MAYBE 805.47/297.03 MAYBE 805.47/297.03 805.47/297.03 We are left with following problem, upon which TcT provides the 805.47/297.03 certificate MAYBE. 805.47/297.03 805.47/297.03 Strict Trs: 805.47/297.03 { 0(#()) -> #() 805.47/297.03 , +(x, #()) -> x 805.47/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 805.47/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 805.47/297.03 , +(#(), x) -> x 805.47/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 805.47/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 805.47/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 805.47/297.03 , *(x, +(y, z)) -> +(*(x, y), *(x, z)) 805.47/297.03 , *(0(x), y) -> 0(*(x, y)) 805.47/297.03 , *(#(), x) -> #() 805.47/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 805.47/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 805.47/297.03 , app(nil(), l) -> l 805.47/297.03 , app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 805.47/297.03 , sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 805.47/297.03 , sum(nil()) -> 0(#()) 805.47/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 805.47/297.03 , prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 805.47/297.03 , prod(nil()) -> 1(#()) 805.47/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 805.47/297.03 Obligation: 805.47/297.03 runtime complexity 805.47/297.03 Answer: 805.47/297.03 MAYBE 805.47/297.03 805.47/297.03 None of the processors succeeded. 805.47/297.03 805.47/297.03 Details of failed attempt(s): 805.47/297.03 ----------------------------- 805.47/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 805.47/297.03 following reason: 805.47/297.03 805.47/297.03 Computation stopped due to timeout after 297.0 seconds. 805.47/297.03 805.47/297.03 2) 'Best' failed due to the following reason: 805.47/297.03 805.47/297.03 None of the processors succeeded. 805.47/297.03 805.47/297.03 Details of failed attempt(s): 805.47/297.03 ----------------------------- 805.47/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 805.47/297.03 seconds)' failed due to the following reason: 805.47/297.03 805.47/297.03 Computation stopped due to timeout after 148.0 seconds. 805.47/297.03 805.47/297.03 2) 'Best' failed due to the following reason: 805.47/297.03 805.47/297.03 None of the processors succeeded. 805.47/297.03 805.47/297.03 Details of failed attempt(s): 805.47/297.03 ----------------------------- 805.47/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 805.47/297.03 to the following reason: 805.47/297.03 805.47/297.03 The processor is inapplicable, reason: 805.47/297.03 Processor only applicable for innermost runtime complexity analysis 805.47/297.03 805.47/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 805.47/297.03 following reason: 805.47/297.03 805.47/297.03 The processor is inapplicable, reason: 805.47/297.03 Processor only applicable for innermost runtime complexity analysis 805.47/297.03 805.47/297.03 805.47/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 805.47/297.03 failed due to the following reason: 805.47/297.03 805.47/297.03 None of the processors succeeded. 805.47/297.03 805.47/297.03 Details of failed attempt(s): 805.47/297.03 ----------------------------- 805.47/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 805.47/297.03 failed due to the following reason: 805.47/297.03 805.47/297.03 match-boundness of the problem could not be verified. 805.47/297.03 805.47/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 805.47/297.03 failed due to the following reason: 805.47/297.03 805.47/297.03 match-boundness of the problem could not be verified. 805.47/297.03 805.47/297.03 805.47/297.03 805.47/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 805.47/297.03 the following reason: 805.47/297.03 805.47/297.03 We add the following weak dependency pairs: 805.47/297.03 805.47/297.03 Strict DPs: 805.47/297.03 { 0^#(#()) -> c_1() 805.47/297.03 , +^#(x, #()) -> c_2(x) 805.47/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , +^#(#(), x) -> c_5(x) 805.47/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , *^#(#(), x) -> c_11() 805.47/297.03 , *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , app^#(nil(), l) -> c_14(l) 805.47/297.03 , app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , prod^#(nil()) -> c_20() 805.47/297.03 , prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) } 805.47/297.03 805.47/297.03 and mark the set of starting terms. 805.47/297.03 805.47/297.03 We are left with following problem, upon which TcT provides the 805.47/297.03 certificate MAYBE. 805.47/297.03 805.47/297.03 Strict DPs: 805.47/297.03 { 0^#(#()) -> c_1() 805.47/297.03 , +^#(x, #()) -> c_2(x) 805.47/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , +^#(#(), x) -> c_5(x) 805.47/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , *^#(#(), x) -> c_11() 805.47/297.03 , *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , app^#(nil(), l) -> c_14(l) 805.47/297.03 , app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , prod^#(nil()) -> c_20() 805.47/297.03 , prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) } 805.47/297.03 Strict Trs: 805.47/297.03 { 0(#()) -> #() 805.47/297.03 , +(x, #()) -> x 805.47/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 805.47/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 805.47/297.03 , +(#(), x) -> x 805.47/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 805.47/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 805.47/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 805.47/297.03 , *(x, +(y, z)) -> +(*(x, y), *(x, z)) 805.47/297.03 , *(0(x), y) -> 0(*(x, y)) 805.47/297.03 , *(#(), x) -> #() 805.47/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 805.47/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 805.47/297.03 , app(nil(), l) -> l 805.47/297.03 , app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 805.47/297.03 , sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 805.47/297.03 , sum(nil()) -> 0(#()) 805.47/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 805.47/297.03 , prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 805.47/297.03 , prod(nil()) -> 1(#()) 805.47/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 805.47/297.03 Obligation: 805.47/297.03 runtime complexity 805.47/297.03 Answer: 805.47/297.03 MAYBE 805.47/297.03 805.47/297.03 We estimate the number of application of {1,11,20} by applications 805.47/297.03 of Pre({1,11,20}) = {2,3,5,8,10,13,14,15,17,19,21}. Here rules are 805.47/297.03 labeled as follows: 805.47/297.03 805.47/297.03 DPs: 805.47/297.03 { 1: 0^#(#()) -> c_1() 805.47/297.03 , 2: +^#(x, #()) -> c_2(x) 805.47/297.03 , 3: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , 4: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , 5: +^#(#(), x) -> c_5(x) 805.47/297.03 , 6: +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , 7: +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , 8: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , 9: *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , 10: *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , 11: *^#(#(), x) -> c_11() 805.47/297.03 , 12: *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , 13: *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , 14: app^#(nil(), l) -> c_14(l) 805.47/297.03 , 15: app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , 16: sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , 17: sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , 18: sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , 19: prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , 20: prod^#(nil()) -> c_20() 805.47/297.03 , 21: prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) } 805.47/297.03 805.47/297.03 We are left with following problem, upon which TcT provides the 805.47/297.03 certificate MAYBE. 805.47/297.03 805.47/297.03 Strict DPs: 805.47/297.03 { +^#(x, #()) -> c_2(x) 805.47/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , +^#(#(), x) -> c_5(x) 805.47/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , app^#(nil(), l) -> c_14(l) 805.47/297.03 , app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) } 805.47/297.03 Strict Trs: 805.47/297.03 { 0(#()) -> #() 805.47/297.03 , +(x, #()) -> x 805.47/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 805.47/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 805.47/297.03 , +(#(), x) -> x 805.47/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 805.47/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 805.47/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 805.47/297.03 , *(x, +(y, z)) -> +(*(x, y), *(x, z)) 805.47/297.03 , *(0(x), y) -> 0(*(x, y)) 805.47/297.03 , *(#(), x) -> #() 805.47/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 805.47/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 805.47/297.03 , app(nil(), l) -> l 805.47/297.03 , app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 805.47/297.03 , sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 805.47/297.03 , sum(nil()) -> 0(#()) 805.47/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 805.47/297.03 , prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 805.47/297.03 , prod(nil()) -> 1(#()) 805.47/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 805.47/297.03 Weak DPs: 805.47/297.03 { 0^#(#()) -> c_1() 805.47/297.03 , *^#(#(), x) -> c_11() 805.47/297.03 , prod^#(nil()) -> c_20() } 805.47/297.03 Obligation: 805.47/297.03 runtime complexity 805.47/297.03 Answer: 805.47/297.03 MAYBE 805.47/297.03 805.47/297.03 We estimate the number of application of {2,7,9,15} by applications 805.47/297.03 of Pre({2,7,9,15}) = {1,3,4,5,6,8,10,11,12,13,14,16,17,18}. Here 805.47/297.03 rules are labeled as follows: 805.47/297.03 805.47/297.03 DPs: 805.47/297.03 { 1: +^#(x, #()) -> c_2(x) 805.47/297.03 , 2: +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , 3: +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , 4: +^#(#(), x) -> c_5(x) 805.47/297.03 , 5: +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , 6: +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , 7: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , 8: *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , 9: *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , 10: *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , 11: *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , 12: app^#(nil(), l) -> c_14(l) 805.47/297.03 , 13: app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , 14: sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , 15: sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , 16: sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , 17: prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , 18: prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) 805.47/297.03 , 19: 0^#(#()) -> c_1() 805.47/297.03 , 20: *^#(#(), x) -> c_11() 805.47/297.03 , 21: prod^#(nil()) -> c_20() } 805.47/297.03 805.47/297.03 We are left with following problem, upon which TcT provides the 805.47/297.03 certificate MAYBE. 805.47/297.03 805.47/297.03 Strict DPs: 805.47/297.03 { +^#(x, #()) -> c_2(x) 805.47/297.03 , +^#(0(x), 1(y)) -> c_4(+^#(x, y)) 805.47/297.03 , +^#(#(), x) -> c_5(x) 805.47/297.03 , +^#(+(x, y), z) -> c_6(+^#(x, +(y, z))) 805.47/297.03 , +^#(1(x), 0(y)) -> c_7(+^#(x, y)) 805.47/297.03 , *^#(x, +(y, z)) -> c_9(+^#(*(x, y), *(x, z))) 805.47/297.03 , *^#(1(x), y) -> c_12(+^#(0(*(x, y)), y)) 805.47/297.03 , *^#(*(x, y), z) -> c_13(*^#(x, *(y, z))) 805.47/297.03 , app^#(nil(), l) -> c_14(l) 805.47/297.03 , app^#(cons(x, l1), l2) -> c_15(x, app^#(l1, l2)) 805.47/297.03 , sum^#(app(l1, l2)) -> c_16(+^#(sum(l1), sum(l2))) 805.47/297.03 , sum^#(cons(x, l)) -> c_18(+^#(x, sum(l))) 805.47/297.03 , prod^#(app(l1, l2)) -> c_19(*^#(prod(l1), prod(l2))) 805.47/297.03 , prod^#(cons(x, l)) -> c_21(*^#(x, prod(l))) } 805.47/297.03 Strict Trs: 805.47/297.03 { 0(#()) -> #() 805.47/297.03 , +(x, #()) -> x 805.47/297.03 , +(0(x), 0(y)) -> 0(+(x, y)) 805.47/297.03 , +(0(x), 1(y)) -> 1(+(x, y)) 805.47/297.03 , +(#(), x) -> x 805.47/297.03 , +(+(x, y), z) -> +(x, +(y, z)) 805.47/297.03 , +(1(x), 0(y)) -> 1(+(x, y)) 805.47/297.03 , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#()))) 805.47/297.03 , *(x, +(y, z)) -> +(*(x, y), *(x, z)) 805.47/297.03 , *(0(x), y) -> 0(*(x, y)) 805.47/297.03 , *(#(), x) -> #() 805.47/297.03 , *(1(x), y) -> +(0(*(x, y)), y) 805.47/297.03 , *(*(x, y), z) -> *(x, *(y, z)) 805.47/297.03 , app(nil(), l) -> l 805.47/297.03 , app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 805.47/297.03 , sum(app(l1, l2)) -> +(sum(l1), sum(l2)) 805.47/297.03 , sum(nil()) -> 0(#()) 805.47/297.03 , sum(cons(x, l)) -> +(x, sum(l)) 805.47/297.03 , prod(app(l1, l2)) -> *(prod(l1), prod(l2)) 805.47/297.03 , prod(nil()) -> 1(#()) 805.47/297.03 , prod(cons(x, l)) -> *(x, prod(l)) } 805.47/297.03 Weak DPs: 805.47/297.03 { 0^#(#()) -> c_1() 805.47/297.03 , +^#(0(x), 0(y)) -> c_3(0^#(+(x, y))) 805.47/297.03 , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#())))) 805.47/297.03 , *^#(0(x), y) -> c_10(0^#(*(x, y))) 805.47/297.03 , *^#(#(), x) -> c_11() 805.47/297.03 , sum^#(nil()) -> c_17(0^#(#())) 805.47/297.03 , prod^#(nil()) -> c_20() } 805.47/297.03 Obligation: 805.47/297.03 runtime complexity 805.47/297.03 Answer: 805.47/297.03 MAYBE 805.47/297.03 805.47/297.03 Empty strict component of the problem is NOT empty. 805.47/297.03 805.47/297.03 805.47/297.03 Arrrr.. 805.68/297.21 EOF