MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { O(0()) -> 0() , +(x, 0()) -> x , +(O(x), O(y)) -> O(+(x, y)) , +(O(x), I(y)) -> I(+(x, y)) , +(0(), x) -> x , +(I(x), O(y)) -> I(+(x, y)) , +(I(x), I(y)) -> O(+(+(x, y), I(0()))) , *(x, 0()) -> 0() , *(O(x), y) -> O(*(x, y)) , *(0(), x) -> 0() , *(I(x), y) -> +(O(*(x, y)), y) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { O^#(0()) -> c_1() , +^#(x, 0()) -> c_2(x) , +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , +^#(O(x), I(y)) -> c_4(+^#(x, y)) , +^#(0(), x) -> c_5(x) , +^#(I(x), O(y)) -> c_6(+^#(x, y)) , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , *^#(x, 0()) -> c_8() , *^#(O(x), y) -> c_9(O^#(*(x, y))) , *^#(0(), x) -> c_10() , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { O^#(0()) -> c_1() , +^#(x, 0()) -> c_2(x) , +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , +^#(O(x), I(y)) -> c_4(+^#(x, y)) , +^#(0(), x) -> c_5(x) , +^#(I(x), O(y)) -> c_6(+^#(x, y)) , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , *^#(x, 0()) -> c_8() , *^#(O(x), y) -> c_9(O^#(*(x, y))) , *^#(0(), x) -> c_10() , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) } Strict Trs: { O(0()) -> 0() , +(x, 0()) -> x , +(O(x), O(y)) -> O(+(x, y)) , +(O(x), I(y)) -> I(+(x, y)) , +(0(), x) -> x , +(I(x), O(y)) -> I(+(x, y)) , +(I(x), I(y)) -> O(+(+(x, y), I(0()))) , *(x, 0()) -> 0() , *(O(x), y) -> O(*(x, y)) , *(0(), x) -> 0() , *(I(x), y) -> +(O(*(x, y)), y) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,8,10} by applications of Pre({1,8,10}) = {2,3,5,7,9}. Here rules are labeled as follows: DPs: { 1: O^#(0()) -> c_1() , 2: +^#(x, 0()) -> c_2(x) , 3: +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , 4: +^#(O(x), I(y)) -> c_4(+^#(x, y)) , 5: +^#(0(), x) -> c_5(x) , 6: +^#(I(x), O(y)) -> c_6(+^#(x, y)) , 7: +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , 8: *^#(x, 0()) -> c_8() , 9: *^#(O(x), y) -> c_9(O^#(*(x, y))) , 10: *^#(0(), x) -> c_10() , 11: *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(x, 0()) -> c_2(x) , +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , +^#(O(x), I(y)) -> c_4(+^#(x, y)) , +^#(0(), x) -> c_5(x) , +^#(I(x), O(y)) -> c_6(+^#(x, y)) , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , *^#(O(x), y) -> c_9(O^#(*(x, y))) , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) } Strict Trs: { O(0()) -> 0() , +(x, 0()) -> x , +(O(x), O(y)) -> O(+(x, y)) , +(O(x), I(y)) -> I(+(x, y)) , +(0(), x) -> x , +(I(x), O(y)) -> I(+(x, y)) , +(I(x), I(y)) -> O(+(+(x, y), I(0()))) , *(x, 0()) -> 0() , *(O(x), y) -> O(*(x, y)) , *(0(), x) -> 0() , *(I(x), y) -> +(O(*(x, y)), y) } Weak DPs: { O^#(0()) -> c_1() , *^#(x, 0()) -> c_8() , *^#(0(), x) -> c_10() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2,6,7} by applications of Pre({2,6,7}) = {1,3,4,5,8}. Here rules are labeled as follows: DPs: { 1: +^#(x, 0()) -> c_2(x) , 2: +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , 3: +^#(O(x), I(y)) -> c_4(+^#(x, y)) , 4: +^#(0(), x) -> c_5(x) , 5: +^#(I(x), O(y)) -> c_6(+^#(x, y)) , 6: +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , 7: *^#(O(x), y) -> c_9(O^#(*(x, y))) , 8: *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) , 9: O^#(0()) -> c_1() , 10: *^#(x, 0()) -> c_8() , 11: *^#(0(), x) -> c_10() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { +^#(x, 0()) -> c_2(x) , +^#(O(x), I(y)) -> c_4(+^#(x, y)) , +^#(0(), x) -> c_5(x) , +^#(I(x), O(y)) -> c_6(+^#(x, y)) , *^#(I(x), y) -> c_11(+^#(O(*(x, y)), y)) } Strict Trs: { O(0()) -> 0() , +(x, 0()) -> x , +(O(x), O(y)) -> O(+(x, y)) , +(O(x), I(y)) -> I(+(x, y)) , +(0(), x) -> x , +(I(x), O(y)) -> I(+(x, y)) , +(I(x), I(y)) -> O(+(+(x, y), I(0()))) , *(x, 0()) -> 0() , *(O(x), y) -> O(*(x, y)) , *(0(), x) -> 0() , *(I(x), y) -> +(O(*(x, y)), y) } Weak DPs: { O^#(0()) -> c_1() , +^#(O(x), O(y)) -> c_3(O^#(+(x, y))) , +^#(I(x), I(y)) -> c_7(O^#(+(+(x, y), I(0())))) , *^#(x, 0()) -> c_8() , *^#(O(x), y) -> c_9(O^#(*(x, y))) , *^#(0(), x) -> c_10() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..