/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: app(app(minus(),0()),y) -> 0() 2: app(app(minus(),app(s(),x)),0()) -> app(s(),x) 3: app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y) 4: app(app(le(),0()),y) -> true() 5: app(app(le(),app(s(),x)),0()) -> false() 6: app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y) 7: app(app(app(if(),true()),x),y) -> x 8: app(app(app(if(),false()),x),y) -> y 9: app(perfectp(),0()) -> false() 10: app(perfectp(),app(s(),x)) -> app(app(app(app(f(),x),app(s(),0())),app(s(),x)),app(s(),x)) 11: app(app(app(app(f(),0()),y),0()),u) -> true() 12: app(app(app(app(f(),0()),y),app(s(),z)),u) -> false() 13: app(app(app(app(f(),app(s(),x)),0()),z),u) -> app(app(app(app(f(),x),u),app(app(minus(),z),app(s(),x))),u) 14: app(app(app(app(f(),app(s(),x)),app(s(),y)),z),u) -> app(app(app(if(),app(app(le(),x),y)),app(app(app(app(f(),app(s(),x)),app(app(minus(),y),x)),z),u)),app(app(app(app(f(),x),u),z),u)) 15: app(app(map(),fun),nil()) -> nil() 16: app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs)) 17: app(app(filter(),fun),nil()) -> nil() 18: app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs) 19: app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs)) 20: app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs) Number of strict rules: 20 Direct POLO(bPol) ... failed. Uncurrying app 1: app^2_minus(0(),y) -> 0() 2: app^2_minus(app^1_s(x),0()) -> app^1_s(x) 3: app^2_minus(app^1_s(x),app^1_s(y)) -> app^2_minus(x,y) 4: app^2_le(0(),y) -> true() 5: app^2_le(app^1_s(x),0()) -> false() 6: app^2_le(app^1_s(x),app^1_s(y)) -> app^2_le(x,y) 7: app^3_if(true(),x,y) -> x 8: app^3_if(false(),x,y) -> y 9: app^1_perfectp(0()) -> false() 10: app^1_perfectp(app^1_s(x)) -> app^4_f(x,app^1_s(0()),app^1_s(x),app^1_s(x)) 11: app^4_f(0(),y,0(),u) -> true() 12: app^4_f(0(),y,app^1_s(z),u) -> false() 13: app^4_f(app^1_s(x),0(),z,u) -> app^4_f(x,u,app^2_minus(z,app^1_s(x)),u) 14: app^4_f(app^1_s(x),app^1_s(y),z,u) -> app^3_if(app^2_le(x,y),app^4_f(app^1_s(x),app^2_minus(y,x),z,u),app^4_f(x,u,z,u)) 15: app^2_map(fun,nil()) -> nil() 16: app^2_map(fun,app^2_cons(x,xs)) -> app^2_cons(app(fun,x),app^2_map(fun,xs)) 17: app^2_filter(fun,nil()) -> nil() 18: app^2_filter(fun,app^2_cons(x,xs)) -> app^4_filter2(app(fun,x),fun,x,xs) 19: app^4_filter2(true(),fun,x,xs) -> app^2_cons(x,app^2_filter(fun,xs)) 20: app^4_filter2(false(),fun,x,xs) -> app^2_filter(fun,xs) 21: app(le(),_1) ->= app^1_le(_1) 22: app(app^1_le(_1),_2) ->= app^2_le(_1,_2) 23: app(if(),_1) ->= app^1_if(_1) 24: app(app^1_if(_1),_2) ->= app^2_if(_1,_2) 25: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3) 26: app(cons(),_1) ->= app^1_cons(_1) 27: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 28: app(s(),_1) ->= app^1_s(_1) 29: app(filter(),_1) ->= app^1_filter(_1) 30: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 31: app(perfectp(),_1) ->= app^1_perfectp(_1) 32: app(map(),_1) ->= app^1_map(_1) 33: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 34: app(minus(),_1) ->= app^1_minus(_1) 35: app(app^1_minus(_1),_2) ->= app^2_minus(_1,_2) 36: app(f(),_1) ->= app^1_f(_1) 37: app(app^1_f(_1),_2) ->= app^2_f(_1,_2) 38: app(app^2_f(_1,_2),_3) ->= app^3_f(_1,_2,_3) 39: app(app^3_f(_1,_2,_3),_4) ->= app^4_f(_1,_2,_3,_4) 40: app(filter2(),_1) ->= app^1_filter2(_1) 41: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 42: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 43: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) Number of strict rules: 20 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #2: #app(app^1_minus(_1),_2) ->? #app^2_minus(_1,_2) #3: #app^2_le(app^1_s(x),app^1_s(y)) -> #app^2_le(x,y) #4: #app^4_f(app^1_s(x),0(),z,u) -> #app^4_f(x,u,app^2_minus(z,app^1_s(x)),u) #5: #app^4_f(app^1_s(x),0(),z,u) -> #app^2_minus(z,app^1_s(x)) #6: #app(perfectp(),_1) ->? #app^1_perfectp(_1) #7: #app^4_f(app^1_s(x),app^1_s(y),z,u) -> #app^3_if(app^2_le(x,y),app^4_f(app^1_s(x),app^2_minus(y,x),z,u),app^4_f(x,u,z,u)) #8: #app^4_f(app^1_s(x),app^1_s(y),z,u) -> #app^2_le(x,y) #9: #app^4_f(app^1_s(x),app^1_s(y),z,u) -> #app^4_f(app^1_s(x),app^2_minus(y,x),z,u) #10: #app^4_f(app^1_s(x),app^1_s(y),z,u) -> #app^2_minus(y,x) #11: #app^4_f(app^1_s(x),app^1_s(y),z,u) -> #app^4_f(x,u,z,u) #12: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #13: #app(app^2_if(_1,_2),_3) ->? #app^3_if(_1,_2,_3) #14: #app^4_filter2(false(),fun,x,xs) -> #app^2_filter(fun,xs) #15: #app(app^3_f(_1,_2,_3),_4) ->? #app^4_f(_1,_2,_3,_4) #16: #app^1_perfectp(app^1_s(x)) -> #app^4_f(x,app^1_s(0()),app^1_s(x),app^1_s(x)) #17: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #18: #app(app^1_le(_1),_2) ->? #app^2_le(_1,_2) #19: #app^4_filter2(true(),fun,x,xs) -> #app^2_filter(fun,xs) #20: #app^2_map(fun,app^2_cons(x,xs)) -> #app(fun,x) #21: #app^2_map(fun,app^2_cons(x,xs)) -> #app^2_map(fun,xs) #22: #app^2_minus(app^1_s(x),app^1_s(y)) -> #app^2_minus(x,y) #23: #app^2_filter(fun,app^2_cons(x,xs)) -> #app^4_filter2(app(fun,x),fun,x,xs) #24: #app^2_filter(fun,app^2_cons(x,xs)) -> #app(fun,x) Number of SCCs: 4, DPs: 14 SCC { #22 } POLO(Sum)... succeeded. #app^3_if w: 0 le w: 0 #app^2_minus w: x1 + x2 s w: 0 app^1_cons w: 0 app^3_f w: 0 #app^2_map w: 0 minus w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^2_f w: 0 #app^2_le w: 0 app^1_le w: 0 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 0 if w: 0 #app^4_f w: 0 #app^4_filter2 w: 0 nil w: 0 app^2_le w: 0 #app w: 0 app^2_minus w: 0 map w: 0 app^1_filter w: 0 #app^1_perfectp w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 perfectp w: 0 app^1_minus w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_perfectp w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app^4_f w: 0 app w: 0 USABLE RULES: { } Removed DPs: #22 Number of SCCs: 3, DPs: 13 SCC { #3 } POLO(Sum)... succeeded. #app^3_if w: 0 le w: 0 #app^2_minus w: 0 s w: 0 app^1_cons w: 0 app^3_f w: 0 #app^2_map w: 0 minus w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^2_f w: 0 #app^2_le w: x2 app^1_le w: 0 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 0 if w: 0 #app^4_f w: 0 #app^4_filter2 w: 0 nil w: 0 app^2_le w: 0 #app w: 0 app^2_minus w: 0 map w: 0 app^1_filter w: 0 #app^1_perfectp w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 perfectp w: 0 app^1_minus w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_perfectp w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app^4_f w: 0 app w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 2, DPs: 12 SCC { #4 #9 #11 } POLO(Sum)... succeeded. #app^3_if w: 0 le w: 0 #app^2_minus w: 0 s w: 0 app^1_cons w: 0 app^3_f w: 0 #app^2_map w: 0 minus w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^2_f w: 0 #app^2_le w: 0 app^1_le w: 0 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 1 if w: 0 #app^4_f w: x1 + x4 #app^4_filter2 w: 0 nil w: 0 app^2_le w: 0 #app w: 0 app^2_minus w: x1 + x2 + 1 map w: 0 app^1_filter w: 0 #app^1_perfectp w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 perfectp w: 0 app^1_minus w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_perfectp w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app^4_f w: 0 app w: 0 USABLE RULES: { } Removed DPs: #4 #11 Number of SCCs: 2, DPs: 10 SCC { #9 } POLO(Sum)... succeeded. #app^3_if w: 0 le w: 0 #app^2_minus w: 0 s w: 0 app^1_cons w: 0 app^3_f w: 0 #app^2_map w: 0 minus w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^2_f w: 0 #app^2_le w: 0 app^1_le w: 0 app^1_filter2 w: 0 true w: 0 f w: 0 filter2 w: 0 0 w: 1 if w: 0 #app^4_f w: x2 #app^4_filter2 w: 0 nil w: 0 app^2_le w: 0 #app w: 0 app^2_minus w: x1 + 1 map w: 0 app^1_filter w: 0 #app^1_perfectp w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 app^1_f w: 0 filter w: 0 perfectp w: 0 app^1_minus w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_if w: 0 app^1_perfectp w: 0 app^1_s w: x1 + 2 app^2_map w: 0 #app^2_filter w: 0 app^4_f w: 0 app w: 0 USABLE RULES: { 1..3 } Removed DPs: #9 Number of SCCs: 1, DPs: 9 SCC { #1 #12 #14 #17 #19..21 #23 #24 } POLO(Sum)... succeeded. #app^3_if w: 0 le w: 1 #app^2_minus w: 0 s w: 1 app^1_cons w: 1 app^3_f w: 1 #app^2_map w: x2 minus w: 1 app^2_filter2 w: 1 app^4_filter2 w: x1 + 2 false w: 0 app^2_f w: 1 #app^2_le w: 0 app^1_le w: 3 app^1_filter2 w: 1 true w: 6 f w: 1 filter2 w: 1 0 w: 2 if w: 1 #app^4_f w: 0 #app^4_filter2 w: x4 + 1 nil w: 4 app^2_le w: x2 + 6 #app w: x2 + 2 app^2_minus w: 1 map w: 1 app^1_filter w: 1 #app^1_perfectp w: 0 cons w: 1 app^2_if w: 1 app^3_if w: x1 + x2 + x3 + 3 app^1_f w: 3 filter w: 1 perfectp w: 1 app^1_minus w: 1 app^3_filter2 w: x1 + x2 + x3 + 3 app^2_filter w: x1 + 3 app^1_map w: 1 app^2_cons w: x1 + x2 + 9 app^1_if w: 1 app^1_perfectp w: x1 + 5 app^1_s w: x1 + 3 app^2_map w: x1 + x2 + 3 #app^2_filter w: x2 app^4_f w: x1 + x2 + 3 app w: x2 + 2 USABLE RULES: { 4 5 } Removed DPs: #1 #12 #14 #17 #19..21 #23 #24 Number of SCCs: 0, DPs: 0