YES(O(1), O(n^1)) 10.95/3.28 YES(O(1), O(n^1)) 11.32/3.36 11.32/3.36 11.32/3.36
11.32/3.36 11.32/3.360 CpxTRS11.32/3.36
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))11.32/3.36
↳2 CdtProblem11.32/3.36
↳3 CdtUnreachableProof (⇔)11.32/3.36
↳4 CdtProblem11.32/3.36
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))11.32/3.36
↳6 CdtProblem11.32/3.36
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))11.32/3.36
↳8 CdtProblem11.32/3.36
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳10 CdtProblem11.32/3.36
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳12 CdtProblem11.32/3.36
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳14 CdtProblem11.32/3.36
↳15 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳16 CdtProblem11.32/3.36
↳17 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳18 CdtProblem11.32/3.36
↳19 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳20 CdtProblem11.32/3.36
↳21 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))11.32/3.36
↳22 CdtProblem11.32/3.36
↳23 SIsEmptyProof (BOTH BOUNDS(ID, ID))11.32/3.36
↳24 BOUNDS(O(1), O(1))11.32/3.36
rec(rec(x)) → sent(rec(x)) 11.32/3.36
rec(sent(x)) → sent(rec(x)) 11.32/3.36
rec(no(x)) → sent(rec(x)) 11.32/3.36
rec(bot) → up(sent(bot)) 11.32/3.36
rec(up(x)) → up(rec(x)) 11.32/3.36
sent(up(x)) → up(sent(x)) 11.32/3.36
no(up(x)) → up(no(x)) 11.32/3.36
top(rec(up(x))) → top(check(rec(x))) 11.32/3.36
top(sent(up(x))) → top(check(rec(x))) 11.32/3.36
top(no(up(x))) → top(check(rec(x))) 11.32/3.36
check(up(x)) → up(check(x)) 11.32/3.36
check(sent(x)) → sent(check(x)) 11.32/3.36
check(rec(x)) → rec(check(x)) 11.32/3.36
check(no(x)) → no(check(x)) 11.32/3.36
check(no(x)) → no(x)
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.32/3.36
rec(sent(z0)) → sent(rec(z0)) 11.32/3.37
rec(no(z0)) → sent(rec(z0)) 11.32/3.37
rec(bot) → up(sent(bot)) 11.32/3.37
rec(up(z0)) → up(rec(z0)) 11.32/3.37
sent(up(z0)) → up(sent(z0)) 11.32/3.37
no(up(z0)) → up(no(z0)) 11.32/3.37
top(rec(up(z0))) → top(check(rec(z0))) 11.32/3.37
top(sent(up(z0))) → top(check(rec(z0))) 11.32/3.37
top(no(up(z0))) → top(check(rec(z0))) 11.32/3.37
check(up(z0)) → up(check(z0)) 11.32/3.37
check(sent(z0)) → sent(check(z0)) 11.32/3.37
check(rec(z0)) → rec(check(z0)) 11.32/3.37
check(no(z0)) → no(check(z0)) 11.32/3.37
check(no(z0)) → no(z0)
S tuples:
REC(rec(z0)) → c(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(bot) → c3(SENT(bot)) 11.32/3.37
REC(up(z0)) → c4(REC(z0)) 11.32/3.37
SENT(up(z0)) → c5(SENT(z0)) 11.32/3.37
NO(up(z0)) → c6(NO(z0)) 11.32/3.37
TOP(rec(up(z0))) → c7(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(sent(up(z0))) → c8(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(no(up(z0))) → c9(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
CHECK(up(z0)) → c10(CHECK(z0)) 11.32/3.37
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(rec(z0)) → c12(REC(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c14(NO(z0))
K tuples:none
REC(rec(z0)) → c(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(bot) → c3(SENT(bot)) 11.32/3.37
REC(up(z0)) → c4(REC(z0)) 11.32/3.37
SENT(up(z0)) → c5(SENT(z0)) 11.32/3.37
NO(up(z0)) → c6(NO(z0)) 11.32/3.37
TOP(rec(up(z0))) → c7(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(sent(up(z0))) → c8(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(no(up(z0))) → c9(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
CHECK(up(z0)) → c10(CHECK(z0)) 11.32/3.37
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(rec(z0)) → c12(REC(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c14(NO(z0))
rec, sent, no, top, check
REC, SENT, NO, TOP, CHECK
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14
TOP(rec(up(z0))) → c7(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(sent(up(z0))) → c8(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0)) 11.32/3.37
TOP(no(up(z0))) → c9(TOP(check(rec(z0))), CHECK(rec(z0)), REC(z0))
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.32/3.37
rec(sent(z0)) → sent(rec(z0)) 11.32/3.37
rec(no(z0)) → sent(rec(z0)) 11.32/3.37
rec(bot) → up(sent(bot)) 11.32/3.37
rec(up(z0)) → up(rec(z0)) 11.32/3.37
sent(up(z0)) → up(sent(z0)) 11.32/3.37
no(up(z0)) → up(no(z0)) 11.32/3.37
top(rec(up(z0))) → top(check(rec(z0))) 11.32/3.37
top(sent(up(z0))) → top(check(rec(z0))) 11.32/3.37
top(no(up(z0))) → top(check(rec(z0))) 11.32/3.37
check(up(z0)) → up(check(z0)) 11.32/3.37
check(sent(z0)) → sent(check(z0)) 11.32/3.37
check(rec(z0)) → rec(check(z0)) 11.32/3.37
check(no(z0)) → no(check(z0)) 11.32/3.37
check(no(z0)) → no(z0)
S tuples:
REC(bot) → c3(SENT(bot)) 11.32/3.37
REC(up(z0)) → c4(REC(z0)) 11.32/3.37
SENT(up(z0)) → c5(SENT(z0)) 11.32/3.37
NO(up(z0)) → c6(NO(z0)) 11.32/3.37
CHECK(up(z0)) → c10(CHECK(z0)) 11.32/3.37
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(rec(z0)) → c12(REC(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c14(NO(z0)) 11.32/3.37
REC(rec(z0)) → c(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0))
K tuples:none
REC(rec(z0)) → c(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.32/3.37
REC(bot) → c3(SENT(bot)) 11.32/3.37
REC(up(z0)) → c4(REC(z0)) 11.32/3.37
SENT(up(z0)) → c5(SENT(z0)) 11.32/3.37
NO(up(z0)) → c6(NO(z0)) 11.32/3.37
CHECK(up(z0)) → c10(CHECK(z0)) 11.32/3.37
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(rec(z0)) → c12(REC(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.32/3.37
CHECK(no(z0)) → c14(NO(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c3, c4, c5, c6, c10, c11, c12, c13, c14, c, c1, c2
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
K tuples:none
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
REC(bot) → c3
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
K tuples:none
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0) 11.71/3.42
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [1] 11.71/3.42
POL(NO(x1)) = 0 11.71/3.42
POL(REC(x1)) = [3] 11.71/3.42
POL(SENT(x1)) = 0 11.71/3.42
POL(bot) = 0 11.71/3.42
POL(c(x1)) = x1 11.71/3.42
POL(c1(x1, x2)) = x1 + x2 11.71/3.42
POL(c10(x1)) = x1 11.71/3.42
POL(c11(x1, x2)) = x1 + x2 11.71/3.42
POL(c12(x1)) = x1 11.71/3.42
POL(c13(x1, x2)) = x1 + x2 11.71/3.42
POL(c14(x1)) = x1 11.71/3.42
POL(c2(x1, x2)) = x1 + x2 11.71/3.42
POL(c3) = 0 11.71/3.42
POL(c4(x1)) = x1 11.71/3.42
POL(c5(x1)) = x1 11.71/3.42
POL(c6(x1)) = x1 11.71/3.42
POL(check(x1)) = 0 11.71/3.42
POL(no(x1)) = [4] 11.71/3.42
POL(rec(x1)) = [3]x1 11.71/3.42
POL(sent(x1)) = 0 11.71/3.42
POL(up(x1)) = 0
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
K tuples:
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
REC(rec(z0)) → c(REC(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0) 11.71/3.42
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [1] 11.71/3.42
POL(NO(x1)) = 0 11.71/3.42
POL(REC(x1)) = [2]x1 11.71/3.42
POL(SENT(x1)) = 0 11.71/3.42
POL(bot) = [4] 11.71/3.42
POL(c(x1)) = x1 11.71/3.42
POL(c1(x1, x2)) = x1 + x2 11.71/3.42
POL(c10(x1)) = x1 11.71/3.42
POL(c11(x1, x2)) = x1 + x2 11.71/3.42
POL(c12(x1)) = x1 11.71/3.42
POL(c13(x1, x2)) = x1 + x2 11.71/3.42
POL(c14(x1)) = x1 11.71/3.42
POL(c2(x1, x2)) = x1 + x2 11.71/3.42
POL(c3) = 0 11.71/3.42
POL(c4(x1)) = x1 11.71/3.42
POL(c5(x1)) = x1 11.71/3.42
POL(c6(x1)) = x1 11.71/3.42
POL(check(x1)) = [4]x1 11.71/3.42
POL(no(x1)) = [4]x1 11.71/3.42
POL(rec(x1)) = [2] + [4]x1 11.71/3.42
POL(sent(x1)) = x1 11.71/3.42
POL(up(x1)) = x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
K tuples:
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
REC(rec(z0)) → c(REC(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0) 11.71/3.42
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [1] + x1 11.71/3.42
POL(NO(x1)) = 0 11.71/3.42
POL(REC(x1)) = [4]x1 11.71/3.42
POL(SENT(x1)) = [1] 11.71/3.42
POL(bot) = [4] 11.71/3.42
POL(c(x1)) = x1 11.71/3.42
POL(c1(x1, x2)) = x1 + x2 11.71/3.42
POL(c10(x1)) = x1 11.71/3.42
POL(c11(x1, x2)) = x1 + x2 11.71/3.42
POL(c12(x1)) = x1 11.71/3.42
POL(c13(x1, x2)) = x1 + x2 11.71/3.42
POL(c14(x1)) = x1 11.71/3.42
POL(c2(x1, x2)) = x1 + x2 11.71/3.42
POL(c3) = 0 11.71/3.42
POL(c4(x1)) = x1 11.71/3.42
POL(c5(x1)) = x1 11.71/3.42
POL(c6(x1)) = x1 11.71/3.42
POL(check(x1)) = 0 11.71/3.42
POL(no(x1)) = [2] + [5]x1 11.71/3.42
POL(rec(x1)) = [2] + [4]x1 11.71/3.42
POL(sent(x1)) = [4] + [2]x1 11.71/3.42
POL(up(x1)) = x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
K tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
REC(rec(z0)) → c(REC(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
REC(up(z0)) → c4(REC(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0) 11.71/3.42
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.42
NO(up(z0)) → c6(NO(z0)) 11.71/3.42
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.42
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.42
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.42
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.42
REC(bot) → c3 11.71/3.42
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.42
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = 0 11.71/3.42
POL(NO(x1)) = 0 11.71/3.42
POL(REC(x1)) = [4]x1 11.71/3.42
POL(SENT(x1)) = 0 11.71/3.42
POL(bot) = [3] 11.71/3.42
POL(c(x1)) = x1 11.71/3.42
POL(c1(x1, x2)) = x1 + x2 11.71/3.42
POL(c10(x1)) = x1 11.71/3.42
POL(c11(x1, x2)) = x1 + x2 11.71/3.42
POL(c12(x1)) = x1 11.71/3.42
POL(c13(x1, x2)) = x1 + x2 11.71/3.42
POL(c14(x1)) = x1 11.71/3.42
POL(c2(x1, x2)) = x1 + x2 11.71/3.42
POL(c3) = 0 11.71/3.42
POL(c4(x1)) = x1 11.71/3.42
POL(c5(x1)) = x1 11.71/3.42
POL(c6(x1)) = x1 11.71/3.42
POL(check(x1)) = x1 11.71/3.42
POL(no(x1)) = [4]x1 11.71/3.42
POL(rec(x1)) = x1 11.71/3.42
POL(sent(x1)) = [4]x1 11.71/3.42
POL(up(x1)) = [4] + x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.42
rec(sent(z0)) → sent(rec(z0)) 11.71/3.42
rec(no(z0)) → sent(rec(z0)) 11.71/3.42
rec(bot) → up(sent(bot)) 11.71/3.42
rec(up(z0)) → up(rec(z0)) 11.71/3.42
sent(up(z0)) → up(sent(z0)) 11.71/3.42
no(up(z0)) → up(no(z0)) 11.71/3.42
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.42
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.42
check(up(z0)) → up(check(z0)) 11.71/3.42
check(sent(z0)) → sent(check(z0)) 11.71/3.42
check(rec(z0)) → rec(check(z0)) 11.71/3.42
check(no(z0)) → no(check(z0)) 11.71/3.42
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.42
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(rec(z0)) → c(REC(z0))
K tuples:
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
REC(rec(z0)) → c(REC(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(up(z0)) → c4(REC(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
CHECK(up(z0)) → c10(CHECK(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.43
rec(sent(z0)) → sent(rec(z0)) 11.71/3.43
rec(no(z0)) → sent(rec(z0)) 11.71/3.43
rec(bot) → up(sent(bot)) 11.71/3.43
sent(up(z0)) → up(sent(z0)) 11.71/3.43
check(sent(z0)) → sent(check(z0)) 11.71/3.43
check(rec(z0)) → rec(check(z0)) 11.71/3.43
check(no(z0)) → no(check(z0)) 11.71/3.43
check(no(z0)) → no(z0) 11.71/3.43
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.43
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [1] + [4]x1 11.71/3.43
POL(NO(x1)) = [2] 11.71/3.43
POL(REC(x1)) = 0 11.71/3.43
POL(SENT(x1)) = 0 11.71/3.43
POL(bot) = [4] 11.71/3.43
POL(c(x1)) = x1 11.71/3.43
POL(c1(x1, x2)) = x1 + x2 11.71/3.43
POL(c10(x1)) = x1 11.71/3.43
POL(c11(x1, x2)) = x1 + x2 11.71/3.43
POL(c12(x1)) = x1 11.71/3.43
POL(c13(x1, x2)) = x1 + x2 11.71/3.43
POL(c14(x1)) = x1 11.71/3.43
POL(c2(x1, x2)) = x1 + x2 11.71/3.43
POL(c3) = 0 11.71/3.43
POL(c4(x1)) = x1 11.71/3.43
POL(c5(x1)) = x1 11.71/3.43
POL(c6(x1)) = x1 11.71/3.43
POL(check(x1)) = [4]x1 11.71/3.43
POL(no(x1)) = [3] + [2]x1 11.71/3.43
POL(rec(x1)) = [2] + [4]x1 11.71/3.43
POL(sent(x1)) = [3] + [2]x1 11.71/3.43
POL(up(x1)) = [1] + x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.43
rec(sent(z0)) → sent(rec(z0)) 11.71/3.43
rec(no(z0)) → sent(rec(z0)) 11.71/3.43
rec(bot) → up(sent(bot)) 11.71/3.43
rec(up(z0)) → up(rec(z0)) 11.71/3.43
sent(up(z0)) → up(sent(z0)) 11.71/3.43
no(up(z0)) → up(no(z0)) 11.71/3.43
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.43
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.43
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.43
check(up(z0)) → up(check(z0)) 11.71/3.43
check(sent(z0)) → sent(check(z0)) 11.71/3.43
check(rec(z0)) → rec(check(z0)) 11.71/3.43
check(no(z0)) → no(check(z0)) 11.71/3.43
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.43
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(rec(z0)) → c(REC(z0))
K tuples:
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
REC(rec(z0)) → c(REC(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(up(z0)) → c4(REC(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
SENT(up(z0)) → c5(SENT(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.43
rec(sent(z0)) → sent(rec(z0)) 11.71/3.43
rec(no(z0)) → sent(rec(z0)) 11.71/3.43
rec(bot) → up(sent(bot)) 11.71/3.43
sent(up(z0)) → up(sent(z0)) 11.71/3.43
check(sent(z0)) → sent(check(z0)) 11.71/3.43
check(rec(z0)) → rec(check(z0)) 11.71/3.43
check(no(z0)) → no(check(z0)) 11.71/3.43
check(no(z0)) → no(z0) 11.71/3.43
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.43
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [1] + [5]x1 11.71/3.43
POL(NO(x1)) = [2] 11.71/3.43
POL(REC(x1)) = [4]x1 11.71/3.43
POL(SENT(x1)) = [4] + x1 11.71/3.43
POL(bot) = [4] 11.71/3.43
POL(c(x1)) = x1 11.71/3.43
POL(c1(x1, x2)) = x1 + x2 11.71/3.43
POL(c10(x1)) = x1 11.71/3.43
POL(c11(x1, x2)) = x1 + x2 11.71/3.43
POL(c12(x1)) = x1 11.71/3.43
POL(c13(x1, x2)) = x1 + x2 11.71/3.43
POL(c14(x1)) = x1 11.71/3.43
POL(c2(x1, x2)) = x1 + x2 11.71/3.43
POL(c3) = 0 11.71/3.43
POL(c4(x1)) = x1 11.71/3.43
POL(c5(x1)) = x1 11.71/3.43
POL(c6(x1)) = x1 11.71/3.43
POL(check(x1)) = [2] + [4]x1 11.71/3.43
POL(no(x1)) = [4] + [4]x1 11.71/3.43
POL(rec(x1)) = [2] + [4]x1 11.71/3.43
POL(sent(x1)) = [3] + [2]x1 11.71/3.43
POL(up(x1)) = [1] + x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.43
rec(sent(z0)) → sent(rec(z0)) 11.71/3.43
rec(no(z0)) → sent(rec(z0)) 11.71/3.43
rec(bot) → up(sent(bot)) 11.71/3.43
rec(up(z0)) → up(rec(z0)) 11.71/3.43
sent(up(z0)) → up(sent(z0)) 11.71/3.43
no(up(z0)) → up(no(z0)) 11.71/3.43
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.43
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.43
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.43
check(up(z0)) → up(check(z0)) 11.71/3.43
check(sent(z0)) → sent(check(z0)) 11.71/3.43
check(rec(z0)) → rec(check(z0)) 11.71/3.43
check(no(z0)) → no(check(z0)) 11.71/3.43
check(no(z0)) → no(z0)
S tuples:
REC(up(z0)) → c4(REC(z0)) 11.71/3.43
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.43
NO(up(z0)) → c6(NO(z0)) 11.71/3.43
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.43
REC(rec(z0)) → c(REC(z0))
K tuples:
NO(up(z0)) → c6(NO(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.43
REC(bot) → c3 11.71/3.43
REC(rec(z0)) → c(REC(z0)) 11.71/3.43
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.43
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.43
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.44
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.44
REC(up(z0)) → c4(REC(z0)) 11.71/3.44
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.44
SENT(up(z0)) → c5(SENT(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c
We considered the (Usable) Rules:
NO(up(z0)) → c6(NO(z0))
And the Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.44
rec(sent(z0)) → sent(rec(z0)) 11.71/3.44
rec(no(z0)) → sent(rec(z0)) 11.71/3.44
rec(bot) → up(sent(bot)) 11.71/3.44
sent(up(z0)) → up(sent(z0)) 11.71/3.44
check(sent(z0)) → sent(check(z0)) 11.71/3.44
check(rec(z0)) → rec(check(z0)) 11.71/3.44
check(no(z0)) → no(check(z0)) 11.71/3.44
check(no(z0)) → no(z0) 11.71/3.44
no(up(z0)) → up(no(z0))
The order we found is given by the following interpretation:
REC(up(z0)) → c4(REC(z0)) 11.71/3.44
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.44
NO(up(z0)) → c6(NO(z0)) 11.71/3.44
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.44
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.44
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.44
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.44
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(bot) → c3 11.71/3.44
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.44
REC(rec(z0)) → c(REC(z0))
POL(CHECK(x1)) = [4] + [2]x1 11.71/3.44
POL(NO(x1)) = [2]x1 11.71/3.44
POL(REC(x1)) = 0 11.71/3.44
POL(SENT(x1)) = 0 11.71/3.44
POL(bot) = [3] 11.71/3.44
POL(c(x1)) = x1 11.71/3.44
POL(c1(x1, x2)) = x1 + x2 11.71/3.44
POL(c10(x1)) = x1 11.71/3.44
POL(c11(x1, x2)) = x1 + x2 11.71/3.44
POL(c12(x1)) = x1 11.71/3.44
POL(c13(x1, x2)) = x1 + x2 11.71/3.44
POL(c14(x1)) = x1 11.71/3.44
POL(c2(x1, x2)) = x1 + x2 11.71/3.44
POL(c3) = 0 11.71/3.44
POL(c4(x1)) = x1 11.71/3.44
POL(c5(x1)) = x1 11.71/3.44
POL(c6(x1)) = x1 11.71/3.44
POL(check(x1)) = [4]x1 11.71/3.44
POL(no(x1)) = [5]x1 11.71/3.44
POL(rec(x1)) = [2] + x1 11.71/3.44
POL(sent(x1)) = [2]x1 11.71/3.44
POL(up(x1)) = [1] + x1
Tuples:
rec(rec(z0)) → sent(rec(z0)) 11.71/3.44
rec(sent(z0)) → sent(rec(z0)) 11.71/3.44
rec(no(z0)) → sent(rec(z0)) 11.71/3.44
rec(bot) → up(sent(bot)) 11.71/3.44
rec(up(z0)) → up(rec(z0)) 11.71/3.44
sent(up(z0)) → up(sent(z0)) 11.71/3.44
no(up(z0)) → up(no(z0)) 11.71/3.44
top(rec(up(z0))) → top(check(rec(z0))) 11.71/3.44
top(sent(up(z0))) → top(check(rec(z0))) 11.71/3.44
top(no(up(z0))) → top(check(rec(z0))) 11.71/3.44
check(up(z0)) → up(check(z0)) 11.71/3.44
check(sent(z0)) → sent(check(z0)) 11.71/3.44
check(rec(z0)) → rec(check(z0)) 11.71/3.44
check(no(z0)) → no(check(z0)) 11.71/3.44
check(no(z0)) → no(z0)
S tuples:none
REC(up(z0)) → c4(REC(z0)) 11.71/3.44
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.44
NO(up(z0)) → c6(NO(z0)) 11.71/3.44
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.44
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.44
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.44
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.44
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(bot) → c3 11.71/3.44
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.44
REC(rec(z0)) → c(REC(z0))
Defined Rule Symbols:
CHECK(no(z0)) → c14(NO(z0)) 11.71/3.44
REC(bot) → c3 11.71/3.44
REC(rec(z0)) → c(REC(z0)) 11.71/3.44
CHECK(sent(z0)) → c11(SENT(check(z0)), CHECK(z0)) 11.71/3.44
CHECK(no(z0)) → c13(NO(check(z0)), CHECK(z0)) 11.71/3.44
REC(sent(z0)) → c1(SENT(rec(z0)), REC(z0)) 11.71/3.44
REC(no(z0)) → c2(SENT(rec(z0)), REC(z0)) 11.71/3.44
CHECK(rec(z0)) → c12(CHECK(z0)) 11.71/3.44
REC(up(z0)) → c4(REC(z0)) 11.71/3.44
CHECK(up(z0)) → c10(CHECK(z0)) 11.71/3.44
SENT(up(z0)) → c5(SENT(z0)) 11.71/3.44
NO(up(z0)) → c6(NO(z0))
rec, sent, no, top, check
REC, SENT, NO, CHECK
c4, c5, c6, c10, c11, c13, c14, c1, c2, c3, c12, c