/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(app(if(),true()),xs),ys) -> xs 2: app(app(app(if(),false()),xs),ys) -> ys 3: app(app(sub(),x),0()) -> x 4: app(app(sub(),app(s(),x)),app(s(),y)) -> app(app(sub(),x),y) 5: app(app(gtr(),0()),y) -> false() 6: app(app(gtr(),app(s(),x)),0()) -> true() 7: app(app(gtr(),app(s(),x)),app(s(),y)) -> app(app(gtr(),x),y) 8: app(app(d(),x),0()) -> true() 9: app(app(d(),app(s(),x)),app(s(),y)) -> app(app(app(if(),app(app(gtr(),x),y)),false()),app(app(d(),app(s(),x)),app(app(sub(),y),x))) 10: app(len(),nil()) -> 0() 11: app(len(),app(app(cons(),x),xs)) -> app(s(),app(len(),xs)) 12: app(app(filter(),p),nil()) -> nil() 13: app(app(filter(),p),app(app(cons(),x),xs)) -> app(app(app(if(),app(p,x)),app(app(cons(),x),app(app(filter(),p),xs))),app(app(filter(),p),xs)) Number of strict rules: 13 Direct POLO(bPol) ... failed. Uncurrying app 1: app^3_if(true(),xs,ys) -> xs 2: app^3_if(false(),xs,ys) -> ys 3: app^2_sub(x,0()) -> x 4: app^2_sub(app^1_s(x),app^1_s(y)) -> app^2_sub(x,y) 5: app^2_gtr(0(),y) -> false() 6: app^2_gtr(app^1_s(x),0()) -> true() 7: app^2_gtr(app^1_s(x),app^1_s(y)) -> app^2_gtr(x,y) 8: app^2_d(x,0()) -> true() 9: app^2_d(app^1_s(x),app^1_s(y)) -> app^3_if(app^2_gtr(x,y),false(),app^2_d(app^1_s(x),app^2_sub(y,x))) 10: app^1_len(nil()) -> 0() 11: app^1_len(app^2_cons(x,xs)) -> app^1_s(app^1_len(xs)) 12: app^2_filter(p,nil()) -> nil() 13: app^2_filter(p,app^2_cons(x,xs)) -> app^3_if(app(p,x),app^2_cons(x,app^2_filter(p,xs)),app^2_filter(p,xs)) 14: app(if(),_1) ->= app^1_if(_1) 15: app(app^1_if(_1),_2) ->= app^2_if(_1,_2) 16: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3) 17: app(cons(),_1) ->= app^1_cons(_1) 18: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 19: app(d(),_1) ->= app^1_d(_1) 20: app(app^1_d(_1),_2) ->= app^2_d(_1,_2) 21: app(s(),_1) ->= app^1_s(_1) 22: app(filter(),_1) ->= app^1_filter(_1) 23: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 24: app(gtr(),_1) ->= app^1_gtr(_1) 25: app(app^1_gtr(_1),_2) ->= app^2_gtr(_1,_2) 26: app(len(),_1) ->= app^1_len(_1) 27: app(sub(),_1) ->= app^1_sub(_1) 28: app(app^1_sub(_1),_2) ->= app^2_sub(_1,_2) Number of strict rules: 13 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app^2_filter(p,app^2_cons(x,xs)) -> #app^3_if(app(p,x),app^2_cons(x,app^2_filter(p,xs)),app^2_filter(p,xs)) #2: #app^2_filter(p,app^2_cons(x,xs)) -> #app(p,x) #3: #app^2_filter(p,app^2_cons(x,xs)) -> #app^2_filter(p,xs) #4: #app^2_filter(p,app^2_cons(x,xs)) -> #app^2_filter(p,xs) #5: #app^2_d(app^1_s(x),app^1_s(y)) -> #app^3_if(app^2_gtr(x,y),false(),app^2_d(app^1_s(x),app^2_sub(y,x))) #6: #app^2_d(app^1_s(x),app^1_s(y)) -> #app^2_gtr(x,y) #7: #app^2_d(app^1_s(x),app^1_s(y)) -> #app^2_d(app^1_s(x),app^2_sub(y,x)) #8: #app^2_d(app^1_s(x),app^1_s(y)) -> #app^2_sub(y,x) #9: #app^1_len(app^2_cons(x,xs)) -> #app^1_len(xs) #10: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #11: #app(app^1_gtr(_1),_2) ->? #app^2_gtr(_1,_2) #12: #app(app^1_d(_1),_2) ->? #app^2_d(_1,_2) #13: #app^2_gtr(app^1_s(x),app^1_s(y)) -> #app^2_gtr(x,y) #14: #app(app^1_sub(_1),_2) ->? #app^2_sub(_1,_2) #15: #app(len(),_1) ->? #app^1_len(_1) #16: #app(app^2_if(_1,_2),_3) ->? #app^3_if(_1,_2,_3) #17: #app^2_sub(app^1_s(x),app^1_s(y)) -> #app^2_sub(x,y) Number of SCCs: 5, DPs: 8 SCC { #9 } POLO(Sum)... succeeded. #app^3_if w: 0 d w: 0 s w: 0 app^1_cons w: 0 app^1_sub w: 0 #app^1_len w: x1 #app^2_d w: 0 false w: 0 gtr w: 0 app^2_sub w: 0 sub w: 0 true w: 0 if w: 0 0 w: 0 nil w: 0 app^2_d w: 0 #app w: 0 app^1_filter w: 0 app^2_gtr w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #app^2_gtr w: 0 filter w: 0 #app^2_sub w: 0 app^1_d w: 0 app^2_filter w: 0 app^1_len w: 0 len w: 0 app^2_cons w: x2 + 1 app^1_if w: 0 app^1_s w: 0 #app^2_filter w: 0 app w: 0 app^1_gtr w: 0 USABLE RULES: { } Removed DPs: #9 Number of SCCs: 4, DPs: 7 SCC { #13 } POLO(Sum)... succeeded. #app^3_if w: 0 d w: 0 s w: 0 app^1_cons w: 0 app^1_sub w: 0 #app^1_len w: 0 #app^2_d w: 0 false w: 0 gtr w: 0 app^2_sub w: 0 sub w: 0 true w: 0 if w: 0 0 w: 0 nil w: 0 app^2_d w: 0 #app w: 0 app^1_filter w: 0 app^2_gtr w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #app^2_gtr w: x2 filter w: 0 #app^2_sub w: 0 app^1_d w: 0 app^2_filter w: 0 app^1_len w: 0 len w: 0 app^2_cons w: 1 app^1_if w: 0 app^1_s w: x1 + 1 #app^2_filter w: 0 app w: 0 app^1_gtr w: 0 USABLE RULES: { } Removed DPs: #13 Number of SCCs: 3, DPs: 6 SCC { #17 } POLO(Sum)... succeeded. #app^3_if w: 0 d w: 0 s w: 0 app^1_cons w: 0 app^1_sub w: 0 #app^1_len w: 0 #app^2_d w: 0 false w: 0 gtr w: 0 app^2_sub w: 0 sub w: 0 true w: 0 if w: 0 0 w: 0 nil w: 0 app^2_d w: 0 #app w: 0 app^1_filter w: 0 app^2_gtr w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #app^2_gtr w: 0 filter w: 0 #app^2_sub w: x2 app^1_d w: 0 app^2_filter w: 0 app^1_len w: 0 len w: 0 app^2_cons w: 1 app^1_if w: 0 app^1_s w: x1 + 1 #app^2_filter w: 0 app w: 0 app^1_gtr w: 0 USABLE RULES: { } Removed DPs: #17 Number of SCCs: 2, DPs: 5 SCC { #7 } POLO(Sum)... succeeded. #app^3_if w: 0 d w: 0 s w: 0 app^1_cons w: 0 app^1_sub w: 0 #app^1_len w: 0 #app^2_d w: x2 false w: 0 gtr w: 0 app^2_sub w: x1 + 1 sub w: 0 true w: 0 if w: 0 0 w: 1 nil w: 0 app^2_d w: 0 #app w: 0 app^1_filter w: 0 app^2_gtr w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #app^2_gtr w: 0 filter w: 0 #app^2_sub w: 0 app^1_d w: 0 app^2_filter w: 0 app^1_len w: 0 len w: 0 app^2_cons w: 1 app^1_if w: 0 app^1_s w: x1 + 2 #app^2_filter w: 0 app w: 0 app^1_gtr w: 0 USABLE RULES: { 3 4 } Removed DPs: #7 Number of SCCs: 1, DPs: 4 SCC { #2..4 #10 } POLO(Sum)... succeeded. #app^3_if w: 0 d w: 0 s w: 0 app^1_cons w: 0 app^1_sub w: 0 #app^1_len w: 0 #app^2_d w: x2 false w: 0 gtr w: 0 app^2_sub w: x1 + 1 sub w: 0 true w: 0 if w: 0 0 w: 1 nil w: 0 app^2_d w: 0 #app w: x1 + x2 app^1_filter w: x1 + 1 app^2_gtr w: 0 cons w: 0 app^2_if w: 0 app^3_if w: 0 #app^2_gtr w: 0 filter w: 0 #app^2_sub w: 0 app^1_d w: 0 app^2_filter w: 0 app^1_len w: 0 len w: 0 app^2_cons w: x1 + x2 + 1 app^1_if w: 0 app^1_s w: x1 + 2 #app^2_filter w: x1 + x2 app w: 0 app^1_gtr w: 0 USABLE RULES: { 3 4 } Removed DPs: #2..4 #10 Number of SCCs: 0, DPs: 0