MAYBE 1173.32/299.88 MAYBE 1173.32/299.88 1173.32/299.88 We are left with following problem, upon which TcT provides the 1173.32/299.88 certificate MAYBE. 1173.32/299.88 1173.32/299.88 Strict Trs: 1173.32/299.88 { a__U11(X1, X2) -> U11(X1, X2) 1173.32/299.88 , a__U11(tt(), N) -> mark(N) 1173.32/299.88 , mark(tt()) -> tt() 1173.32/299.88 , mark(s(X)) -> s(mark(X)) 1173.32/299.88 , mark(0()) -> 0() 1173.32/299.88 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1173.32/299.88 , mark(isNat(X)) -> a__isNat(X) 1173.32/299.88 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1173.32/299.88 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1173.32/299.88 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1173.32/299.88 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1173.32/299.88 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1173.32/299.88 , a__plus(X1, X2) -> plus(X1, X2) 1173.32/299.88 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1173.32/299.88 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1173.32/299.88 , a__and(X1, X2) -> and(X1, X2) 1173.32/299.88 , a__and(tt(), X) -> mark(X) 1173.32/299.88 , a__isNat(X) -> isNat(X) 1173.32/299.88 , a__isNat(s(V1)) -> a__isNat(V1) 1173.32/299.88 , a__isNat(0()) -> tt() 1173.32/299.88 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1173.32/299.88 Obligation: 1173.32/299.88 runtime complexity 1173.32/299.88 Answer: 1173.32/299.88 MAYBE 1173.32/299.88 1173.32/299.88 None of the processors succeeded. 1173.32/299.88 1173.32/299.88 Details of failed attempt(s): 1173.32/299.88 ----------------------------- 1173.32/299.88 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1173.32/299.88 following reason: 1173.32/299.88 1173.32/299.88 Computation stopped due to timeout after 297.0 seconds. 1173.32/299.88 1173.32/299.88 2) 'Best' failed due to the following reason: 1173.32/299.88 1173.32/299.88 None of the processors succeeded. 1173.32/299.88 1173.32/299.88 Details of failed attempt(s): 1173.32/299.88 ----------------------------- 1173.32/299.88 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1173.32/299.88 seconds)' failed due to the following reason: 1173.32/299.88 1173.32/299.88 Computation stopped due to timeout after 148.0 seconds. 1173.32/299.88 1173.32/299.88 2) 'Best' failed due to the following reason: 1173.32/299.88 1173.32/299.88 None of the processors succeeded. 1173.32/299.88 1173.32/299.88 Details of failed attempt(s): 1173.32/299.88 ----------------------------- 1173.32/299.88 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1173.32/299.88 to the following reason: 1173.32/299.88 1173.32/299.88 The processor is inapplicable, reason: 1173.32/299.88 Processor only applicable for innermost runtime complexity analysis 1173.32/299.88 1173.32/299.88 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1173.32/299.88 following reason: 1173.32/299.88 1173.32/299.88 The processor is inapplicable, reason: 1173.32/299.88 Processor only applicable for innermost runtime complexity analysis 1173.32/299.88 1173.32/299.88 1173.32/299.88 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1173.32/299.88 failed due to the following reason: 1173.32/299.88 1173.32/299.88 None of the processors succeeded. 1173.32/299.88 1173.32/299.88 Details of failed attempt(s): 1173.32/299.88 ----------------------------- 1173.32/299.88 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1173.32/299.88 failed due to the following reason: 1173.32/299.88 1173.32/299.88 match-boundness of the problem could not be verified. 1173.32/299.88 1173.32/299.88 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1173.32/299.88 failed due to the following reason: 1173.32/299.88 1173.32/299.88 match-boundness of the problem could not be verified. 1173.32/299.88 1173.32/299.88 1173.32/299.88 1173.32/299.88 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1173.32/299.88 the following reason: 1173.32/299.88 1173.32/299.88 We add the following weak dependency pairs: 1173.32/299.88 1173.32/299.88 Strict DPs: 1173.32/299.88 { a__U11^#(X1, X2) -> c_1(X1, X2) 1173.32/299.88 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1173.32/299.88 , mark^#(tt()) -> c_3() 1173.32/299.88 , mark^#(s(X)) -> c_4(mark^#(X)) 1173.32/299.88 , mark^#(0()) -> c_5() 1173.32/299.88 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1173.32/299.88 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1173.32/299.88 , mark^#(U11(X1, X2)) -> c_8(a__U11^#(mark(X1), X2)) 1173.32/299.88 , mark^#(U21(X1, X2, X3)) -> c_9(a__U21^#(mark(X1), X2, X3)) 1173.32/299.88 , mark^#(and(X1, X2)) -> c_10(a__and^#(mark(X1), X2)) 1173.32/299.88 , a__plus^#(X1, X2) -> c_13(X1, X2) 1173.32/299.88 , a__plus^#(N, s(M)) -> 1173.32/299.88 c_14(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1173.32/299.88 , a__plus^#(N, 0()) -> c_15(a__U11^#(a__isNat(N), N)) 1173.32/299.88 , a__isNat^#(X) -> c_18(X) 1173.32/299.88 , a__isNat^#(s(V1)) -> c_19(a__isNat^#(V1)) 1173.32/299.88 , a__isNat^#(0()) -> c_20() 1173.32/299.88 , a__isNat^#(plus(V1, V2)) -> 1173.32/299.88 c_21(a__and^#(a__isNat(V1), isNat(V2))) 1173.32/299.88 , a__U21^#(X1, X2, X3) -> c_11(X1, X2, X3) 1173.32/299.88 , a__U21^#(tt(), M, N) -> c_12(a__plus^#(mark(N), mark(M))) 1173.32/299.88 , a__and^#(X1, X2) -> c_16(X1, X2) 1173.32/299.88 , a__and^#(tt(), X) -> c_17(mark^#(X)) } 1173.32/299.88 1173.32/299.88 and mark the set of starting terms. 1173.32/299.88 1173.32/299.88 We are left with following problem, upon which TcT provides the 1173.32/299.88 certificate MAYBE. 1173.32/299.88 1173.32/299.88 Strict DPs: 1173.32/299.88 { a__U11^#(X1, X2) -> c_1(X1, X2) 1173.32/299.88 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1173.32/299.88 , mark^#(tt()) -> c_3() 1173.32/299.88 , mark^#(s(X)) -> c_4(mark^#(X)) 1173.32/299.88 , mark^#(0()) -> c_5() 1173.32/299.88 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1173.32/299.88 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1173.32/299.88 , mark^#(U11(X1, X2)) -> c_8(a__U11^#(mark(X1), X2)) 1173.32/299.88 , mark^#(U21(X1, X2, X3)) -> c_9(a__U21^#(mark(X1), X2, X3)) 1173.32/299.88 , mark^#(and(X1, X2)) -> c_10(a__and^#(mark(X1), X2)) 1173.32/299.88 , a__plus^#(X1, X2) -> c_13(X1, X2) 1173.32/299.88 , a__plus^#(N, s(M)) -> 1173.32/299.88 c_14(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1173.32/299.88 , a__plus^#(N, 0()) -> c_15(a__U11^#(a__isNat(N), N)) 1173.32/299.88 , a__isNat^#(X) -> c_18(X) 1173.32/299.88 , a__isNat^#(s(V1)) -> c_19(a__isNat^#(V1)) 1173.32/299.88 , a__isNat^#(0()) -> c_20() 1173.32/299.88 , a__isNat^#(plus(V1, V2)) -> 1173.32/299.88 c_21(a__and^#(a__isNat(V1), isNat(V2))) 1173.32/299.88 , a__U21^#(X1, X2, X3) -> c_11(X1, X2, X3) 1173.32/299.88 , a__U21^#(tt(), M, N) -> c_12(a__plus^#(mark(N), mark(M))) 1173.32/299.88 , a__and^#(X1, X2) -> c_16(X1, X2) 1173.32/299.88 , a__and^#(tt(), X) -> c_17(mark^#(X)) } 1173.32/299.88 Strict Trs: 1173.32/299.88 { a__U11(X1, X2) -> U11(X1, X2) 1173.32/299.88 , a__U11(tt(), N) -> mark(N) 1173.32/299.88 , mark(tt()) -> tt() 1173.32/299.88 , mark(s(X)) -> s(mark(X)) 1173.32/299.88 , mark(0()) -> 0() 1173.32/299.88 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1173.32/299.88 , mark(isNat(X)) -> a__isNat(X) 1173.32/299.88 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1173.32/299.88 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1173.32/299.88 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1173.32/299.88 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1173.32/299.88 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1173.32/299.88 , a__plus(X1, X2) -> plus(X1, X2) 1173.32/299.88 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1173.32/299.88 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1173.32/299.88 , a__and(X1, X2) -> and(X1, X2) 1173.32/299.88 , a__and(tt(), X) -> mark(X) 1173.32/299.88 , a__isNat(X) -> isNat(X) 1173.32/299.88 , a__isNat(s(V1)) -> a__isNat(V1) 1173.32/299.88 , a__isNat(0()) -> tt() 1173.32/299.88 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1173.32/299.88 Obligation: 1173.32/299.88 runtime complexity 1173.32/299.88 Answer: 1173.32/299.88 MAYBE 1173.32/299.88 1173.32/299.88 We estimate the number of application of {3,5,16} by applications 1173.32/299.88 of Pre({3,5,16}) = {1,2,4,7,11,14,15,18,20,21}. Here rules are 1173.32/299.88 labeled as follows: 1173.32/299.88 1173.32/299.88 DPs: 1173.32/299.88 { 1: a__U11^#(X1, X2) -> c_1(X1, X2) 1173.32/299.88 , 2: a__U11^#(tt(), N) -> c_2(mark^#(N)) 1173.32/299.88 , 3: mark^#(tt()) -> c_3() 1173.32/299.88 , 4: mark^#(s(X)) -> c_4(mark^#(X)) 1173.32/299.88 , 5: mark^#(0()) -> c_5() 1173.32/299.88 , 6: mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1173.32/299.88 , 7: mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1173.32/299.88 , 8: mark^#(U11(X1, X2)) -> c_8(a__U11^#(mark(X1), X2)) 1173.32/299.88 , 9: mark^#(U21(X1, X2, X3)) -> c_9(a__U21^#(mark(X1), X2, X3)) 1173.32/299.88 , 10: mark^#(and(X1, X2)) -> c_10(a__and^#(mark(X1), X2)) 1173.32/299.88 , 11: a__plus^#(X1, X2) -> c_13(X1, X2) 1173.32/299.88 , 12: a__plus^#(N, s(M)) -> 1173.32/299.88 c_14(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1173.32/299.88 , 13: a__plus^#(N, 0()) -> c_15(a__U11^#(a__isNat(N), N)) 1173.32/299.88 , 14: a__isNat^#(X) -> c_18(X) 1173.32/299.88 , 15: a__isNat^#(s(V1)) -> c_19(a__isNat^#(V1)) 1173.32/299.88 , 16: a__isNat^#(0()) -> c_20() 1173.32/299.88 , 17: a__isNat^#(plus(V1, V2)) -> 1173.32/299.88 c_21(a__and^#(a__isNat(V1), isNat(V2))) 1173.32/299.88 , 18: a__U21^#(X1, X2, X3) -> c_11(X1, X2, X3) 1173.32/299.88 , 19: a__U21^#(tt(), M, N) -> c_12(a__plus^#(mark(N), mark(M))) 1173.32/299.88 , 20: a__and^#(X1, X2) -> c_16(X1, X2) 1173.32/299.88 , 21: a__and^#(tt(), X) -> c_17(mark^#(X)) } 1173.32/299.88 1173.32/299.88 We are left with following problem, upon which TcT provides the 1173.32/299.88 certificate MAYBE. 1173.32/299.88 1173.32/299.88 Strict DPs: 1173.32/299.88 { a__U11^#(X1, X2) -> c_1(X1, X2) 1173.32/299.88 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1173.32/299.88 , mark^#(s(X)) -> c_4(mark^#(X)) 1173.32/299.88 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1173.32/299.88 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1173.32/299.88 , mark^#(U11(X1, X2)) -> c_8(a__U11^#(mark(X1), X2)) 1173.32/299.88 , mark^#(U21(X1, X2, X3)) -> c_9(a__U21^#(mark(X1), X2, X3)) 1173.32/299.88 , mark^#(and(X1, X2)) -> c_10(a__and^#(mark(X1), X2)) 1173.32/299.88 , a__plus^#(X1, X2) -> c_13(X1, X2) 1173.32/299.88 , a__plus^#(N, s(M)) -> 1173.32/299.88 c_14(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1173.32/299.88 , a__plus^#(N, 0()) -> c_15(a__U11^#(a__isNat(N), N)) 1173.32/299.88 , a__isNat^#(X) -> c_18(X) 1173.32/299.88 , a__isNat^#(s(V1)) -> c_19(a__isNat^#(V1)) 1173.32/299.88 , a__isNat^#(plus(V1, V2)) -> 1173.32/299.88 c_21(a__and^#(a__isNat(V1), isNat(V2))) 1173.32/299.88 , a__U21^#(X1, X2, X3) -> c_11(X1, X2, X3) 1173.32/299.88 , a__U21^#(tt(), M, N) -> c_12(a__plus^#(mark(N), mark(M))) 1173.32/299.88 , a__and^#(X1, X2) -> c_16(X1, X2) 1173.32/299.88 , a__and^#(tt(), X) -> c_17(mark^#(X)) } 1173.32/299.88 Strict Trs: 1173.32/299.88 { a__U11(X1, X2) -> U11(X1, X2) 1173.32/299.88 , a__U11(tt(), N) -> mark(N) 1173.32/299.88 , mark(tt()) -> tt() 1173.32/299.88 , mark(s(X)) -> s(mark(X)) 1173.32/299.88 , mark(0()) -> 0() 1173.32/299.88 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1173.32/299.88 , mark(isNat(X)) -> a__isNat(X) 1173.32/299.88 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1173.32/299.88 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1173.32/299.88 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1173.32/299.88 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1173.32/299.88 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1173.32/299.88 , a__plus(X1, X2) -> plus(X1, X2) 1173.32/299.88 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1173.32/299.88 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1173.32/299.88 , a__and(X1, X2) -> and(X1, X2) 1173.32/299.88 , a__and(tt(), X) -> mark(X) 1173.32/299.88 , a__isNat(X) -> isNat(X) 1173.32/299.88 , a__isNat(s(V1)) -> a__isNat(V1) 1173.32/299.88 , a__isNat(0()) -> tt() 1173.32/299.88 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1173.32/299.88 Weak DPs: 1173.32/299.88 { mark^#(tt()) -> c_3() 1173.32/299.88 , mark^#(0()) -> c_5() 1173.32/299.88 , a__isNat^#(0()) -> c_20() } 1173.32/299.88 Obligation: 1173.32/299.88 runtime complexity 1173.32/299.88 Answer: 1173.32/299.88 MAYBE 1173.32/299.88 1173.32/299.88 Empty strict component of the problem is NOT empty. 1173.32/299.88 1173.32/299.88 1173.32/299.88 Arrrr.. 1173.76/300.55 EOF