/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(plus(),0()),y) -> y 2: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) 3: app(app(times(),0()),y) -> 0() 4: app(app(times(),app(s(),x)),y) -> app(app(plus(),app(app(times(),x),y)),y) 5: app(app(map(),f),nil()) -> nil() 6: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 7: inc() -> app(map(),app(plus(),app(s(),0()))) 8: double() -> app(map(),app(times(),app(s(),app(s(),0())))) Number of strict rules: 8 Direct POLO(bPol) ... failed. Uncurrying app 1: app^2_plus(0(),y) -> y 2: app^2_plus(app^1_s(x),y) -> app^1_s(app^2_plus(x,y)) 3: app^2_times(0(),y) -> 0() 4: app^2_times(app^1_s(x),y) -> app^2_plus(app^2_times(x,y),y) 5: app^2_map(f,nil()) -> nil() 6: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 7: inc() -> app^1_map(app^1_plus(app^1_s(0()))) 8: double() -> app^1_map(app^1_times(app^1_s(app^1_s(0())))) 9: app(plus(),_1) ->= app^1_plus(_1) 10: app(app^1_plus(_1),_2) ->= app^2_plus(_1,_2) 11: app(cons(),_1) ->= app^1_cons(_1) 12: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 13: app(times(),_1) ->= app^1_times(_1) 14: app(app^1_times(_1),_2) ->= app^2_times(_1,_2) 15: app(s(),_1) ->= app^1_s(_1) 16: app(map(),_1) ->= app^1_map(_1) 17: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) Number of strict rules: 8 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app^2_plus(app^1_s(x),y) -> #app^2_plus(x,y) #2: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x) #3: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs) #4: #app(app^1_times(_1),_2) ->? #app^2_times(_1,_2) #5: #app(app^1_plus(_1),_2) ->? #app^2_plus(_1,_2) #6: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #7: #app^2_times(app^1_s(x),y) -> #app^2_plus(app^2_times(x,y),y) #8: #app^2_times(app^1_s(x),y) -> #app^2_times(x,y) Number of SCCs: 3, DPs: 5 SCC { #8 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 #inc w: 0 inc w: 0 #app^2_plus w: 0 app^2_plus w: 0 0 w: 0 #double w: 0 double w: 0 times w: 0 nil w: 0 #app w: 0 map w: 0 plus w: 0 cons w: 0 app^1_times w: 0 #app^2_times w: x1 app^1_map w: 0 app^2_cons w: 0 app^1_s w: x1 + 1 app^2_map w: 0 app w: 0 app^2_times w: 0 USABLE RULES: { } Removed DPs: #8 Number of SCCs: 2, DPs: 4 SCC { #1 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: 0 #inc w: 0 inc w: 0 #app^2_plus w: x1 app^2_plus w: 0 0 w: 0 #double w: 0 double w: 0 times w: 0 nil w: 0 #app w: 0 map w: 0 plus w: 0 cons w: 0 app^1_times w: 0 #app^2_times w: 0 app^1_map w: 0 app^2_cons w: 0 app^1_s w: x1 + 1 app^2_map w: 0 app w: 0 app^2_times w: 0 USABLE RULES: { } Removed DPs: #1 Number of SCCs: 1, DPs: 3 SCC { #2 #3 #6 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: x1 + 1 #inc w: 0 inc w: 0 #app^2_plus w: 0 app^2_plus w: 0 0 w: 0 #double w: 0 double w: 0 times w: 0 nil w: 0 #app w: x1 map w: 0 plus w: 0 cons w: 0 app^1_times w: 0 #app^2_times w: 0 app^1_map w: x1 + 2 app^2_cons w: 1 app^1_s w: 1 app^2_map w: 0 app w: 0 app^2_times w: 0 USABLE RULES: { } Removed DPs: #2 #6 Number of SCCs: 1, DPs: 1 SCC { #3 } POLO(Sum)... succeeded. s w: 0 app^1_cons w: 0 app^1_plus w: 0 #app^2_map w: x2 + 1 #inc w: 0 inc w: 0 #app^2_plus w: 0 app^2_plus w: 0 0 w: 0 #double w: 0 double w: 0 times w: 0 nil w: 0 #app w: 0 map w: 0 plus w: 0 cons w: 0 app^1_times w: 0 #app^2_times w: 0 app^1_map w: 2 app^2_cons w: x2 + 1 app^1_s w: 1 app^2_map w: 0 app w: 0 app^2_times w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 0, DPs: 0