/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(D(),t()) -> 1() 2: app(D(),constant()) -> 0() 3: app(D(),app(app(+(),x),y)) -> app(app(+(),app(D(),x)),app(D(),y)) 4: app(D(),app(app(*(),x),y)) -> app(app(+(),app(app(*(),y),app(D(),x))),app(app(*(),x),app(D(),y))) 5: app(D(),app(app(-(),x),y)) -> app(app(-(),app(D(),x)),app(D(),y)) 6: app(D(),app(minus(),x)) -> app(minus(),app(D(),x)) 7: app(D(),app(app(div(),x),y)) -> app(app(-(),app(app(div(),app(D(),x)),y)),app(app(div(),app(app(*(),x),app(D(),y))),app(app(pow(),y),2()))) 8: app(D(),app(ln(),x)) -> app(app(div(),app(D(),x)),x) 9: app(D(),app(app(pow(),x),y)) -> app(app(+(),app(app(*(),app(app(*(),y),app(app(pow(),x),app(app(-(),y),1())))),app(D(),x))),app(app(*(),app(app(*(),app(app(pow(),x),y)),app(ln(),x))),app(D(),y))) 10: app(app(map(),f),nil()) -> nil() 11: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) 12: app(app(filter(),f),nil()) -> nil() 13: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) 14: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) 15: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Number of strict rules: 15 Direct POLO(bPol) ... failed. Uncurrying app 1: app^1_D(t()) -> 1() 2: app^1_D(constant()) -> 0() 3: app^1_D(app^2_+(x,y)) -> app^2_+(app^1_D(x),app^1_D(y)) 4: app^1_D(app^2_*(x,y)) -> app^2_+(app^2_*(y,app^1_D(x)),app^2_*(x,app^1_D(y))) 5: app^1_D(app^2_-(x,y)) -> app^2_-(app^1_D(x),app^1_D(y)) 6: app^1_D(app^1_minus(x)) -> app^1_minus(app^1_D(x)) 7: app^1_D(app^2_div(x,y)) -> app^2_-(app^2_div(app^1_D(x),y),app^2_div(app^2_*(x,app^1_D(y)),app^2_pow(y,2()))) 8: app^1_D(app^1_ln(x)) -> app^2_div(app^1_D(x),x) 9: app^1_D(app^2_pow(x,y)) -> app^2_+(app^2_*(app^2_*(y,app^2_pow(x,app^2_-(y,1()))),app^1_D(x)),app^2_*(app^2_*(app^2_pow(x,y),app^1_ln(x)),app^1_D(y))) 10: app^2_map(f,nil()) -> nil() 11: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs)) 12: app^2_filter(f,nil()) -> nil() 13: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs) 14: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs)) 15: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs) 16: app(cons(),_1) ->= app^1_cons(_1) 17: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2) 18: app(div(),_1) ->= app^1_div(_1) 19: app(app^1_div(_1),_2) ->= app^2_div(_1,_2) 20: app(ln(),_1) ->= app^1_ln(_1) 21: app(filter(),_1) ->= app^1_filter(_1) 22: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2) 23: app(+(),_1) ->= app^1_+(_1) 24: app(app^1_+(_1),_2) ->= app^2_+(_1,_2) 25: app(-(),_1) ->= app^1_-(_1) 26: app(app^1_-(_1),_2) ->= app^2_-(_1,_2) 27: app(map(),_1) ->= app^1_map(_1) 28: app(app^1_map(_1),_2) ->= app^2_map(_1,_2) 29: app(minus(),_1) ->= app^1_minus(_1) 30: app(D(),_1) ->= app^1_D(_1) 31: app(pow(),_1) ->= app^1_pow(_1) 32: app(app^1_pow(_1),_2) ->= app^2_pow(_1,_2) 33: app(filter2(),_1) ->= app^1_filter2(_1) 34: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2) 35: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3) 36: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4) 37: app(*(),_1) ->= app^1_*(_1) 38: app(app^1_*(_1),_2) ->= app^2_*(_1,_2) Number of strict rules: 15 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #app^1_D(app^1_minus(x)) -> #app^1_D(x) #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^1_D(app^2_pow(x,y)) -> #app^1_D(x) #5: #app^1_D(app^2_pow(x,y)) -> #app^1_D(y) #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(D(),_1) ->? #app^1_D(_1) #10: #app^1_D(app^2_div(x,y)) -> #app^1_D(x) #11: #app^1_D(app^2_div(x,y)) -> #app^1_D(y) #12: #app^1_D(app^2_-(x,y)) -> #app^1_D(x) #13: #app^1_D(app^2_-(x,y)) -> #app^1_D(y) #14: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2) #15: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2) #16: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4) #17: #app^1_D(app^2_+(x,y)) -> #app^1_D(x) #18: #app^1_D(app^2_+(x,y)) -> #app^1_D(y) #19: #app^1_D(app^1_ln(x)) -> #app^1_D(x) #20: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs) #21: #app^1_D(app^2_*(x,y)) -> #app^1_D(x) #22: #app^1_D(app^2_*(x,y)) -> #app^1_D(y) Number of SCCs: 2, DPs: 20 SCC { #3 #6..8 #14..16 #20 } POLO(Sum)... succeeded. 1 w: 0 ln w: 0 app^1_div w: 0 app^1_cons w: 0 app^1_+ w: 0 #app^2_map w: x1 + x2 constant w: 0 app^1_pow w: 0 minus w: 0 pow w: 0 app^1_D w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 t w: 0 false w: 1 div w: 0 app^1_* w: 0 app^2_* w: 0 app^2_- w: 0 app^1_- w: 0 D w: 0 app^2_pow w: 0 app^1_filter2 w: 0 true w: 1 filter2 w: 0 app^1_ln w: 0 0 w: 0 #app^4_filter2 w: x1 + x2 + x4 nil w: 0 - w: 0 #app w: x1 + x2 map w: 0 app^1_filter w: x1 + 1 app^2_+ w: 0 2 w: 0 app^2_div w: 0 #app^1_D w: 0 cons w: 0 filter w: 0 + w: 0 app^1_minus w: 0 app^3_filter2 w: x1 + x2 + x3 + 1 app^2_filter w: 0 app^1_map w: x1 + 1 app^2_cons w: x1 + x2 + 1 app^2_map w: 0 #app^2_filter w: x1 + x2 * w: 0 app w: 0 USABLE RULES: { } Removed DPs: #3 #6..8 #14..16 #20 Number of SCCs: 1, DPs: 12 SCC { #1 #4 #5 #10..13 #17..19 #21 #22 } POLO(Sum)... succeeded. 1 w: 0 ln w: 0 app^1_div w: 0 app^1_cons w: 0 app^1_+ w: 0 #app^2_map w: 0 constant w: 0 app^1_pow w: 0 minus w: 0 pow w: 0 app^1_D w: 0 app^2_filter2 w: 0 app^4_filter2 w: 0 t w: 0 false w: 1 div w: 0 app^1_* w: 0 app^2_* w: x1 + x2 + 1 app^2_- w: x1 + x2 + 1 app^1_- w: 0 D w: 0 app^2_pow w: x1 + x2 + 1 app^1_filter2 w: 0 true w: 1 filter2 w: 0 app^1_ln w: x1 + 1 0 w: 0 #app^4_filter2 w: 0 nil w: 0 - w: 0 #app w: 0 map w: 0 app^1_filter w: 1 app^2_+ w: x1 + x2 + 1 2 w: 0 app^2_div w: x1 + x2 + 1 #app^1_D w: x1 cons w: 0 filter w: 0 + w: 0 app^1_minus w: x1 + 1 app^3_filter2 w: 1 app^2_filter w: 0 app^1_map w: 1 app^2_cons w: 1 app^2_map w: 0 #app^2_filter w: 0 * w: 0 app w: 0 USABLE RULES: { } Removed DPs: #1 #4 #5 #10..13 #17..19 #21 #22 Number of SCCs: 0, DPs: 0