/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: app(app(times(),x),app(app(plus(),y),app(s(),z))) -> app(app(plus(),app(app(times(),x),app(app(plus(),y),app(app(times(),app(s(),z)),0())))),app(app(times(),x),app(s(),z))) 2: app(app(times(),x),0()) -> 0() 3: app(app(times(),x),app(s(),y)) -> app(app(plus(),app(app(times(),x),y)),x) 4: app(app(plus(),x),0()) -> x 5: app(app(plus(),x),app(s(),y)) -> app(s(),app(app(plus(),x),y)) 6: app(app(map(),f),nil()) -> nil() 7: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 8: app(app(filter(),f),nil()) -> nil() 9: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) 10: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) 11: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Number of strict rules: 11 Direct POLO(bPol) ... failed. Uncurrying app 1: app^2_times(x,app^2_plus(y,app^1_s(z))) -> app^2_plus(app^2_times(x,app^2_plus(y,app^2_times(app^1_s(z),0()))),app^2_times(x,app^1_s(z))) 2: app^2_times(x,0()) -> 0() 3: app^2_times(x,app^1_s(y)) -> app^2_plus(app^2_times(x,y),x) 4: app^2_plus(x,0()) -> x 5: app^2_plus(x,app^1_s(y)) -> app^1_s(app^2_plus(x,y)) 6: app^2_map(f,nil()) -> nil() 7: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 8: app^2_filter(f,nil()) -> nil() 9: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs) 10: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs)) 11: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs) 12: app(plus(),_1) ->= app^1_plus(_1) 13: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2) 14: app(cons(),_1) ->= app^1_cons(_1) 15: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 16: app(times(),_1) ->= app^1_times(_1) 17: app(app^1_times(_1),_2) ->= app^2_times(_1,_2) 18: app(s(),_1) ->= app^1_s(_1) 19: app(filter(),_1) ->= app^1_filter(_1) 20: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 21: app(map(),_1) ->= app^1_map(_1) 22: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 23: app(filter2(),_1) ->= app^1_filter2(_1) 24: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 25: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 26: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) Number of strict rules: 11 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2) #2: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs) #3: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x) #4: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs) #5: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #6: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x) #7: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs) #8: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs) #9: #app^2_plus(x,app^1_s(y)) -> #app^2_plus(x,y) #10: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #11: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2) #12: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #13: #app^2_times(x,app^1_s(y)) -> #app^2_plus(app^2_times(x,y),x) #14: #app^2_times(x,app^1_s(y)) -> #app^2_times(x,y) #15: #app^2_times(x,app^2_plus(y,app^1_s(z))) -> #app^2_plus(app^2_times(x,app^2_plus(y,app^2_times(app^1_s(z),0()))),app^2_times(x,app^1_s(z))) #16: #app^2_times(x,app^2_plus(y,app^1_s(z))) -> #app^2_times(x,app^2_plus(y,app^2_times(app^1_s(z),0()))) #17: #app^2_times(x,app^2_plus(y,app^1_s(z))) -> #app^2_plus(y,app^2_times(app^1_s(z),0())) #18: #app^2_times(x,app^2_plus(y,app^1_s(z))) -> #app^2_times(app^1_s(z),0()) #19: #app^2_times(x,app^2_plus(y,app^1_s(z))) -> #app^2_times(x,app^1_s(z)) Number of SCCs: 3, DPs: 13 SCC { #9 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^1_filter2 w: 0 true w: 0 #app^2_plus w: x2 filter2 w: 0 app^2_plus w: 0 0 w: 0 times w: 0 #app^4_filter2 w: 0 nil w: 0 #app w: 0 map w: 0 app^1_filter w: 0 plus w: 0 cons w: 0 app^1_times w: 0 filter w: 0 #app^2_times w: 0 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_s w: x1 + 1 app^2_map w: 0 #app^2_filter w: 0 app w: 0 app^2_times w: 0 USABLE RULES: { } Removed DPs: #9 Number of SCCs: 2, DPs: 12 SCC { #14 #16 #19 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 false w: 0 app^1_filter2 w: 0 true w: 0 #app^2_plus w: 0 filter2 w: 0 app^2_plus w: x1 + x2 + 1 0 w: 1 times w: 0 #app^4_filter2 w: 0 nil w: 0 #app w: 0 map w: 0 app^1_filter w: 0 plus w: 0 cons w: 0 app^1_times w: 0 filter w: 0 #app^2_times w: x2 app^3_filter2 w: 0 app^2_filter w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_s w: x1 + 2 app^2_map w: 0 #app^2_filter w: 0 app w: 0 app^2_times w: 1 USABLE RULES: { 2 4 5 } Removed DPs: #14 #16 #19 Number of SCCs: 1, DPs: 9 SCC { #2..8 #10 #12 } POLO(Sum)... succeeded. s w: 1 app^1_cons w: 3 app^1_plus w: x1 + 2 #app^2_map w: x2 app^2_filter2 w: x1 + 1 app^4_filter2 w: x3 + x4 + 4 false w: 1 app^1_filter2 w: x1 + 3 true w: 1 #app^2_plus w: 0 filter2 w: 1 app^2_plus w: x1 + x2 + 1 0 w: 1 times w: 1 #app^4_filter2 w: x4 + 1 nil w: 6 #app w: x2 + 2 map w: 1 app^1_filter w: 3 plus w: 1 cons w: 1 app^1_times w: x1 + 1 filter w: 1 #app^2_times w: x2 app^3_filter2 w: 2 app^2_filter w: x2 + 5 app^1_map w: x1 + 3 app^2_cons w: x1 + x2 + 5 app^1_s w: x1 + 3 app^2_map w: 5 #app^2_filter w: x2 app w: x1 + x2 + 1 app^2_times w: x2 + 1 USABLE RULES: { 2 4 5 } Removed DPs: #2..8 #10 #12 Number of SCCs: 0, DPs: 0