MAYBE 756.51/297.04 MAYBE 756.51/297.04 756.51/297.04 We are left with following problem, upon which TcT provides the 756.51/297.04 certificate MAYBE. 756.51/297.04 756.51/297.04 Strict Trs: 756.51/297.04 { 0(#()) -> #() 756.51/297.04 , +(x, #()) -> x 756.51/297.04 , +(0(x), 0(y)) -> 0(+(x, y)) 756.51/297.04 , +(0(x), 1(y)) -> 1(+(x, y)) 756.51/297.04 , +(#(), x) -> x 756.51/297.04 , +(1(x), 0(y)) -> 1(+(x, y)) 756.51/297.04 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 756.51/297.04 , *(0(x), y) -> 0(*(x, y)) 756.51/297.04 , *(#(), x) -> #() 756.51/297.04 , *(1(x), y) -> +(0(*(x, y)), y) 756.51/297.04 , sum(nil()) -> 0(#()) 756.51/297.04 , sum(cons(x, l)) -> +(x, sum(l)) 756.51/297.04 , prod(nil()) -> 1(#()) 756.51/297.04 , prod(cons(x, l)) -> *(x, prod(l)) } 756.51/297.04 Obligation: 756.51/297.04 runtime complexity 756.51/297.04 Answer: 756.51/297.04 MAYBE 756.51/297.04 756.51/297.04 None of the processors succeeded. 756.51/297.04 756.51/297.04 Details of failed attempt(s): 756.51/297.04 ----------------------------- 756.51/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 756.51/297.04 following reason: 756.51/297.04 756.51/297.04 Computation stopped due to timeout after 297.0 seconds. 756.51/297.04 756.51/297.04 2) 'Best' failed due to the following reason: 756.51/297.04 756.51/297.04 None of the processors succeeded. 756.51/297.04 756.51/297.04 Details of failed attempt(s): 756.51/297.04 ----------------------------- 756.51/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 756.51/297.04 seconds)' failed due to the following reason: 756.51/297.04 756.51/297.04 Computation stopped due to timeout after 148.0 seconds. 756.51/297.04 756.51/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 756.51/297.04 failed due to the following reason: 756.51/297.04 756.51/297.04 None of the processors succeeded. 756.51/297.04 756.51/297.04 Details of failed attempt(s): 756.51/297.04 ----------------------------- 756.51/297.04 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 756.51/297.04 failed due to the following reason: 756.51/297.04 756.51/297.04 match-boundness of the problem could not be verified. 756.51/297.04 756.51/297.04 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 756.51/297.04 failed due to the following reason: 756.51/297.04 756.51/297.04 match-boundness of the problem could not be verified. 756.51/297.04 756.51/297.04 756.51/297.04 3) 'Best' failed due to the following reason: 756.51/297.04 756.51/297.04 None of the processors succeeded. 756.51/297.04 756.51/297.04 Details of failed attempt(s): 756.51/297.04 ----------------------------- 756.51/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 756.51/297.04 to the following reason: 756.51/297.04 756.51/297.04 The processor is inapplicable, reason: 756.51/297.04 Processor only applicable for innermost runtime complexity analysis 756.51/297.04 756.51/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 756.51/297.04 following reason: 756.51/297.04 756.51/297.04 The processor is inapplicable, reason: 756.51/297.04 Processor only applicable for innermost runtime complexity analysis 756.51/297.04 756.51/297.04 756.51/297.04 756.51/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 756.51/297.04 the following reason: 756.51/297.04 756.51/297.04 We add the following weak dependency pairs: 756.51/297.04 756.51/297.04 Strict DPs: 756.51/297.04 { 0^#(#()) -> c_1() 756.51/297.04 , +^#(x, #()) -> c_2(x) 756.51/297.04 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , +^#(#(), x) -> c_5(x) 756.51/297.04 , +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , *^#(#(), x) -> c_9() 756.51/297.04 , *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , prod^#(nil()) -> c_13() 756.51/297.04 , prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) } 756.51/297.04 756.51/297.04 and mark the set of starting terms. 756.51/297.04 756.51/297.04 We are left with following problem, upon which TcT provides the 756.51/297.04 certificate MAYBE. 756.51/297.04 756.51/297.04 Strict DPs: 756.51/297.04 { 0^#(#()) -> c_1() 756.51/297.04 , +^#(x, #()) -> c_2(x) 756.51/297.04 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , +^#(#(), x) -> c_5(x) 756.51/297.04 , +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , *^#(#(), x) -> c_9() 756.51/297.04 , *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , prod^#(nil()) -> c_13() 756.51/297.04 , prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) } 756.51/297.04 Strict Trs: 756.51/297.04 { 0(#()) -> #() 756.51/297.04 , +(x, #()) -> x 756.51/297.04 , +(0(x), 0(y)) -> 0(+(x, y)) 756.51/297.04 , +(0(x), 1(y)) -> 1(+(x, y)) 756.51/297.04 , +(#(), x) -> x 756.51/297.04 , +(1(x), 0(y)) -> 1(+(x, y)) 756.51/297.04 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 756.51/297.04 , *(0(x), y) -> 0(*(x, y)) 756.51/297.04 , *(#(), x) -> #() 756.51/297.04 , *(1(x), y) -> +(0(*(x, y)), y) 756.51/297.04 , sum(nil()) -> 0(#()) 756.51/297.04 , sum(cons(x, l)) -> +(x, sum(l)) 756.51/297.04 , prod(nil()) -> 1(#()) 756.51/297.04 , prod(cons(x, l)) -> *(x, prod(l)) } 756.51/297.04 Obligation: 756.51/297.04 runtime complexity 756.51/297.04 Answer: 756.51/297.04 MAYBE 756.51/297.04 756.51/297.04 We estimate the number of application of {1,9,13} by applications 756.51/297.04 of Pre({1,9,13}) = {2,3,5,7,8,11,14}. Here rules are labeled as 756.51/297.04 follows: 756.51/297.04 756.51/297.04 DPs: 756.51/297.04 { 1: 0^#(#()) -> c_1() 756.51/297.04 , 2: +^#(x, #()) -> c_2(x) 756.51/297.04 , 3: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , 4: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , 5: +^#(#(), x) -> c_5(x) 756.51/297.04 , 6: +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , 7: +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , 8: *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , 9: *^#(#(), x) -> c_9() 756.51/297.04 , 10: *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , 11: sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , 12: sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , 13: prod^#(nil()) -> c_13() 756.51/297.04 , 14: prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) } 756.51/297.04 756.51/297.04 We are left with following problem, upon which TcT provides the 756.51/297.04 certificate MAYBE. 756.51/297.04 756.51/297.04 Strict DPs: 756.51/297.04 { +^#(x, #()) -> c_2(x) 756.51/297.04 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , +^#(#(), x) -> c_5(x) 756.51/297.04 , +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) } 756.51/297.04 Strict Trs: 756.51/297.04 { 0(#()) -> #() 756.51/297.04 , +(x, #()) -> x 756.51/297.04 , +(0(x), 0(y)) -> 0(+(x, y)) 756.51/297.04 , +(0(x), 1(y)) -> 1(+(x, y)) 756.51/297.04 , +(#(), x) -> x 756.51/297.04 , +(1(x), 0(y)) -> 1(+(x, y)) 756.51/297.04 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 756.51/297.04 , *(0(x), y) -> 0(*(x, y)) 756.51/297.04 , *(#(), x) -> #() 756.51/297.04 , *(1(x), y) -> +(0(*(x, y)), y) 756.51/297.04 , sum(nil()) -> 0(#()) 756.51/297.04 , sum(cons(x, l)) -> +(x, sum(l)) 756.51/297.04 , prod(nil()) -> 1(#()) 756.51/297.04 , prod(cons(x, l)) -> *(x, prod(l)) } 756.51/297.04 Weak DPs: 756.51/297.04 { 0^#(#()) -> c_1() 756.51/297.04 , *^#(#(), x) -> c_9() 756.51/297.04 , prod^#(nil()) -> c_13() } 756.51/297.04 Obligation: 756.51/297.04 runtime complexity 756.51/297.04 Answer: 756.51/297.04 MAYBE 756.51/297.04 756.51/297.04 We estimate the number of application of {2,6,7,9} by applications 756.51/297.04 of Pre({2,6,7,9}) = {1,3,4,5,8,10,11}. Here rules are labeled as 756.51/297.04 follows: 756.51/297.04 756.51/297.04 DPs: 756.51/297.04 { 1: +^#(x, #()) -> c_2(x) 756.51/297.04 , 2: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , 3: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , 4: +^#(#(), x) -> c_5(x) 756.51/297.04 , 5: +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , 6: +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , 7: *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , 8: *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , 9: sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , 10: sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , 11: prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) 756.51/297.04 , 12: 0^#(#()) -> c_1() 756.51/297.04 , 13: *^#(#(), x) -> c_9() 756.51/297.04 , 14: prod^#(nil()) -> c_13() } 756.51/297.04 756.51/297.04 We are left with following problem, upon which TcT provides the 756.51/297.04 certificate MAYBE. 756.51/297.04 756.51/297.04 Strict DPs: 756.51/297.04 { +^#(x, #()) -> c_2(x) 756.51/297.04 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 756.51/297.04 , +^#(#(), x) -> c_5(x) 756.51/297.04 , +^#(1(x), 0(y)) -> c_6(+^#(x, y)) 756.51/297.04 , *^#(1(x), y) -> c_10(+^#(0(*(x, y)), y)) 756.51/297.04 , sum^#(cons(x, l)) -> c_12(+^#(x, sum(l))) 756.51/297.04 , prod^#(cons(x, l)) -> c_14(*^#(x, prod(l))) } 756.51/297.04 Strict Trs: 756.51/297.04 { 0(#()) -> #() 756.51/297.04 , +(x, #()) -> x 756.51/297.04 , +(0(x), 0(y)) -> 0(+(x, y)) 756.51/297.04 , +(0(x), 1(y)) -> 1(+(x, y)) 756.51/297.04 , +(#(), x) -> x 756.51/297.04 , +(1(x), 0(y)) -> 1(+(x, y)) 756.51/297.04 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 756.51/297.04 , *(0(x), y) -> 0(*(x, y)) 756.51/297.04 , *(#(), x) -> #() 756.51/297.04 , *(1(x), y) -> +(0(*(x, y)), y) 756.51/297.04 , sum(nil()) -> 0(#()) 756.51/297.04 , sum(cons(x, l)) -> +(x, sum(l)) 756.51/297.04 , prod(nil()) -> 1(#()) 756.51/297.04 , prod(cons(x, l)) -> *(x, prod(l)) } 756.51/297.04 Weak DPs: 756.51/297.04 { 0^#(#()) -> c_1() 756.51/297.04 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 756.51/297.04 , +^#(1(x), 1(y)) -> c_7(0^#(+(+(x, y), 1(#())))) 756.51/297.04 , *^#(0(x), y) -> c_8(0^#(*(x, y))) 756.51/297.04 , *^#(#(), x) -> c_9() 756.51/297.04 , sum^#(nil()) -> c_11(0^#(#())) 756.51/297.04 , prod^#(nil()) -> c_13() } 756.51/297.04 Obligation: 756.51/297.04 runtime complexity 756.51/297.04 Answer: 756.51/297.04 MAYBE 756.51/297.04 756.51/297.04 Empty strict component of the problem is NOT empty. 756.51/297.04 756.51/297.04 756.51/297.04 Arrrr.. 756.93/297.42 EOF