MAYBE 935.98/297.02 MAYBE 935.98/297.02 935.98/297.02 We are left with following problem, upon which TcT provides the 935.98/297.02 certificate MAYBE. 935.98/297.02 935.98/297.02 Strict Trs: 935.98/297.02 { a__zeros() -> cons(0(), zeros()) 935.98/297.02 , a__zeros() -> zeros() 935.98/297.02 , a__U11(X1, X2) -> U11(X1, X2) 935.98/297.02 , a__U11(tt(), L) -> s(a__length(mark(L))) 935.98/297.02 , a__length(X) -> length(X) 935.98/297.02 , a__length(cons(N, L)) -> 935.98/297.02 a__U11(a__and(a__isNatList(L), isNat(N)), L) 935.98/297.02 , a__length(nil()) -> 0() 935.98/297.02 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 935.98/297.02 , mark(0()) -> 0() 935.98/297.02 , mark(zeros()) -> a__zeros() 935.98/297.02 , mark(tt()) -> tt() 935.98/297.02 , mark(s(X)) -> s(mark(X)) 935.98/297.02 , mark(length(X)) -> a__length(mark(X)) 935.98/297.02 , mark(isNatIList(X)) -> a__isNatIList(X) 935.98/297.02 , mark(nil()) -> nil() 935.98/297.02 , mark(isNatList(X)) -> a__isNatList(X) 935.98/297.02 , mark(isNat(X)) -> a__isNat(X) 935.98/297.02 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 935.98/297.02 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 935.98/297.02 , a__and(X1, X2) -> and(X1, X2) 935.98/297.02 , a__and(tt(), X) -> mark(X) 935.98/297.02 , a__isNat(X) -> isNat(X) 935.98/297.02 , a__isNat(0()) -> tt() 935.98/297.02 , a__isNat(s(V1)) -> a__isNat(V1) 935.98/297.02 , a__isNat(length(V1)) -> a__isNatList(V1) 935.98/297.02 , a__isNatList(X) -> isNatList(X) 935.98/297.02 , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 935.98/297.02 , a__isNatList(nil()) -> tt() 935.98/297.02 , a__isNatIList(V) -> a__isNatList(V) 935.98/297.02 , a__isNatIList(X) -> isNatIList(X) 935.98/297.02 , a__isNatIList(cons(V1, V2)) -> 935.98/297.02 a__and(a__isNat(V1), isNatIList(V2)) 935.98/297.02 , a__isNatIList(zeros()) -> tt() } 935.98/297.02 Obligation: 935.98/297.02 runtime complexity 935.98/297.02 Answer: 935.98/297.02 MAYBE 935.98/297.02 935.98/297.02 None of the processors succeeded. 935.98/297.02 935.98/297.02 Details of failed attempt(s): 935.98/297.02 ----------------------------- 935.98/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 935.98/297.02 following reason: 935.98/297.02 935.98/297.02 Computation stopped due to timeout after 297.0 seconds. 935.98/297.02 935.98/297.02 2) 'Best' failed due to the following reason: 935.98/297.02 935.98/297.02 None of the processors succeeded. 935.98/297.02 935.98/297.02 Details of failed attempt(s): 935.98/297.02 ----------------------------- 935.98/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 935.98/297.02 seconds)' failed due to the following reason: 935.98/297.02 935.98/297.02 Computation stopped due to timeout after 148.0 seconds. 935.98/297.02 935.98/297.02 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 935.98/297.02 failed due to the following reason: 935.98/297.02 935.98/297.02 None of the processors succeeded. 935.98/297.02 935.98/297.02 Details of failed attempt(s): 935.98/297.02 ----------------------------- 935.98/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 935.98/297.02 failed due to the following reason: 935.98/297.02 935.98/297.02 match-boundness of the problem could not be verified. 935.98/297.02 935.98/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 935.98/297.02 failed due to the following reason: 935.98/297.02 935.98/297.02 match-boundness of the problem could not be verified. 935.98/297.02 935.98/297.02 935.98/297.02 3) 'Best' failed due to the following reason: 935.98/297.02 935.98/297.02 None of the processors succeeded. 935.98/297.02 935.98/297.02 Details of failed attempt(s): 935.98/297.02 ----------------------------- 935.98/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 935.98/297.02 following reason: 935.98/297.02 935.98/297.02 The processor is inapplicable, reason: 935.98/297.02 Processor only applicable for innermost runtime complexity analysis 935.98/297.02 935.98/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 935.98/297.02 to the following reason: 935.98/297.02 935.98/297.02 The processor is inapplicable, reason: 935.98/297.02 Processor only applicable for innermost runtime complexity analysis 935.98/297.02 935.98/297.02 935.98/297.02 935.98/297.02 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 935.98/297.02 the following reason: 935.98/297.02 935.98/297.02 We add the following weak dependency pairs: 935.98/297.02 935.98/297.02 Strict DPs: 935.98/297.02 { a__zeros^#() -> c_1() 935.98/297.02 , a__zeros^#() -> c_2() 935.98/297.02 , a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , a__length^#(X) -> c_5(X) 935.98/297.02 , a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , a__length^#(nil()) -> c_7() 935.98/297.02 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , mark^#(0()) -> c_9() 935.98/297.02 , mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.02 , mark^#(tt()) -> c_11() 935.98/297.02 , mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , mark^#(nil()) -> c_15() 935.98/297.02 , mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , a__isNatIList^#(zeros()) -> c_32() 935.98/297.02 , a__isNatList^#(X) -> c_26(X) 935.98/297.02 , a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , a__isNatList^#(nil()) -> c_28() 935.98/297.02 , a__isNat^#(X) -> c_22(X) 935.98/297.02 , a__isNat^#(0()) -> c_23() 935.98/297.02 , a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , a__and^#(tt(), X) -> c_21(mark^#(X)) } 935.98/297.02 935.98/297.02 and mark the set of starting terms. 935.98/297.02 935.98/297.02 We are left with following problem, upon which TcT provides the 935.98/297.02 certificate MAYBE. 935.98/297.02 935.98/297.02 Strict DPs: 935.98/297.02 { a__zeros^#() -> c_1() 935.98/297.02 , a__zeros^#() -> c_2() 935.98/297.02 , a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , a__length^#(X) -> c_5(X) 935.98/297.02 , a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , a__length^#(nil()) -> c_7() 935.98/297.02 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , mark^#(0()) -> c_9() 935.98/297.02 , mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.02 , mark^#(tt()) -> c_11() 935.98/297.02 , mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , mark^#(nil()) -> c_15() 935.98/297.02 , mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , a__isNatIList^#(zeros()) -> c_32() 935.98/297.02 , a__isNatList^#(X) -> c_26(X) 935.98/297.02 , a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , a__isNatList^#(nil()) -> c_28() 935.98/297.02 , a__isNat^#(X) -> c_22(X) 935.98/297.02 , a__isNat^#(0()) -> c_23() 935.98/297.02 , a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , a__and^#(tt(), X) -> c_21(mark^#(X)) } 935.98/297.02 Strict Trs: 935.98/297.02 { a__zeros() -> cons(0(), zeros()) 935.98/297.02 , a__zeros() -> zeros() 935.98/297.02 , a__U11(X1, X2) -> U11(X1, X2) 935.98/297.02 , a__U11(tt(), L) -> s(a__length(mark(L))) 935.98/297.02 , a__length(X) -> length(X) 935.98/297.02 , a__length(cons(N, L)) -> 935.98/297.02 a__U11(a__and(a__isNatList(L), isNat(N)), L) 935.98/297.02 , a__length(nil()) -> 0() 935.98/297.02 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 935.98/297.02 , mark(0()) -> 0() 935.98/297.02 , mark(zeros()) -> a__zeros() 935.98/297.02 , mark(tt()) -> tt() 935.98/297.02 , mark(s(X)) -> s(mark(X)) 935.98/297.02 , mark(length(X)) -> a__length(mark(X)) 935.98/297.02 , mark(isNatIList(X)) -> a__isNatIList(X) 935.98/297.02 , mark(nil()) -> nil() 935.98/297.02 , mark(isNatList(X)) -> a__isNatList(X) 935.98/297.02 , mark(isNat(X)) -> a__isNat(X) 935.98/297.02 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 935.98/297.02 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 935.98/297.02 , a__and(X1, X2) -> and(X1, X2) 935.98/297.02 , a__and(tt(), X) -> mark(X) 935.98/297.02 , a__isNat(X) -> isNat(X) 935.98/297.02 , a__isNat(0()) -> tt() 935.98/297.02 , a__isNat(s(V1)) -> a__isNat(V1) 935.98/297.02 , a__isNat(length(V1)) -> a__isNatList(V1) 935.98/297.02 , a__isNatList(X) -> isNatList(X) 935.98/297.02 , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 935.98/297.02 , a__isNatList(nil()) -> tt() 935.98/297.02 , a__isNatIList(V) -> a__isNatList(V) 935.98/297.02 , a__isNatIList(X) -> isNatIList(X) 935.98/297.02 , a__isNatIList(cons(V1, V2)) -> 935.98/297.02 a__and(a__isNat(V1), isNatIList(V2)) 935.98/297.02 , a__isNatIList(zeros()) -> tt() } 935.98/297.02 Obligation: 935.98/297.02 runtime complexity 935.98/297.02 Answer: 935.98/297.02 MAYBE 935.98/297.02 935.98/297.02 We estimate the number of application of {1,2,7,9,11,15,23,26,28} 935.98/297.02 by applications of Pre({1,2,7,9,11,15,23,26,28}) = 935.98/297.02 {3,4,5,8,10,12,13,14,16,17,20,21,24,27,29,30,31,32}. Here rules are 935.98/297.02 labeled as follows: 935.98/297.02 935.98/297.02 DPs: 935.98/297.02 { 1: a__zeros^#() -> c_1() 935.98/297.02 , 2: a__zeros^#() -> c_2() 935.98/297.02 , 3: a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , 4: a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , 5: a__length^#(X) -> c_5(X) 935.98/297.02 , 6: a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , 7: a__length^#(nil()) -> c_7() 935.98/297.02 , 8: mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , 9: mark^#(0()) -> c_9() 935.98/297.02 , 10: mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.02 , 11: mark^#(tt()) -> c_11() 935.98/297.02 , 12: mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , 13: mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , 14: mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , 15: mark^#(nil()) -> c_15() 935.98/297.02 , 16: mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , 17: mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , 18: mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , 19: mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , 20: a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , 21: a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , 22: a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , 23: a__isNatIList^#(zeros()) -> c_32() 935.98/297.02 , 24: a__isNatList^#(X) -> c_26(X) 935.98/297.02 , 25: a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , 26: a__isNatList^#(nil()) -> c_28() 935.98/297.02 , 27: a__isNat^#(X) -> c_22(X) 935.98/297.02 , 28: a__isNat^#(0()) -> c_23() 935.98/297.02 , 29: a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , 30: a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , 31: a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , 32: a__and^#(tt(), X) -> c_21(mark^#(X)) } 935.98/297.02 935.98/297.02 We are left with following problem, upon which TcT provides the 935.98/297.02 certificate MAYBE. 935.98/297.02 935.98/297.02 Strict DPs: 935.98/297.02 { a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , a__length^#(X) -> c_5(X) 935.98/297.02 , a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.02 , mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , a__isNatList^#(X) -> c_26(X) 935.98/297.02 , a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , a__isNat^#(X) -> c_22(X) 935.98/297.02 , a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , a__and^#(tt(), X) -> c_21(mark^#(X)) } 935.98/297.02 Strict Trs: 935.98/297.02 { a__zeros() -> cons(0(), zeros()) 935.98/297.02 , a__zeros() -> zeros() 935.98/297.02 , a__U11(X1, X2) -> U11(X1, X2) 935.98/297.02 , a__U11(tt(), L) -> s(a__length(mark(L))) 935.98/297.02 , a__length(X) -> length(X) 935.98/297.02 , a__length(cons(N, L)) -> 935.98/297.02 a__U11(a__and(a__isNatList(L), isNat(N)), L) 935.98/297.02 , a__length(nil()) -> 0() 935.98/297.02 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 935.98/297.02 , mark(0()) -> 0() 935.98/297.02 , mark(zeros()) -> a__zeros() 935.98/297.02 , mark(tt()) -> tt() 935.98/297.02 , mark(s(X)) -> s(mark(X)) 935.98/297.02 , mark(length(X)) -> a__length(mark(X)) 935.98/297.02 , mark(isNatIList(X)) -> a__isNatIList(X) 935.98/297.02 , mark(nil()) -> nil() 935.98/297.02 , mark(isNatList(X)) -> a__isNatList(X) 935.98/297.02 , mark(isNat(X)) -> a__isNat(X) 935.98/297.02 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 935.98/297.02 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 935.98/297.02 , a__and(X1, X2) -> and(X1, X2) 935.98/297.02 , a__and(tt(), X) -> mark(X) 935.98/297.02 , a__isNat(X) -> isNat(X) 935.98/297.02 , a__isNat(0()) -> tt() 935.98/297.02 , a__isNat(s(V1)) -> a__isNat(V1) 935.98/297.02 , a__isNat(length(V1)) -> a__isNatList(V1) 935.98/297.02 , a__isNatList(X) -> isNatList(X) 935.98/297.02 , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 935.98/297.02 , a__isNatList(nil()) -> tt() 935.98/297.02 , a__isNatIList(V) -> a__isNatList(V) 935.98/297.02 , a__isNatIList(X) -> isNatIList(X) 935.98/297.02 , a__isNatIList(cons(V1, V2)) -> 935.98/297.02 a__and(a__isNat(V1), isNatIList(V2)) 935.98/297.02 , a__isNatIList(zeros()) -> tt() } 935.98/297.02 Weak DPs: 935.98/297.02 { a__zeros^#() -> c_1() 935.98/297.02 , a__zeros^#() -> c_2() 935.98/297.02 , a__length^#(nil()) -> c_7() 935.98/297.02 , mark^#(0()) -> c_9() 935.98/297.02 , mark^#(tt()) -> c_11() 935.98/297.02 , mark^#(nil()) -> c_15() 935.98/297.02 , a__isNatIList^#(zeros()) -> c_32() 935.98/297.02 , a__isNatList^#(nil()) -> c_28() 935.98/297.02 , a__isNat^#(0()) -> c_23() } 935.98/297.02 Obligation: 935.98/297.02 runtime complexity 935.98/297.02 Answer: 935.98/297.02 MAYBE 935.98/297.02 935.98/297.02 We estimate the number of application of {6} by applications of 935.98/297.02 Pre({6}) = {1,3,5,7,15,17,19,22,23}. Here rules are labeled as 935.98/297.02 follows: 935.98/297.02 935.98/297.02 DPs: 935.98/297.02 { 1: a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , 2: a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , 3: a__length^#(X) -> c_5(X) 935.98/297.02 , 4: a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , 5: mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , 6: mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.02 , 7: mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , 8: mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , 9: mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , 10: mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , 11: mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , 12: mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , 13: mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , 14: a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , 15: a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , 16: a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , 17: a__isNatList^#(X) -> c_26(X) 935.98/297.02 , 18: a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , 19: a__isNat^#(X) -> c_22(X) 935.98/297.02 , 20: a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , 21: a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , 22: a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , 23: a__and^#(tt(), X) -> c_21(mark^#(X)) 935.98/297.02 , 24: a__zeros^#() -> c_1() 935.98/297.02 , 25: a__zeros^#() -> c_2() 935.98/297.02 , 26: a__length^#(nil()) -> c_7() 935.98/297.02 , 27: mark^#(0()) -> c_9() 935.98/297.02 , 28: mark^#(tt()) -> c_11() 935.98/297.02 , 29: mark^#(nil()) -> c_15() 935.98/297.02 , 30: a__isNatIList^#(zeros()) -> c_32() 935.98/297.02 , 31: a__isNatList^#(nil()) -> c_28() 935.98/297.02 , 32: a__isNat^#(0()) -> c_23() } 935.98/297.02 935.98/297.02 We are left with following problem, upon which TcT provides the 935.98/297.02 certificate MAYBE. 935.98/297.02 935.98/297.02 Strict DPs: 935.98/297.02 { a__U11^#(X1, X2) -> c_3(X1, X2) 935.98/297.02 , a__U11^#(tt(), L) -> c_4(a__length^#(mark(L))) 935.98/297.02 , a__length^#(X) -> c_5(X) 935.98/297.02 , a__length^#(cons(N, L)) -> 935.98/297.02 c_6(a__U11^#(a__and(a__isNatList(L), isNat(N)), L)) 935.98/297.02 , mark^#(cons(X1, X2)) -> c_8(mark^#(X1), X2) 935.98/297.02 , mark^#(s(X)) -> c_12(mark^#(X)) 935.98/297.02 , mark^#(length(X)) -> c_13(a__length^#(mark(X))) 935.98/297.02 , mark^#(isNatIList(X)) -> c_14(a__isNatIList^#(X)) 935.98/297.02 , mark^#(isNatList(X)) -> c_16(a__isNatList^#(X)) 935.98/297.02 , mark^#(isNat(X)) -> c_17(a__isNat^#(X)) 935.98/297.02 , mark^#(U11(X1, X2)) -> c_18(a__U11^#(mark(X1), X2)) 935.98/297.02 , mark^#(and(X1, X2)) -> c_19(a__and^#(mark(X1), X2)) 935.98/297.02 , a__isNatIList^#(V) -> c_29(a__isNatList^#(V)) 935.98/297.02 , a__isNatIList^#(X) -> c_30(X) 935.98/297.02 , a__isNatIList^#(cons(V1, V2)) -> 935.98/297.02 c_31(a__and^#(a__isNat(V1), isNatIList(V2))) 935.98/297.02 , a__isNatList^#(X) -> c_26(X) 935.98/297.02 , a__isNatList^#(cons(V1, V2)) -> 935.98/297.02 c_27(a__and^#(a__isNat(V1), isNatList(V2))) 935.98/297.02 , a__isNat^#(X) -> c_22(X) 935.98/297.02 , a__isNat^#(s(V1)) -> c_24(a__isNat^#(V1)) 935.98/297.02 , a__isNat^#(length(V1)) -> c_25(a__isNatList^#(V1)) 935.98/297.02 , a__and^#(X1, X2) -> c_20(X1, X2) 935.98/297.02 , a__and^#(tt(), X) -> c_21(mark^#(X)) } 935.98/297.03 Strict Trs: 935.98/297.03 { a__zeros() -> cons(0(), zeros()) 935.98/297.03 , a__zeros() -> zeros() 935.98/297.03 , a__U11(X1, X2) -> U11(X1, X2) 935.98/297.03 , a__U11(tt(), L) -> s(a__length(mark(L))) 935.98/297.03 , a__length(X) -> length(X) 935.98/297.03 , a__length(cons(N, L)) -> 935.98/297.03 a__U11(a__and(a__isNatList(L), isNat(N)), L) 935.98/297.03 , a__length(nil()) -> 0() 935.98/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 935.98/297.03 , mark(0()) -> 0() 935.98/297.03 , mark(zeros()) -> a__zeros() 935.98/297.03 , mark(tt()) -> tt() 935.98/297.03 , mark(s(X)) -> s(mark(X)) 935.98/297.03 , mark(length(X)) -> a__length(mark(X)) 935.98/297.03 , mark(isNatIList(X)) -> a__isNatIList(X) 935.98/297.03 , mark(nil()) -> nil() 935.98/297.03 , mark(isNatList(X)) -> a__isNatList(X) 935.98/297.03 , mark(isNat(X)) -> a__isNat(X) 935.98/297.03 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 935.98/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 935.98/297.03 , a__and(X1, X2) -> and(X1, X2) 935.98/297.03 , a__and(tt(), X) -> mark(X) 935.98/297.03 , a__isNat(X) -> isNat(X) 935.98/297.03 , a__isNat(0()) -> tt() 935.98/297.03 , a__isNat(s(V1)) -> a__isNat(V1) 935.98/297.03 , a__isNat(length(V1)) -> a__isNatList(V1) 935.98/297.03 , a__isNatList(X) -> isNatList(X) 935.98/297.03 , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) 935.98/297.03 , a__isNatList(nil()) -> tt() 935.98/297.03 , a__isNatIList(V) -> a__isNatList(V) 935.98/297.03 , a__isNatIList(X) -> isNatIList(X) 935.98/297.03 , a__isNatIList(cons(V1, V2)) -> 935.98/297.03 a__and(a__isNat(V1), isNatIList(V2)) 935.98/297.03 , a__isNatIList(zeros()) -> tt() } 935.98/297.03 Weak DPs: 935.98/297.03 { a__zeros^#() -> c_1() 935.98/297.03 , a__zeros^#() -> c_2() 935.98/297.03 , a__length^#(nil()) -> c_7() 935.98/297.03 , mark^#(0()) -> c_9() 935.98/297.03 , mark^#(zeros()) -> c_10(a__zeros^#()) 935.98/297.03 , mark^#(tt()) -> c_11() 935.98/297.03 , mark^#(nil()) -> c_15() 935.98/297.03 , a__isNatIList^#(zeros()) -> c_32() 935.98/297.03 , a__isNatList^#(nil()) -> c_28() 935.98/297.03 , a__isNat^#(0()) -> c_23() } 935.98/297.03 Obligation: 935.98/297.03 runtime complexity 935.98/297.03 Answer: 935.98/297.03 MAYBE 935.98/297.03 935.98/297.03 Empty strict component of the problem is NOT empty. 935.98/297.03 935.98/297.03 935.98/297.03 Arrrr.. 936.10/297.10 EOF