proper(U31(z0)) → U31(proper(z0)) 380.03/114.17
proper(0) → ok(0) 380.03/114.17
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.03/114.17
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.03/114.17
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.03/114.17
proper(isNat(z0)) → isNat(proper(z0)) 380.03/114.17
isNat(ok(z0)) → ok(isNat(z0)) 380.03/114.17
top(mark(z0)) → top(proper(z0)) 380.03/114.17
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.18
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.18
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.18
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.18
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.18
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.18
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.18
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.18
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.18
S(mark(z0)) → c27(S(z0)) 380.03/114.18
S(ok(z0)) → c28(S(z0)) 380.03/114.18
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.18
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.18
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.18
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.18
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.18
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.18
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.18
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.18
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.18
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.18
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.18
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.18
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.18
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.18
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.18
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.18
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.18
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.18
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.18
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.18
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.18
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.18
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.18
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.18
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.18
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.18
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.18
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.18
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.18
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.18
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.18
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.18
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.18
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.18
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.18
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.18
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.18
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.18
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.18
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.18
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.18
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.18
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.18
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.18
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.18
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.18
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.18
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.18
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.18
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.18
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.18
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.18
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.18
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.18
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.18
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.18
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.18
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.18
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.18
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.18
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.18
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.18
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.18
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.18
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.18
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.18
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.18
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.18
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.18
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.18
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.18
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.18
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.18
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.18
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.18
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.18
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.18
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.18
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.18
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.18
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.18
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.18
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.18
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.18
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.18
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.18
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.18
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.18
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.18
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.18
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.18
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.18
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.18
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.18
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.18
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.18
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.18
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.18
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.18
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.18
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.18
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.18
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.18
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.18
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.18
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.18
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.18
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.18
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.18
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.18
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.18
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.18
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.18
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.18
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.18
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.18
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.18
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.18
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.18
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.18
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.18
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.18
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.18
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.18
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.18
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.18
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.18
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.18
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.18
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.18
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.18
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.18
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.18
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.18
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.18
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.18
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.18
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.18
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.18
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.18
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.03/114.19
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.03/114.19
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.19
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.19
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.19
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.03/114.19
PROPER(s(tt)) → c44(S(ok(tt)), PROPER(tt)) 380.03/114.19
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.03/114.19
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.03/114.19
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.03/114.19
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.03/114.19
PROPER(s(0)) → c44(S(ok(0)), PROPER(0)) 380.03/114.19
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.03/114.19
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.03/114.19
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.03/114.19
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.19
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.19
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.19
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.19
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.19
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.19
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.19
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.19
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.19
S(mark(z0)) → c27(S(z0)) 380.03/114.19
S(ok(z0)) → c28(S(z0)) 380.03/114.19
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.19
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.19
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.19
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.19
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.19
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.19
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.19
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.19
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.19
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.19
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.19
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.19
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.19
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.19
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.19
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.19
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.19
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.19
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.19
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.19
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.19
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.19
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.19
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.19
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.19
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.19
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.19
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.19
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.19
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.19
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.19
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.19
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.19
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.19
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.19
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.19
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.19
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.19
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.19
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.19
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.19
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.19
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.19
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.19
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.19
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.19
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.19
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.19
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.19
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.19
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.19
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.19
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.19
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.19
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.19
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.19
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.19
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.19
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.19
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.19
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.19
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.19
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.19
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.19
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.19
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.19
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.19
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.19
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.19
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.19
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.19
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.19
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.19
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.19
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.19
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.19
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.19
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.19
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.19
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.19
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.19
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.19
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.19
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.19
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.19
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.19
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.19
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.19
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.19
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.19
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.19
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.19
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.19
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.19
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.19
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.19
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.19
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.19
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.19
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.19
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.19
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.19
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.19
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.19
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.19
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.19
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.19
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.19
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.19
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.19
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.19
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.19
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.19
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.19
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.19
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.03/114.19
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.03/114.19
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.03/114.19
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.03/114.19
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.03/114.20
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.03/114.20
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.03/114.20
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.03/114.20
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.03/114.20
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.03/114.20
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.03/114.20
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.03/114.20
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.03/114.20
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.03/114.20
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.03/114.20
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.03/114.20
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.03/114.20
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.03/114.20
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.03/114.20
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.03/114.20
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.03/114.20
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.03/114.20
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.03/114.20
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.03/114.20
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.20
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.03/114.20
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.03/114.20
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.03/114.20
PROPER(s(tt)) → c44(S(ok(tt)), PROPER(tt)) 380.03/114.20
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.03/114.20
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.03/114.20
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.03/114.20
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.03/114.20
PROPER(s(0)) → c44(S(ok(0)), PROPER(0)) 380.03/114.20
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.03/114.20
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.03/114.20
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.03/114.20
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44
Tuples:
active(U11(tt, z0)) → mark(z0) 380.03/114.20
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.03/114.20
active(U31(tt)) → mark(0) 380.03/114.20
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.03/114.20
active(and(tt, z0)) → mark(z0) 380.03/114.20
active(isNat(0)) → mark(tt) 380.03/114.20
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.20
active(isNat(s(z0))) → mark(isNat(z0)) 380.03/114.20
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.03/114.20
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.03/114.20
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.20
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.03/114.20
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.03/114.20
active(U11(z0, z1)) → U11(active(z0), z1) 380.03/114.20
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.03/114.20
active(s(z0)) → s(active(z0)) 380.03/114.20
active(plus(z0, z1)) → plus(active(z0), z1) 380.03/114.20
active(plus(z0, z1)) → plus(z0, active(z1)) 380.03/114.20
active(U31(z0)) → U31(active(z0)) 380.03/114.20
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.03/114.20
active(x(z0, z1)) → x(active(z0), z1) 380.03/114.20
active(x(z0, z1)) → x(z0, active(z1)) 380.03/114.20
active(and(z0, z1)) → and(active(z0), z1) 380.03/114.20
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.03/114.20
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.03/114.20
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.03/114.20
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.03/114.20
s(mark(z0)) → mark(s(z0)) 380.03/114.20
s(ok(z0)) → ok(s(z0)) 380.03/114.20
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.03/114.20
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.03/114.20
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.03/114.20
U31(mark(z0)) → mark(U31(z0)) 380.03/114.20
U31(ok(z0)) → ok(U31(z0)) 380.03/114.20
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.03/114.20
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.03/114.20
x(mark(z0), z1) → mark(x(z0, z1)) 380.03/114.20
x(z0, mark(z1)) → mark(x(z0, z1)) 380.03/114.20
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.03/114.20
and(mark(z0), z1) → mark(and(z0, z1)) 380.03/114.20
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.03/114.20
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.03/114.20
proper(tt) → ok(tt) 380.03/114.20
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.03/114.20
proper(s(z0)) → s(proper(z0)) 380.03/114.20
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.03/114.20
proper(U31(z0)) → U31(proper(z0)) 380.03/114.20
proper(0) → ok(0) 380.03/114.20
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.03/114.20
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.03/114.20
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.03/114.20
proper(isNat(z0)) → isNat(proper(z0)) 380.03/114.20
isNat(ok(z0)) → ok(isNat(z0)) 380.03/114.20
top(mark(z0)) → top(proper(z0)) 380.03/114.20
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.03/114.20
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.03/114.20
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.03/114.20
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.03/114.20
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.03/114.20
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.03/114.20
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.03/114.20
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.03/114.20
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.03/114.20
S(mark(z0)) → c27(S(z0)) 380.03/114.20
S(ok(z0)) → c28(S(z0)) 380.03/114.20
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.03/114.20
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.03/114.20
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.03/114.20
U31'(mark(z0)) → c32(U31'(z0)) 380.03/114.20
U31'(ok(z0)) → c33(U31'(z0)) 380.03/114.20
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.03/114.20
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.03/114.20
X(mark(z0), z1) → c36(X(z0, z1)) 380.03/114.20
X(z0, mark(z1)) → c37(X(z0, z1)) 380.03/114.20
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.03/114.20
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.03/114.20
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.03/114.20
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.20
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.03/114.20
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.03/114.20
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.20
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.03/114.20
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.03/114.20
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.03/114.20
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.03/114.20
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.03/114.20
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.03/114.20
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.03/114.20
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.03/114.20
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.03/114.20
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.03/114.20
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.03/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.03/114.20
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.03/114.20
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.03/114.20
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.03/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.03/114.20
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.20
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.03/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.03/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.20
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.03/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.03/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.03/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.03/114.20
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.03/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.03/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.03/114.20
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.03/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.03/114.20
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.03/114.20
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.03/114.20
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.20
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.03/114.20
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.03/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.03/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.03/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.03/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.20
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.03/114.20
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.03/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.03/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.03/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.03/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.03/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.03/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.03/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.03/114.20
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.03/114.20
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.03/114.20
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.03/114.20
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.03/114.20
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.03/114.20
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.03/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.03/114.20
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.03/114.20
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.03/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.03/114.20
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.03/114.20
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.03/114.20
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.03/114.20
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.03/114.20
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.03/114.20
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.03/114.20
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.20
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.03/114.20
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.03/114.20
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.03/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.03/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.03/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.03/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.03/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.03/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.03/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.03/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.03/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.03/114.20
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.03/114.20
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.03/114.20
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.03/114.20
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.03/114.20
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.03/114.20
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.03/114.20
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.03/114.20
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.03/114.20
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.03/114.20
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.03/114.20
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.20
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.20
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.20
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.20
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.20
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.20
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.20
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.20
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.20
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.20
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.20
PROPER(s(0)) → c44(S(ok(0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.20
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.20
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.20
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.20
S(mark(z0)) → c27(S(z0)) 380.42/114.20
S(ok(z0)) → c28(S(z0)) 380.42/114.20
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.20
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.20
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.20
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.20
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.20
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.20
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.20
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.20
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.20
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.20
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.20
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.20
PROPER(plus(z0, z1)) → c45(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.42/114.20
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.20
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.20
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.20
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.20
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.20
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.20
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.20
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.20
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.20
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.20
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.20
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.20
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.20
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.20
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.20
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.20
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.20
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.20
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.20
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.20
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.20
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.20
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.20
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.20
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.20
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.20
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.20
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.20
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.20
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.20
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.20
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.20
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.20
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.20
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.20
PROPER(s(0)) → c44(S(ok(0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c45, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.20
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.20
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.20
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.20
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.20
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.20
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.20
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.20
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.20
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.20
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.20
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.20
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.20
active(U31(tt)) → mark(0) 380.42/114.20
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.20
active(and(tt, z0)) → mark(z0) 380.42/114.20
active(isNat(0)) → mark(tt) 380.42/114.20
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.20
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.20
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.20
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.20
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.20
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.20
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.20
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.20
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.20
active(s(z0)) → s(active(z0)) 380.42/114.20
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.20
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.20
active(U31(z0)) → U31(active(z0)) 380.42/114.20
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.20
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.20
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.20
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.20
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.20
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.20
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.20
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.20
s(mark(z0)) → mark(s(z0)) 380.42/114.20
s(ok(z0)) → ok(s(z0)) 380.42/114.20
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.20
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.20
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.20
U31(mark(z0)) → mark(U31(z0)) 380.42/114.20
U31(ok(z0)) → ok(U31(z0)) 380.42/114.20
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.20
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.20
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.20
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.20
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.20
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.20
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.20
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.20
proper(tt) → ok(tt) 380.42/114.20
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.20
proper(s(z0)) → s(proper(z0)) 380.42/114.20
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.20
proper(U31(z0)) → U31(proper(z0)) 380.42/114.20
proper(0) → ok(0) 380.42/114.20
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.20
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.20
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.20
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.20
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.20
top(mark(z0)) → top(proper(z0)) 380.42/114.20
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.20
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.20
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.20
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.20
S(mark(z0)) → c27(S(z0)) 380.42/114.20
S(ok(z0)) → c28(S(z0)) 380.42/114.20
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.20
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.20
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.20
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.20
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.20
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.20
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.20
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.20
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.20
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.20
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.20
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.20
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.42/114.20
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.20
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.20
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.20
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.20
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.20
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.20
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.20
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.20
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.20
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.20
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.20
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.20
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.20
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.20
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.20
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.20
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.20
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.20
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.20
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.20
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.20
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.20
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.20
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.20
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.20
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.20
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.20
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.20
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.20
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.20
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.20
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.20
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.20
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.20
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.20
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.20
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.20
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.20
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.20
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.20
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.20
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.20
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.20
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.20
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.20
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.20
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.20
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.20
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.20
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.20
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.20
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.20
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.20
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.20
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.20
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.20
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.20
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.20
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.20
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.20
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.20
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.20
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.20
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.20
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.20
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.20
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.20
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.20
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.20
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.20
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.20
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.20
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.20
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.20
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.20
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.20
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.20
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.20
S(mark(z0)) → c27(S(z0)) 380.42/114.20
S(ok(z0)) → c28(S(z0)) 380.42/114.20
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.20
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.20
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.20
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.20
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.20
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.20
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.20
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.20
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.20
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.20
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.20
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.20
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.42/114.20
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.20
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.20
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.20
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.20
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.20
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.20
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.20
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.20
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.20
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.20
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.20
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.20
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.20
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.20
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.20
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.20
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.20
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.20
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.20
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.20
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.20
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.20
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.20
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.20
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.20
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.20
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.20
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.20
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.20
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.21
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.21
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.21
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.21
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.21
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.21
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.21
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.21
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.21
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.21
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.21
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.21
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.21
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.21
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.21
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.21
active(U31(tt)) → mark(0) 380.42/114.21
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.21
active(and(tt, z0)) → mark(z0) 380.42/114.21
active(isNat(0)) → mark(tt) 380.42/114.21
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.21
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.21
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.21
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.21
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.21
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.21
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.21
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.21
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.21
active(s(z0)) → s(active(z0)) 380.42/114.21
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.21
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.21
active(U31(z0)) → U31(active(z0)) 380.42/114.21
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.21
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.21
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.21
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.21
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.21
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.21
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.21
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.21
s(mark(z0)) → mark(s(z0)) 380.42/114.21
s(ok(z0)) → ok(s(z0)) 380.42/114.21
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.21
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.21
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.21
U31(mark(z0)) → mark(U31(z0)) 380.42/114.21
U31(ok(z0)) → ok(U31(z0)) 380.42/114.21
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.21
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.21
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.21
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.21
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.21
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.21
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.21
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.21
proper(tt) → ok(tt) 380.42/114.21
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.21
proper(s(z0)) → s(proper(z0)) 380.42/114.21
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.21
proper(U31(z0)) → U31(proper(z0)) 380.42/114.21
proper(0) → ok(0) 380.42/114.21
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.21
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.21
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.21
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.21
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.21
top(mark(z0)) → top(proper(z0)) 380.42/114.21
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.21
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.21
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.21
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.21
S(mark(z0)) → c27(S(z0)) 380.42/114.21
S(ok(z0)) → c28(S(z0)) 380.42/114.21
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.21
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.21
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.21
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.21
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.21
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.21
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.21
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.21
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.21
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.21
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.21
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.21
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.42/114.21
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.21
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.21
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.21
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.21
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.21
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.21
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.21
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.21
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.21
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.21
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.21
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.21
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.21
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.21
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.21
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.21
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.21
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.21
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.21
S(mark(z0)) → c27(S(z0)) 380.42/114.21
S(ok(z0)) → c28(S(z0)) 380.42/114.21
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.21
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.21
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.21
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.21
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.21
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.21
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.21
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.21
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.21
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.21
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.21
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.21
PROPER(U31(z0)) → c46(U31'(proper(z0)), PROPER(z0)) 380.42/114.21
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.21
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.21
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.21
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.21
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.21
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.21
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.21
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.21
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.21
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.21
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.21
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.21
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.21
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.21
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.21
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c46, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U31(tt)) → c46(U31'(ok(tt)), PROPER(tt)) 380.42/114.21
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(U31(0)) → c46(U31'(ok(0)), PROPER(0)) 380.42/114.21
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.21
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.21
active(U31(tt)) → mark(0) 380.42/114.21
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.21
active(and(tt, z0)) → mark(z0) 380.42/114.21
active(isNat(0)) → mark(tt) 380.42/114.21
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.21
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.21
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.21
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.21
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.21
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.21
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.21
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.21
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.21
active(s(z0)) → s(active(z0)) 380.42/114.21
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.21
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.21
active(U31(z0)) → U31(active(z0)) 380.42/114.21
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.21
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.21
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.21
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.21
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.21
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.21
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.21
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.21
s(mark(z0)) → mark(s(z0)) 380.42/114.21
s(ok(z0)) → ok(s(z0)) 380.42/114.21
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.21
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.21
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.21
U31(mark(z0)) → mark(U31(z0)) 380.42/114.21
U31(ok(z0)) → ok(U31(z0)) 380.42/114.21
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.21
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.21
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.21
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.21
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.21
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.21
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.21
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.21
proper(tt) → ok(tt) 380.42/114.21
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.21
proper(s(z0)) → s(proper(z0)) 380.42/114.21
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.21
proper(U31(z0)) → U31(proper(z0)) 380.42/114.21
proper(0) → ok(0) 380.42/114.21
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.21
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.21
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.21
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.21
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.21
top(mark(z0)) → top(proper(z0)) 380.42/114.21
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.21
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.21
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.21
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.21
S(mark(z0)) → c27(S(z0)) 380.42/114.21
S(ok(z0)) → c28(S(z0)) 380.42/114.21
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.21
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.21
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.21
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.21
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.21
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.21
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.21
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.21
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.21
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.21
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.21
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.21
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.21
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.21
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.21
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.21
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.21
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.21
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.21
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.21
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.21
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.21
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.21
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.21
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.21
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.21
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.21
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.21
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.21
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.21
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.21
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.21
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.21
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.21
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.21
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.21
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.21
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.21
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.21
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.21
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.21
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.21
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.21
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.21
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.21
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.21
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.21
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.21
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.21
PROPER(U31(tt)) → c46(U31'(ok(tt)), PROPER(tt)) 380.42/114.21
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.21
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.21
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.21
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.21
PROPER(U31(0)) → c46(U31'(ok(0)), PROPER(0)) 380.42/114.21
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.21
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.21
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.21
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.21
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.21
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.21
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.21
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.21
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.21
S(mark(z0)) → c27(S(z0)) 380.42/114.21
S(ok(z0)) → c28(S(z0)) 380.42/114.21
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.21
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.21
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.21
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.21
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.21
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.21
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.21
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.21
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.21
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.21
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.21
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.21
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.21
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.21
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.21
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.21
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.21
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.21
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.21
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.21
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.21
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.21
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.21
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.21
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.21
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.21
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.21
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.21
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.21
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.21
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.21
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.21
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.21
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.21
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.21
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.21
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.21
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.21
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.21
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.21
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.21
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.21
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.21
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.21
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.22
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.22
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.22
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.22
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.22
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.22
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U31(tt)) → c46(U31'(ok(tt)), PROPER(tt)) 380.42/114.22
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(U31(0)) → c46(U31'(ok(0)), PROPER(0)) 380.42/114.22
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.22
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.22
active(U31(tt)) → mark(0) 380.42/114.22
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.22
active(and(tt, z0)) → mark(z0) 380.42/114.22
active(isNat(0)) → mark(tt) 380.42/114.22
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.22
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.22
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.22
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.22
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.22
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.22
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.22
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.22
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.22
active(s(z0)) → s(active(z0)) 380.42/114.22
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.22
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.22
active(U31(z0)) → U31(active(z0)) 380.42/114.22
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.22
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.22
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.22
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.22
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.22
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.22
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.22
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.22
s(mark(z0)) → mark(s(z0)) 380.42/114.22
s(ok(z0)) → ok(s(z0)) 380.42/114.22
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.22
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.22
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.22
U31(mark(z0)) → mark(U31(z0)) 380.42/114.22
U31(ok(z0)) → ok(U31(z0)) 380.42/114.22
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.22
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.22
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.22
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.22
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.22
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.22
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.22
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.22
proper(tt) → ok(tt) 380.42/114.22
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.22
proper(s(z0)) → s(proper(z0)) 380.42/114.22
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.22
proper(U31(z0)) → U31(proper(z0)) 380.42/114.22
proper(0) → ok(0) 380.42/114.22
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.22
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.22
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.22
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.22
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.22
top(mark(z0)) → top(proper(z0)) 380.42/114.22
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.22
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.22
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.22
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.22
S(mark(z0)) → c27(S(z0)) 380.42/114.22
S(ok(z0)) → c28(S(z0)) 380.42/114.22
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.22
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.22
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.22
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.22
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.22
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.22
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.22
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.22
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.22
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.22
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.22
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.22
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.22
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.22
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.22
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.22
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.22
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.22
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.22
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.22
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.22
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.22
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.22
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.22
PROPER(U31(0)) → c46(U31'(ok(0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.22
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.22
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.22
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.22
S(mark(z0)) → c27(S(z0)) 380.42/114.22
S(ok(z0)) → c28(S(z0)) 380.42/114.22
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.22
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.22
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.22
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.22
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.22
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.22
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.22
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.22
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.22
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.22
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.22
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.22
PROPER(U41(z0, z1, z2)) → c48(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 380.42/114.22
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.22
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.22
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.22
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.22
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.22
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.22
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.22
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.22
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.22
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.22
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.22
PROPER(U31(0)) → c46(U31'(ok(0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c48, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.42/114.22
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.42/114.22
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.22
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.22
active(U31(tt)) → mark(0) 380.42/114.22
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.22
active(and(tt, z0)) → mark(z0) 380.42/114.22
active(isNat(0)) → mark(tt) 380.42/114.22
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.22
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.22
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.22
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.22
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.22
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.22
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.22
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.22
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.22
active(s(z0)) → s(active(z0)) 380.42/114.22
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.22
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.22
active(U31(z0)) → U31(active(z0)) 380.42/114.22
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.22
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.22
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.22
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.22
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.22
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.22
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.22
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.22
s(mark(z0)) → mark(s(z0)) 380.42/114.22
s(ok(z0)) → ok(s(z0)) 380.42/114.22
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.22
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.22
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.22
U31(mark(z0)) → mark(U31(z0)) 380.42/114.22
U31(ok(z0)) → ok(U31(z0)) 380.42/114.22
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.22
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.22
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.22
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.22
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.22
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.22
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.22
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.22
proper(tt) → ok(tt) 380.42/114.22
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.22
proper(s(z0)) → s(proper(z0)) 380.42/114.22
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.22
proper(U31(z0)) → U31(proper(z0)) 380.42/114.22
proper(0) → ok(0) 380.42/114.22
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.22
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.22
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.22
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.22
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.22
top(mark(z0)) → top(proper(z0)) 380.42/114.22
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.22
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.22
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.22
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.22
S(mark(z0)) → c27(S(z0)) 380.42/114.22
S(ok(z0)) → c28(S(z0)) 380.42/114.22
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.22
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.22
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.22
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.22
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.22
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.22
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.22
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.22
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.22
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.22
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.22
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.22
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.22
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.22
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.22
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.22
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.22
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.22
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.22
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.22
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.22
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.22
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.22
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.22
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.22
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.22
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.22
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.22
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.22
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.22
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.22
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.22
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.22
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.22
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.22
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.22
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.22
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.22
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.22
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.22
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.22
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.22
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.22
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.22
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.22
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.22
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.22
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.22
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.22
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.22
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.22
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.22
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.22
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.22
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.22
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.22
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.22
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.22
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.22
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.22
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.22
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.22
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.22
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.22
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.22
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.22
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.22
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.22
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.22
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.22
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.22
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.22
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.42/114.22
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.22
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.22
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.22
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.42/114.22
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.22
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.22
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.22
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.22
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.22
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.22
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.22
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.22
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.22
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.22
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.22
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.22
S(mark(z0)) → c27(S(z0)) 380.42/114.22
S(ok(z0)) → c28(S(z0)) 380.42/114.22
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.22
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.22
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.22
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.22
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.22
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.22
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.22
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.22
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.22
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.22
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.22
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.22
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.22
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.22
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.22
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.22
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.22
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.23
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.23
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.23
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.23
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.23
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.23
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.23
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.23
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.23
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 380.42/114.23
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 380.42/114.23
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.23
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.23
active(U31(tt)) → mark(0) 380.42/114.23
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.23
active(and(tt, z0)) → mark(z0) 380.42/114.23
active(isNat(0)) → mark(tt) 380.42/114.23
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.23
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.23
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.23
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.23
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.23
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.23
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.23
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.23
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.23
active(s(z0)) → s(active(z0)) 380.42/114.23
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.23
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.23
active(U31(z0)) → U31(active(z0)) 380.42/114.23
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.23
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.23
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.23
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.23
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.23
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.23
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.23
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.23
s(mark(z0)) → mark(s(z0)) 380.42/114.23
s(ok(z0)) → ok(s(z0)) 380.42/114.23
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.23
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.23
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.23
U31(mark(z0)) → mark(U31(z0)) 380.42/114.23
U31(ok(z0)) → ok(U31(z0)) 380.42/114.23
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.23
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.23
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.23
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.23
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.23
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.23
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.23
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.23
proper(tt) → ok(tt) 380.42/114.23
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.23
proper(s(z0)) → s(proper(z0)) 380.42/114.23
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.23
proper(U31(z0)) → U31(proper(z0)) 380.42/114.23
proper(0) → ok(0) 380.42/114.23
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.23
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.23
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.23
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.23
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.23
top(mark(z0)) → top(proper(z0)) 380.42/114.23
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.23
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.23
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.23
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.23
S(mark(z0)) → c27(S(z0)) 380.42/114.23
S(ok(z0)) → c28(S(z0)) 380.42/114.23
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.23
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.23
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.23
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.23
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.23
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.23
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.23
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.23
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.23
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.23
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.23
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.23
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.23
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.23
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.23
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.23
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.23
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.23
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.23
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.23
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.23
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.23
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.23
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.23
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.23
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.23
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.23
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.23
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.23
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.23
S(mark(z0)) → c27(S(z0)) 380.42/114.23
S(ok(z0)) → c28(S(z0)) 380.42/114.23
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.23
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.23
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.23
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.23
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.23
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.23
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.23
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.23
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.23
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.23
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.23
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.23
PROPER(x(z0, z1)) → c49(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.23
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.23
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.23
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.23
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.23
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.23
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.23
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.23
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.23
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.23
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.23
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.23
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.23
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.23
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.23
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.23
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.23
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.23
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.23
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.23
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.23
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.23
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.23
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.23
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.23
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.23
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.23
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.23
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.23
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.23
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c49, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.23
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.23
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.23
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.23
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.23
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.23
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.23
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.23
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.23
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.23
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.23
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.23
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.23
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.23
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.23
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.23
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.23
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.23
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.23
active(U31(tt)) → mark(0) 380.42/114.23
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.23
active(and(tt, z0)) → mark(z0) 380.42/114.23
active(isNat(0)) → mark(tt) 380.42/114.23
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.23
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.23
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.23
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.23
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.23
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.23
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.23
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.23
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.23
active(s(z0)) → s(active(z0)) 380.42/114.23
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.23
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.23
active(U31(z0)) → U31(active(z0)) 380.42/114.23
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.23
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.23
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.23
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.23
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.23
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.23
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.23
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.23
s(mark(z0)) → mark(s(z0)) 380.42/114.23
s(ok(z0)) → ok(s(z0)) 380.42/114.23
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.23
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.23
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.23
U31(mark(z0)) → mark(U31(z0)) 380.42/114.23
U31(ok(z0)) → ok(U31(z0)) 380.42/114.23
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.23
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.23
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.23
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.23
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.23
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.23
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.23
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.23
proper(tt) → ok(tt) 380.42/114.23
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.23
proper(s(z0)) → s(proper(z0)) 380.42/114.23
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.23
proper(U31(z0)) → U31(proper(z0)) 380.42/114.23
proper(0) → ok(0) 380.42/114.23
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.23
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.23
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.23
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.23
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.23
top(mark(z0)) → top(proper(z0)) 380.42/114.23
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.23
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.23
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.23
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.23
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.23
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.23
S(mark(z0)) → c27(S(z0)) 380.42/114.23
S(ok(z0)) → c28(S(z0)) 380.42/114.23
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.23
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.23
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.23
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.23
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.23
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.23
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.23
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.23
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.23
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.23
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.23
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.23
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.23
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.23
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.23
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.23
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.23
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.23
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.23
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.23
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.23
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.23
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.23
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.23
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.23
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.23
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.23
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.23
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.23
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.23
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.23
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.23
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.23
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.23
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.23
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.23
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.23
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.23
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.23
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.23
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.23
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.23
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.23
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.23
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.23
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.23
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.23
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.23
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.23
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.23
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.23
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.23
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.24
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.24
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.24
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.24
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.24
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.24
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.24
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.24
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.24
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.24
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.24
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.24
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.24
S(mark(z0)) → c27(S(z0)) 380.42/114.24
S(ok(z0)) → c28(S(z0)) 380.42/114.24
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.24
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.24
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.24
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.24
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.24
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.24
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.24
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.24
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.24
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.24
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.24
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.24
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.24
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.24
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.24
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.24
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.24
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.24
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.24
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.24
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.24
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.24
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.24
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.24
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.24
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.24
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.24
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.24
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.24
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.24
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.24
active(U31(tt)) → mark(0) 380.42/114.24
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.24
active(and(tt, z0)) → mark(z0) 380.42/114.24
active(isNat(0)) → mark(tt) 380.42/114.24
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.24
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.24
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.24
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.24
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.24
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.24
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.24
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.24
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.24
active(s(z0)) → s(active(z0)) 380.42/114.24
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.24
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.24
active(U31(z0)) → U31(active(z0)) 380.42/114.24
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.24
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.24
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.24
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.24
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.24
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.24
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.24
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.24
s(mark(z0)) → mark(s(z0)) 380.42/114.24
s(ok(z0)) → ok(s(z0)) 380.42/114.24
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.24
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.24
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.24
U31(mark(z0)) → mark(U31(z0)) 380.42/114.24
U31(ok(z0)) → ok(U31(z0)) 380.42/114.24
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.24
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.24
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.24
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.24
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.24
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.24
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.24
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.24
proper(tt) → ok(tt) 380.42/114.24
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.24
proper(s(z0)) → s(proper(z0)) 380.42/114.24
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.24
proper(U31(z0)) → U31(proper(z0)) 380.42/114.24
proper(0) → ok(0) 380.42/114.24
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.24
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.24
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.24
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.24
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.24
top(mark(z0)) → top(proper(z0)) 380.42/114.24
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.24
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.24
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.24
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.24
S(mark(z0)) → c27(S(z0)) 380.42/114.24
S(ok(z0)) → c28(S(z0)) 380.42/114.24
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.24
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.24
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.24
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.24
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.24
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.24
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.24
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.24
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.24
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.24
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.24
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.24
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.24
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.24
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.24
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.24
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.24
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.24
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.24
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.24
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.24
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.24
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.24
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.24
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.24
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.24
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.24
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.24
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.24
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.24
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.24
S(mark(z0)) → c27(S(z0)) 380.42/114.24
S(ok(z0)) → c28(S(z0)) 380.42/114.24
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.24
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.24
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.24
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.24
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.24
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.24
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.24
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.24
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.24
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.24
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.24
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.24
PROPER(and(z0, z1)) → c50(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 380.42/114.24
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.24
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.24
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.24
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.24
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.24
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.24
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.24
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.24
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.24
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.24
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.24
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.24
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.24
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.24
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.24
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.24
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.24
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.24
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.24
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.24
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.24
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.24
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.24
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.24
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.24
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.24
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.24
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.24
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.24
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.24
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.24
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.24
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.24
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.24
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.24
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.24
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.24
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.24
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.24
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.24
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.24
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.24
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.24
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.24
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.24
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.24
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.24
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.24
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.24
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.24
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.24
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.24
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.24
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.24
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.24
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.24
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.24
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.24
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.24
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.24
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.24
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.24
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.24
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.24
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.24
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.24
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.24
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c50, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.25
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.25
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.25
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.25
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.25
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.25
active(U31(tt)) → mark(0) 380.42/114.25
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.25
active(and(tt, z0)) → mark(z0) 380.42/114.25
active(isNat(0)) → mark(tt) 380.42/114.25
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.25
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.25
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.25
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.25
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.25
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.25
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.25
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.25
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.25
active(s(z0)) → s(active(z0)) 380.42/114.25
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.25
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.25
active(U31(z0)) → U31(active(z0)) 380.42/114.25
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.25
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.25
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.25
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.25
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.25
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.25
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.25
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.25
s(mark(z0)) → mark(s(z0)) 380.42/114.25
s(ok(z0)) → ok(s(z0)) 380.42/114.25
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.25
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.25
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.25
U31(mark(z0)) → mark(U31(z0)) 380.42/114.25
U31(ok(z0)) → ok(U31(z0)) 380.42/114.25
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.25
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.25
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.25
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.25
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.25
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.25
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.25
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.25
proper(tt) → ok(tt) 380.42/114.25
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.25
proper(s(z0)) → s(proper(z0)) 380.42/114.25
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.25
proper(U31(z0)) → U31(proper(z0)) 380.42/114.25
proper(0) → ok(0) 380.42/114.25
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.25
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.25
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.25
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.25
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.25
top(mark(z0)) → top(proper(z0)) 380.42/114.25
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.25
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.25
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.25
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.25
S(mark(z0)) → c27(S(z0)) 380.42/114.25
S(ok(z0)) → c28(S(z0)) 380.42/114.25
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.25
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.25
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.25
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.25
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.25
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.25
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.25
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.25
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.25
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.25
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.25
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.25
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.25
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.25
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.25
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.25
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.25
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.25
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.25
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.25
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.25
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.25
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.25
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.25
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.25
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.25
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.25
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.25
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.25
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.25
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.25
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.25
S(mark(z0)) → c27(S(z0)) 380.42/114.25
S(ok(z0)) → c28(S(z0)) 380.42/114.25
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.25
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.25
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.25
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.25
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.25
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.25
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.25
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.25
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.25
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.25
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.25
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.25
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.25
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.25
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.25
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.25
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.25
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.25
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.25
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.25
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.25
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.25
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.25
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.25
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 380.42/114.25
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 380.42/114.25
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 380.42/114.25
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 380.42/114.25
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.25
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.25
active(U31(tt)) → mark(0) 380.42/114.25
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.25
active(and(tt, z0)) → mark(z0) 380.42/114.25
active(isNat(0)) → mark(tt) 380.42/114.25
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.25
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.25
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.25
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.25
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.25
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.25
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.25
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.25
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.25
active(s(z0)) → s(active(z0)) 380.42/114.25
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.25
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.25
active(U31(z0)) → U31(active(z0)) 380.42/114.25
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.25
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.25
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.25
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.25
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.25
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.25
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.25
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.25
s(mark(z0)) → mark(s(z0)) 380.42/114.25
s(ok(z0)) → ok(s(z0)) 380.42/114.25
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.25
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.25
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.25
U31(mark(z0)) → mark(U31(z0)) 380.42/114.25
U31(ok(z0)) → ok(U31(z0)) 380.42/114.25
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.25
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.25
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.25
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.25
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.25
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.25
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.25
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.25
proper(tt) → ok(tt) 380.42/114.25
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.25
proper(s(z0)) → s(proper(z0)) 380.42/114.25
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.25
proper(U31(z0)) → U31(proper(z0)) 380.42/114.25
proper(0) → ok(0) 380.42/114.25
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.25
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.25
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.25
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.25
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.25
top(mark(z0)) → top(proper(z0)) 380.42/114.25
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.25
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.25
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.25
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.25
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.25
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.25
S(mark(z0)) → c27(S(z0)) 380.42/114.25
S(ok(z0)) → c28(S(z0)) 380.42/114.25
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.25
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.25
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.25
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.25
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.25
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.25
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.25
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.25
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.25
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.25
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.25
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.25
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.25
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.25
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.25
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.25
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.25
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.25
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.25
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.25
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.25
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.25
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.25
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.25
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.25
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.25
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.25
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.25
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.25
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.25
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.25
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.25
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.25
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.25
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.25
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.25
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.25
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.25
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.25
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.25
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.25
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.25
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.25
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.25
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.25
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.25
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.25
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.25
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.25
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.25
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.25
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.25
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.25
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.25
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.25
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.25
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.25
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.25
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.25
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.25
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.25
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.25
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.25
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.25
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.25
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.25
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.25
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.25
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.25
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.25
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.25
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.25
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.25
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.25
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.25
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.25
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.25
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.25
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.25
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.25
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.25
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.25
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.25
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.26
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.26
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.26
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.26
S(mark(z0)) → c27(S(z0)) 380.42/114.26
S(ok(z0)) → c28(S(z0)) 380.42/114.26
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.26
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.26
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.26
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.26
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.26
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.26
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.26
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.26
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.26
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.26
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.26
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.26
PROPER(isNat(z0)) → c51(ISNAT(proper(z0)), PROPER(z0)) 380.42/114.26
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.26
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.26
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.26
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.26
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.26
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.26
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.26
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.26
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.26
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.26
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.26
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, PROPER, ISNAT, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c51, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(isNat(tt)) → c51(ISNAT(ok(tt)), PROPER(tt)) 380.42/114.26
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(isNat(0)) → c51(ISNAT(ok(0)), PROPER(0)) 380.42/114.26
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.26
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.26
active(U31(tt)) → mark(0) 380.42/114.26
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.26
active(and(tt, z0)) → mark(z0) 380.42/114.26
active(isNat(0)) → mark(tt) 380.42/114.26
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.26
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.26
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.26
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.26
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.26
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.26
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.26
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.26
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.26
active(s(z0)) → s(active(z0)) 380.42/114.26
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.26
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.26
active(U31(z0)) → U31(active(z0)) 380.42/114.26
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.26
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.26
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.26
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.26
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.26
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.26
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.26
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.26
s(mark(z0)) → mark(s(z0)) 380.42/114.26
s(ok(z0)) → ok(s(z0)) 380.42/114.26
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.26
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.26
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.26
U31(mark(z0)) → mark(U31(z0)) 380.42/114.26
U31(ok(z0)) → ok(U31(z0)) 380.42/114.26
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.26
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.26
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.26
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.26
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.26
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.26
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.26
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.26
proper(tt) → ok(tt) 380.42/114.26
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.26
proper(s(z0)) → s(proper(z0)) 380.42/114.26
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.26
proper(U31(z0)) → U31(proper(z0)) 380.42/114.26
proper(0) → ok(0) 380.42/114.26
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.26
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.26
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.26
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.26
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.26
top(mark(z0)) → top(proper(z0)) 380.42/114.26
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.26
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.26
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.26
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.26
S(mark(z0)) → c27(S(z0)) 380.42/114.26
S(ok(z0)) → c28(S(z0)) 380.42/114.26
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.26
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.26
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.26
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.26
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.26
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.26
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.26
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.26
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.26
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.26
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.26
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.26
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.26
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.26
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.26
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.26
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.26
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.26
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.26
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.26
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.26
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.26
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.26
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(isNat(tt)) → c51(ISNAT(ok(tt)), PROPER(tt)) 380.42/114.26
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(isNat(0)) → c51(ISNAT(ok(0)), PROPER(0)) 380.42/114.26
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.26
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.26
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.26
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.26
S(mark(z0)) → c27(S(z0)) 380.42/114.26
S(ok(z0)) → c28(S(z0)) 380.42/114.26
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.26
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.26
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.26
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.26
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.26
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.26
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.26
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.26
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.26
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.26
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.26
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.26
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.26
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.26
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.26
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.26
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.26
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.26
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.26
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.26
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.26
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.26
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.26
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.26
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.26
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.26
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.26
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.26
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.26
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.26
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.26
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.26
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.26
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.26
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.26
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.26
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.26
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.26
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.26
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.26
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.26
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.26
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.26
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.26
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.26
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.26
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.26
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.26
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.26
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.26
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.26
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.26
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.26
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.26
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.26
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.26
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.26
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.26
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.26
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.26
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.26
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.26
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.26
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.26
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.26
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.26
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.26
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.26
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.26
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.26
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.26
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.26
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.26
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.26
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.26
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.26
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.26
PROPER(isNat(tt)) → c51(ISNAT(ok(tt)), PROPER(tt)) 380.42/114.26
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.26
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.26
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.26
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.26
PROPER(isNat(0)) → c51(ISNAT(ok(0)), PROPER(0)) 380.42/114.26
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.26
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.26
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.26
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP, PROPER
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50, c51
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.26
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.26
active(U31(tt)) → mark(0) 380.42/114.26
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.26
active(and(tt, z0)) → mark(z0) 380.42/114.26
active(isNat(0)) → mark(tt) 380.42/114.26
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.26
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.26
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.26
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.26
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.26
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.26
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.26
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.26
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.26
active(s(z0)) → s(active(z0)) 380.42/114.26
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.26
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.26
active(U31(z0)) → U31(active(z0)) 380.42/114.26
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.26
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.26
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.26
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.26
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.26
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.26
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.26
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.26
s(mark(z0)) → mark(s(z0)) 380.42/114.26
s(ok(z0)) → ok(s(z0)) 380.42/114.26
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.26
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.26
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.26
U31(mark(z0)) → mark(U31(z0)) 380.42/114.26
U31(ok(z0)) → ok(U31(z0)) 380.42/114.26
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.26
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.26
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.26
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.26
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.26
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.26
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.26
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.26
proper(tt) → ok(tt) 380.42/114.26
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.26
proper(s(z0)) → s(proper(z0)) 380.42/114.26
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.26
proper(U31(z0)) → U31(proper(z0)) 380.42/114.26
proper(0) → ok(0) 380.42/114.26
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.26
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.26
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.26
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.26
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.26
top(mark(z0)) → top(proper(z0)) 380.42/114.26
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.26
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.26
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.26
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.26
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.26
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.26
S(mark(z0)) → c27(S(z0)) 380.42/114.26
S(ok(z0)) → c28(S(z0)) 380.42/114.26
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.26
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.26
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.27
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.27
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.27
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.27
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.27
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.27
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.27
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.27
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.27
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.27
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.27
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.27
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.27
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.27
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.27
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.27
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.27
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.27
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.27
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.27
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.27
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.27
PROPER(isNat(0)) → c51(ISNAT(ok(0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.27
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.27
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.27
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.27
S(mark(z0)) → c27(S(z0)) 380.42/114.27
S(ok(z0)) → c28(S(z0)) 380.42/114.27
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.27
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.27
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.27
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.27
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.27
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.27
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.27
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.27
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.27
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.27
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.27
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.27
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.27
TOP(mark(z0)) → c53(TOP(proper(z0)), PROPER(z0)) 380.42/114.27
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.27
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.27
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.27
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.27
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.27
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.27
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.27
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.27
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.27
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.27
PROPER(isNat(0)) → c51(ISNAT(ok(0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP, PROPER
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c53, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50, c51, c51
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
TOP(mark(tt)) → c53(TOP(ok(tt)), PROPER(tt)) 380.42/114.27
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
TOP(mark(0)) → c53(TOP(ok(0)), PROPER(0)) 380.42/114.27
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.27
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.27
active(U31(tt)) → mark(0) 380.42/114.27
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.27
active(and(tt, z0)) → mark(z0) 380.42/114.27
active(isNat(0)) → mark(tt) 380.42/114.27
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.27
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.27
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.27
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.27
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.27
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.27
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.27
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.27
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.27
active(s(z0)) → s(active(z0)) 380.42/114.27
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.27
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.27
active(U31(z0)) → U31(active(z0)) 380.42/114.27
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.27
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.27
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.27
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.27
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.27
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.27
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.27
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.27
s(mark(z0)) → mark(s(z0)) 380.42/114.27
s(ok(z0)) → ok(s(z0)) 380.42/114.27
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.27
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.27
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.27
U31(mark(z0)) → mark(U31(z0)) 380.42/114.27
U31(ok(z0)) → ok(U31(z0)) 380.42/114.27
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.27
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.27
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.27
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.27
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.27
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.27
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.27
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.27
proper(tt) → ok(tt) 380.42/114.27
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.27
proper(s(z0)) → s(proper(z0)) 380.42/114.27
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.27
proper(U31(z0)) → U31(proper(z0)) 380.42/114.27
proper(0) → ok(0) 380.42/114.27
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.27
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.27
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.27
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.27
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.27
top(mark(z0)) → top(proper(z0)) 380.42/114.27
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.27
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.27
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.27
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.27
S(mark(z0)) → c27(S(z0)) 380.42/114.27
S(ok(z0)) → c28(S(z0)) 380.42/114.27
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.27
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.27
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.27
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.27
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.27
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.27
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.27
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.27
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.27
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.27
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.27
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.27
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.27
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.27
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.27
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.27
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.27
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.27
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.27
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.27
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.27
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.27
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.27
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.27
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.27
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.27
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.27
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.27
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.27
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.27
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.27
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.27
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.27
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.27
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.27
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.27
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.27
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.27
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.27
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.27
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.27
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.27
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.27
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.27
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.27
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.27
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.27
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.27
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.27
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.27
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.27
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.27
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.27
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.27
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.27
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.27
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.27
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.27
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.27
TOP(mark(tt)) → c53(TOP(ok(tt)), PROPER(tt)) 380.42/114.27
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.27
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.27
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.27
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.27
TOP(mark(0)) → c53(TOP(ok(0)), PROPER(0)) 380.42/114.27
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.27
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.27
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.27
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.27
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.27
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.27
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.27
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.27
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.27
S(mark(z0)) → c27(S(z0)) 380.42/114.27
S(ok(z0)) → c28(S(z0)) 380.42/114.27
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.27
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.27
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.27
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.27
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.27
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.27
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.27
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.27
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.27
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.27
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.27
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.27
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.27
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.27
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.27
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.27
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.27
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.27
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.27
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.27
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.27
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.27
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.27
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.27
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.27
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.27
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.27
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.27
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.27
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.27
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.27
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.27
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.28
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.28
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.28
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.28
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.28
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.28
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.28
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.28
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.28
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.28
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.28
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
TOP(mark(tt)) → c53(TOP(ok(tt)), PROPER(tt)) 380.42/114.28
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
TOP(mark(0)) → c53(TOP(ok(0)), PROPER(0)) 380.42/114.28
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP, PROPER
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50, c51, c51, c53
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.28
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.28
active(U31(tt)) → mark(0) 380.42/114.28
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.28
active(and(tt, z0)) → mark(z0) 380.42/114.28
active(isNat(0)) → mark(tt) 380.42/114.28
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.28
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.28
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.28
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.28
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.28
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.28
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.28
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.28
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.28
active(s(z0)) → s(active(z0)) 380.42/114.28
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.28
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.28
active(U31(z0)) → U31(active(z0)) 380.42/114.28
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.28
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.28
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.28
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.28
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.28
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.28
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.28
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.28
s(mark(z0)) → mark(s(z0)) 380.42/114.28
s(ok(z0)) → ok(s(z0)) 380.42/114.28
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.28
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.28
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.28
U31(mark(z0)) → mark(U31(z0)) 380.42/114.28
U31(ok(z0)) → ok(U31(z0)) 380.42/114.28
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.28
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.28
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.28
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.28
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.28
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.28
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.28
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.28
proper(tt) → ok(tt) 380.42/114.28
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.28
proper(s(z0)) → s(proper(z0)) 380.42/114.28
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.28
proper(U31(z0)) → U31(proper(z0)) 380.42/114.28
proper(0) → ok(0) 380.42/114.28
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.28
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.28
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.28
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.28
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.28
top(mark(z0)) → top(proper(z0)) 380.42/114.28
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.28
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.28
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.28
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.28
S(mark(z0)) → c27(S(z0)) 380.42/114.28
S(ok(z0)) → c28(S(z0)) 380.42/114.28
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.28
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.28
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.28
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.28
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.28
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.28
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.28
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.28
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.28
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.28
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.28
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.28
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.28
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.28
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.28
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.28
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.28
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.28
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.28
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.28
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.28
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.28
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.28
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.28
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.28
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.28
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.28
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.28
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.28
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.28
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.28
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.28
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.28
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.28
TOP(mark(0)) → c53(TOP(ok(0)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.28
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.28
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.28
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.28
S(mark(z0)) → c27(S(z0)) 380.42/114.28
S(ok(z0)) → c28(S(z0)) 380.42/114.28
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.28
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.28
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.28
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.28
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.28
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.28
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.28
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.28
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.28
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.28
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.28
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.28
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.28
TOP(ok(z0)) → c54(TOP(active(z0)), ACTIVE(z0)) 380.42/114.28
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.28
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.28
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.28
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.28
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.28
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.28
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.28
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.28
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.28
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.28
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.28
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.28
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.28
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.28
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.28
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.28
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.28
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.28
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.28
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.28
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.28
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.28
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.28
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.28
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.28
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.28
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.28
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.28
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.28
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.28
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.28
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.28
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.28
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.28
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.28
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.28
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.28
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.28
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.28
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.28
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.28
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.28
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.28
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.28
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.28
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.28
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.28
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.28
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.28
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.28
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.28
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.28
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.28
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.28
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.28
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.28
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.28
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.28
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.28
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.28
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.28
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.28
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.28
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.28
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.28
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.28
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.28
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.28
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.28
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.28
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.28
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.28
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.28
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.28
TOP(mark(0)) → c53(TOP(ok(0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP, PROPER
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c54, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50, c51, c51, c53, c53
TOP(ok(U11(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(U11(tt, z0))) 380.42/114.28
TOP(ok(U21(tt, z0, z1))) → c54(TOP(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 380.42/114.28
TOP(ok(U31(tt))) → c54(TOP(mark(0)), ACTIVE(U31(tt))) 380.42/114.28
TOP(ok(U41(tt, z0, z1))) → c54(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 380.42/114.28
TOP(ok(and(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(and(tt, z0))) 380.42/114.28
TOP(ok(isNat(0))) → c54(TOP(mark(tt)), ACTIVE(isNat(0))) 380.42/114.28
TOP(ok(isNat(plus(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 380.42/114.28
TOP(ok(isNat(s(z0)))) → c54(TOP(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 380.42/114.28
TOP(ok(isNat(x(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 380.42/114.28
TOP(ok(plus(z0, 0))) → c54(TOP(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.28
TOP(ok(plus(z0, s(z1)))) → c54(TOP(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.28
TOP(ok(x(z0, 0))) → c54(TOP(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.28
TOP(ok(x(z0, s(z1)))) → c54(TOP(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.28
TOP(ok(U11(z0, z1))) → c54(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.28
TOP(ok(U21(z0, z1, z2))) → c54(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.28
TOP(ok(s(z0))) → c54(TOP(s(active(z0))), ACTIVE(s(z0))) 380.42/114.28
TOP(ok(plus(z0, z1))) → c54(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.28
TOP(ok(plus(z0, z1))) → c54(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.28
TOP(ok(U31(z0))) → c54(TOP(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.28
TOP(ok(U41(z0, z1, z2))) → c54(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.28
TOP(ok(x(z0, z1))) → c54(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.28
TOP(ok(x(z0, z1))) → c54(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.28
TOP(ok(and(z0, z1))) → c54(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.28
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.28
active(U31(tt)) → mark(0) 380.42/114.28
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.28
active(and(tt, z0)) → mark(z0) 380.42/114.28
active(isNat(0)) → mark(tt) 380.42/114.28
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.28
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.28
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.28
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.28
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.28
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.28
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.28
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.28
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.28
active(s(z0)) → s(active(z0)) 380.42/114.28
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.28
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.28
active(U31(z0)) → U31(active(z0)) 380.42/114.28
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.28
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.28
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.28
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.28
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.28
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.28
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.28
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.28
s(mark(z0)) → mark(s(z0)) 380.42/114.28
s(ok(z0)) → ok(s(z0)) 380.42/114.28
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.28
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.28
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.28
U31(mark(z0)) → mark(U31(z0)) 380.42/114.28
U31(ok(z0)) → ok(U31(z0)) 380.42/114.28
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.28
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.28
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.28
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.28
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.28
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.28
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.28
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.28
proper(tt) → ok(tt) 380.42/114.28
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.28
proper(s(z0)) → s(proper(z0)) 380.42/114.28
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.28
proper(U31(z0)) → U31(proper(z0)) 380.42/114.28
proper(0) → ok(0) 380.42/114.28
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.28
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.28
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.28
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.28
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.28
top(mark(z0)) → top(proper(z0)) 380.42/114.28
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.28
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.28
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.28
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.28
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.28
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.28
S(mark(z0)) → c27(S(z0)) 380.42/114.28
S(ok(z0)) → c28(S(z0)) 380.42/114.28
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.28
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.28
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.28
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.28
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.28
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.28
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.28
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.28
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.29
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.29
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.29
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.29
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.29
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.29
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.29
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.29
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.29
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.29
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.29
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.29
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.29
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.29
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.29
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.29
TOP(mark(0)) → c53(TOP(ok(0))) 380.42/114.29
TOP(ok(U11(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(U11(tt, z0))) 380.42/114.29
TOP(ok(U21(tt, z0, z1))) → c54(TOP(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 380.42/114.29
TOP(ok(U31(tt))) → c54(TOP(mark(0)), ACTIVE(U31(tt))) 380.42/114.29
TOP(ok(U41(tt, z0, z1))) → c54(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 380.42/114.29
TOP(ok(and(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(and(tt, z0))) 380.42/114.29
TOP(ok(isNat(0))) → c54(TOP(mark(tt)), ACTIVE(isNat(0))) 380.42/114.29
TOP(ok(isNat(plus(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
TOP(ok(isNat(s(z0)))) → c54(TOP(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 380.42/114.29
TOP(ok(isNat(x(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
TOP(ok(plus(z0, 0))) → c54(TOP(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
TOP(ok(plus(z0, s(z1)))) → c54(TOP(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
TOP(ok(x(z0, 0))) → c54(TOP(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
TOP(ok(x(z0, s(z1)))) → c54(TOP(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
TOP(ok(U11(z0, z1))) → c54(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
TOP(ok(U21(z0, z1, z2))) → c54(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
TOP(ok(s(z0))) → c54(TOP(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(U31(z0))) → c54(TOP(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
TOP(ok(U41(z0, z1, z2))) → c54(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(and(z0, z1))) → c54(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))
K tuples:none
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.29
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.29
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.29
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.29
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.29
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.29
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.29
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.29
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.29
S(mark(z0)) → c27(S(z0)) 380.42/114.29
S(ok(z0)) → c28(S(z0)) 380.42/114.29
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.29
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.29
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.29
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.29
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.29
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.29
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.29
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.29
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.29
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.29
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.29
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.29
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.29
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.29
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.29
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.29
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.29
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.29
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.29
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.29
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.29
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.29
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.29
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.29
TOP(mark(0)) → c53(TOP(ok(0))) 380.42/114.29
TOP(ok(U11(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(U11(tt, z0))) 380.42/114.29
TOP(ok(U21(tt, z0, z1))) → c54(TOP(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 380.42/114.29
TOP(ok(U31(tt))) → c54(TOP(mark(0)), ACTIVE(U31(tt))) 380.42/114.29
TOP(ok(U41(tt, z0, z1))) → c54(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 380.42/114.29
TOP(ok(and(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(and(tt, z0))) 380.42/114.29
TOP(ok(isNat(0))) → c54(TOP(mark(tt)), ACTIVE(isNat(0))) 380.42/114.29
TOP(ok(isNat(plus(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
TOP(ok(isNat(s(z0)))) → c54(TOP(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 380.42/114.29
TOP(ok(isNat(x(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
TOP(ok(plus(z0, 0))) → c54(TOP(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
TOP(ok(plus(z0, s(z1)))) → c54(TOP(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
TOP(ok(x(z0, 0))) → c54(TOP(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
TOP(ok(x(z0, s(z1)))) → c54(TOP(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
TOP(ok(U11(z0, z1))) → c54(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
TOP(ok(U21(z0, z1, z2))) → c54(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
TOP(ok(s(z0))) → c54(TOP(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(U31(z0))) → c54(TOP(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
TOP(ok(U41(z0, z1, z2))) → c54(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(and(z0, z1))) → c54(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
ACTIVE, U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, PROPER, TOP
c7, c16, c17, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c, c13, c13, c1, c14, c14, c2, c15, c15, c3, c18, c18, c4, c19, c19, c5, c22, c22, c6, c41, c41, c43, c43, c44, c44, c45, c45, c46, c46, c48, c48, c49, c49, c50, c50, c51, c51, c53, c53, c54
ACTIVE(isNat(s(z0))) → c7(ISNAT(z0)) 380.42/114.29
ACTIVE(plus(z0, z1)) → c16(PLUS(active(z0), z1), ACTIVE(z0)) 380.42/114.29
ACTIVE(plus(z0, z1)) → c17(PLUS(z0, active(z1)), ACTIVE(z1)) 380.42/114.29
ACTIVE(x(z0, z1)) → c20(X(active(z0), z1), ACTIVE(z0)) 380.42/114.29
ACTIVE(x(z0, z1)) → c21(X(z0, active(z1)), ACTIVE(z1)) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(S(plus(z1, z0))) 380.42/114.29
ACTIVE(U21(tt, z0, z1)) → c(PLUS(z1, z0)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(PLUS(x(z1, z0), z1)) 380.42/114.29
ACTIVE(U41(tt, z0, z1)) → c(X(z1, z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(plus(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(AND(isNat(z0), isNat(z1))) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(isNat(x(z0, z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(U11'(isNat(z0), z0)) 380.42/114.29
ACTIVE(plus(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, 0)) → c(U31'(isNat(z0))) 380.42/114.29
ACTIVE(x(z0, 0)) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(plus(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z1)) 380.42/114.29
ACTIVE(x(z0, s(z1))) → c(ISNAT(z0)) 380.42/114.29
ACTIVE(U11(plus(z0, 0), x1)) → c13(U11'(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U11(plus(z0, s(z1)), x1)) → c13(U11'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(x(z0, 0), x1)) → c13(U11'(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U11(x(z0, s(z1)), x1)) → c13(U11'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U11(U11(z0, z1), x1)) → c13(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U11(U21(z0, z1, z2), x1)) → c13(U11'(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(s(z0), x1)) → c13(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(plus(z0, z1), x1)) → c13(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(z0), x1)) → c13(U11'(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U11(U41(z0, z1, z2), x1)) → c13(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(x(z0, z1), x1)) → c13(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U11(and(z0, z1), x1)) → c13(U11'(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U11(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U11(isNat(0), x1)) → c13(U11'(mark(tt), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c1(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(U11'(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(U11(isNat(s(z0)), x1)) → c1(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(U11'(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c1(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U21(plus(z0, 0), x1, x2)) → c14(U21'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c14(U21'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(x(z0, 0), x1, x2)) → c14(U21'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c14(U21'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U21(U11(z0, z1), x1, x2)) → c14(U21'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c14(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(s(z0), x1, x2)) → c14(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(plus(z0, z1), x1, x2)) → c14(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U21(U31(z0), x1, x2)) → c14(U21'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U21(U41(z0, z1, z2), x1, x2)) → c14(U21'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(x(z0, z1), x1, x2)) → c14(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U21(and(z0, z1), x1, x2)) → c14(U21'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U21(U11(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(0), x1, x2)) → c14(U21'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(U11'(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(U11(U21(tt, z0, z1), x1)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(U21'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c2(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(plus(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(U21'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(s(z0)), x1, x2)) → c2(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(U21'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U21(isNat(x(z0, z1)), x1, x2)) → c2(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(s(plus(z0, 0))) → c15(S(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(s(plus(z0, s(z1)))) → c15(S(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(s(x(z0, 0))) → c15(S(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(s(x(z0, s(z1)))) → c15(S(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(s(U11(z0, z1))) → c15(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(s(U21(z0, z1, z2))) → c15(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(s(s(z0))) → c15(S(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(plus(z0, z1))) → c15(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(s(U31(z0))) → c15(S(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(s(U41(z0, z1, z2))) → c15(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(x(z0, z1))) → c15(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(s(and(z0, z1))) → c15(S(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(s(U11(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(s(isNat(0))) → c15(S(mark(tt))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(S(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(s(U21(tt, z0, z1))) → c3(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(S(mark(isNat(z0)))) 380.42/114.29
ACTIVE(s(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(S(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(s(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U31(plus(z0, 0))) → c18(U31'(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U31(plus(z0, s(z1)))) → c18(U31'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(x(z0, 0))) → c18(U31'(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U31(x(z0, s(z1)))) → c18(U31'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U31(U11(z0, z1))) → c18(U31'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U31(U21(z0, z1, z2))) → c18(U31'(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(s(z0))) → c18(U31'(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(plus(z0, z1))) → c18(U31'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U31(U31(z0))) → c18(U31'(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U31(U41(z0, z1, z2))) → c18(U31'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(x(z0, z1))) → c18(U31'(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U31(and(z0, z1))) → c18(U31'(and(active(z0), z1)), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(U31(tt), x1)) → c13(U11'(mark(0), x1)) 380.42/114.29
ACTIVE(U21(U31(tt), x1, x2)) → c14(U21'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(s(U31(tt))) → c15(S(mark(0))) 380.42/114.29
ACTIVE(U31(U11(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U31(U31(tt))) → c18(U31'(mark(0))) 380.42/114.29
ACTIVE(U31(isNat(0))) → c18(U31'(mark(tt))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(U31'(mark(s(plus(z1, z0))))) 380.42/114.29
ACTIVE(U31(U21(tt, z0, z1))) → c4(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(plus(z0, z1)))) → c4(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(U31'(mark(isNat(z0)))) 380.42/114.29
ACTIVE(U31(isNat(s(z0)))) → c4(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(U31'(mark(and(isNat(z0), isNat(z1))))) 380.42/114.29
ACTIVE(U31(isNat(x(z0, z1)))) → c4(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(U41(plus(z0, 0), x1, x2)) → c19(U41'(mark(U11(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c19(U41'(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(x(z0, 0), x1, x2)) → c19(U41'(mark(U31(isNat(z0))), x1, x2), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(U41(x(z0, s(z1)), x1, x2)) → c19(U41'(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(U41(U11(z0, z1), x1, x2)) → c19(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(U41(U21(z0, z1, z2), x1, x2)) → c19(U41'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(s(z0), x1, x2)) → c19(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(plus(z0, z1), x1, x2)) → c19(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(U41(U31(z0), x1, x2)) → c19(U41'(U31(active(z0)), x1, x2), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c19(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(x(z0, z1), x1, x2)) → c19(U41'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(U41(and(z0, z1), x1, x2)) → c19(U41'(and(active(z0), z1), x1, x2), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U41(U11(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(U41(U31(tt), x1, x2)) → c19(U41'(mark(0), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(0), x1, x2)) → c19(U41'(mark(tt), x1, x2)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U21(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(S(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(s(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(U31'(mark(plus(x(z1, z0), z1)))) 380.42/114.29
ACTIVE(U31(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(U41'(mark(s(plus(z1, z0))), x1, x2)) 380.42/114.29
ACTIVE(U41(U21(tt, z0, z1), x1, x2)) → c5(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(plus(x(z1, z0), z1)), x1, x2)) 380.42/114.29
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(isNat(z0)), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(U41'(mark(and(isNat(z0), isNat(z1))), x1, x2)) 380.42/114.29
ACTIVE(U41(isNat(x(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
ACTIVE(and(plus(z0, 0), x1)) → c22(AND(mark(U11(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 380.42/114.29
ACTIVE(and(plus(z0, s(z1)), x1)) → c22(AND(mark(U21(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
ACTIVE(and(x(z0, 0), x1)) → c22(AND(mark(U31(isNat(z0))), x1), ACTIVE(x(z0, 0))) 380.42/114.29
ACTIVE(and(x(z0, s(z1)), x1)) → c22(AND(mark(U41(and(isNat(z1), isNat(z0)), z1, z0)), x1), ACTIVE(x(z0, s(z1)))) 380.42/114.29
ACTIVE(and(U11(z0, z1), x1)) → c22(AND(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 380.42/114.29
ACTIVE(and(U21(z0, z1, z2), x1)) → c22(AND(U21(active(z0), z1, z2), x1), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
ACTIVE(and(s(z0), x1)) → c22(AND(s(active(z0)), x1), ACTIVE(s(z0))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(plus(z0, z1), x1)) → c22(AND(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 380.42/114.29
ACTIVE(and(U31(z0), x1)) → c22(AND(U31(active(z0)), x1), ACTIVE(U31(z0))) 380.42/114.29
ACTIVE(and(U41(z0, z1, z2), x1)) → c22(AND(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(active(z0), z1), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(x(z0, z1), x1)) → c22(AND(x(z0, active(z1)), x1), ACTIVE(x(z0, z1))) 380.42/114.29
ACTIVE(and(and(z0, z1), x1)) → c22(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1))) 380.42/114.29
ACTIVE(U11(and(tt, z0), x1)) → c13(U11'(mark(z0), x1)) 380.42/114.29
ACTIVE(U21(and(tt, z0), x1, x2)) → c14(U21'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(s(and(tt, z0))) → c15(S(mark(z0))) 380.42/114.29
ACTIVE(U31(and(tt, z0))) → c18(U31'(mark(z0))) 380.42/114.29
ACTIVE(U41(and(tt, z0), x1, x2)) → c19(U41'(mark(z0), x1, x2)) 380.42/114.29
ACTIVE(and(U11(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(U31(tt), x1)) → c22(AND(mark(0), x1)) 380.42/114.29
ACTIVE(and(and(tt, z0), x1)) → c22(AND(mark(z0), x1)) 380.42/114.29
ACTIVE(and(isNat(0), x1)) → c22(AND(mark(tt), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(AND(mark(s(plus(z1, z0))), x1)) 380.42/114.29
ACTIVE(and(U21(tt, z0, z1), x1)) → c6(ACTIVE(U21(tt, z0, z1))) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(AND(mark(plus(x(z1, z0), z1)), x1)) 380.42/114.29
ACTIVE(and(U41(tt, z0, z1), x1)) → c6(ACTIVE(U41(tt, z0, z1))) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(AND(mark(isNat(z0)), x1)) 380.42/114.29
ACTIVE(and(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0)))) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(AND(mark(and(isNat(z0), isNat(z1))), x1)) 380.42/114.29
ACTIVE(and(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
PROPER(U11(x0, U11(z0, z1))) → c41(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U11(x0, U21(z0, z1, z2))) → c41(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, s(z0))) → c41(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(U11(x0, plus(z0, z1))) → c41(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U11(x0, U31(z0))) → c41(U11'(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(U11(x0, U41(z0, z1, z2))) → c41(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U11(x0, x(z0, z1))) → c41(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U11(x0, and(z0, z1))) → c41(U11'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U11(x0, isNat(z0))) → c41(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(U11(U11(z0, z1), x1)) → c41(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U21(z0, z1, z2), x1)) → c41(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(s(z0), x1)) → c41(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(plus(z0, z1), x1)) → c41(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(U31(z0), x1)) → c41(U11'(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(U41(z0, z1, z2), x1)) → c41(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(U11(x(z0, z1), x1)) → c41(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(and(z0, z1), x1)) → c41(U11'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(U11(isNat(z0), x1)) → c41(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(U11(x0, tt)) → c41(U11'(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(U11(x0, 0)) → c41(U11'(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(U11(tt, x1)) → c41(U11'(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U11(0, x1)) → c41(U11'(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, U11(z0, z1))) → c43(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, s(z0))) → c43(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U21(x0, x1, plus(z0, z1))) → c43(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, U31(z0))) → c43(U21'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U21(x0, x1, U41(z0, z1, z2))) → c43(U21'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U21(x0, x1, x(z0, z1))) → c43(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, and(z0, z1))) → c43(U21'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U21(x0, x1, isNat(z0))) → c43(U21'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U21(x0, U11(z0, z1), x2)) → c43(U21'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c43(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, s(z0), x2)) → c43(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, plus(z0, z1), x2)) → c43(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U31(z0), x2)) → c43(U21'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, U41(z0, z1, z2), x2)) → c43(U21'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x(z0, z1), x2)) → c43(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, and(z0, z1), x2)) → c43(U21'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, isNat(z0), x2)) → c43(U21'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U21(U11(z0, z1), x1, x2)) → c43(U21'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c43(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(s(z0), x1, x2)) → c43(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(plus(z0, z1), x1, x2)) → c43(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U31(z0), x1, x2)) → c43(U21'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(U41(z0, z1, z2), x1, x2)) → c43(U21'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x(z0, z1), x1, x2)) → c43(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(and(z0, z1), x1, x2)) → c43(U21'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(isNat(z0), x1, x2)) → c43(U21'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, x1, tt)) → c43(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, x1, 0)) → c43(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U21(x0, tt, x2)) → c43(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(x0, 0, x2)) → c43(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U21(tt, x1, x2)) → c43(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U21(0, x1, x2)) → c43(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(s(U11(z0, z1))) → c44(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(s(U21(z0, z1, z2))) → c44(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(s(s(z0))) → c44(S(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(s(plus(z0, z1))) → c44(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(s(U31(z0))) → c44(S(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(s(U41(z0, z1, z2))) → c44(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(s(x(z0, z1))) → c44(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(s(and(z0, z1))) → c44(S(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(s(isNat(z0))) → c44(S(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(s(tt)) → c44(S(ok(tt))) 380.42/114.29
PROPER(s(0)) → c44(S(ok(0))) 380.42/114.29
PROPER(plus(x0, U11(z0, z1))) → c45(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(plus(x0, U21(z0, z1, z2))) → c45(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, s(z0))) → c45(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(plus(x0, plus(z0, z1))) → c45(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(plus(x0, U31(z0))) → c45(PLUS(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(plus(x0, U41(z0, z1, z2))) → c45(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(plus(x0, x(z0, z1))) → c45(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(plus(x0, and(z0, z1))) → c45(PLUS(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(plus(x0, isNat(z0))) → c45(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(plus(U11(z0, z1), x1)) → c45(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U21(z0, z1, z2), x1)) → c45(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(s(z0), x1)) → c45(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(plus(z0, z1), x1)) → c45(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(U31(z0), x1)) → c45(PLUS(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(U41(z0, z1, z2), x1)) → c45(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(plus(x(z0, z1), x1)) → c45(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(and(z0, z1), x1)) → c45(PLUS(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(plus(isNat(z0), x1)) → c45(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(plus(x0, tt)) → c45(PLUS(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(plus(x0, 0)) → c45(PLUS(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(plus(tt, x1)) → c45(PLUS(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(plus(0, x1)) → c45(PLUS(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(U31(U11(z0, z1))) → c46(U31'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U31(U21(z0, z1, z2))) → c46(U31'(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U31(s(z0))) → c46(U31'(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(U31(plus(z0, z1))) → c46(U31'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U31(U31(z0))) → c46(U31'(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(U31(U41(z0, z1, z2))) → c46(U31'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U31(x(z0, z1))) → c46(U31'(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U31(and(z0, z1))) → c46(U31'(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U31(isNat(z0))) → c46(U31'(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(U31(tt)) → c46(U31'(ok(tt))) 380.42/114.29
PROPER(U31(0)) → c46(U31'(ok(0))) 380.42/114.29
PROPER(U41(x0, x1, U11(z0, z1))) → c48(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U21(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, s(z0))) → c48(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 380.42/114.29
PROPER(U41(x0, x1, plus(z0, z1))) → c48(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, U31(z0))) → c48(U41'(proper(x0), proper(x1), U31(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U31(z0))) 380.42/114.29
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c48(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(U41(x0, x1, x(z0, z1))) → c48(U41'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, and(z0, z1))) → c48(U41'(proper(x0), proper(x1), and(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(and(z0, z1))) 380.42/114.29
PROPER(U41(x0, x1, isNat(z0))) → c48(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 380.42/114.29
PROPER(U41(x0, U11(z0, z1), x2)) → c48(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U21(z0, z1, z2), x2)) → c48(U41'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, s(z0), x2)) → c48(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, plus(z0, z1), x2)) → c48(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U31(z0), x2)) → c48(U41'(proper(x0), U31(proper(z0)), proper(x2)), PROPER(x0), PROPER(U31(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c48(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x(z0, z1), x2)) → c48(U41'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, and(z0, z1), x2)) → c48(U41'(proper(x0), and(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(and(z0, z1)), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, isNat(z0), x2)) → c48(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 380.42/114.29
PROPER(U41(U11(z0, z1), x1, x2)) → c48(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U21(z0, z1, z2), x1, x2)) → c48(U41'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(s(z0), x1, x2)) → c48(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(plus(z0, z1), x1, x2)) → c48(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U31(z0), x1, x2)) → c48(U41'(U31(proper(z0)), proper(x1), proper(x2)), PROPER(U31(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c48(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x(z0, z1), x1, x2)) → c48(U41'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(and(z0, z1), x1, x2)) → c48(U41'(and(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(and(z0, z1)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(isNat(z0), x1, x2)) → c48(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, x1, tt)) → c48(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, x1, 0)) → c48(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 380.42/114.29
PROPER(U41(x0, tt, x2)) → c48(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(x0, 0, x2)) → c48(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 380.42/114.29
PROPER(U41(tt, x1, x2)) → c48(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(U41(0, x1, x2)) → c48(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 380.42/114.29
PROPER(x(x0, U11(z0, z1))) → c49(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(x(x0, U21(z0, z1, z2))) → c49(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, s(z0))) → c49(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(x(x0, plus(z0, z1))) → c49(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(x(x0, U31(z0))) → c49(X(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(x(x0, U41(z0, z1, z2))) → c49(X(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(x(x0, x(z0, z1))) → c49(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(x(x0, and(z0, z1))) → c49(X(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(x(x0, isNat(z0))) → c49(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(x(U11(z0, z1), x1)) → c49(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U21(z0, z1, z2), x1)) → c49(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(s(z0), x1)) → c49(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(plus(z0, z1), x1)) → c49(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(U31(z0), x1)) → c49(X(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(U41(z0, z1, z2), x1)) → c49(X(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(x(x(z0, z1), x1)) → c49(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(and(z0, z1), x1)) → c49(X(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(x(isNat(z0), x1)) → c49(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(x(x0, tt)) → c49(X(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(x(x0, 0)) → c49(X(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(x(tt, x1)) → c49(X(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(x(0, x1)) → c49(X(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, U11(z0, z1))) → c50(AND(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(and(x0, U21(z0, z1, z2))) → c50(AND(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, s(z0))) → c50(AND(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 380.42/114.29
PROPER(and(x0, plus(z0, z1))) → c50(AND(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(and(x0, U31(z0))) → c50(AND(proper(x0), U31(proper(z0))), PROPER(x0), PROPER(U31(z0))) 380.42/114.29
PROPER(and(x0, U41(z0, z1, z2))) → c50(AND(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(and(x0, x(z0, z1))) → c50(AND(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 380.42/114.29
PROPER(and(x0, and(z0, z1))) → c50(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1))) 380.42/114.29
PROPER(and(x0, isNat(z0))) → c50(AND(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 380.42/114.29
PROPER(and(U11(z0, z1), x1)) → c50(AND(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U21(z0, z1, z2), x1)) → c50(AND(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(s(z0), x1)) → c50(AND(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(plus(z0, z1), x1)) → c50(AND(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(U31(z0), x1)) → c50(AND(U31(proper(z0)), proper(x1)), PROPER(U31(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(U41(z0, z1, z2), x1)) → c50(AND(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 380.42/114.29
PROPER(and(x(z0, z1), x1)) → c50(AND(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(and(z0, z1), x1)) → c50(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1)) 380.42/114.29
PROPER(and(isNat(z0), x1)) → c50(AND(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 380.42/114.29
PROPER(and(x0, tt)) → c50(AND(proper(x0), ok(tt)), PROPER(x0)) 380.42/114.29
PROPER(and(x0, 0)) → c50(AND(proper(x0), ok(0)), PROPER(x0)) 380.42/114.29
PROPER(and(tt, x1)) → c50(AND(ok(tt), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(and(0, x1)) → c50(AND(ok(0), proper(x1)), PROPER(x1)) 380.42/114.29
PROPER(isNat(U11(z0, z1))) → c51(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
PROPER(isNat(U21(z0, z1, z2))) → c51(ISNAT(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
PROPER(isNat(s(z0))) → c51(ISNAT(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
PROPER(isNat(plus(z0, z1))) → c51(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
PROPER(isNat(U31(z0))) → c51(ISNAT(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
PROPER(isNat(U41(z0, z1, z2))) → c51(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
PROPER(isNat(x(z0, z1))) → c51(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
PROPER(isNat(and(z0, z1))) → c51(ISNAT(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
PROPER(isNat(isNat(z0))) → c51(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
PROPER(isNat(tt)) → c51(ISNAT(ok(tt))) 380.42/114.29
PROPER(isNat(0)) → c51(ISNAT(ok(0))) 380.42/114.29
TOP(mark(U11(z0, z1))) → c53(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 380.42/114.29
TOP(mark(U21(z0, z1, z2))) → c53(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 380.42/114.29
TOP(mark(s(z0))) → c53(TOP(s(proper(z0))), PROPER(s(z0))) 380.42/114.29
TOP(mark(plus(z0, z1))) → c53(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 380.42/114.29
TOP(mark(U31(z0))) → c53(TOP(U31(proper(z0))), PROPER(U31(z0))) 380.42/114.29
TOP(mark(U41(z0, z1, z2))) → c53(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 380.42/114.29
TOP(mark(x(z0, z1))) → c53(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 380.42/114.29
TOP(mark(and(z0, z1))) → c53(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1))) 380.42/114.29
TOP(mark(isNat(z0))) → c53(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 380.42/114.29
TOP(ok(U11(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(U11(tt, z0))) 380.42/114.29
TOP(ok(U21(tt, z0, z1))) → c54(TOP(mark(s(plus(z1, z0)))), ACTIVE(U21(tt, z0, z1))) 380.42/114.29
TOP(ok(U31(tt))) → c54(TOP(mark(0)), ACTIVE(U31(tt))) 380.42/114.29
TOP(ok(U41(tt, z0, z1))) → c54(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U41(tt, z0, z1))) 380.42/114.29
TOP(ok(and(tt, z0))) → c54(TOP(mark(z0)), ACTIVE(and(tt, z0))) 380.42/114.29
TOP(ok(isNat(0))) → c54(TOP(mark(tt)), ACTIVE(isNat(0))) 380.42/114.29
TOP(ok(isNat(plus(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(plus(z0, z1)))) 380.42/114.29
TOP(ok(isNat(s(z0)))) → c54(TOP(mark(isNat(z0))), ACTIVE(isNat(s(z0)))) 380.42/114.29
TOP(ok(isNat(x(z0, z1)))) → c54(TOP(mark(and(isNat(z0), isNat(z1)))), ACTIVE(isNat(x(z0, z1)))) 380.42/114.29
TOP(ok(plus(z0, 0))) → c54(TOP(mark(U11(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 380.42/114.29
TOP(ok(plus(z0, s(z1)))) → c54(TOP(mark(U21(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(plus(z0, s(z1)))) 380.42/114.29
TOP(ok(x(z0, 0))) → c54(TOP(mark(U31(isNat(z0)))), ACTIVE(x(z0, 0))) 380.42/114.29
TOP(ok(x(z0, s(z1)))) → c54(TOP(mark(U41(and(isNat(z1), isNat(z0)), z1, z0))), ACTIVE(x(z0, s(z1)))) 380.42/114.29
TOP(ok(U11(z0, z1))) → c54(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 380.42/114.29
TOP(ok(U21(z0, z1, z2))) → c54(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 380.42/114.29
TOP(ok(s(z0))) → c54(TOP(s(active(z0))), ACTIVE(s(z0))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(plus(z0, z1))) → c54(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 380.42/114.29
TOP(ok(U31(z0))) → c54(TOP(U31(active(z0))), ACTIVE(U31(z0))) 380.42/114.29
TOP(ok(U41(z0, z1, z2))) → c54(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(x(z0, z1))) → c54(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1))) 380.42/114.29
TOP(ok(and(z0, z1))) → c54(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.29
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.29
active(U31(tt)) → mark(0) 380.42/114.29
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.29
active(and(tt, z0)) → mark(z0) 380.42/114.29
active(isNat(0)) → mark(tt) 380.42/114.29
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.29
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.29
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.29
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.29
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.29
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.29
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.29
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.29
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.29
active(s(z0)) → s(active(z0)) 380.42/114.29
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.29
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.29
active(U31(z0)) → U31(active(z0)) 380.42/114.29
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.29
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.29
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.29
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.29
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.29
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.29
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.29
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.29
s(mark(z0)) → mark(s(z0)) 380.42/114.29
s(ok(z0)) → ok(s(z0)) 380.42/114.29
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.29
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.29
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.29
U31(mark(z0)) → mark(U31(z0)) 380.42/114.29
U31(ok(z0)) → ok(U31(z0)) 380.42/114.29
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.29
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.29
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.29
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.29
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.29
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.29
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.30
TOP(mark(0)) → c53(TOP(ok(0)))
K tuples:none
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
TOP(mark(tt)) → c53(TOP(ok(tt))) 380.42/114.30
TOP(mark(0)) → c53(TOP(ok(0)))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c53
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
TOP(mark(tt)) → c53 380.42/114.30
TOP(mark(0)) → c53
K tuples:none
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
TOP(mark(tt)) → c53 380.42/114.30
TOP(mark(0)) → c53
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT, TOP
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52, c53
TOP(mark(0)) → c53 380.42/114.30
TOP(mark(tt)) → c53
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:none
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [2]x12 380.42/114.30
POL(PLUS(x1, x2)) = 0 380.42/114.30
POL(S(x1)) = 0 380.42/114.30
POL(U11'(x1, x2)) = x22 380.42/114.30
POL(U21'(x1, x2, x3)) = 0 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = 0 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = 0 380.42/114.30
POL(ok(x1)) = [1] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
X(ok(z0), ok(z1)) → c38(X(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = 0 380.42/114.30
POL(S(x1)) = 0 380.42/114.30
POL(U11'(x1, x2)) = [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = 0 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = x1 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = x1 380.42/114.30
POL(ok(x1)) = [1] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = 0 380.42/114.30
POL(S(x1)) = 0 380.42/114.30
POL(U11'(x1, x2)) = [2]x1 + [3]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = x1 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = 0 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [1] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = x1 380.42/114.30
POL(S(x1)) = [2]x1 380.42/114.30
POL(U11'(x1, x2)) = [3]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = 0 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = 0 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [1] + x1 380.42/114.30
POL(ok(x1)) = [2] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
X(mark(z0), z1) → c36(X(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [3]x1 380.42/114.30
POL(PLUS(x1, x2)) = [3]x1 380.42/114.30
POL(S(x1)) = [3]x1 380.42/114.30
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = x2 + x3 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = x2 380.42/114.30
POL(X(x1, x2)) = x1 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [1] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
X(z0, mark(z1)) → c37(X(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = [5]x1 380.42/114.30
POL(S(x1)) = [5]x1 380.42/114.30
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = 0 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = [5]x1 + [4]x2 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [4] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = [3]x1 380.42/114.30
POL(S(x1)) = [3]x1 380.42/114.30
POL(U11'(x1, x2)) = [5]x1 + [3]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = [2]x3 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = 0 380.42/114.30
POL(X(x1, x2)) = [3]x1 + [3]x2 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = x1 380.42/114.30
POL(ok(x1)) = [1] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = x2 380.42/114.30
POL(ISNAT(x1)) = [3]x1 380.42/114.30
POL(PLUS(x1, x2)) = [3]x1 + [2]x2 380.42/114.30
POL(S(x1)) = [3]x1 380.42/114.30
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = [5]x1 + [5]x2 + [3]x3 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = x2 + x3 380.42/114.30
POL(X(x1, x2)) = [5]x1 + [3]x2 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [1] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = x2 380.42/114.30
POL(ISNAT(x1)) = [3]x1 380.42/114.30
POL(PLUS(x1, x2)) = [3]x1 + [3]x2 380.42/114.30
POL(S(x1)) = [3]x1 380.42/114.30
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = [3]x1 + [3]x2 + [3]x3 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = x1 + x2 + x3 380.42/114.30
POL(X(x1, x2)) = [5]x1 + [5]x2 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [2] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.30
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.30
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.30
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.30
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.30
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.30
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.30
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.30
proper(tt) → ok(tt) 380.42/114.30
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(s(z0)) → s(proper(z0)) 380.42/114.30
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.30
proper(U31(z0)) → U31(proper(z0)) 380.42/114.30
proper(0) → ok(0) 380.42/114.30
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.30
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.30
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.30
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.30
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.30
top(mark(z0)) → top(proper(z0)) 380.42/114.30
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
AND(mark(z0), z1) → c39(AND(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.30
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.30
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.30
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.30
S(mark(z0)) → c27(S(z0)) 380.42/114.30
S(ok(z0)) → c28(S(z0)) 380.42/114.30
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.30
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.30
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.30
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.30
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.30
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.30
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.30
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.30
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.30
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.30
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.30
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.30
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = x1 + x2 380.42/114.30
POL(ISNAT(x1)) = [5]x1 380.42/114.30
POL(PLUS(x1, x2)) = [3]x1 + [5]x2 380.42/114.30
POL(S(x1)) = [5]x1 380.42/114.30
POL(U11'(x1, x2)) = [3]x1 + [5]x2 380.42/114.30
POL(U21'(x1, x2, x3)) = [3]x1 + [3]x2 + [5]x3 380.42/114.30
POL(U31'(x1)) = 0 380.42/114.30
POL(U41'(x1, x2, x3)) = x1 + x2 + x3 380.42/114.30
POL(X(x1, x2)) = [5]x1 + [3]x2 380.42/114.30
POL(c23(x1)) = x1 380.42/114.30
POL(c24(x1)) = x1 380.42/114.30
POL(c25(x1)) = x1 380.42/114.30
POL(c26(x1)) = x1 380.42/114.30
POL(c27(x1)) = x1 380.42/114.30
POL(c28(x1)) = x1 380.42/114.30
POL(c29(x1)) = x1 380.42/114.30
POL(c30(x1)) = x1 380.42/114.30
POL(c31(x1)) = x1 380.42/114.30
POL(c32(x1)) = x1 380.42/114.30
POL(c33(x1)) = x1 380.42/114.30
POL(c34(x1)) = x1 380.42/114.30
POL(c35(x1)) = x1 380.42/114.30
POL(c36(x1)) = x1 380.42/114.30
POL(c37(x1)) = x1 380.42/114.30
POL(c38(x1)) = x1 380.42/114.30
POL(c39(x1)) = x1 380.42/114.30
POL(c40(x1)) = x1 380.42/114.30
POL(c52(x1)) = x1 380.42/114.30
POL(mark(x1)) = [1] + x1 380.42/114.30
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.30
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.30
active(U31(tt)) → mark(0) 380.42/114.30
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.30
active(and(tt, z0)) → mark(z0) 380.42/114.30
active(isNat(0)) → mark(tt) 380.42/114.30
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(isNat(s(z0))) → mark(isNat(z0)) 380.42/114.30
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.42/114.30
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.42/114.30
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.42/114.30
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.42/114.30
active(U11(z0, z1)) → U11(active(z0), z1) 380.42/114.30
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.42/114.30
active(s(z0)) → s(active(z0)) 380.42/114.30
active(plus(z0, z1)) → plus(active(z0), z1) 380.42/114.30
active(plus(z0, z1)) → plus(z0, active(z1)) 380.42/114.30
active(U31(z0)) → U31(active(z0)) 380.42/114.30
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.42/114.30
active(x(z0, z1)) → x(active(z0), z1) 380.42/114.30
active(x(z0, z1)) → x(z0, active(z1)) 380.42/114.30
active(and(z0, z1)) → and(active(z0), z1) 380.42/114.30
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.42/114.30
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.42/114.30
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.42/114.30
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.42/114.30
s(mark(z0)) → mark(s(z0)) 380.42/114.30
s(ok(z0)) → ok(s(z0)) 380.42/114.30
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.42/114.30
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.42/114.30
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.42/114.30
U31(mark(z0)) → mark(U31(z0)) 380.42/114.30
U31(ok(z0)) → ok(U31(z0)) 380.42/114.30
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.42/114.31
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.42/114.31
x(mark(z0), z1) → mark(x(z0, z1)) 380.42/114.31
x(z0, mark(z1)) → mark(x(z0, z1)) 380.42/114.31
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.42/114.31
and(mark(z0), z1) → mark(and(z0, z1)) 380.42/114.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.42/114.31
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.42/114.31
proper(tt) → ok(tt) 380.42/114.31
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.42/114.31
proper(s(z0)) → s(proper(z0)) 380.42/114.31
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.42/114.31
proper(U31(z0)) → U31(proper(z0)) 380.42/114.31
proper(0) → ok(0) 380.42/114.31
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.42/114.31
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.42/114.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.42/114.31
proper(isNat(z0)) → isNat(proper(z0)) 380.42/114.31
isNat(ok(z0)) → ok(isNat(z0)) 380.42/114.31
top(mark(z0)) → top(proper(z0)) 380.42/114.31
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.31
S(mark(z0)) → c27(S(z0)) 380.42/114.31
S(ok(z0)) → c28(S(z0)) 380.42/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.42/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.31
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.31
S(mark(z0)) → c27(S(z0)) 380.42/114.31
S(ok(z0)) → c28(S(z0)) 380.42/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.31
AND(mark(z0), z1) → c39(AND(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U31'(mark(z0)) → c32(U31'(z0))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.42/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.42/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.42/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.42/114.31
S(mark(z0)) → c27(S(z0)) 380.42/114.31
S(ok(z0)) → c28(S(z0)) 380.42/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.42/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.42/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.42/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.42/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.42/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.42/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.42/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.42/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.42/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.42/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.42/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.42/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.42/114.31
POL(ISNAT(x1)) = [3]x1 380.42/114.31
POL(PLUS(x1, x2)) = [3]x1 + [5]x2 380.42/114.31
POL(S(x1)) = [5]x1 380.42/114.31
POL(U11'(x1, x2)) = [5]x1 + [3]x2 380.42/114.31
POL(U21'(x1, x2, x3)) = [3]x1 + [3]x2 + [5]x3 380.42/114.31
POL(U31'(x1)) = [2]x1 380.42/114.31
POL(U41'(x1, x2, x3)) = x1 + x2 380.42/114.31
POL(X(x1, x2)) = [5]x1 + [3]x2 380.42/114.31
POL(c23(x1)) = x1 380.42/114.31
POL(c24(x1)) = x1 380.42/114.31
POL(c25(x1)) = x1 380.42/114.31
POL(c26(x1)) = x1 380.42/114.31
POL(c27(x1)) = x1 380.42/114.31
POL(c28(x1)) = x1 380.42/114.31
POL(c29(x1)) = x1 380.42/114.31
POL(c30(x1)) = x1 380.42/114.31
POL(c31(x1)) = x1 380.42/114.31
POL(c32(x1)) = x1 380.42/114.31
POL(c33(x1)) = x1 380.42/114.31
POL(c34(x1)) = x1 380.42/114.31
POL(c35(x1)) = x1 380.42/114.31
POL(c36(x1)) = x1 380.42/114.31
POL(c37(x1)) = x1 380.42/114.31
POL(c38(x1)) = x1 380.42/114.31
POL(c39(x1)) = x1 380.42/114.31
POL(c40(x1)) = x1 380.42/114.31
POL(c52(x1)) = x1 380.42/114.31
POL(mark(x1)) = [1] + x1 380.42/114.31
POL(ok(x1)) = x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.42/114.31
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.42/114.31
active(U31(tt)) → mark(0) 380.42/114.31
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.42/114.31
active(and(tt, z0)) → mark(z0) 380.42/114.31
active(isNat(0)) → mark(tt) 380.66/114.31
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(isNat(s(z0))) → mark(isNat(z0)) 380.66/114.31
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.66/114.31
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.66/114.31
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(U11(z0, z1)) → U11(active(z0), z1) 380.66/114.31
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.66/114.31
active(s(z0)) → s(active(z0)) 380.66/114.31
active(plus(z0, z1)) → plus(active(z0), z1) 380.66/114.31
active(plus(z0, z1)) → plus(z0, active(z1)) 380.66/114.31
active(U31(z0)) → U31(active(z0)) 380.66/114.31
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.66/114.31
active(x(z0, z1)) → x(active(z0), z1) 380.66/114.31
active(x(z0, z1)) → x(z0, active(z1)) 380.66/114.31
active(and(z0, z1)) → and(active(z0), z1) 380.66/114.31
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.66/114.31
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.66/114.31
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.66/114.31
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.66/114.31
s(mark(z0)) → mark(s(z0)) 380.66/114.31
s(ok(z0)) → ok(s(z0)) 380.66/114.31
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.66/114.31
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.66/114.31
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.66/114.31
U31(mark(z0)) → mark(U31(z0)) 380.66/114.31
U31(ok(z0)) → ok(U31(z0)) 380.66/114.31
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.66/114.31
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.66/114.31
x(mark(z0), z1) → mark(x(z0, z1)) 380.66/114.31
x(z0, mark(z1)) → mark(x(z0, z1)) 380.66/114.31
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.66/114.31
and(mark(z0), z1) → mark(and(z0, z1)) 380.66/114.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.66/114.31
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.66/114.31
proper(tt) → ok(tt) 380.66/114.31
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(s(z0)) → s(proper(z0)) 380.66/114.31
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.66/114.31
proper(U31(z0)) → U31(proper(z0)) 380.66/114.31
proper(0) → ok(0) 380.66/114.31
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.66/114.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.66/114.31
proper(isNat(z0)) → isNat(proper(z0)) 380.66/114.31
isNat(ok(z0)) → ok(isNat(z0)) 380.66/114.31
top(mark(z0)) → top(proper(z0)) 380.66/114.31
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U31'(ok(z0)) → c33(U31'(z0))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.66/114.31
POL(ISNAT(x1)) = [5]x1 380.66/114.31
POL(PLUS(x1, x2)) = [3]x1 + [3]x2 380.66/114.31
POL(S(x1)) = [5]x1 380.66/114.31
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.66/114.31
POL(U21'(x1, x2, x3)) = [3]x1 + [5]x2 + [3]x3 380.66/114.31
POL(U31'(x1)) = [2]x1 380.66/114.31
POL(U41'(x1, x2, x3)) = 0 380.66/114.31
POL(X(x1, x2)) = [5]x1 + [3]x2 380.66/114.31
POL(c23(x1)) = x1 380.66/114.31
POL(c24(x1)) = x1 380.66/114.31
POL(c25(x1)) = x1 380.66/114.31
POL(c26(x1)) = x1 380.66/114.31
POL(c27(x1)) = x1 380.66/114.31
POL(c28(x1)) = x1 380.66/114.31
POL(c29(x1)) = x1 380.66/114.31
POL(c30(x1)) = x1 380.66/114.31
POL(c31(x1)) = x1 380.66/114.31
POL(c32(x1)) = x1 380.66/114.31
POL(c33(x1)) = x1 380.66/114.31
POL(c34(x1)) = x1 380.66/114.31
POL(c35(x1)) = x1 380.66/114.31
POL(c36(x1)) = x1 380.66/114.31
POL(c37(x1)) = x1 380.66/114.31
POL(c38(x1)) = x1 380.66/114.31
POL(c39(x1)) = x1 380.66/114.31
POL(c40(x1)) = x1 380.66/114.31
POL(c52(x1)) = x1 380.66/114.31
POL(mark(x1)) = x1 380.66/114.31
POL(ok(x1)) = [1] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.66/114.31
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.66/114.31
active(U31(tt)) → mark(0) 380.66/114.31
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.66/114.31
active(and(tt, z0)) → mark(z0) 380.66/114.31
active(isNat(0)) → mark(tt) 380.66/114.31
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(isNat(s(z0))) → mark(isNat(z0)) 380.66/114.31
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.66/114.31
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.66/114.31
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(U11(z0, z1)) → U11(active(z0), z1) 380.66/114.31
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.66/114.31
active(s(z0)) → s(active(z0)) 380.66/114.31
active(plus(z0, z1)) → plus(active(z0), z1) 380.66/114.31
active(plus(z0, z1)) → plus(z0, active(z1)) 380.66/114.31
active(U31(z0)) → U31(active(z0)) 380.66/114.31
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.66/114.31
active(x(z0, z1)) → x(active(z0), z1) 380.66/114.31
active(x(z0, z1)) → x(z0, active(z1)) 380.66/114.31
active(and(z0, z1)) → and(active(z0), z1) 380.66/114.31
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.66/114.31
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.66/114.31
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.66/114.31
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.66/114.31
s(mark(z0)) → mark(s(z0)) 380.66/114.31
s(ok(z0)) → ok(s(z0)) 380.66/114.31
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.66/114.31
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.66/114.31
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.66/114.31
U31(mark(z0)) → mark(U31(z0)) 380.66/114.31
U31(ok(z0)) → ok(U31(z0)) 380.66/114.31
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.66/114.31
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.66/114.31
x(mark(z0), z1) → mark(x(z0, z1)) 380.66/114.31
x(z0, mark(z1)) → mark(x(z0, z1)) 380.66/114.31
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.66/114.31
and(mark(z0), z1) → mark(and(z0, z1)) 380.66/114.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.66/114.31
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.66/114.31
proper(tt) → ok(tt) 380.66/114.31
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(s(z0)) → s(proper(z0)) 380.66/114.31
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.66/114.31
proper(U31(z0)) → U31(proper(z0)) 380.66/114.31
proper(0) → ok(0) 380.66/114.31
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.66/114.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.66/114.31
proper(isNat(z0)) → isNat(proper(z0)) 380.66/114.31
isNat(ok(z0)) → ok(isNat(z0)) 380.66/114.31
top(mark(z0)) → top(proper(z0)) 380.66/114.31
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = 0 380.66/114.31
POL(ISNAT(x1)) = [5]x1 380.66/114.31
POL(PLUS(x1, x2)) = [5]x1 + [3]x2 380.66/114.31
POL(S(x1)) = [5]x1 380.66/114.31
POL(U11'(x1, x2)) = [3]x1 + [5]x2 380.66/114.31
POL(U21'(x1, x2, x3)) = [3]x1 + [3]x2 + [5]x3 380.66/114.31
POL(U31'(x1)) = [3]x1 380.66/114.31
POL(U41'(x1, x2, x3)) = x3 380.66/114.31
POL(X(x1, x2)) = [5]x1 + [3]x2 380.66/114.31
POL(c23(x1)) = x1 380.66/114.31
POL(c24(x1)) = x1 380.66/114.31
POL(c25(x1)) = x1 380.66/114.31
POL(c26(x1)) = x1 380.66/114.31
POL(c27(x1)) = x1 380.66/114.31
POL(c28(x1)) = x1 380.66/114.31
POL(c29(x1)) = x1 380.66/114.31
POL(c30(x1)) = x1 380.66/114.31
POL(c31(x1)) = x1 380.66/114.31
POL(c32(x1)) = x1 380.66/114.31
POL(c33(x1)) = x1 380.66/114.31
POL(c34(x1)) = x1 380.66/114.31
POL(c35(x1)) = x1 380.66/114.31
POL(c36(x1)) = x1 380.66/114.31
POL(c37(x1)) = x1 380.66/114.31
POL(c38(x1)) = x1 380.66/114.31
POL(c39(x1)) = x1 380.66/114.31
POL(c40(x1)) = x1 380.66/114.31
POL(c52(x1)) = x1 380.66/114.31
POL(mark(x1)) = x1 380.66/114.31
POL(ok(x1)) = [1] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.66/114.31
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.66/114.31
active(U31(tt)) → mark(0) 380.66/114.31
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.66/114.31
active(and(tt, z0)) → mark(z0) 380.66/114.31
active(isNat(0)) → mark(tt) 380.66/114.31
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(isNat(s(z0))) → mark(isNat(z0)) 380.66/114.31
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.66/114.31
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.66/114.31
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(U11(z0, z1)) → U11(active(z0), z1) 380.66/114.31
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.66/114.31
active(s(z0)) → s(active(z0)) 380.66/114.31
active(plus(z0, z1)) → plus(active(z0), z1) 380.66/114.31
active(plus(z0, z1)) → plus(z0, active(z1)) 380.66/114.31
active(U31(z0)) → U31(active(z0)) 380.66/114.31
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.66/114.31
active(x(z0, z1)) → x(active(z0), z1) 380.66/114.31
active(x(z0, z1)) → x(z0, active(z1)) 380.66/114.31
active(and(z0, z1)) → and(active(z0), z1) 380.66/114.31
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.66/114.31
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.66/114.31
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.66/114.31
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.66/114.31
s(mark(z0)) → mark(s(z0)) 380.66/114.31
s(ok(z0)) → ok(s(z0)) 380.66/114.31
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.66/114.31
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.66/114.31
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.66/114.31
U31(mark(z0)) → mark(U31(z0)) 380.66/114.31
U31(ok(z0)) → ok(U31(z0)) 380.66/114.31
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.66/114.31
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.66/114.31
x(mark(z0), z1) → mark(x(z0, z1)) 380.66/114.31
x(z0, mark(z1)) → mark(x(z0, z1)) 380.66/114.31
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.66/114.31
and(mark(z0), z1) → mark(and(z0, z1)) 380.66/114.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.66/114.31
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.66/114.31
proper(tt) → ok(tt) 380.66/114.31
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(s(z0)) → s(proper(z0)) 380.66/114.31
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.66/114.31
proper(U31(z0)) → U31(proper(z0)) 380.66/114.31
proper(0) → ok(0) 380.66/114.31
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.66/114.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.66/114.31
proper(isNat(z0)) → isNat(proper(z0)) 380.66/114.31
isNat(ok(z0)) → ok(isNat(z0)) 380.66/114.31
top(mark(z0)) → top(proper(z0)) 380.66/114.31
top(ok(z0)) → top(active(z0))
S tuples:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
K tuples:
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52
We considered the (Usable) Rules:none
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
The order we found is given by the following interpretation:
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
POL(AND(x1, x2)) = x1 380.66/114.31
POL(ISNAT(x1)) = [3]x1 380.66/114.31
POL(PLUS(x1, x2)) = [3]x1 + [3]x2 380.66/114.31
POL(S(x1)) = [5]x1 380.66/114.31
POL(U11'(x1, x2)) = [5]x1 + [5]x2 380.66/114.31
POL(U21'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3 380.66/114.31
POL(U31'(x1)) = [5]x1 380.66/114.31
POL(U41'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3 380.66/114.31
POL(X(x1, x2)) = [3]x1 + [5]x2 380.66/114.31
POL(c23(x1)) = x1 380.66/114.31
POL(c24(x1)) = x1 380.66/114.31
POL(c25(x1)) = x1 380.66/114.31
POL(c26(x1)) = x1 380.66/114.31
POL(c27(x1)) = x1 380.66/114.31
POL(c28(x1)) = x1 380.66/114.31
POL(c29(x1)) = x1 380.66/114.31
POL(c30(x1)) = x1 380.66/114.31
POL(c31(x1)) = x1 380.66/114.31
POL(c32(x1)) = x1 380.66/114.31
POL(c33(x1)) = x1 380.66/114.31
POL(c34(x1)) = x1 380.66/114.31
POL(c35(x1)) = x1 380.66/114.31
POL(c36(x1)) = x1 380.66/114.31
POL(c37(x1)) = x1 380.66/114.31
POL(c38(x1)) = x1 380.66/114.31
POL(c39(x1)) = x1 380.66/114.31
POL(c40(x1)) = x1 380.66/114.31
POL(c52(x1)) = x1 380.66/114.31
POL(mark(x1)) = x1 380.66/114.31
POL(ok(x1)) = [2] + x1
Tuples:
active(U11(tt, z0)) → mark(z0) 380.66/114.31
active(U21(tt, z0, z1)) → mark(s(plus(z1, z0))) 380.66/114.31
active(U31(tt)) → mark(0) 380.66/114.31
active(U41(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 380.66/114.31
active(and(tt, z0)) → mark(z0) 380.66/114.31
active(isNat(0)) → mark(tt) 380.66/114.31
active(isNat(plus(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(isNat(s(z0))) → mark(isNat(z0)) 380.66/114.31
active(isNat(x(z0, z1))) → mark(and(isNat(z0), isNat(z1))) 380.66/114.31
active(plus(z0, 0)) → mark(U11(isNat(z0), z0)) 380.66/114.31
active(plus(z0, s(z1))) → mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(x(z0, 0)) → mark(U31(isNat(z0))) 380.66/114.31
active(x(z0, s(z1))) → mark(U41(and(isNat(z1), isNat(z0)), z1, z0)) 380.66/114.31
active(U11(z0, z1)) → U11(active(z0), z1) 380.66/114.31
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 380.66/114.31
active(s(z0)) → s(active(z0)) 380.66/114.31
active(plus(z0, z1)) → plus(active(z0), z1) 380.66/114.31
active(plus(z0, z1)) → plus(z0, active(z1)) 380.66/114.31
active(U31(z0)) → U31(active(z0)) 380.66/114.31
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 380.66/114.31
active(x(z0, z1)) → x(active(z0), z1) 380.66/114.31
active(x(z0, z1)) → x(z0, active(z1)) 380.66/114.31
active(and(z0, z1)) → and(active(z0), z1) 380.66/114.31
U11(mark(z0), z1) → mark(U11(z0, z1)) 380.66/114.31
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 380.66/114.31
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 380.66/114.31
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 380.66/114.31
s(mark(z0)) → mark(s(z0)) 380.66/114.31
s(ok(z0)) → ok(s(z0)) 380.66/114.31
plus(mark(z0), z1) → mark(plus(z0, z1)) 380.66/114.31
plus(z0, mark(z1)) → mark(plus(z0, z1)) 380.66/114.31
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 380.66/114.31
U31(mark(z0)) → mark(U31(z0)) 380.66/114.31
U31(ok(z0)) → ok(U31(z0)) 380.66/114.31
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 380.66/114.31
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 380.66/114.31
x(mark(z0), z1) → mark(x(z0, z1)) 380.66/114.31
x(z0, mark(z1)) → mark(x(z0, z1)) 380.66/114.31
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 380.66/114.31
and(mark(z0), z1) → mark(and(z0, z1)) 380.66/114.31
and(ok(z0), ok(z1)) → ok(and(z0, z1)) 380.66/114.31
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 380.66/114.31
proper(tt) → ok(tt) 380.66/114.31
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(s(z0)) → s(proper(z0)) 380.66/114.31
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 380.66/114.31
proper(U31(z0)) → U31(proper(z0)) 380.66/114.31
proper(0) → ok(0) 380.66/114.31
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 380.66/114.31
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 380.66/114.31
proper(and(z0, z1)) → and(proper(z0), proper(z1)) 380.66/114.31
proper(isNat(z0)) → isNat(proper(z0)) 380.66/114.31
isNat(ok(z0)) → ok(isNat(z0)) 380.66/114.31
top(mark(z0)) → top(proper(z0)) 380.66/114.31
top(ok(z0)) → top(active(z0))
S tuples:none
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0))
Defined Rule Symbols:
U11'(ok(z0), ok(z1)) → c24(U11'(z0, z1)) 380.66/114.31
ISNAT(ok(z0)) → c52(ISNAT(z0)) 380.66/114.31
X(ok(z0), ok(z1)) → c38(X(z0, z1)) 380.66/114.31
U11'(mark(z0), z1) → c23(U11'(z0, z1)) 380.66/114.31
U21'(mark(z0), z1, z2) → c25(U21'(z0, z1, z2)) 380.66/114.31
S(mark(z0)) → c27(S(z0)) 380.66/114.31
S(ok(z0)) → c28(S(z0)) 380.66/114.31
PLUS(mark(z0), z1) → c29(PLUS(z0, z1)) 380.66/114.31
PLUS(ok(z0), ok(z1)) → c31(PLUS(z0, z1)) 380.66/114.31
X(mark(z0), z1) → c36(X(z0, z1)) 380.66/114.31
X(z0, mark(z1)) → c37(X(z0, z1)) 380.66/114.31
U21'(ok(z0), ok(z1), ok(z2)) → c26(U21'(z0, z1, z2)) 380.66/114.31
PLUS(z0, mark(z1)) → c30(PLUS(z0, z1)) 380.66/114.31
U41'(mark(z0), z1, z2) → c34(U41'(z0, z1, z2)) 380.66/114.31
AND(mark(z0), z1) → c39(AND(z0, z1)) 380.66/114.31
U31'(mark(z0)) → c32(U31'(z0)) 380.66/114.31
U31'(ok(z0)) → c33(U31'(z0)) 380.66/114.31
U41'(ok(z0), ok(z1), ok(z2)) → c35(U41'(z0, z1, z2)) 380.66/114.31
AND(ok(z0), ok(z1)) → c40(AND(z0, z1))
active, U11, U21, s, plus, U31, U41, x, and, proper, isNat, top
U11', U21', S, PLUS, U31', U41', X, AND, ISNAT
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c52